Advanced quantum theory and its applications through Feynman diagrams

International Nuclear Information System (INIS)

Scadron, M.D.

1979-01-01

The two themes of scattering diagrams and the fundamental forces characterize this book. Transformation theory is developed to review the concepts of nonrelativistic quantum mechanics and to formulate the relativistic Klein-Gordon, Maxwell, and Dirac wave equations for relativistic spin-0, massless spin-1, and spin-1/2 particles, respectively. The language of group theory is used to write relativistic Lorentz transformations in a form similar to ordinary rotations and to describe the important discrete symmetries of C, P, and T. Then quantum mechanics is reformulated in the language of scattering theory, with the momentum-space S matrix replacing the coordinate-space hamiltonian as the central dynamical operator. Nonrelativistic perturbation scattering diagrams are then developed, and simple applications given for nuclear, atomic, and solid-state scattering problems. Next, relativistic scattering diagrams built up from covariant Feynman propagators and vertices in a manner consistent with the CPT theorem are considered. The theory is systematically applied to the lowest-order fundamental electromagnetic, strong, weak, and gravitational interactions. Finally, the use of higher-order Feynman diagrams to explain more detailed aspects of quantum electrodynamics (QED) and strong-interaction elementary-particle physics is surveyed. Throughout, the notion of currents is used to exploit the underlying symmetries and dynamical interactions of the various quantum forces. 258 references, 77 figures, 1 table

FF. A package to evaluate one-loop Feynman diagrams

International Nuclear Information System (INIS)

Oldenborgh, G.J. van

1990-09-01

A short description and a user's guide of the FF package are given. This package contains routines to evaluate numerically the scalar one-loop integrals occurring in the evaluation in one-loop Feynman diagrams. The algorithms chosen are numerically stable over most parameter space. (author). 5 refs.; 1 tab

Some remarks on non-planar Feynman diagrams

International Nuclear Information System (INIS)

Bielas, Krzysztof; Dubovyk, Ievgen; Gluza, Janusz

2013-12-01

Two criteria for planarity of a Feynman diagram upon its propagators (momentum ows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.

Some remarks on non-planar Feynman diagrams

Energy Technology Data Exchange (ETDEWEB)

Bielas, Krzysztof; Dubovyk, Ievgen; Gluza, Janusz [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2013-12-15

Two criteria for planarity of a Feynman diagram upon its propagators (momentum ows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.

Penguin-like diagrams from the standard model

International Nuclear Information System (INIS)

Ping, Chia Swee

2015-01-01

The Standard Model is highly successful in describing the interactions of leptons and quarks. There are, however, rare processes that involve higher order effects in electroweak interactions. One specific class of processes is the penguin-like diagram. Such class of diagrams involves the neutral change of quark flavours accompanied by the emission of a gluon (gluon penguin), a photon (photon penguin), a gluon and a photon (gluon-photon penguin), a Z-boson (Z penguin), or a Higgs-boson (Higgs penguin). Such diagrams do not arise at the tree level in the Standard Model. They are, however, induced by one-loop effects. In this paper, we present an exact calculation of the penguin diagram vertices in the ‘tHooft-Feynman gauge. Renormalization of the vertex is effected by a prescription by Chia and Chong which gives an expression for the counter term identical to that obtained by employing Ward-Takahashi identity. The on-shell vertex functions for the penguin diagram vertices are obtained. The various penguin diagram vertex functions are related to one another via Ward-Takahashi identity. From these, a set of relations is obtained connecting the vertex form factors of various penguin diagrams. Explicit expressions for the gluon-photon penguin vertex form factors are obtained, and their contributions to the flavor changing processes estimated

Penguin-like diagrams from the standard model

Energy Technology Data Exchange (ETDEWEB)

Ping, Chia Swee [High Impact Research, University of Malaya, 50603 Kuala Lumpur (Malaysia)

2015-04-24

The Standard Model is highly successful in describing the interactions of leptons and quarks. There are, however, rare processes that involve higher order effects in electroweak interactions. One specific class of processes is the penguin-like diagram. Such class of diagrams involves the neutral change of quark flavours accompanied by the emission of a gluon (gluon penguin), a photon (photon penguin), a gluon and a photon (gluon-photon penguin), a Z-boson (Z penguin), or a Higgs-boson (Higgs penguin). Such diagrams do not arise at the tree level in the Standard Model. They are, however, induced by one-loop effects. In this paper, we present an exact calculation of the penguin diagram vertices in the ‘tHooft-Feynman gauge. Renormalization of the vertex is effected by a prescription by Chia and Chong which gives an expression for the counter term identical to that obtained by employing Ward-Takahashi identity. The on-shell vertex functions for the penguin diagram vertices are obtained. The various penguin diagram vertex functions are related to one another via Ward-Takahashi identity. From these, a set of relations is obtained connecting the vertex form factors of various penguin diagrams. Explicit expressions for the gluon-photon penguin vertex form factors are obtained, and their contributions to the flavor changing processes estimated.

A guide to Feynman diagrams in the many-body problem

CERN Document Server

Mattuck, Richard D

1976-01-01

Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. ""A great delight to read."" - Physics Today. 1974 edition.

Construction of renormalized coefficient functions of the Feynman diagrams by means of a computer

International Nuclear Information System (INIS)

Tarasov, O.V.

1978-01-01

An algorithm and short description of computer program, written in SCHOONSCHIP, are given. The program is assigned for construction of integrands of renormalized coefficient functions of the Feynman diagrams in scalar theories in the case of arbitrary subtraction point. For the given Feynman graph computer completely realizes the R-operation of Bogolubov-Parasjuk and gives the result as an integral over Feynman parameters. With the help of the program the time construction of the whole renormalized coefficient function is equal approximately 30 s on the CDC-6500 computer

Teaching Electron--Positron--Photon Interactions with Hands-on Feynman Diagrams

Science.gov (United States)

Kontokostas, George; Kalkanis, George

2013-01-01

Feynman diagrams are introduced in many physics textbooks, such as those by Alonso and Finn and Serway, and their use in physics education has been discussed by various authors. They have an appealing simplicity and can give insight into events in the microworld. Yet students often do not understand their significance and often cannot combine the…

Asymptotic expansions of Feynman diagrams and the Mellin-Barnes representation

International Nuclear Information System (INIS)

Friot, Samuel; Greynat, David

2007-01-01

In this talk, we describe part of our recent work [S. Friot, D. Greynat and E. de Rafael, Phys. Lett. B 628 (2005) 73 [ (arXiv:hep-ph/0505038)] (see also [S. Friot, PhD Thesis (2005); D. Greynat, PhD Thesis (2005)]) that gives new results in the context of asymptotic expansions of Feynman diagrams using the Mellin-Barnes representation

Differential reduction of generalized hypergeometric functions from Feynman diagrams. One-variable case

Energy Technology Data Exchange (ETDEWEB)

Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Kniehl, Bernd A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik

2010-03-15

The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed. (orig.)

Do we need Feynman diagrams for higher order perturbation theory?

International Nuclear Information System (INIS)

Jora, Renata

2012-01-01

We compute the two loop and three loop corrections to the beta function for Yang-Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes contributions and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.

Generalized internal multiple imaging (GIMI) using Feynman-like diagrams

KAUST Repository

Zuberi, M. A. H.; Alkhalifah, Tariq Ali

2014-01-01

Single scattering events recorded in surface seismic data do not fully illuminate the subsurface structure, especially if it is complicated. In such cases, multiple internal scatterings (internal multiples) can help improve the illumination. We devise a generalized internal multiple imaging (GIMI) procedure that maps internal multiple energy to their true location with a relatively mild addition to the computational cost. GIMI theory relies heavily on seismic interferometry, which often involves cumbersome algebra, especially when one is dealing with high-order terms in the perturbation series. To make the derivations, and inference of the results easier, we introduce Feynman-like diagrams to represent different terms of the perturbation series (solution to the Lippman–Schwinger equation). The rules we define for the diagrams allow operations like convolution and cross-correlation in the series to be compressed in diagram form. The application of the theory to a double scattering example demonstrates the power of the method.

Generalized internal multiple imaging (GIMI) using Feynman-like diagrams

KAUST Repository

Zuberi, M. A. H.

2014-05-19

Single scattering events recorded in surface seismic data do not fully illuminate the subsurface structure, especially if it is complicated. In such cases, multiple internal scatterings (internal multiples) can help improve the illumination. We devise a generalized internal multiple imaging (GIMI) procedure that maps internal multiple energy to their true location with a relatively mild addition to the computational cost. GIMI theory relies heavily on seismic interferometry, which often involves cumbersome algebra, especially when one is dealing with high-order terms in the perturbation series. To make the derivations, and inference of the results easier, we introduce Feynman-like diagrams to represent different terms of the perturbation series (solution to the Lippman–Schwinger equation). The rules we define for the diagrams allow operations like convolution and cross-correlation in the series to be compressed in diagram form. The application of the theory to a double scattering example demonstrates the power of the method.

The diamond rule for multi-loop Feynman diagrams

International Nuclear Information System (INIS)

Ruijl, B.; Ueda, T.; Vermaseren, J.A.M.

2015-01-01

An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed

Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation

International Nuclear Information System (INIS)

Gonzalez, Ivan; Schmidt, Ivan

2007-01-01

We present an improved form of the integration technique known as NDIM (negative dimensional integration method), which is a powerful tool in the analytical evaluation of Feynman diagrams. Using this technique we study a φ 3 +φ 4 theory in D=4-2ε dimensions, considering generic topologies of L loops and E independent external momenta, and where the propagator powers are arbitrary. The method transforms the Schwinger parametric integral associated to the diagram into a multiple series expansion, whose main characteristic is that the argument contains several Kronecker deltas which appear naturally in the application of the method, and which we call diagram presolution. The optimization we present here consists in a procedure that minimizes the series multiplicity, through appropriate factorizations in the multinomials that appear in the parametric integral, and which maximizes the number of Kronecker deltas that are generated in the process. The solutions are presented in terms of generalized hypergeometric functions, obtained once the Kronecker deltas have been used in the series. Although the technique is general, we apply it to cases in which there are 2 or 3 different energy scales (masses or kinematic variables associated to the external momenta), obtaining solutions in terms of a finite sum of generalized hypergeometric series 1 and 2 variables respectively, each of them expressible as ratios between the different energy scales that characterize the topology. The main result is a method capable of solving Feynman integrals, expressing the solutions as hypergeometric series of multiplicity (n-1), where n is the number of energy scales present in the diagram

On the scattering of gluons in the GKP string

International Nuclear Information System (INIS)

Bianchi, Lorenzo; Hamburg Univ.; Bianchi, Marco S.

2015-11-01

We compute the one-loop S-matrix for the light bosonic excitations of the GKP string at strong coupling. These correspond, on the gauge theory side, to gluon insertions in the GKP vacuum. We perform the calculation by Feynman diagrams in the worldsheet theory and we compare the result to the integrability prediction, finding perfect agreement for the scheme independent part. For scheme dependent rational terms we test different schemes and find that a recent proposal reproduces exactly the integrability prediction.

Appell functions and the scalar one-loop three-point integrals in Feynman diagrams

Energy Technology Data Exchange (ETDEWEB)

Cabral-Rosetti, L G [Departamento de Posgrado, Centro Interdisciplinario de Investigacion y Docencia en Educacion Tecnica (CIIDET), Av. Universidad 282 Pte., Col. Centro, A. Postal 752, C.P. 76000, Santiago de Queretaro, Qro. (Mexico); Sanchis-Lozano, M A [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, 46100 Burjassot, Valencia (Spain)

2006-05-15

The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms coming from a previous investigation. Special cases are obtained for particular values of internal masses and external momenta.

TMD splitting functions in kT factorization. The real contribution to the gluon-to-gluon splitting

International Nuclear Information System (INIS)

Hentschinski, M.; Kusina, A.; Kutak, K.; Serino, M.

2018-01-01

We calculate the transverse momentum dependent gluon-to-gluon splitting function within k T -factorization, generalizing the framework employed in the calculation of the quark splitting functions in Hautmann et al. (Nucl Phys B 865:54-66, arXiv:1205.1759, 2012), Gituliar et al. (JHEP 01:181, arXiv:1511.08439, 2016), Hentschinski et al. (Phys Rev D 94(11):114013, arXiv:1607.01507, 2016) and demonstrate at the same time the consistency of the extended formalism with previous results. While existing versions of k T factorized evolution equations contain already a gluon-to-gluon splitting function i.e. the leading order Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel or the Ciafaloni-Catani-Fiorani-Marchesini (CCFM) kernel, the obtained splitting function has the important property that it reduces both to the leading order BFKL kernel in the high energy limit, to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) gluon-to-gluon splitting function in the collinear limit as well as to the CCFM kernel in the soft limit. At the same time we demonstrate that this splitting kernel can be obtained from a direct calculation of the QCD Feynman diagrams, based on a combined implementation of the Curci-Furmanski-Petronzio formalism for the calculation of the collinear splitting functions and the framework of high energy factorization. (orig.)

Gravitational lensing of the CMB: A Feynman diagram approach

Directory of Open Access Journals (Sweden)

Elizabeth E. Jenkins

2014-09-01

Full Text Available We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS. We study the Hu–Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to O(ϕ4 in the lensing potential ϕ. By identifying the diagrams responsible for the previously noted large O(ϕ4 term, we conclude that the lensing expansion does not break down. The convergence can be significantly improved by a reorganization of the ϕ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel, including many previously unexplored cases. We briefly discuss other applications to cosmology of this diagrammatic approach, such as distortions of the CMB due to patchy reionization, or due to Faraday rotation from primordial axion fields.

Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams

International Nuclear Information System (INIS)

Ablinger, Jakob; Bluemlein, Johannes; Klein, Sebastian; Schneider, Carsten

2010-01-01

By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion.

One-loop Higgs plus four gluon amplitudes. Full analytic results

International Nuclear Information System (INIS)

Badger, Simon; Nigel Glover, E.W.; Williams, Ciaran; Mastrolia, Pierpaolo

2009-10-01

We consider one-loop amplitudes of a Higgs boson coupled to gluons in the limit of a large top quark mass. We treat the Higgs as the real part of a complex field φ that couples to the self-dual field strengths and compute the one-loop corrections to the φ-NMHV amplitude, which contains one gluon of positive helicity whilst the remaining three have negative helicity. We use four-dimensional unitarity to construct the cut-containing contributions and a hybrid of Feynman diagram and recursive based techniques to determine the rational piece. Knowledge of the φ-NMHV contribution completes the analytic calculation of the Higgs plus four gluon amplitude. For completeness we also include expressions for the remaining helicity configurations which have been calculated elsewhere. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark is large compared to all other scales in the problem. (orig.)

Modern summation methods and the computation of 2- and 3-loop Feynman diagrams

International Nuclear Information System (INIS)

Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Klein, Sebastian

2010-06-01

By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion. (orig.)

Modern summation methods and the computation of 2- and 3-loop Feynman diagrams

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Schneider, Carsten [Linz Univ. (AT). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, Sebastian [RWTH Aachen (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie

2010-06-15

By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion. (orig.)

Feynman diagrams sampling for quantum field theories on the QPACE 2 supercomputer

Energy Technology Data Exchange (ETDEWEB)

Rappl, Florian

2016-08-01

This work discusses the application of Feynman diagram sampling in quantum field theories. The method uses a computer simulation to sample the diagrammatic space obtained in a series expansion. For running large physical simulations powerful computers are obligatory, effectively splitting the thesis in two parts. The first part deals with the method of Feynman diagram sampling. Here the theoretical background of the method itself is discussed. Additionally, important statistical concepts and the theory of the strong force, quantum chromodynamics, are introduced. This sets the context of the simulations. We create and evaluate a variety of models to estimate the applicability of diagrammatic methods. The method is then applied to sample the perturbative expansion of the vertex correction. In the end we obtain the value for the anomalous magnetic moment of the electron. The second part looks at the QPACE 2 supercomputer. This includes a short introduction to supercomputers in general, as well as a closer look at the architecture and the cooling system of QPACE 2. Guiding benchmarks of the InfiniBand network are presented. At the core of this part, a collection of best practices and useful programming concepts are outlined, which enables the development of efficient, yet easily portable, applications for the QPACE 2 system.

ALOHA: Automatic libraries of helicity amplitudes for Feynman diagram computations

Science.gov (United States)

de Aquino, Priscila; Link, William; Maltoni, Fabio; Mattelaer, Olivier; Stelzer, Tim

2012-10-01

We present an application that automatically writes the HELAS (HELicity Amplitude Subroutines) library corresponding to the Feynman rules of any quantum field theory Lagrangian. The code is written in Python and takes the Universal FeynRules Output (UFO) as an input. From this input it produces the complete set of routines, wave-functions and amplitudes, that are needed for the computation of Feynman diagrams at leading as well as at higher orders. The representation is language independent and currently it can output routines in Fortran, C++, and Python. A few sample applications implemented in the MADGRAPH 5 framework are presented. Program summary Program title: ALOHA Catalogue identifier: AEMS_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: http://www.opensource.org/licenses/UoI-NCSA.php No. of lines in distributed program, including test data, etc.: 6094320 No. of bytes in distributed program, including test data, etc.: 7479819 Distribution format: tar.gz Programming language: Python2.6 Computer: 32/64 bit Operating system: Linux/Mac/Windows RAM: 512 Mbytes Classification: 4.4, 11.6 Nature of problem: An effcient numerical evaluation of a squared matrix element can be done with the help of the helicity routines implemented in the HELAS library [1]. This static library contains a limited number of helicity functions and is therefore not always able to provide the needed routine in the presence of an arbitrary interaction. This program provides a way to automatically create the corresponding routines for any given model. Solution method: ALOHA takes the Feynman rules associated to the vertex obtained from the model information (in the UFO format [2]), and multiplies it by the different wavefunctions or propagators. As a result the analytical expression of the helicity routines is obtained. Subsequently, this expression is

FeynRules - Feynman rules made easy

OpenAIRE

Christensen, Neil D.; Duhr, Claude

2008-01-01

In this paper we present FeynRules, a new Mathematica package that facilitates the implementation of new particle physics models. After the user implements the basic model information (e.g. particle content, parameters and Lagrangian), FeynRules derives the Feynman rules and stores them in a generic form suitable for translation to any Feynman diagram calculation program. The model can then be translated to the format specific to a particular Feynman diagram calculator via F...

A T-matrix calculation for in-medium heavy-quark gluon scattering

International Nuclear Information System (INIS)

Huggins, K.; Rapp, R.

2012-01-01

The interactions of charm and bottom quarks in a quark-gluon plasma (QGP) are evaluated using a thermodynamic 2-body T-matrix. We specifically focus on heavy-quark (HQ) interactions with thermal gluons with an input potential motivated by lattice-QCD computations of the HQ free energy. The latter is implemented into a field-theoretic ansatz for color-Coulomb and (remnants of) confining interactions. This, in particular, enables to discuss corrections to the potential approach, specifically hard-thermal-loop corrections to the vertices, relativistic corrections deduced from pertinent Feynman diagrams, and a suitable projection on transverse thermal gluons. The resulting potentials are applied to compute scattering amplitudes in different color channels and utilized for a calculation of the corresponding HQ drag coefficient in the QGP. A factor of ∼2-3 enhancement over perturbative results is obtained, mainly driven by the resummation in the attractive color-channels.

The unitary mechanism of infrared freezing in QCD with massive gluons

International Nuclear Information System (INIS)

Shirkov, D.V.

1999-01-01

A 'natural' model for the QCD invariant (running) coupling, free of the IR singularity, is proposed. It is based upon the hypothesis of finite gluon mass m gl existence and, technically, uses an accurate treating of threshold behaviour of Feynman diagram contribution. The model correlates with the unitarity condition. Quantitative estimate, performed in the one-loop approximation yields a reasonable lower bound for this mass m gl > 150 MeV and a smooth IR freezing at the level α s (Q 2 ) < or ∼ 1

A new approach to the Taylor expansion of multiloop Feynman diagrams

International Nuclear Information System (INIS)

Tarasov, O.V.

1996-01-01

We present a new method for the Taylor expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function for the coefficients of the small momentum expansion of an arbitrary diagram. The method is applicable for the expansion with respect to all or a subset of external momenta. The coefficients of the expansion are obtained by applying a differential operator to a given integral with shifted value of the space-time dimension d and the expansion momenta set equal to zero. Integrals with changed d are evaluated by using the generalized recurrence relations recently proposed [O.V. Tarasov, Connection between Feynman integrals having different values of the space-time dimension, preprint DESY 96-068, JINR E2-96-62 (hep-th/9606018), to be published in Phys. Rev. D 54, No. 10 (1996)]. We show how the method works for one- and two-loop integrals. It is also illustrated that our method is simpler and more efficient than others. (orig.)

Quarks and gluons in the phase diagram of quantum chromodynamics

Energy Technology Data Exchange (ETDEWEB)

Welzbacher, Christian Andreas

2016-07-14

In this dissertation we study the phase diagram of strongly interacting matter by approaching the theory of quantum chromodynamics in the functional approach of Dyson-Schwinger equations. With these quantum (field) equations of motions we calculate the non-perturbative quark propagator within the Matsubara formalism. We built up on previous works and extend the so-called truncation scheme, which is necessary to render the infinite tower of Dyson-Schwinger equations finite and study phase transitions of chiral symmetry and the confinement/deconfinement transition. In the first part of this thesis we discuss general aspects of quantum chromodynamics and introduce the Dyson-Schwinger equations in general and present the quark Dyson-Schwinger equation together with its counterpart for the gluon. The Bethe-Salpeter equation is introduced which is necessary to perform two-body bound state calculations. A view on the phase diagram of quantum chromodynamics is given, including the discussion of order parameter for chiral symmetry and confinement. Here we also discuss the dependence of the phase structure on the masses of the quarks. In the following we present the truncation and our results for an unquenched N{sub f} = 2+1 calculation and compare it to previous studies. We highlight some complementary details for the quark and gluon propagator and discus the resulting phase diagram, which is in agreement with previous work. Results for an equivalent of the Columbia plot and the critical surface are discussed. A systematically improved truncation, where the charm quark as a dynamical quark flavour is added, will be presented in Ch. 4. An important aspect in this investigation is the proper adjustment of the scales. This is done by matching vacuum properties of the relevant pseudoscalar mesons separately for N{sub f} = 2+1 and N f = 2+1+1 via a solution of the Bethe-Salpeter equation. A comparison of the resulting N{sub f} = 2+1 and N{sub f} = 2+1+1 phase diagram indicates

Equivalence between the Arquès-Walsh sequence formula and the number of connected Feynman diagrams for every perturbation order in the fermionic many-body problem

Science.gov (United States)

Castro, E.

2018-02-01

From the perturbative expansion of the exact Green function, an exact counting formula is derived to determine the number of different types of connected Feynman diagrams. This formula coincides with the Arquès-Walsh sequence formula in the rooted map theory, supporting the topological connection between Feynman diagrams and rooted maps. A classificatory summing-terms approach is used, in connection to discrete mathematical theory.

Gluon fragmentation in T(1S) decays

International Nuclear Information System (INIS)

Bienlein, J.K.

1983-05-01

In T(1S) decays most observables (sphericity, charged multiplicity, photonic energy fraction, inclusive spectra) can be understood assuming that gluons fragment like quarks. New results from LENA use the (axis-independent) Fox-Wolfram moments for the photonic energy deposition. Continuum reactions show 'standard' Field-Feynman fragmentation. T(1S) decays show a significant difference in the photonic energy topology. It is more isotropic than with the Field-Feynman fragmentation scheme. Gluon fragmentation into isoscalar mesons (a la Peterson and Walsh) is excluded. But if one forces the leading particle to be isoscalar, one gets good agreement with the data. (orig.)

Systematic implementation of implicit regularization for multi-loop Feynman Diagrams

International Nuclear Information System (INIS)

Cherchiglia, Adriano Lana; Sampaio, Marcos; Nemes, Maria Carolina

2011-01-01

Full text: Implicit Regularization (IR) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. The essence of the method is to write the divergences in terms of loop integrals in one internal momentum which do not need to be explicitly evaluated. Moreover it acts in the physical dimension of the theory and gauge invariance is controlled by regularization dependent surface terms which when set to zero define a constrained version of IR (CIR) and deliver gauge invariant amplitudes automatically. Therefore it is in principle applicable to all physical relevant quantum field theories, supersymmetric gauge theories included. A non trivial question is whether we can generalize this program to arbitrary loop order in consonance with locality, unitarity and Lorentz invariance, especially when overlapping divergences occur. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IR program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multi-loop amplitude in a well defined set of basic divergent integrals in one internal momentum. We present several examples (from 1-loop to n-loops) using scalar φ 6 3 theory in order to help the reader understand and visualize the essence of the IR program. The choice of a scalar theory does not reduce the generality of the method presented since all other physical theories can be treated within the same strategy after space time and internal algebra are performed. Another result of this contribution is to show that if the surface terms are not set to zero they will contaminate the renormalization group coefficients. Thus, we are forced to adopt CIR which is equivalent to demand momentum routing invariance

Looking at the gluon moment of the nucleon with dynamical twisted mass fermions

International Nuclear Information System (INIS)

Alexandrou, Constantia; Cyprus Institute, Nicosia; Drach, Vincent; Wiese, Christian; Hadjiyiannakou, Kyriakos; Jansen, Karl; Deutsches Elektronen-Synchrotron; Kostrzewa, Bartosz

2013-11-01

To understand the structure of hadrons it is important to know the PDF of their constituents, the quarks and gluons. In our work we aim to compute the first moment of the gluon PDF left angle x right angle g for the nucleon. We follow two possible approaches in order to extract the gluon moment: the Feynman-Hellmann theorem and a direct method with smearing of the gluon operator. We present preliminary results computed on 24 3 x 48 lattices for the case where the Feynman-Hellman theorem is used and 32 3 x 64 lattices for the direct method, employing N f =2+1+1 maximally twisted mass fermions.

Feynman versus Bakamjian-Thomas in light-front dynamics

International Nuclear Information System (INIS)

Araujo, W.R.B. de; Beyer, M.; Weber, H.J.; Frederico, T.

1999-01-01

We compare the Bakamjian-Thomas (BT) formulation of relativistic few-body systems with light-front field theories that maintain closer contact with Feynman diagrams. We find that Feynman diagrams distinguish Melosh rotations and other kinematical quantities belonging to various composite subsystem frames that correspond to different loop integrals. The BT formalism knows only the rest frame of the whole composite system, where everything is evaluated. (author)

JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes

Science.gov (United States)

Binosi, D.; Collins, J.; Kaufhold, C.; Theussl, L.

2009-09-01

A new version of the Feynman graph plotting tool JaxoDraw is presented. Version 2.0 is a fundamental re-write of most of the JaxoDraw core and some functionalities, in particular importing graphs, are not backward-compatible with the 1.x branch. The most prominent new features include: drawing of Bézier curves for all particle modes, on-the-fly update of edited objects, multiple undo/redo functionality, the addition of a plugin infrastructure, and a general improved memory performance. A new LaTeX style file is presented that has been written specifically on top of the original axodraw.sty to meet the needs of this new version. New version program summaryProgram title: JaxoDraw Catalogue identifier: ADUA_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUA_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL No. of lines in distributed program, including test data, etc.: 103 544 No. of bytes in distributed program, including test data, etc.: 3 745 814 Distribution format: tar.gz Programming language: Java Computer: Any Java-enabled platform Operating system: Any Java-enabled platform, tested on Linux, Windows XP, Mac OS X Classification: 14 Catalogue identifier of previous version: ADUA_v1_0 Journal reference of previous version: Comput. Phys. Comm. 161 (2004) 76 Does the new version supersede the previous version?: Yes Nature of problem: Existing methods for drawing Feynman diagrams usually require some hard-coding in one or the other programming or scripting language. It is not very convenient and often time consuming, to generate relatively simple diagrams. Solution method: A program is provided that allows for the interactive drawing of Feynman diagrams with a graphical user interface. The program is easy to learn and use, produces high quality output in several formats and runs on any operating system where a Java Runtime Environment is available. Reasons for new version: A

Critical exponents predicted by grouping of Feynman diagrams in φ4 model

International Nuclear Information System (INIS)

Kaupuzs, J.

2001-01-01

Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams of φ 4 model with O(n) symmetry. As a result, equations for calculation of the two-point correlation function are obtained which allow to predict possible exact values of critical exponents in two and three dimensions by proving relevant scaling properties of the asymptotic solution at (and near) the criticality. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments. (orig.)

Automatically generating Feynman rules for improved lattice field theories

International Nuclear Information System (INIS)

Hart, A.; Hippel, G.M. von; Horgan, R.R.; Storoni, L.C.

2005-01-01

Deriving the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially when improvement terms are present. This physically important task is, however, suitable for automation. We describe a flexible algorithm for generating Feynman rules for a wide range of lattice field theories including gluons, relativistic fermions and heavy quarks. We also present an efficient implementation of this in a freely available, multi-platform programming language (PYTHON), optimised to deal with a wide class of lattice field theories

Exact Maximum-Entropy Estimation with Feynman Diagrams

Science.gov (United States)

Netser Zernik, Amitai; Schlank, Tomer M.; Tessler, Ran J.

2018-02-01

A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.

One gluon, two gluon: multigluon production via high energy evolution

International Nuclear Information System (INIS)

Kovner, Alex; Lublinsky, Michael

2006-01-01

We develop an approach for calculating the inclusive multigluon production within the JIMWLK high energy evolution. We give a formal expression of multigluon cross section in terms of a generating functional for arbitrary number of gluons n. In the dipole limit the expression simplifies dramatically. We recover the previously known results for single and double gluon inclusive cross section and generalize those for arbitrary multigluon amplitude in terms of Feynman diagramms of Pomeron - like objects coupled to external rapidity dependent field s(η). We confirm the conclusion that the AGK cutting rules in general are violated in multigluon production. However we present an argument to the effect that for doubly inclusive cross section the AGK diagramms give the leading contribution at high energy, while genuine violation only occurs for triple and higher inclusive gluon production. We discuss some general properties of our expressions and suggest a line of argument to simplify the approach further

A mapping between Feynman and string motivated one-loop rules in gauge theories

International Nuclear Information System (INIS)

Bern, Z.

1992-01-01

Recently, computationally efficient rules for one-loop gauge theory amplitudes have been derived from string theory. We demonstrate the relationship of the compact string organization of the amplitude to Feynman diagrams. In particular, we explicitly show how large cancellations inherent in conventional Feynman diagram computations are avoided by the string motivated rules. (orig.)

The algebraic locus of Feynman integrals

OpenAIRE

Kol, Barak

2016-01-01

In the Symmetries of Feynman Integrals (SFI) approach, a diagram's parameter space is foliated by orbits of a Lie group associated with the diagram. SFI is related to the important methods of Integrations By Parts and of Differential Equations. It is shown that sometimes there exist a locus in parameter space where the set of SFI differential equations degenerates into an algebraic equation, thereby enabling a solution in terms of integrals associated with degenerations of the diagram. This i...

The effect of the vertical part of the path on the real time Feynman rules in finite temperature field theory 2-point functions and vacuum diagrams

International Nuclear Information System (INIS)

Gelis, F.

1996-01-01

The effect of the contribution of the vertical part of the real time path is studied completely in the case of two points functions and vacuum diagrams. Indeed, this vertical part generally contributes in the calculation of a given graph. Moreover, this contribution is essential in order to have a consistent equilibrium theory: thanks to this contribution, the Green functions are effectively invariant by time translation, as they should be. As a by product, it is shown that the perturbative calculations give a result which does not depend on the initial time t I and final time t F of the path. The property of independence with respect to t I is closely related to the KMS conditions, i.e. to the fact the system is in thermal equilibrium. In the case of two point functions and vacuum diagrams, the contribution of the vertical part can be taken into account by the n(vertical stroke k 0 vertical stroke) prescription in the usual RTF Feynman rules. The extra Feynman rule needed for vacuum diagrams is shown not to be related directly to the contribution of the vertical part of the path. (orig.). With 4 figs

Non-planar Feynman diagrams and Mellin-Barnes representations with AMBRE 3.0

International Nuclear Information System (INIS)

Dubovyk, Ievgen; Gluza, Janusz; Riemann, Tord

2016-04-01

We introduce the Mellin-Barnes representation of general Feynman integrals and discuss their evaluation. The Mathematica package AMBRE has been recently extended in order to cover consistently non-planar Feynman integrals with two loops. Prospects for the near future are outlined. This write-up is an introduction to new results which have also been presented elsewhere.

Ring diagrams and phase transitions

International Nuclear Information System (INIS)

Takahashi, K.

1986-01-01

Ring diagrams at finite temperatures carry most infrared-singular parts among Feynman diagrams. Their effect to effective potentials are in general so significant that one must incorporate them as well as 1-loop diagrams. The author expresses these circumstances in some examples of supercooled phase transitions

Dynamical quark and gluon condensates from a modified perturbative QCD

International Nuclear Information System (INIS)

Cabo Montes de Oca, A.; Martinez Pedrera, D.

2004-12-01

As it was suggested by previous works on a modified perturbation expansion for QCD, the possibility for the generation of large quark condensates in the massless version of the theory is explored. For this purpose, it is firstly presented a way to well define the Feynman diagrams at any number of loops by just employing dimensional regularization. After that, the calculated zero and one loop corrections to the effective potential indicate a strong instability of the system under the generation of quark condensates even in the absence of the gluon one. The quark condensate dependence of particular two loop terms does not modify the instability picture arising at one loop. The results suggest a possible mechanism for a sort of Top Condensate Model to be a dynamically fixed effective action for massless QCD. The inability of lattice calculations in detecting this possibility could be related to the current limitations in treating the fermion determinants. (author)

Gluon quasidistribution function at one loop

Energy Technology Data Exchange (ETDEWEB)

Wang, Wei; Zhao, Shuai [Shanghai Jiao Tong University, INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, School of Physics and Astronomy, Shanghai (China); Zhu, Ruilin [Shanghai Jiao Tong University, INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, School of Physics and Astronomy, Shanghai (China); Nanjing Normal University, Department of Physics and Institute of Theoretical Physics, Nanjing, Jiangsu (China)

2018-02-15

We study the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory. For the quark quasidistribution, power law ultraviolet divergences arise in the cut-off scheme and an important observation is that they all are subjected to Wilson lines. However for the gluon quasidistribution function, we first point out that the linear ultraviolet divergences also exist in the real diagram which is not connected to any Wilson line. We then study the one loop corrections to parton distribution functions in both cut-off scheme and dimensional regularization to deal with the ultraviolet divergences. In addition to the ordinary quark and gluon distributions, we also include the quark to gluon and gluon to quark splitting diagrams. The complete one-loop matching factors between the quasi and light cone parton distribution functions are presented in the cut-off scheme. We derive the P{sup z} evolution equation for quasi parton distribution functions, and find that the P{sup z} evolution kernels are identical to the DGLAP evolution kernels. (orig.)

Factorization in QCD in Feynman gauge

International Nuclear Information System (INIS)

Tucci, R.R.

1985-01-01

We present a mass divergence power counting technique for QCD in the Feynman gauge. For the process γ/sup */ → qq, we find the leading regions of integration and show that single diagrams are at worst logarithmically divergent. Using the Weyl representation facilities the γ matrix manipulations necessary for power counting and adds much physical insight. We prove Ward type identities which are needed in the proof of factorization of the Drill Yan process. Previous treatments prove them only for an axial gauge, and the proofs are diagrammatic in nature. We, on the other hand, establish the identities for the Feynman gauge and through symmetry considerations at the Lagrangian level. The strategy is to first derive exact results in a background field gauge and then to show that to leading order in the mass divergences the background field gauge results can be used in the Feynman gauge

Gluing Ladder Feynman Diagrams into Fishnets

International Nuclear Information System (INIS)

Basso, Benjamin; Dixon, Lance J.; Stanford University, CA; University of California, Santa Barbara, CA

2017-01-01

We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar Φ "4 theory. Our results are always multilinear combinations of ladder integrals, which are in turn built out of classical polylogarithms. The Steinmann relations provide a powerful constraint on such linear combinations, which leads to a natural conjecture for any fishnet diagram as the determinant of a matrix of ladder integrals.

Off-shell gluon production in interaction of a projectile with 2 or 3 targets

Energy Technology Data Exchange (ETDEWEB)

Braun, M.A.; Salykin, M.Yu. [Saint-Petersburg State University, Department of High Energy physics, Saint Petersburg (Russian Federation)

2017-07-15

Within the effective QCD action for the Regge kinematics, the amplitudes for virtual gluon emission are studied in collision of a projectile with two and three targets. It is demonstrated that all non-Feynman singularities cancel between induced vertices and rescattering contributions. Formulas simplify considerably in a special gauge, which is a straightforward generalization of the light-cone gauge for emission of real gluons. (orig.)

On application of analytical transformation system using a computer for Feynman intearal calculation

International Nuclear Information System (INIS)

Gerdt, V.P.

1978-01-01

Various systems of analytic transformations for the calculation of Feynman integrals using computers are discussed. The hyperspheric technique Which is used to calculate Feynman integrals enables to perform angular integration for a set of diagrams, thus reducing the multiplicity of integral. All calculations based on this method are made with the ASHMEDAL program. Feynman integrals are calculated in Euclidean space using integration by parts and some differential identities. Analytic calculation of Feynman integral is performed by the MACSYMA system. Dispersion method of integral calculation is implemented in the SCHOONSCHIP system, calculations based on features of Nielsen function are made using efficient SINAC and RSIN programs. A tube of basic Feynman integral parameters calculated using the above techniques is given

Infrared finite ghost propagator in the Feynman gauge

International Nuclear Information System (INIS)

Aguilar, A. C.; Papavassiliou, J.

2008-01-01

We demonstrate how to obtain from the Schwinger-Dyson equations of QCD an infrared finite ghost propagator in the Feynman gauge. The key ingredient in this construction is the longitudinal form factor of the nonperturbative gluon-ghost vertex, which, contrary to what happens in the Landau gauge, contributes nontrivially to the gap equation of the ghost. The detailed study of the corresponding vertex equation reveals that in the presence of a dynamical infrared cutoff this form factor remains finite in the limit of vanishing ghost momentum. This, in turn, allows the ghost self-energy to reach a finite value in the infrared, without having to assume any additional properties for the gluon-ghost vertex, such as the presence of massless poles. The implications of this result and possible future directions are briefly outlined

Twistor Spinoffs for Collider Physics

International Nuclear Information System (INIS)

Dixon, Lance

2006-01-01

In the coming decade, the search for the Higgs boson, and for new particles representing physics beyond the Standard Model, will be carried out by colliding protons at the Tevatron and the Large Hadron Collider. A collision of two protons, each of which is made out of quarks and gluons, is inherently messy. Feynman likened it to smashing two Swiss watches together to figure out how they work. In recent decades, we have learned better how the Swiss watches work, using the theory of quark-gluon interactions, quantum chromodynamics. Armed with this knowledge, we can better predict the results of collisions at the Tevatron and the LHC, to see whether the Standard Model holds up or fails, or whether new particles are in the data. But a major bottleneck is simply in adding up Feynman diagrams, for which the rules are well known, yet there can be thousands of extremely complicated diagrams. In fact, the sum of all diagrams is often much simpler than the typical one, suggesting hidden symmetries and better ways to compute. In the past two years, spinoffs from a new theory, 'twistor string theory', have led to very efficient alternatives to Feynman diagrams for making such predictions, as I will explain.

A development of an accelerator board dedicated for multi-precision arithmetic operations and its application to Feynman loop integrals

International Nuclear Information System (INIS)

Motoki, S; Ishikawa, T; Yuasa, F; Daisaka, H; Nakasato, N; Fukushige, T; Kawai, A; Makino, J

2015-01-01

Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagrams with multi-loop integrals which may require multi-precision calculation. We developed a dedicated accelerator system for multiprecision calculations (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision. (paper)

Thermal single-gluon exchange potential for heavy quarkonium in the static limit

International Nuclear Information System (INIS)

Zhu, Jia-Qing; Ma, Zhi-Lei; Shi, Chao-Yi; Li, Yun-De

2015-01-01

The calculations of thermal single-gluon exchange potential for heavy quarkonium in Feynman and Coulomb gauges are presented, and the comparisons between them and the hard thermal loop approximation ones which were first calculated by Laine et al. are illustrated. The numerical results show that the hard thermal loop thermal single-gluon exchange potential (especially its imaginary part) which used in many researches make some errors in the practical calculations at the temperature range accessible in the present experiment, and the problem of gauge dependent cannot be avoided when the complete self energy is used in the derivation of potential

Connection between Feynman integrals having different values of the space-time dimension

International Nuclear Information System (INIS)

Tarasov, O.V.

1996-05-01

A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension d is proposed. The relation between d and d-2 dimensional integrals is given in terms of a differential operator for which an explicit formula can be obtained for each Feynman diagram. We show how the method works for one-, two- and three-loop integrals. The new recurrence relations w.r.t. d are complementary to the recurrence relations which derive from the method of integration by parts. We find that the problem of the irreducible numerators in Feynman integrals can be naturally solved in the framework of the proposed generalized recurrence relations. (orig.)

Selected topics on the nonrelativistic diagram technique

International Nuclear Information System (INIS)

Blokhintsev, L.D.; Narodetskij, I.M.

1983-01-01

The construction of the diagrams describing various processes in the four-particle systems is considered. It is shown that these diagrams, in particular the diagrams corresponding to the simple mechanisms often used in nuclear and atomic reaction theory, are readily obtained from the Faddeev-Yakubovsky equations. The covariant four-dimensional formalism of nonrelativistic Feynman graphs and its connection to the three-dimensional graph technique are briefly discussed

Constituent gluons and the static quark potential

Energy Technology Data Exchange (ETDEWEB)

Greensite, Jeff [San Francisco State Univ., CA (United States); Szczepaniak, Adam P. [Indiana Univ., Bloomington, IN (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

2016-04-01

We suggest that Hamiltonian matrix elements between physical states in QCD might be approximated, in Coulomb gauge, by "lattice-improved" tree diagrams; i.e. tree diagram contributions with dressed ghost, transverse gluon, and Coulomb propagators obtained from lattice simulations. Such matrix elements can be applied to a variational treatment of hadronic states which include constituent gluons. As an illustration and first application of this hybrid approach, we derive a variational estimate of the heavy quark potential for distances up to 2.5 fm. The Coulomb string tension in SU(3) gauge theory is about a factor of four times greater than the asymptotic string tension. In our variational approach, using for simplicity a single variational parameter, we can reduce this overshoot by nearly the factor required. The building blocks of our approach are Coulomb gauge propagators, and in this connection we present new lattice results for the ghost and transverse gluon propagators in position space.

Analytic computations of massive one-loop amplitudes

International Nuclear Information System (INIS)

Badger, Simon; Yundin, Valery; Sattler, Ralf

2010-06-01

We show some new applications of on-shell methods to calculate compact helicity amplitudes for t anti t production through gluon fusion. The rational and mass renormalisation contributions are extracted from two independent Feynman diagram based approaches. (orig.)

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

International Nuclear Information System (INIS)

Groote, S.; Koerner, J.G.; Pivovarov, A.A.

2007-01-01

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases in their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their numerical evaluation in the general case of D-dimensional space-time as well as in integer dimensions D = D 0 for different values of dimensions including the most important practical cases D 0 = 2, 3, 4. Substantial simplifications occur for odd integer space-time dimensions where the final results can be expressed in closed form through elementary functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology where an irreducible loop is added

Solving recurrence relations for multi-loop Feynman integrals

International Nuclear Information System (INIS)

Smirnov, Vladimir A.; Steinhauser, Matthias

2003-01-01

We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, i.e., the problem of expressing any Feynman integral from this class as a linear combination of master integrals. We show how the parametric representation invented by Baikov [Phys. Lett. B 385 (1996) 404, Nucl. Instrum. Methods A 389 (1997) 347] can be used to characterize the master integrals and to construct an algorithm for evaluating the corresponding coefficient functions. To illustrate this procedure we use simple one-loop examples as well as the class of diagrams appearing in the calculation of the two-loop heavy quark potential

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in φ4-Theory

International Nuclear Information System (INIS)

Finster, Felix; Tolksdorf, Juergen

2012-01-01

Solutions of the classical φ 4 -theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a ''classical measurement process'' in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

Science.gov (United States)

Finster, Felix; Tolksdorf, Jürgen

2012-05-01

Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

AMBRE - a mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Gluza, J.; Kajda, K. [Silesia Univ, Katowice (Poland). Dept. of Field Theory and Particle Physics, Inst. of Phsyics; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2007-05-15

The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2{epsilon} dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. AMBRE uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version of AMBRE works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in {epsilon}. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops. (orig.)

The five-gluon amplitude and one-loop integrals

International Nuclear Information System (INIS)

Bern, Z.; Dixon, L.; Kosower, D.A.

1992-12-01

We review the conventional field theory description of the string motivated technique. This technique is applied to the one-loop five-gluon amplitude. To evaluate the amplitude a general method for computing dimensionally regulated one-loop integrals is outlined including results for one-loop integrals required for the pentagon diagram and beyond. Finally, two five-gluon helicity amplitudes are given

Diagrams in the polaron model

International Nuclear Information System (INIS)

Smondyrev, M.A.

1985-01-01

The perturbation theory for the polaron energy is systematically treated on the diagrammatic basis. Feynman diagrams being constructed allow to calculate the polaron energy up to the third order in powers of the coupling constant. Similar calculations are performed for the average number of virtual phonons

A complete algebraic reduction of one-loop tensor Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Fleischer, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2010-09-15

Guided by the need to eliminate inverse Gram determinants (){sub 5} from tensorial 5-point functions and sub-Gram determinants (){sub 4} from tensorial 4-point functions, we set up a new and very efficient approach for the tensor reduction of Feynman integrals. We eliminate all Gram determinants for one-loop 5-point integrals up to tensors of rank R=5 by reducing their tensor coefficients to higherdimensional 4-point tensor coefficients. These in turn are reduced to expressions which are free of inverse powers of (){sub 4}, but depend on higher-dimensional integrals I{sub 4}{sup (d)} with d{<=}2R. Their expression in terms of scalar integrals defined in the generic dimension, I{sub 4}; I{sub 3}; I{sub 2}; I{sub 1}, however, introduces coefficients [1=(){sub 4}]{sup R} for tensors of rank R. For small or vanishing (){sub 4}, an efficient expansion is found so that a stable numerical evaluation of massive and massless Feynman integrals at arbitrary values of the Gram determinants is made possible. Finally, some relations are mentioned which may be useful for analytic simplifications of the original Feynman diagrams. (orig.)

Feynman integral calculus

CERN Document Server

Smirnov, Vladimir A

2006-01-01

The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. `Feynman Integral Calculus' characterizes the most powerful methods in a systematic way. It concentrates on the methods that have been employed recently for most sophisticated calculations and illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples. It also shows how to choose adequate methods and combine them in a non-trivial way. This is a textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. Problems and solutions have been included, Appendix G has been added, more details have been presented, recent publications on evaluating Feynman integrals have been taken into account and the bibliography has been updated.

Two-loop ladder diagram contributions to Bhabha scattering. III

International Nuclear Information System (INIS)

Bjoerkevoll, K.S.; Osland, P.; Faeldt, G.

1992-01-01

The authors evaluate, in the high-energy limit, the sum of the Feynman amplitudes corresponding the six two-loop ladder-like diagrams in Bhabha scattering. This is the limit where s→∞, while t, the electron mass m and the photon mass λ are all being held fixed. In this limit the sum of the six Feynman amplitudes does not depend on the electron mass. When specialized to the region s>>t>>m 2 >>λ 2 , this result complements the one previously obtained. The connection with Φ 3 theory is also investigated. 6 refs

Folded diagram theory, time-dependent approach of Johnson and Baranger

International Nuclear Information System (INIS)

Johnson, M.B.

1975-01-01

The folded diagram expansion of Brandow and extensively developed by Johnson and Baranger is discussed in detail. The time-dependent approach is reviewed through Feynman-Goldstone diagrams to establish the conventions used. The problem of calculating the effective interaction for nuclei beyond 208 Pb is then considered as an example. Finally, examples are given which show how to do the time integrations. (17 figures) (SDF)

Automatic numerical integration methods for Feynman integrals through 3-loop

International Nuclear Information System (INIS)

De Doncker, E; Olagbemi, O; Yuasa, F; Ishikawa, T; Kato, K

2015-01-01

We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities. (paper)

Universal Regge slope α' from QCD gluon propagator

International Nuclear Information System (INIS)

Nielsen, H.B.; Ninomiya, M.

1980-02-01

An effective gluon propagator is estimated in the presence of a fluctuating color magnetic field in vacuum. Using the dual honeycomb diagram tlhe universal slope is estimated to yield Λsub(p) = 0.34 GeV when corrected by instanton, for α' = 0.88 GeV -2 . (Auth.)

Large momentum expansion of two-loop self-energy diagrams with arbitrary masses

International Nuclear Information System (INIS)

Davydychev, A.I.; Smirnov, V.A.; Tausk, J.B.

1993-01-01

For two-loop two-point diagrams with arbitrary masses, an algorithm to derive the asymptotic expansion at large external momentum squared is constructed. By using a general theorem on asymptotic expansions of Feynman diagrams, the coefficients of the expansion are calculated analytically. For some two-loop diagrams occurring in the Standard Model, comparison with results of numerical integration shows that our expansion works well in the region above the highest physical threshold. (orig.)

Self-consistence equations for extended Feynman rules in quantum chromodynamics

International Nuclear Information System (INIS)

Wielenberg, A.

2005-01-01

In this thesis improved solutions for Green's functions are obtained. First the for this thesis essential techniques and concepts of QCD as euclidean field theory are presented. After a discussion of the foundations of the extended approach for the Feynman rules of QCD with a systematic approach for the 4-gluon vertex a modified renormalization scheme for the extended approach is developed. Thereafter the resummation of the Dyson-Schwinger equations (DSE) by the appropriately modified Bethe-Salpeter equation is discussed. Then the leading divergences for the 1-loop graphs of the resummed DSE are determined. Thereafter the equation-of-motion condensate is defined as result of an operator-product expansion. Then the self-consistency equations for the extended approaches are defined and numerically solved. (HSI)

Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Bergbauer, Christoph

2009-06-11

The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the

Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

International Nuclear Information System (INIS)

Bergbauer, Christoph

2009-01-01

The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the

Covariant diagrams for one-loop matching

International Nuclear Information System (INIS)

Zhang, Zhengkang

2016-10-01

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Covariant diagrams for one-loop matching

Energy Technology Data Exchange (ETDEWEB)

Zhang, Zhengkang [Michigan Center for Theoretical Physics (MCTP), University of Michigan,450 Church Street, Ann Arbor, MI 48109 (United States); Deutsches Elektronen-Synchrotron (DESY),Notkestraße 85, 22607 Hamburg (Germany)

2017-05-30

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Covariant diagrams for one-loop matching

Energy Technology Data Exchange (ETDEWEB)

Zhang, Zhengkang [Michigan Univ., Ann Arbor, MI (United States). Michigan Center for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2016-10-15

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Covariant diagrams for one-loop matching

International Nuclear Information System (INIS)

Zhang, Zhengkang

2017-01-01

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation

International Nuclear Information System (INIS)

Matevosyan, Hrayr H.; Thomas, Anthony W.; Tandy, Peter C.

2007-01-01

We include a generalized infinite class of quark-gluon vertex dressing diagrams in a study of how dynamics beyond the ladder-rainbow truncation influences the Bethe-Salpeter description of light-quark pseudoscalar and vector mesons. The diagrammatic specification of the vertex is mapped into a corresponding specification of the Bethe-Salpeter kernel, which preserves chiral symmetry. This study adopts the algebraic format afforded by the simple interaction kernel used in previous work on this topic. The new feature of the present work is that in every diagram summed for the vertex and the corresponding Bethe-Salpeter kernel, each quark-gluon vertex is required to be the self-consistent vertex solution. We also adopt from previous work the effective accounting for the role of the explicitly non-Abelian three-gluon coupling in a global manner through one parameter determined from recent lattice-QCD data for the vertex. Within the current model, the more consistent dressed vertex limits the ladder-rainbow truncation error for vector mesons to be never more than 10% as the current quark mass is varied from the u/d region to the b region

Block diagrams and the cancellation of divergencies in energy-level perturbation theory

International Nuclear Information System (INIS)

Michels, M.A.J.; Suttorp, L.G.

1979-01-01

The effective Hamiltonian for the degenerate energy-eigenvalue problem in adiabatic perturbation theory is cast in a form that permits an expansion in Feynman diagrams. By means of a block representation a resummation of these diagrams is carried out such that in the adiabatic limit no divergencies are encountered. The resummed form of the effective Hamiltonian is used to establish a connexion with the S matrix. (Auth.)

Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation

International Nuclear Information System (INIS)

Kalmykov, Mikhail Yu.; Kniehl, Bernd A.

2017-06-01

A number of irreducible master integrals for L-loop sunrise and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via the Mellin-Barnes representation.

Soft gluon emission in coloured quark scattering

International Nuclear Information System (INIS)

Frenkel, J.; Meuldemans, R.; Mohammad, I.; Taylor, J.C.

1977-01-01

In order to investigate the infrared behaviour of non-Abelian gauge theories the leading logarithms in the bremsstrahlung of two soft gluons by a coloured quark scattered in an external colourless potential have been calculated. In the calculations only diagrams containing exactly one Yang-Mills vertex have been used alongside with the dimensional infrared regularization. An expression is obtained exhibiting a crucial difference between QCD and QED

Professor Richard Feynman colloquium

CERN Multimedia

1965-01-01

Richard P. Feynman received the Nobel Prize for physics in 1965. Following the ceremony in Stockholm, Feynman gave the colloquium "Development of the space-time view of quantum electrodynamics" at CERN on 17th December.

Feynman Lectures on Computation

CERN Document Server

Feynman, Richard Phillips; Allen, Robin W

1999-01-01

"When, in 1984-86, Richard P. Feynman gave his famous course on computation at the California Institute of Technology, he asked Tony Hey to adapt his lecture notes into a book. Although led by Feynman,"

Worldline Green functions for multiloop diagrams

International Nuclear Information System (INIS)

Schmidt, M.G.; Heidelberg Univ.; Schubert, C.

1994-03-01

We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop graph, and for a loop with an arbitrary number of propagator insertions. For scalar and abelian gauge theories, the resulting integral representations allow to combine whole classes of Feynman diagrams into compact expressions. (orig.)

Feynman rules for the Standard Model Effective Field Theory in R ξ -gauges

Science.gov (United States)

Dedes, A.; Materkowska, W.; Paraskevas, M.; Rosiek, J.; Suxho, K.

2017-06-01

We assume that New Physics effects are parametrized within the Standard Model Effective Field Theory (SMEFT) written in a complete basis of gauge invariant operators up to dimension 6, commonly referred to as "Warsaw basis". We discuss all steps necessary to obtain a consistent transition to the spontaneously broken theory and several other important aspects, including the BRST-invariance of the SMEFT action for linear R ξ -gauges. The final theory is expressed in a basis characterized by SM-like propagators for all physical and unphysical fields. The effect of the non-renormalizable operators appears explicitly in triple or higher multiplicity vertices. In this mass basis we derive the complete set of Feynman rules, without resorting to any simplifying assumptions such as baryon-, lepton-number or CP conservation. As it turns out, for most SMEFT vertices the expressions are reasonably short, with a noticeable exception of those involving 4, 5 and 6 gluons. We have also supplemented our set of Feynman rules, given in an appendix here, with a publicly available Mathematica code working with the FeynRules package and producing output which can be integrated with other symbolic algebra or numerical codes for automatic SMEFT amplitude calculations.

Exploring the QCD phase diagram through relativistic heavy ion collisions

Directory of Open Access Journals (Sweden)

Mohanty Bedangadas

2014-03-01

Full Text Available We present a review of the studies related to establishing the QCD phase diagram through high energy nucleus-nucleus collisions. We particularly focus on the experimental results related to the formation of a quark-gluon phase, crossover transition and search for a critical point in the QCD phase diagram.

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

Energy Technology Data Exchange (ETDEWEB)

Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de [Bauman Moscow State Technical University, 2nd Baumanskaya street, 5, Moscow 105005, Russia and University of Saarland, Postfach 151150, D-66041 Saarbrücken (Germany); Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de [University of Kaiserslautern, 67653 Kaiserslautern (Germany); Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru [Lomonosov Moscow State University, Vorob’evy gory 1, Moscow 119992 (Russian Federation)

2016-02-15

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

International Nuclear Information System (INIS)

Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G.

2016-01-01

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures

Iterated elliptic and hypergeometric integrals for Feynman diagrams

Energy Technology Data Exchange (ETDEWEB)

Ablinger, J.; Radu, C.S.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Van Hoeij, M.; Imamoglu, E. [Florida State Univ., Tallahassee, FL (United States). Dept. of Mathematics; Raab, C.G. [Linz Univ. (Austria). Inst. for Algebra

2017-05-15

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as {sub 2}F{sub 1} Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ{sub i} functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η{sup κ}(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

Iterated elliptic and hypergeometric integrals for Feynman diagrams

International Nuclear Information System (INIS)

Ablinger, J.; Radu, C.S.; Schneider, C.; Bluemlein, J.; Freitas, A. de; Van Hoeij, M.; Imamoglu, E.; Raab, C.G.

2017-05-01

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as _2F_1 Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ_i functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η"κ(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

Detailed balance of the Feynman micromotor

Science.gov (United States)

Abbott, Derek; Davis, Bruce R.; Parrondo, Juan M. R.

1999-09-01

One existing implication of micromotors is that they can be powered by rectifying non-equilibrium thermal fluctuations or mechanical vibrations via the so-called Feynman- micromotor. An example of mechanical rectification is found in the batteryless wristwatch. The original concept was described in as early as 1912 by Smoluchowski and was later revisited in 1963 by Feynman, in the context of rectifying thermal fluctuations to obtain useful motion. It has been shown that, although rectification is impossible at equilibrium, it is possible for the Feynman-micromotor to perform work under non-equilibrium conditions. These concepts can now be realized by MEMS technology and may have exciting implications in biomedicine - where the Feynman- micromotor can be used to power a smart pill, for example. Previously, Feynman's analysis of the motor's efficiency has been shown to be flawed by Parrondo and Espanol. We now show there are further problems in Feynman's treatment of detailed balance. In order to design and understand this device correctly, the equations of detailed balance must be found. Feynman's approach was to use probabilities based on energies and we show that this is problematic. In this paper, we demonstrate corrected equations using level crossing probabilities instead. A potential application of the Feynman-micromotor is a batteryless nanopump that consists of a small MEMS chip that adheres to the skin of a patient and dispense nanoliter quantities of medication. Either mechanical or thermal rectification via a Feynman- micromotor, as the power source, is open for possible investigation.

Feynman integrals and hyperlogarithms

Energy Technology Data Exchange (ETDEWEB)

Panzer, Erik

2015-02-05

We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the ε-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless φ{sup 4} theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by the √(3)). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.

Feynman integrals and hyperlogarithms

International Nuclear Information System (INIS)

Panzer, Erik

2015-01-01

We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the ε-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless φ 4 theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by the √(3)). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.

Quasi-particles and quantum condensate in the Quantum Chromodynamics

International Nuclear Information System (INIS)

Herrmann, J.

1987-01-01

The non-perturbative structure of Quantum Chromodynamics is investigated with the help of a generalisation of the formalism of Green's functions according to Gorkow and Nambu's studies in the theory of superconductivity methods. Taking into account the existence of the gluon condensation, the self-energy of the gluon-quasi-particles in the form of integral-equations is calculated with the help of modified rules for Feynman diagrams. The form of these equations implies the existence of particular solutions with an energy gap in the spectrum of the quasi-particles and a phase transition at a critical momentum. (author)

Numerical evaluation of one-loop diagrams near exceptional momentum configurations

International Nuclear Information System (INIS)

Giele, Walter T.; Zanderighi, Giulia; Glover, E.W.N.

2004-01-01

One problem which plagues the numerical evaluation of one-loop Feynman diagrams using recursive integration by part relations is a numerical instability near exceptional momentum configurations. In this contribution we will discuss a generic solution to this problem. As an example we consider the case of forward light-by-light scattering

Baikov-Lee representations of cut Feynman integrals

International Nuclear Information System (INIS)

Harley, Mark; Moriello, Francesco; Schabinger, Robert M.

2017-01-01

We develop a general framework for the evaluation of d-dimensional cut Feynman integrals based on the Baikov-Lee representation of purely-virtual Feynman integrals. We implement the generalized Cutkosky cutting rule using Cauchy’s residue theorem and identify a set of constraints which determine the integration domain. The method applies equally well to Feynman integrals with a unitarity cut in a single kinematic channel and to maximally-cut Feynman integrals. Our cut Baikov-Lee representation reproduces the expected relation between cuts and discontinuities in a given kinematic channel and furthermore makes the dependence on the kinematic variables manifest from the beginning. By combining the Baikov-Lee representation of maximally-cut Feynman integrals and the properties of periods of algebraic curves, we are able to obtain complete solution sets for the homogeneous differential equations satisfied by Feynman integrals which go beyond multiple polylogarithms. We apply our formalism to the direct evaluation of a number of interesting cut Feynman integrals.

Small-threshold behaviour of two-loop self-energy diagrams: two-particle thresholds

International Nuclear Information System (INIS)

Berends, F.A.; Davydychev, A.I.; Moskovskij Gosudarstvennyj Univ., Moscow; Smirnov, V.A.; Moskovskij Gosudarstvennyj Univ., Moscow

1996-01-01

The behaviour of two-loop two-point diagrams at non-zero thresholds corresponding to two-particle cuts is analyzed. The masses involved in a cut and the external momentum are assumed to be small as compared to some of the other masses of the diagram. By employing general formulae of asymptotic expansions of Feynman diagrams in momenta and masses, we construct an algorithm to derive analytic approximations to the diagrams. In such a way, we calculate several first coefficients of the expansion. Since no conditions on relative values of the small masses and the external momentum are imposed, the threshold irregularities are described analytically. Numerical examples, using diagrams occurring in the standard model, illustrate the convergence of the expansion below the first large threshold. (orig.)

From quarks and gluons to baryon form factors.

Science.gov (United States)

Eichmann, Gernot

2012-04-01

I briefly summarize recent results for nucleon and [Formula: see text] electromagnetic, axial and transition form factors in the Dyson-Schwinger approach. The calculation of the current diagrams from the quark-gluon level enables a transparent discussion of common features such as: the implications of dynamical chiral symmetry breaking and quark orbital angular momentum, the timelike structure of the form factors, and their interpretation in terms of missing pion-cloud effects.

Gluon chains and multiquark hadrons

International Nuclear Information System (INIS)

Jadach, S.; Jezabek, M.

1979-01-01

A monopole approximation to the confining potential is proposed. In this approximation spatially separated groups of quarks carry a definite total colour charge. The potentials which lead to the formation of gluon chains are discussed. The generalization of a (3,3bar) chain notion, studied by Tiktopoulos, to the case of arbitrary colour charges is given. It is argued that these generalized chains may be unstable with respect to splitting into a system of weakly interacting chains of the (3,3bar) type. A unified picture of the high energy hadronic collisions, based on the gluon chain notion and the monopole approximation is proposed. In the meson-meson sector this picture is equivalent to the topological approach. For the other processes it is similar to the approach of Rossi and Veneziano. However, it is argued that the introduction of the junction line into the quark frame is superfluous. The results are expressed in the language of the coloured dual diagrams which provide a generalization of those of Harari and Rosner. (author)

Feynman Lectures on Gravitation

International Nuclear Information System (INIS)

Borcherds, P

2003-01-01

In the early 1960s Feynman lectured to physics undergraduates and, with the assistance of his colleagues Leighton and Sands, produced the three-volume classic Feynman Lectures in Physics. These lectures were delivered in the mornings. In the afternoons Feynman was giving postgraduate lectures on gravitation. This book is based on notes compiled by two students on that course: Morinigo and Wagner. Their notes were checked and approved by Feynman and were available at Caltech. They have now been edited by Brian Hatfield and made more widely available. The book has a substantial preface by John Preskill and Kip Thorne, and an introduction entitled 'Quantum Gravity' by Brian Hatfield. You should read these before going on to the lectures themselves. Preskill and Thorne identify three categories of potential readers of this book. 1. Those with a postgraduate training in theoretical physics. 2. 'Readers with a solid undergraduate training in physics'. 3. 'Admirers of Feynman who do not have a strong physics background'. The title of the book is perhaps misleading: readers in category 2 who think that this book is an extension of the Feynman Lectures in Physics may be disappointed. It is not: it is a book aimed mainly at those in category 1. If you want to get to grips with gravitation (and general relativity) then you need to read an introductory text first e.g. General Relativity by I R Kenyon (Oxford: Oxford University Press) or A Unified Grand Tour of Theoretical Physics by Ian D Lawrie (Bristol: IoP). But there is no Royal Road. As pointed out in the preface and in the introduction, the book represents Feynman's thinking about gravitation some 40 years ago: the lecture course was part of his attempts to understand the subject himself, and for readers in all three categories it is this that makes the book one of interest: the opportunity to observe how a great physicist attempts to tackle some of the hardest challenges of physics. However, the book was written 40

Charmed baryon production in hadronic collisions

International Nuclear Information System (INIS)

Boreskov, K.G.; Kaidalov, A.B.

1982-01-01

Quantitative description of charmed baryon production in pp and πp collisions is obtained in the framework of the soft, peripheral quark-gluon approach. The quark-gluon model, based on the topological expansion, is used for determination of the planar part of the multiperipheral diagrams. The parameters of the D*-D** Regge trajectories and residues are estimated in this model. The total contribution of the peripheral mechanism is calculated by substitution of this planar part to the cylinder-type multiperipheral diagram with π-meson exchange. The energy dependence, absolute value of the inclusive cross section for #betta#sub(c) production and its xsub(F) and psub(perpendicular)-distributions (where xsub(F) is the Feynman variable and psub(perpendicular) is transverse momentum) are calculated and found to be in an agreement with experimental data. Connection with orher models of charm production is discussed

Analytic Tools for Feynman Integrals

CERN Document Server

Smirnov, Vladimir A

2012-01-01

The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice.  This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added:  One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, “Applied Asymptotic Expansions in Momenta and Masses,” by the author. This chapter describes, on t...

Decorated-box-diagram contributions to Bhabha scattering. Pt. 1

International Nuclear Information System (INIS)

Faeldt, G.; Osland, P.

1994-01-01

We evaluate, in the light-energy limit, s>>vertical stroke tvertical stroke >>m 2 >>λ 2 , the sum of amplitudes corresponding to a class of Feynman diagrams describing two-loop virtual photonic corrections to Bhabha scattering. The diagrams considered are box and crossed-box diagrams with an extra photon decorating one of the fermion lines. The mathematical method employed is that of Mellin transforms. In the eikonal approximation, this sum of two-loop amplitudes has previously been evaluated, and found to be equal to the sum of the box and crossed-box amplitudes, multiplied by the electric form factor of the electron. We obtain a similar factorization, but with the form factor replaced by another expression involving the logarithms log(λ 2 /m 2 ) and log(λ 2 /vertical stroke tvertical stroke ). (orig.)

Counting loop diagrams: computational complexity of higher-order amplitude evaluation

International Nuclear Information System (INIS)

Eijk, E. van; Kleiss, R.; Lazopoulos, A.

2004-01-01

We discuss the computational complexity of the perturbative evaluation of scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct evaluation of the individual diagrams. For a self-interacting scalar theory, we determine the complexity as a function of the number of external legs. We describe a method for obtaining the number of topologically inequivalent Feynman graphs containing closed loops, and apply this to 1- and 2-loop amplitudes. We also compute the number of graphs weighted by their symmetry factors, thus arriving at exact and asymptotic estimates for the average symmetry factor of diagrams. We present results for the asymptotic number of diagrams up to 10 loops, and prove that the average symmetry factor approaches unity as the number of external legs becomes large. (orig.)

Quantum Simulations of Strongly Coupled Quark-Gluon Plasma

International Nuclear Information System (INIS)

Filinov, V.S.; Bonitz, M.; Ivanov, Yu.B.

2013-01-01

In recent years, there has been an increasing interest in dynamics and thermodynamics of non-Abelian plasmas at both very high temperature and density. It is expected that a specific state of matter with unconfined quarks and gluons - the so called quark - gluon plasma (QGP) - can exist. The most fundamental way to compute properties of the strongly interacting matter is provided by the lattice QCD. Interpretation of these very complicated computations requires application of various QCD motivated, albeit schematic, models simulating various aspects of the full theory. Moreover, such models are needed in cases when the lattice QCD fails, e.g. at large baryon chemical potentials and out of equilibrium. A semi-classical approximation, based on a point like quasi-particle picture has been recently introduced in literature. It is expected that it allows to treat soft processes in the QGP which are not accessible by the perturbative means and the main features of non-Abelian plasmas can be understood in simple semi-classical terms without the difficulties inherent to a full quantum field theoretical analysis. Here we propose stochastic simulation of thermodynamics and kinetic properties for QGP in semi-classical approximation in the wide region of temperature, density and quasi-particles masses. We extend previous classical nonrelativistic simulations based on a color Coulomb interaction to the quantum regime and take into account the Fermi (Bose) statistics of quarks (gluons) and quantum degeneracy self-consistently. In grand canonical ensemble for finite and zero baryon chemical potential we use the direct quantum path integral Monte Carlo method (PIMC) developed for finite temperature within Feynman formulation of quantum mechanics to do calculations of internal energy, pressure and pair correlation functions. The QGP quasi-particles representing dressed quarks, antiquarks and gluons interact via color quantum Kelbg pseudopotential rigorously derived in for Coulomb

Quest for the QCD phase diagram in extreme environments

Energy Technology Data Exchange (ETDEWEB)

Fukushima, Kenji, E-mail: fuku@rk.phys.keio.ac.jp [Keio University, Department of Physics (Japan)

2013-03-15

We review the state-of-the-art status of the research on the phase diagram of QCD matter out of quarks and gluons. Our discussions particularly include the extreme environments such as the high temperature, the high baryon density, and the strong magnetic field.

Feynman integral calculus

International Nuclear Information System (INIS)

Smirnov, V.A.

2006-01-01

The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. (orig.)

Feynman integral calculus

Energy Technology Data Exchange (ETDEWEB)

Smirnov, V.A. [Lomonosov Moscow State Univ. (Russian Federation). Skobeltsyn Inst. of Nuclear Physics

2006-07-01

The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. (orig.)

Planar quark diagrams and binary spin processes

International Nuclear Information System (INIS)

Grigoryan, A.A.; Ivanov, N.Ya.

1986-01-01

Contributions of planar diagrams to the binary scattering processes are analyzed. The analysis is based on the predictions of quark-gluon picture of strong interactions for the coupling of reggeons with quarks as well as on the SU(6)-classification of hadrons. The dependence of contributions of nonplanar corrections on spins and quark composition of interacting particles is discussed

Constituent quarks as clusters in quark-gluon-parton model. [Total cross sections, probability distributions

Energy Technology Data Exchange (ETDEWEB)

Kanki, T [Osaka Univ., Toyonaka (Japan). Coll. of General Education

1976-12-01

We present a quark-gluon-parton model in which quark-partons and gluons make clusters corresponding to two or three constituent quarks (or anti-quarks) in the meson or in the baryon, respectively. We explicitly construct the constituent quark state (cluster), by employing the Kuti-Weisskopf theory and by requiring the scaling. The quark additivity of the hadronic total cross sections and the quark counting rules on the threshold powers of various distributions are satisfied. For small x (Feynman fraction), it is shown that the constituent quarks and quark-partons have quite different probability distributions. We apply our model to hadron-hadron inclusive reactions, and clarify that the fragmentation and the diffractive processes relate to the constituent quark distributions, while the processes in or near the central region are controlled by the quark-partons. Our model gives the reasonable interpretation for the experimental data and much improves the usual ''constituent interchange model'' result near and in the central region (x asymptotically equals x sub(T) asymptotically equals 0).

Richard Feynman Quarks, Bombs, and Bongos

CERN Document Server

Henderson, Harry

2010-01-01

Described by his peers as the "finest physicist of his generation," Richard Feynman defied scientist stereotypes. This brash New York-born American physicist startled the more conservative giants of European physics with his endless ability to improvise. Indeed, later in life, Feynman became an accomplished bongo player. Feynman's legacy to physics was his ability to simplify complex equations and clarify fundamental principles through the use of graphs. He developed the theory of quantum electrodynamics, which illustrates the behavior of electrically charged particles, such as elect

A note on relativistic Feynman-type integrals

International Nuclear Information System (INIS)

Namsrai, Kh.

1979-01-01

An attempt is made to generalize the definition of Feynman path integral to the relativistic case within the framework of the Kershaw stochastic model. The Smoluchowski type equations are used which allow one to obtain easily the Schrodinger, Klein-Gordon and Dirac equations. The interaction is introduced by using Weyl's gaude theory. In the model developed the Feynman process may formally by interpreted as a stochastic diffusion process in complex times with a real probability measure which occurs in the Euclidean space. Feynman path integrals themselves are not obtained in the model, nonetheless it represents an interest as one of possibilities of the relativistic generalization of Feynman type integrals

Analytic tools for Feynman integrals

International Nuclear Information System (INIS)

Smirnov, Vladimir A.

2012-01-01

Most powerful methods of evaluating Feynman integrals are presented. Reader will be able to apply them in practice. Contains numerous examples. The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author's previous Springer book ''Evaluating Feynman Integrals'' and its textbook version ''Feynman Integral Calculus.'' Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, ''Applied Asymptotic Expansions in Momenta and Masses,'' by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes.

Approximation of hadron interactions by Regge diagrams with multipomeron exchange

International Nuclear Information System (INIS)

Barashenkov, V.S.

1988-01-01

A good agreement of hadron diffraction interaction total cross section and their elastic scattering at small angles calculated by summarizing Regge multipomeron exchange diagrams with experiment mentioned by a number of authors results from the fitting of a great variety of the parameters contained in the formulas. The agreement of the other hadron characteristcs with experiment is worse. Distribution of hadron interactions over the number of fragmenting quark-gluon strings calculated by utilizing Regge diagrams is discussed

Mathematical aspects of Feynman integrals

International Nuclear Information System (INIS)

Bogner, Christian

2009-08-01

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals. The integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph. Starting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative

Mathematical aspects of Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Bogner, Christian

2009-08-15

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals. The integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph. Starting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative

Some remarks on Feynman rules for non-commutative gauge theories based on groups G≠U(N)

International Nuclear Information System (INIS)

Dorn, Harald; Sieg, Christoph

2002-01-01

We study for subgroups G is a subset of U(N) partial summations of the θ-expanded perturbation theory. On diagrammatic level a summation procedure is established, which in the U(N) case delivers the full star-product induced rules. Thereby we uncover a cancellation mechanism between certain diagrams, which is crucial in the U(N) case, but set out of work for G is a subset of U(N). In addition, an explicit proof is given that for G is a subset of U(N), G≠U(M), M< N there is no partial summation of the θ-expanded rules resulting in new Feynman rules using the U(N) star-product vertices and besides suitable modified propagators at most a finite number of additional building blocks. Finally, we show that certain SO(N) Feynman rules conjectured in the literature cannot be derived from the enveloping algebra approach. (author)

Analytic tools for Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Smirnov, Vladimir A. [Moscow State Univ. (Russian Federation). Skobeltsyn Inst. of Nuclear Physics

2012-07-01

Most powerful methods of evaluating Feynman integrals are presented. Reader will be able to apply them in practice. Contains numerous examples. The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author's previous Springer book ''Evaluating Feynman Integrals'' and its textbook version ''Feynman Integral Calculus.'' Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, ''Applied Asymptotic Expansions in Momenta and Masses,'' by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes.

Quantum many-body physics in a nutshell

CERN Document Server

Shuryak, Edward

2018-01-01

This book provides an essential introduction to the physics of quantum many-body systems, which are at the heart of atomic and nuclear physics, condensed matter, and particle physics. Unlike other textbooks on the subject, it covers topics across a broad range of physical fields―phenomena as well as theoretical tools―and does so in a simple and accessible way. Edward Shuryak begins with Feynman diagrams of the quantum and statistical mechanics of a particle―in these applications, the diagrams are easy to calculate and there are no divergencies. He discusses the renormalization group and illustrates its uses and covers systems such as weakly and strongly coupled Bose and Fermi gases, electron gas, nuclear matter, and quark-gluon plasmas. Phenomena include Bose condensation and superfluidity. Shuryak also looks at Cooper pairing and superconductivity for electrons in metals, liquid 3He, nuclear matter, and quark-gluon plasma. A recurring topic throughout is topological matter, ranging from ensembles of q...

Excluding scalar gluons

International Nuclear Information System (INIS)

Koller, K.; Krasemann, H.

1979-08-01

We investigate the Dalitz plot population and thrust angular distribution for the Orthoquarkonium decay Q anti Q → 3 scalar gluons. The Dalitz plot for scalar gluons is populated in corners where events are 2 jet like and this disagrees with existing Upsilon data. The scalar gluon thrust angular distribution is also in striking disagreement with the UPSILON data and so scalar gluons are completely ruled out. (orig.)

Analytic continuation of dual Feynman amplitudes

International Nuclear Information System (INIS)

Bleher, P.M.

1981-01-01

A notion of dual Feynman amplitude is introduced and a theorem on the existence of analytic continuation of this amplitude from the convergence domain to the whole complex is proved. The case under consideration corresponds to massless power propagators and the analytic continuation is constructed on the propagators powers. Analytic continuation poles and singular set of external impulses are found explicitly. The proof of the theorem on the existence of analytic continuation is based on the introduction of α-representation for dual Feynman amplitudes. In proving, the so-called ''trees formula'' and ''trees-with-cycles formula'' are established that are dual by formulation to the trees and 2-trees formulae for usual Feynman amplitudes. (Auth.)

Feynman integrals in QCD made simple

CERN Multimedia

CERN. Geneva

2015-01-01

A key insight is that important properties of these functions can be predicted by inspecting the singularity structure of the Feynman integrand. Combined with the differential equations technique, this gives a powerful method for computing the necessary Feynman integrals. I will review these ideas, based on Phys.Rev.Lett. 110 (2013) 25, and present recent new results relevant for QCD scattering amplitudes.

(U) Feynman-Y calculations using PARTISN

Energy Technology Data Exchange (ETDEWEB)

Favorite, Jeffrey A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-08-31

A prescription for computing the Feynman Y as a function of coincidence gate width using a deterministic multigroup neutron transport code has been published and the results compared favorably with measurements of the BeRP ball. In this paper, we report on our project to implement the method and reproduce the results. There are several clarifications and corrections of the published prescription. We show results using two multigroup cross section libraries compared with measurements and with Monte Carlo results. Deterministic simulations of the mean count rates compare very favorably with previously published Monte Carlo results, and deterministic simulations of the Feynman Y asymptote compare somewhat favorably. In Feynman beta plots, the deterministic simulations reached the asymptotic value much sooner than did a fit to the measured data.

The Feynman-Dyson view

International Nuclear Information System (INIS)

Gill, Tepper L.

2017-01-01

This paper is a survey of our work on the mathematical foundations for the Feynman-Dyson program in quantum electrodynamics (QED). After a brief discussion of the history, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson’s second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman’s path integral, and to prove Dyson’s first conjecture that the divergences are in part due to a violation of Heisenberg’s uncertainly relations. As a by-product, we also prove Feynman’s conjecture about the relationship between the operator calculus and has path integral. Thus, providing the first rigorous justification for the Feynman formulation of quantum mechanics. (paper)

The Feynman-Dyson view

Science.gov (United States)

Gill, Tepper L.

2017-05-01

This paper is a survey of our work on the mathematical foundations for the Feynman-Dyson program in quantum electrodynamics (QED). After a brief discussion of the history, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson’s second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman’s path integral, and to prove Dyson’s first conjecture that the divergences are in part due to a violation of Heisenberg’s uncertainly relations. As a by-product, we also prove Feynman’s conjecture about the relationship between the operator calculus and has path integral. Thus, providing the first rigorous justification for the Feynman formulation of quantum mechanics.

Surface terms and radiative corrections to the VVA triangle diagram

International Nuclear Information System (INIS)

Chowdhury, A.M.; McKeon, G.

1986-01-01

The two-loop radiative corrections to the divergence of the axial-vector current are analyzed in the context of spinor electrodynamics. It is found that the arbitrariness that occurs in the relevant Feynman diagrams due to the appearance of surface terms associated with linearly divergent integrals is sufficient to ensure that at two-loop order the Ward identity can be satisfied, irrespective of how the divergences that occur are parametrized. This indicates that the Adler-Bardeen theorem is satisfied

Quark jets, gluon jets and the three-gluon vertex

International Nuclear Information System (INIS)

Fodor, Z.

1989-11-01

Using hadronic jets in electron-positron annihilation, we suggest a simple and model-independent method to see the differences between quark and gluon jets. We define and analyse special energy dependent moments of jets and choose those which are the most characteristic to the jet type. The method handles the energy of a jet in an adequate way. We discuss new methods using jet flavor tagging, ordinary flavor tagging of a definite quark jet or discrimination between quark and gluon jets, to test the triple-gluon vertex in electron-positron annihilation. An enriched sample of gluon jets, jets with the smallest energy in four-jet events, as well as a continuous tagging variable are also studied. 21 refs., 6 figs. (Author)

Some recent results on evaluating Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Smirnov, V.A. [Nuclear Physics Institute of Moscow State University, Moscow 119992 (Russian Federation)

2006-07-15

Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner bases to solve integration by parts relations in an automatic way is described.

Some recent results on evaluating Feynman integrals

International Nuclear Information System (INIS)

Smirnov, V.A.

2006-01-01

Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner bases to solve integration by parts relations in an automatic way is described

Gluon attributes

International Nuclear Information System (INIS)

Weiler, T.

1981-01-01

An overview is presented of the attributes of gluons, deducible from experimental data. Particular attention is given to the photon-gluon fusion model of charm leptoproduction. The agreement with QCD and theoretical prejudice is qualitatively good

A Feynman graph selection tool in GRACE system

International Nuclear Information System (INIS)

Yuasa, Fukuko; Ishikawa, Tadashi; Kaneko, Toshiaki

2001-01-01

We present a Feynman graph selection tool grcsel, which is an interpreter written in C language. In the framework of GRACE, it enables us to get a subset of Feynman graphs according to given conditions

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

Energy Technology Data Exchange (ETDEWEB)

Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2010-10-15

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)

Quark and Gluon Relaxation in Quark-Gluon Plasmas

Science.gov (United States)

Heiselberg, H.; Pethick, C. J.

1993-01-01

The quasiparticle decay rates for quarks and gluons in quark-gluon plasmas are calculated by solving the kinetic equation. Introducing an infrared cutoff to allow for nonperturbative effects, we evaluate the quasiparticle lifetime at momenta greater than the inverse Debye screening length to leading order in the coupling constant.

Complete algebraic reduction of one-loop tensor Feynman integrals

International Nuclear Information System (INIS)

Fleischer, J.; Riemann, T.

2011-01-01

We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals. The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point Gram determinant is avoided. The 4-point tensor coefficients are represented in terms of 4-point integrals, defined in d dimensions, 4-2ε≤d≤4-2ε+2(R-1), with higher powers of the propagators. They can be further reduced to expressions which stay free of the inverse 4-point Gram determinants but contain higher-dimensional 4-point integrals with only the first power of scalar propagators, plus 3-point tensor coefficients. A direct evaluation of the higher-dimensional 4-point functions would avoid the appearance of inverse powers of the Gram determinants completely. The simplest approach, however, is to apply here dimensional recurrence relations in order to reduce them to the familiar 2- to 4-point functions in generic dimension d=4-2ε, introducing thereby coefficients with inverse 4-point Gram determinants up to power R for tensors of rank R. For small or vanishing Gram determinants--where this reduction is not applicable--we use analytic expansions in positive powers of the Gram determinants. Improving the convergence of the expansions substantially with Pade approximants we close up to the evaluation of the 4-point tensor coefficients for larger Gram determinants. Finally, some relations are discussed which may be useful for analytic simplifications of Feynman diagrams.

A dynamical mechanism for the hairpin diagram

International Nuclear Information System (INIS)

Chang Chaohsi; Guo Xinheng; Li Xueqian.

1989-09-01

Based on the non-valence quark-antiquark and gluon constituent structure of mesons we give a reasonable dynamical mechanism which can induce the hairpin diagram without violating the well-observed OZI rule. We calculate the hairpin amplitudes of D deg. → K-bar deg.η and K-bar deg.η' normalized by D deg. → K-bar deg.π deg. and have found that the hairpin diagram can give rise to substantial contribution to the decays where a meson with a SU(3) flavor singlet component is involved in the final state. In this scenario, we also obtain the branching ratio of D deg. → K-bar deg. φ as 0.55% in comparison with the experimental data of 0.83%. (autor). 33 refs, 3 figs

Application of difference filter to Feynman-α analysis

International Nuclear Information System (INIS)

Mouri, Tomoaki; Ohtani, Nobuo

1997-11-01

The Feynman-α method has been developed for monitoring sub-criticality in nuclear fuel facilities. It is difficult to apply the Feynman-α method which estimates statistical variation of the number of neutron counts per unit time, to the system in transient condition such that the averaged neutron flux varies with time. In the application of Feynman-α method to such system, it is suggested to remove the averaged variation of neutron flux from neutron count data by the use of the difference filter. In this study, we applied the difference filter to reactor noise data at sub-criticality near to criticality, where the prompt decay constant was difficult to estimate due to the large effect of delayed neutron. With the difference filter, accurate prompt decay constants for effective multiplication factors from 0.999 to 0.994 were obtained by Feynman-α method. It was cleared that the difference filter is effective to estimate accurate prompt decay constant, so that there is the prospect to be able to apply Feynman-α method having the difference filter to the system in the transient condition. (author)

Critical point in the phase diagram of primordial quark-gluon matter from black hole physics

Science.gov (United States)

Critelli, Renato; Noronha, Jorge; Noronha-Hostler, Jacquelyn; Portillo, Israel; Ratti, Claudia; Rougemont, Romulo

2017-11-01

Strongly interacting matter undergoes a crossover phase transition at high temperatures T ˜1012 K and zero net-baryon density. A fundamental question in the theory of strong interactions, QCD, is whether a hot and dense system of quarks and gluons displays critical phenomena when doped with more quarks than antiquarks, where net-baryon number fluctuations diverge. Recent lattice QCD work indicates that such a critical point can only occur in the baryon dense regime of the theory, which defies a description from first principles calculations. Here we use the holographic gauge/gravity correspondence to map the fluctuations of baryon charge in the dense quark-gluon liquid onto a numerically tractable gravitational problem involving the charge fluctuations of holographic black holes. This approach quantitatively reproduces ab initio results for the lowest order moments of the baryon fluctuations and makes predictions for the higher-order baryon susceptibilities and also for the location of the critical point, which is found to be within the reach of heavy-ion collision experiments.

Feynman maps without improper integrals

International Nuclear Information System (INIS)

Exner, P.; Kolerov, G.I.

1980-01-01

The Feynman maps introduced first by Truman are examined. The domain considered here consists of the Fresnel-inteo-rable functions in the sense of Albeverio and Hoegh-Krohn. The original definition of the F-maps is slightly modified: it is started from the underlying measures on the Hilbert space of paths in order to avoid use of improper integrals. Some new properties of the F-maps are derived. In particular, the dominated convergence theorem is shown to be not valid for the F 1 -map (or Feynman integral); this fact is of a certain importance for classical limit of quantum mechanics

Quantum chromodynamics

CERN Document Server

Neubert, Matthias

1996-01-01

Quantum chromodynamics (QCD) is the fundamental theory of the strong interactions. It is local, non-abelian gauge theory descripting the interactions between quarks and gluons, the constituents of hadrons. In these lectures, the basic concepts and ph will be introduced in a pedagogical way. Topics will include : asymptotically free partons, colour and confinement ; non-abelian gauge invariance and quantization ; the running coupling constant ; deep-inelastic scattering and scaling violations ; th chiral and heavy-quark symmetries. Some elementary knowledge of field theory, abelian gauge invariance and Feynman diagrams will be helpful in following the course.

Reggeons in pQCD

International Nuclear Information System (INIS)

Griffiths, S.

1999-06-01

We consider the description of deep inelastic scattering by perturbative quantum chromo dynamics in the Regge-limit, specifically via the Reggeization of fundamental particles (gluons and quarks) and the description of processes by integro-differential equations such as the BFKL equation. We review the Reggeization of the gluon via Feynman diagrams in the leading-log approximation and then extend this to an original demonstration of the quark's Reggeization. In analogy to the hard Pomeron's description in terms of Reggeized gluons we consider the ρ-meson's trajectory in terms of the exchange of Reggeized quarks and derive the evolution equation describing this. The solutions of this equation, both analytic and numeric, are then looked at in some detail, and we demonstrate how the low-x behaviour is enhanced. We then make modifications to include a running coupling constant and massive propagators, and investigate the effects that these have on the asymptotics of the ρ-trajectory. (author)

Evaluation of physical constants and operators in the SU(2) and SU(3) lattice gauge theory

International Nuclear Information System (INIS)

Tsuchida, R.H.

1987-01-01

Wilson loops and Wilson lines in the fundamental and the adjoint representations of SU(2) on the lattice are measured using the icosahedral subgroup and a noise reduction technique. The string tension was evaluated by fitting the expectation value of loops of all sizes to a 6-parameter curve. From the Wilson lines in the adjoint representation of SU(2), two kinds of gluon potentials were measured: the gluon-gluon interaction potential and the gluon-image interaction potential. The effective mass of the gluon was evaluated on each of those potentials and compared. In SU(3), the contribution of s anti σ/sub μnu/F/sub μnu/d operator to the correction of effective weak four-quark operator in the measurement of ΔI = 1/2 amplitude of kaon decay is examined. The renormalization of the critical hopping parameter is calculated perturbatively and compared with the Monte Carlo results. The VEV of psi anti psi operator is measured on the lattice. In the hopping parameter renormalization calculation and the psi anti psi measurements, the effects of expanding of Feynman diagrams in power of a, the lattice spacing, are examined

Rigorous time slicing approach to Feynman path integrals

CERN Document Server

Fujiwara, Daisuke

2017-01-01

This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved. The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by...

Properties of gluon jets

International Nuclear Information System (INIS)

Sugano, K.

1987-01-01

The properties of gluon jets are reviewed, and the measured characteristics are compared to the theoretical expectations. Although neither data nor models for the gluon jets are in the mature stage, in general the agreement between experiment and theory is remarkable. There are some intriguing differences. Since the properties of gluon jets are deeply rooted in the basic structure of non-Abelian gauge theory, the study of gluon jets casts further light on our understanding of QCD. Finally, the future prospects are discussed

Counting the number of Feynman graphs in QCD

Science.gov (United States)

Kaneko, T.

2018-05-01

Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A method of counting the number of Feynman graphs with weight of symmetry factor was established based on zero-dimensional field theory, and was used in scalar theories and QED. In this article this method is generalized to more complicated models by direct calculation of generating functions on a computer algebra system. This method is applied to QCD with and without counter terms, where many higher order are being calculated automatically.

Richard Phillips Feynman

Indian Academy of Sciences (India)

ARTICLE-IN-A-BOX. 797. RESONANCE │ September 2011. The war years interrupted the efforts of both Feynman and Schwinger to tackle the divergence problems in quantum electrodynamics, another of Dirac's pioneering creations from 1927. In 1965 the Physics Nobel Prize was shared by the two of them and Sin-Ichiro ...

Properties of gluon jets

International Nuclear Information System (INIS)

Sugano, K.

1988-01-01

The properties of gluon jets are reviewed from an experimental point of view. The measured characteristics are compared to theoretical expectations. Although neither data nor models for the gluon jets are in the mature stage, there are remarkable agreements and also intriguing disagreements between experiment and theory. Since much interesting data have begun to emerge from various experiments and the properties of gluon jets are deeply rooted in the basic structure of non-Abelian gauge theory, the study of gluon jets casts further light on understanding of QCD. The future prospects are discussed

The Feynman integral for time-dependent anharmonic oscillators

International Nuclear Information System (INIS)

Grothaus, M.; Khandekar, D.C.; da Silva, J.L.; Streit, L.

1997-01-01

We review some basic notions and results of white noise analysis that are used in the construction of the Feynman integrand as a generalized white noise functional. We show that the Feynman integrand for the time-dependent harmonic oscillator in an external potential is a Hida distribution. copyright 1997 American Institute of Physics

Richard Phillips Feynman

Indian Academy of Sciences (India)

While the two relativity theories were largely the creation of Albert Einstein, the quantum ... of what may lie in store for anyone who dares to follow the beat of a different drum. ... saw Feynman's exceptional talents and in a special lecture explained to him the beautiful principle ... The Character of Physical Law – 1965. c).

Gluons in quarkonium decay

International Nuclear Information System (INIS)

Koller, K.; Walsh, T.

1978-03-01

We discuss what can be learned of the 3 S 1 quarkonium decay QantiQ → 3 gluoans QantiQ → γ + 2 gluons. The former is a way to find gluon jets and test QCD. The latter also allows us to measure gluoan + gluon → hadrons and look for pure gluonic resonances (glueballs). (orig.) [de

To Have Been a Student of Richard Feynman

Indian Academy of Sciences (India)

Excerpt from Most of the Good Stuff: Memories of Richard Feynman, 1993, ... of Feynman, but while it inspired us to try for originality after we left Cornell, it also lowered our productivity to a point that at times was dangerous to our academic careers. In truth .... (However, my actual thesis topic turned out to be a different one.).

Classical gluon and graviton radiation from the bi-adjoint scalar double copy

Science.gov (United States)

Goldberger, Walter D.; Prabhu, Siddharth G.; Thompson, Jedidiah O.

2017-09-01

We find double-copy relations between classical radiating solutions in Yang-Mills theory coupled to dynamical color charges and their counterparts in a cubic bi-adjoint scalar field theory which interacts linearly with particles carrying bi-adjoint charge. The particular color-to-kinematics replacements we employ are motivated by the Bern-Carrasco-Johansson double-copy correspondence for on-shell amplitudes in gauge and gravity theories. They are identical to those recently used to establish relations between classical radiating solutions in gauge theory and in dilaton gravity. Our explicit bi-adjoint solutions are constructed to second order in a perturbative expansion, and map under the double copy onto gauge theory solutions which involve at most cubic gluon self-interactions. If the correspondence is found to persist to higher orders in perturbation theory, our results suggest the possibility of calculating gravitational radiation from colliding compact objects, directly from a scalar field with vastly simpler (purely cubic) Feynman vertices.

Multiple production of hadrons at high energies in the model of quark-gluon strings

International Nuclear Information System (INIS)

Kaidalov, A.B.; Ter-Martirosyan, K.A.

1983-01-01

Multiple production of hadrons at high energies is considered in the framework of the approach based on a picture of formation and subsequent fission of the quark-gluon strings, corresponding to the Pomeron with αsub(P)(0) > 1. The topological (1/nsub(f))-expansion and the colour-tube model is used. Inclusive cross-sections are expressed in therms of the structure functions and fragmentation functions of quarks and their limiting values are in an agreement with the results of the reggeon theory. It is pointed out that an account of rapidity fluctuations of the ends of the quark-gluon strings, connected to valence or sea quarks, allows one to explain a number of characteristic features of the multiple production of hadrons. In particular the model, which takes into account multipomeron configurations, reproduces the experimentally observed rise of inclusive spectra in a central region and well describes both rapidity and multiplicity distributions of charged particles up to energies of the SPS-collider. It is shown that in this approach the KNO-scaling is only approximately satisfied and the pattern of its violation at energies √ s approximately 10 3 GeV is predicted. Inclusive spectra are investigated in the whole region 0 or approximately 0.1) Feynman scaling is violated only logarithmically and deviations from it are very rsmall at s 3 +10 4 GeV

Feynman rules for fermion-number-violating interactions

International Nuclear Information System (INIS)

Denner, A.; Eck, H.; Hahn, O.; Kueblbeck, J.

1992-01-01

We present simple algorithmic Feynman rules for fermion-number-violating interactions. They do not involve explicit charge-conjugation matrices and resemble closely the familiar rules for Dirac fermions. We insist on a fermion flow through the graphs along fermion lines and get the correct relative signs between different interfering Feynman graphs as in the case of Dirac fermions. We only need the familiar Dirac propagator and fewer vertices than in the usual treatment of fermion-number-violating interactions. (orig.)

The Hellman-Feynman theorem at finite temperature

International Nuclear Information System (INIS)

Cabrera, A.; Calles, A.

1990-01-01

The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)

Feynman path integral and the interaction picture

International Nuclear Information System (INIS)

Pugh, R.E.

1986-01-01

The role of interaction-picture fields in the construction of coherent states and in the derivation of the Feynman path integral for interacting scalar quantum fields is examined. Special attention is paid to the dependence of the integrand on the intermediate times and it is shown that the Feynman rules are valid prior to taking the limit wherein the number of intermediate times goes to infinity; thus, this number does not act as a cutoff in divergent amplitudes. Specific normalization factors are determined

The signed permutation group on Feynman graphs

Energy Technology Data Exchange (ETDEWEB)

Purkart, Julian, E-mail: purkart@physik.hu-berlin.de [Institute of Physics, Humboldt University, D-12489 Berlin (Germany)

2016-08-15

The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization scheme and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.

Gluon exchange in elastic hadron scattering

International Nuclear Information System (INIS)

Jenkovszky, L.L.; Paccanoni, F.; Chikovani, Z.E.

1991-01-01

It is generally accepted that the Pomeron, which determines the long-range component of the strong interaction, corresponds to exchange of gluons with the corresponding quantum numbers (the minimum number of such gluons is two). The C-odd partner of the Pomeron, the odderon, corresponds to exchange of an odd number of gluons (three or more). By means of a model of the nonperturbative gluon propagator, restrictions are obtained on the parameters of two-gluon (Pomeron) and three-gluon (odderon) exchange in hadron scattering. In the framework of this model an interpretation is proposed for the various asymptotic regimes in the behavior of the total cross section and of the differential cross section of elastic scattering at high energies

Gluon mass generation without seagull divergences

International Nuclear Information System (INIS)

Aguilar, Arlene C.; Papavassiliou, Joannis

2010-01-01

Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses. In this work we show how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger the aforementioned identity hinges crucially on the particular Ansatz employed for the three-gluon vertex entering into the Schwinger-Dyson equation governing the gluon propagator. The use of the appropriate three-gluon vertex brings about an additional advantage: one obtains two separate (but coupled) integral equations, one for the effective charge and one for the gluon mass. This system of integral equations has a unique solution, which unambiguously determines these two quantities. Most notably, the effective charge freezes in the infrared, and the gluon mass displays power-law running in the ultraviolet, in agreement with earlier considerations.

Generalized statistics and the formation of a quark-gluon plasma

International Nuclear Information System (INIS)

Teweldeberhan, A.M.; Miller, H.G.; Tegen, R.

2003-01-01

The aim of this paper is to investigate the effect of a non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quark-gluon plasma (QGP). We suggest to account for the effects of the dominant part of the long-range interactions among the constituents in the QGP by a change in the statistics of the system in this phase, and we study the relevance of this statistics for the phase transition. The results show that small deviations (≈ 10%) from Boltzmann–Gibbs statistics in the QGP produce a noticeable change in the phase diagram, which can, in principle, be tested experimentally. (author)

Applying Groebner bases to solve reduction problems for Feynman integrals

International Nuclear Information System (INIS)

Smirnov, Alexander V.; Smirnov, Vladimir A.

2006-01-01

We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. We illustrate it through various examples of reduction problems for families of one- and two-loop Feynman integrals. We also solve the reduction problem for a family of integrals contributing to the three-loop static quark potential

Applying Groebner bases to solve reduction problems for Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Smirnov, Alexander V. [Mechanical and Mathematical Department and Scientific Research Computer Center of Moscow State University, Moscow 119992 (Russian Federation); Smirnov, Vladimir A. [Nuclear Physics Institute of Moscow State University, Moscow 119992 (Russian Federation)

2006-01-15

We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. We illustrate it through various examples of reduction problems for families of one- and two-loop Feynman integrals. We also solve the reduction problem for a family of integrals contributing to the three-loop static quark potential.

Gluon Saturation and EIC

Energy Technology Data Exchange (ETDEWEB)

Sichtermann, Ernst

2016-12-15

The fundamental structure of nucleons and nuclear matter is described by the properties and dynamics of quarks and gluons in quantum chromodynamics. Electron-nucleon collisions are a powerful method to study this structure. As one increases the energy of the collisions, the interaction process probes regions of progressively higher gluon density. This density must eventually saturate. An high-energy polarized Electron-Ion Collider (EIC) has been proposed to observe and study the saturated gluon density regime. Selected measurements will be discussed, following a brief introduction.

Coupled oscillators and Feynman's three papers

International Nuclear Information System (INIS)

Kim, Y S

2007-01-01

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the 'rest of the universe' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators

A convergence theorem for asymptotic expansions of Feynman amplitudes

International Nuclear Information System (INIS)

Mabouisson, A.P.C.

1999-06-01

The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to ∞, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)

Comments on gluon 6-point scattering amplitudes in N = 4 SYM at strong coupling

International Nuclear Information System (INIS)

Astefanesei, Dumitru; Dobashi, Suguru; Ito, Katsushi; Nastase, Horatiu

2007-01-01

We use the AdS-CFT prescription of Alday and Maldacena [1] to analyze gluon 6-point scattering amplitudes at strong coupling in N = 4 SYM. By cutting and gluing we obtain AdS 6-point amplitudes that contain extra boundary conditions and come close to matching the field theory results. We interpret them as parts of the field theory amplitudes, containing only certain diagrams. We also analyze the collinear limits of 6- and 5-point amplitudes and discuss the results

Quantum Man: Richard Feynman's Life in Science

CERN Document Server

CERN. Geneva

2011-01-01

It took a man who was willing to break all the rules to tame a theory that breaks all the rules. This talk will be based on my new book Quantum Man: Richard Feynman's life in science. I will try and present a scientific overview of the contributions of Richard Feynman, as seen through the arc of his fascinating life. From Quantum Mechanics to Antiparticles, from Rio de Janeiro to Los Alamos, a whirlwind tour will provide insights into the character, life and accomplishments of one of the 20th centuries most important scientists, and provide an object lesson in scientific integrity.

Duality and multi-gluon scattering

International Nuclear Information System (INIS)

Mangano, M.; Parke, S.; Xu Zhan

1988-01-01

For the six-gluon scattering process we give explicit and simple expressions for the amplitude and its square. To achieve this we use an analogy with string theories to identify a unique procedure for writing the multi-gluon scattering amplitudes in terms of a sum of gauge invariant dual sub-amplitudes multiplied by an appropriate color (Chan-Paton) factor. The sub-amplitudes defined in this way are invariant under cyclic permutations, satisfy powerful identities which relate different non-cyclic permutations and factorize in the soft gluon limit, the two-gluon collinear limit and on multi-gluon poles. Also, to leading order in the number of colors these sub-amplitudes sum incoherently in the square of the full matrix element. The results contained here are important for Monte Carlo studies of multi-jet processes at hadron colliders as well as for understanding the general structure of QCD. (orig.)

The quark gluon plasma; Le plasma de quarks et de gluons

Energy Technology Data Exchange (ETDEWEB)

Granier de Cassagnac, R. [Ecole Polytechnique, Lab. Leprince-Ringuet, 91 - Palaiseau (France)

2010-05-15

The quark-gluon plasma (QGP) is a state of matter in which the universe was expected to be a few micro-seconds after the big-bang. Violent collisions of heavy ions are supposed to re-create this state in particle accelerators. Numerous signatures of this fugacious state have already been observed at the RHIC (relativistic heavy ion collider). The first evidence of the violence of collisions is the number of generated particles: about 6000 per collision, mostly hadrons. This figure seems high but in fact is less than theoretically expected and is the first sign of the formation of a QGP that saturates the density of gluons. Another sign, observed at the RHIC is the damping of the particle jets that are produced in the collision. This damping is consistent with the crossing of a medium whose density is so high that it can not be made of hadrons but of partons. In the RHIC experiments the collective behaviour of quarks and gluons shows that they are strongly interacting with one another. This fact supports the idea that the QGP is more a perfect liquid rather than an ideal gas in which quarks and gluons move freely. (A.C.)

Mathematical theory of Feynman path integrals an introduction

CERN Document Server

Albeverio, Sergio A; Mazzucchi, Sonia

2008-01-01

Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

Constructive Representation Theory for the Feynman Operator Calculus

CERN Document Server

Gill, T L

2006-01-01

In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. We first develop an operator version of the Henstock-Kurzweil integral, and a new Hilbert space that allows us to construct the elementary path integral in the manner originally envisioned by Feynman. After developing our time-ordered operator theory we extend a few of the important theorems of semigroup theory, including the Hille-Yosida theorem. As an application, we unify and extend the theory of time-dependent parabolic and hyperbolic evolution equations. We then develop a general perturbation theory and use it to prove that all theories generated by semigroups are asympotic in the operator-valued sense of Poincar e. This allows us to provide a general theory for the interaction representation of relativistic quantum theory. We then show that our theory can be reformulated as a physically motivated sum over paths, and use this version to extend the Feynman path integral to include more general interaction...

Modelling the gluon propagator

Energy Technology Data Exchange (ETDEWEB)

Leinweber, D.B.; Parrinello, C.; Skullerud, J.I.; Williams, A.G

1999-03-01

Scaling of the Landau gauge gluon propagator calculated at {beta} = 6.0 and at {beta} = 6.2 is demonstrated. A variety of functional forms for the gluon propagator calculated on a large (32{sup 3} x 64) lattice at {beta} = 6.0 are investigated.

Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory.

Science.gov (United States)

Baaquie, Belal E

2007-01-01

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

Quark ACM with topologically generated gluon mass

Science.gov (United States)

Choudhury, Ishita Dutta; Lahiri, Amitabha

2016-03-01

We investigate the effect of a small, gauge-invariant mass of the gluon on the anomalous chromomagnetic moment (ACM) of quarks by perturbative calculations at one-loop level. The mass of the gluon is taken to have been generated via a topological mass generation mechanism, in which the gluon acquires a mass through its interaction with an antisymmetric tensor field Bμν. For a small gluon mass ( ACM at momentum transfer q2 = -M Z2. We compare those with the ACM calculated for the gluon mass arising from a Proca mass term. We find that the ACM of up, down, strange and charm quarks vary significantly with the gluon mass, while the ACM of top and bottom quarks show negligible gluon mass dependence. The mechanism of gluon mass generation is most important for the strange quarks ACM, but not so much for the other quarks. We also show the results at q2 = -m t2. We find that the dependence on gluon mass at q2 = -m t2 is much less than at q2 = -M Z2 for all quarks.

Gluon Polarisation Measurements at COMPASS

CERN Document Server

Silva, Luís

2012-01-01

One of the missing keys in the present understanding of the spin structure of the nucleon is the contribution from the gluons: the so-called gluon polarisation. This quantity can be determined in DIS through the photon-gluon fusion process, in which two analysis methods may be used: (i) identifying open charm events or (ii) selecting events with high $p_{T}$ hadrons. The data used in the present work were collected in the COMPASS experiment, where a 160 GeV/c naturally polarised muon beam, impinging on a polarised nucleon fixed target is used. Preliminary results for the gluon polarisation from high $p_{T}$ and open charm analyses are presented. The gluon polarisation result for high $p_{T}$ hadrons is divided, for the first time, into three statistically independent measurements at LO. The result from open charm analysis is obtained at LO and NLO. In both analyses a new weighted method based on a neural network approach is used.

Feynman integrals and the moment problem

International Nuclear Information System (INIS)

Pusterla, M.; Turchetti, G.; Vitali, G.

1976-01-01

In this letter it is illustrated a general procedure, based on the momentum method, to estimate the scalar Feynman integrals. In order to illustrate the various situations discussed, some numerical examples are presented

New framework for the Feynman path integral

International Nuclear Information System (INIS)

Shaharir, M.Z.

1986-01-01

The well-known Fourier integral solution of the free diffusion equation in an arbitrary Euclidean space is reduced to Feynmannian integrals using the method partly contained in the formulation of the Fresnelian integral. By replacing the standard Hilbert space underlying the present mathematical formulation of the Feynman path integral by a new Hilbert space, the space of classical paths on the tangent bundle to the Euclidean space (and more general to an arbitrary Riemannian manifold) equipped with a natural inner product, we show that our Feynmannian integral is in better agreement with the qualitative features of the original Feynman path integral than the previous formulations of the integral

Gluons and gravitons at one loop from ambitwistor strings

Science.gov (United States)

Geyer, Yvonne; Monteiro, Ricardo

2018-03-01

We present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results exhibit the colour-kinematics duality in gauge theory and the double-copy relation to gravity, in a form that was recently observed in supersymmetric theories. The new formulae are expressed in a particular representation of the loop integrand, with only one quadratic propagator, which arises naturally from the framework of the loop-level scattering equations. The starting point in our work are the expressions based on the scattering equations that were recently derived from ambitwistor string theory. We turn these expressions into explicit formulae depending only on the loop momentum, the external momenta and the external polarisations. These formulae are valid in any number of spacetime dimensions for pure Yang-Mills theory (gluon) and its natural double copy, NS-NS gravity (graviton, dilaton, B-field), and we also present formulae in four spacetime dimensions for pure gravity (graviton). We perform several tests of our results, such as checking gauge invariance and directly matching our four-particle formulae to previously known expressions. While these tests would be elaborate in a Feynman-type representation of the loop integrand, they become straightforward in the representation we use.

Field theory

CERN Multimedia

1999-11-08

In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.

A New Comment on Dyson's Exposition of Feynman's Proof of Maxwell Equations

International Nuclear Information System (INIS)

Pombo, Claudia

2009-01-01

A paper by Dyson, published nearly two decades ago, describing Feynman's proof of Maxwell equations, has generated many comments, analysis, discussions and generalizations of the proof. Feynman's derivation is assumed to be based on two main sets of equations. One is supposed to be the second law of Newton and the other a set of basic commutation relations from quantum physics.Here we present a new comment on this paper, focusing mainly on the initial arguments and applying a new method of analysis and interpretation of physics, named observational realism. The present discussion does not alter the technical steps of Feynman, but do clarify their basis. We show that Newton's physics is not a starting point in Feynman's derivation, neither is quantum physics involved in it, but the foundations of relativity only.

arXiv Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case

CERN Document Server

Abreu, Samuel; Duhr, Claude; Gardi, Einan

2017-12-15

We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the dimensional regulator are multiple polylogarithms (MPLs). Our main result is the conjecture that this diagrammatic coaction reproduces the combinatorics of the coaction on MPLs order by order in the Laurent expansion. We show that our conjecture holds in a broad range of nontrivial one-loop integrals. We then explore its consequences for the study of discontinuities of Feynman integrals, and the differential equations that they satisfy. In particular, using the diagrammatic coaction along with information from cuts, we explicitly derive differential equations for any one-loop Feynman integral. We also explain how to construct the symbol of any one-loop Feynman integral recursively. Finally, we show that our diagrammatic coaction follows, in the special case of o...

A proposal of a renormalizable Nambu-Jona-Lasinio model

Science.gov (United States)

Cabo Montes de Oca, Alejandro

2018-03-01

A local and gauge invariant gauge field model including Nambu-Jona-Lasinio (NJL) and QCD Lagrangian terms in its action is introduced. Surprisingly, it becomes power counting renormalizable. This occurs thanks to the presence of action terms which modify the quark propagators, to become more decreasing that the Dirac one at large momenta in a Lee-Wick form, implying power counting renormalizability. The appearance of finite quark masses already in the tree approximation in the scheme is determined by the fact that the new action terms explicitly break chiral invariance. In this starting work we present the renormalized Feynman diagram expansion of the model and derive the formula for the degree of divergence of the diagrams. An explanation for the usual exclusion of the added Lagrangian terms is presented. In addition, the primitíve divergent graphs are identified. We start their evaluation by calculating the simpler contribution to the gluon polarization operator. The divergent and finite parts both result transverse as required by gauge invariance. The full evaluation of the various primitive divergences, which are required for completely defining the counterterm Feynman expansion will be considered in coming works, for further allowing to discuss the flavour symmetry breaking and unitarity.

Quark contribution to the gluon Regge trajectory at NLO from the high energy effective action

International Nuclear Information System (INIS)

Chachamis, G.; Hentschinski, M.; Madrigal Martínez, J.D.; Sabio Vera, A.

2012-01-01

The two loop (NLO) diagrams with quark content contributing to the gluon Regge trajectory are computed within the framework of Lipatov's effective action for QCD, using the regularization procedure for longitudinal divergencies recently proposed by two of us in (M. Hentschinski and A. Sabio Vera, 2011). Perfect agreement with previous results in the literature is found, providing a robust check of the regularization prescription and showing that the high energy effective action is a very useful computational tool in the quasi-multi-Regge limit.

Bound states of quarks and gluons and hadronic transitions; Estados ligados de quarks e gluons e transicoes hadronicas

Energy Technology Data Exchange (ETDEWEB)

Castro, Antonio Soares de

1990-05-01

A potential which incorporates the concepts of confinement and asymptotic freedom, previously utilized in the description of the spectroscopy of mesons and baryons, is extended to the gluon sector. The mass spectroscopy of glueballs and hybrids is analyzed considering only pairwise potentials and massive constituent gluons. The mass spectrum of the color octet two-gluon system is adopted as a suitable description of the intermediate states of hadronic transitions, within the framework of the multipole expansion for quantum chromodynamics. The spin-dependent effects in the gluonium spectrum, associated with the Coulombian potential, are calculated through the inverted first Born approximation for the gluon-gluon scattering. (author). 102 refs, 1 fig, 13 tabs.

Path-integral quantization of solitons using the zero-mode Feynman rule

International Nuclear Information System (INIS)

Sung Sheng Chang

1978-01-01

We propose a direct expansion treatment to quantize solitons without collective coordinates. Feynman's path integral for a free particle subject to an external force is directly used as the generating functional for the zero-frequency mode. The generating functional has no infrared singularity and defines a zero-mode Feynman rule which also gives a correct perturbative expansion for the harmonic-oscillator Green's function by treating the quadratic potential as a perturbation. We use the zero-mode Feynman rule to calculate the energy shift due to the second-order quantum corrections for solitons. Our result agrees with previous predictions using the collective-coordinate method or the method of Goldstone and Jackiw

Feynman variance-to-mean method

International Nuclear Information System (INIS)

Dowdy, E.J.; Hansen, G.E.; Robba, A.A.

1985-01-01

The Feynman and other fluctuation techniques have been shown to be useful for determining the multiplication of subcritical systems. The moments of the counting distribution from neutron detectors is analyzed to yield the multiplication value. The authors present the methodology and some selected applications and results and comparisons with Monte Carlo calculations

Algorithm FIRE-Feynman Integral REduction

International Nuclear Information System (INIS)

Smirnov, A.V.

2008-01-01

The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over loop momenta when possible. Currently it is being used in complicated three-loop calculations.

The Gluon Sivers Distribution: Status and Future Prospects

International Nuclear Information System (INIS)

Zhou, Jian; Boer, Daniël; Pisano, Cristian; Lorcé, Cédric

2015-01-01

We review what is currently known about the gluon Sivers distribution and what are the opportunities to learn more about it. Because single transverse spin asymmetries in p"↑p→πX provide only indirect information about the gluon Sivers function through the relation with the quark-gluon and tri-gluon Qiu-Sterman functions, current data from hadronic collisions at RHIC have not yet been translated into a solid constraint on the gluon Sivers function. SIDIS data, including the COMPASS deuteron data, allow for a gluon Sivers contribution of natural size expected from large N_c arguments, which is O(1/N_c) times the nonsinglet quark Sivers contribution. Several very promising processes to measure the gluon Sivers effect directly have been suggested, which besides RHIC investigations, would strongly favor experiments at AFTER@LHC and a possible future Electron-Ion Collider. Due to the inherent process dependence of TMDs, the gluon Sivers TMD probed in the various processes are different linear combinations of two universal gluon Sivers functions that have different behavior under charge conjugation and that therefore satisfy different theoretical constraints. For this reason both hadronic and DIS type of collisions are essential in the study of the role of gluons in transversely polarized protons.

The Elusive Gluon

CERN Document Server

Chala, Mikael; Perez, Gilad; Santiago, Jose

2015-01-01

We study the phenomenology of vector resonances in the context of natural composite Higgs models. A mild hierarchy between the fermionic partners and the vector resonances can be expected in these models based on the following arguments. Both direct and indirect (electroweak and flavor precision) constraints on fermionic partners are milder than the ones on spin one resonances. Also the naturalness pressure coming from the top partners is stronger than that induced by the gauge partners. This observation implies that the search strategy for vector resonances at the LHC needs to be modified. In particular, we point out the importance of heavy gluon decays (or other vector resonances) to top partner pairs that were overlooked in previous experimental searches at the LHC. These searches focused on simplified benchmark models in which the only new particle beyond the Standard Model was the heavy gluon. It turns out that, when kinematically allowed, such heavy-heavy decays make the heavy gluon elusive, and the bou...

Quark gluon plasma

CERN Document Server

Nayak, Tapan; Sarkar, Sourav

2014-01-01

At extremely high temperatures and densities, protons and neutrons may dissolve into a "soup" of quarks and gluons, called the Quark-Gluon Plasma (QGP). For a few microseconds, shortly after the Big Bang, the Universe was filled with the QGP matter. The search and study of Quark-Gluon Plasma (QGP) is one of the most fundamental research topics of our times. The QGP matter has been probed by colliding heavy ions at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory, New York and the Large Hadron Collider at CERN, Geneva. By colliding heavy-ions at a speed close to that of light, scientists aim to obtain - albeit over a tiny volume of the size of a nucleus and for an infinitesimally short instant - a QGP state. This QGP state can be observed by dedicated experiments, as it reverts to hadronic matter through expansion and cooling. This volume presents some of the current theoretical and experimental understandings in the field of QGP.

Feynman's operational calculus and beyond noncommutativity and time-ordering

CERN Document Server

Johnson, George W; Nielsen, Lance

2015-01-01

This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections wi...

A multi-region multi-energy formalism for the Feynman-alpha formulas

International Nuclear Information System (INIS)

Malinovitch, T.; Dubi, C.

2015-01-01

Highlights: • A formalism of N regions and M groups for the Feynman-α method is introduced. • Using a space-energy cell notation the expressions are simplified significantly. • A simple way to incorporate the detectors in the system is used. • The results have been verified by a Monte Carlo simulation in a two-region case. - Abstract: The stochastic transport equation, describing the dynamics in time of the neutron population in a nuclear system, is used to gain expressions for the higher moments of the neutron population in a sub-critical system. Such expressions are the bone structure of the so called Feynman-α method to analyze noise experiments, aimed to determine the reactivity of sub-critical systems. In the present study, a general formalism for the stochastic transport equation in an N regions system, under the M energy groups approximation will be introduced. In particular, expressions for the Feynman variance to mean (or the Feynman-Y function) under the above mentioned restriction will be sought by using the steady state mode of the solution

Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.

Science.gov (United States)

Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan

2017-04-07

In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.

The quark gluon plasma

International Nuclear Information System (INIS)

Granier de Cassagnac, R.

2010-01-01

The quark-gluon plasma (QGP) is a state of matter in which the universe was expected to be a few micro-seconds after the big-bang. Violent collisions of heavy ions are supposed to re-create this state in particle accelerators. Numerous signatures of this fugacious state have already been observed at the RHIC (relativistic heavy ion collider). The first evidence of the violence of collisions is the number of generated particles: about 6000 per collision, mostly hadrons. This figure seems high but in fact is less than theoretically expected and is the first sign of the formation of a QGP that saturates the density of gluons. Another sign, observed at the RHIC is the damping of the particle jets that are produced in the collision. This damping is consistent with the crossing of a medium whose density is so high that it can not be made of hadrons but of partons. In the RHIC experiments the collective behaviour of quarks and gluons shows that they are strongly interacting with one another. This fact supports the idea that the QGP is more a perfect liquid rather than an ideal gas in which quarks and gluons move freely. (A.C.)

Extension of a theory of Feynman

International Nuclear Information System (INIS)

Blaquiere, Augustin

1979-01-01

We propose a relativistic extension of a method through which Feynman derives the Schroedinger equation. The equation of Klein-Gordon for a charged particle in a magnetic field is obtained. Some connections with the nonrelativistic and the classical approximations are discussed [fr

Acceleration of Feynman loop integrals in high-energy physics on many core GPUs

International Nuclear Information System (INIS)

Yuasa, F; Ishikawa, T; Hamaguchi, N; Koike, T; Nakasato, N

2013-01-01

The current and future colliders in high-energy physics require theorists to carry out a large scale computation for a precise comparison between experimental results and theoretical ones. In a perturbative approach several methods to evaluate Feynman loop integrals which appear in the theoretical calculation of cross-sections are well established in the one-loop level, however, more studies are necessary for higher-order levels. Direct Computation Method (DCM) is developed to evaluate multi-loop integrals. DCM is based on a combination of multidimensional numerical integration and extrapolation on a sequence of integrals. It is a fully numerical method and is applicable to a wide class of integrals with various physics parameters. The computation time depends on physics parameters and the topology of loop diagrams and it becomes longer for the two-loop integrals. In this paper we present our approach to the acceleration of the two-loop integrals by DCM on multiple GPU boards

Gluon saturation in a saturated environment

International Nuclear Information System (INIS)

Kopeliovich, B. Z.; Potashnikova, I. K.; Schmidt, Ivan

2011-01-01

A bootstrap equation for self-quenched gluon shadowing leads to a reduced magnitude of broadening for partons propagating through a nucleus. Saturation of small-x gluons in a nucleus, which has the form of transverse momentum broadening of projectile gluons in pA collisions in the nuclear rest frame, leads to a modification of the parton distribution functions in the beam compared with pp collisions. In nucleus-nucleus collisions all participating nucleons acquire enhanced gluon density at small x, which boosts further the saturation scale. Solution of the reciprocity equations for central collisions of two heavy nuclei demonstrate a significant, up to several times, enhancement of Q sA 2 , in AA compared with pA collisions.

Role of the QCD induced gluon-gluon coupling to gauge boson pairs in the multitev region

International Nuclear Information System (INIS)

Ametller, L.; Gava, E.; Paver, N.; Treleani, D.

1985-02-01

We discuss the production of γγ and Zsup(O)γ pairs induced by the gluon-gluon fusion mechanism at typical supercollider energies. Due to the large flux of gluons with small fractional momenta, it is found that in certain kinematical configurations that subprocess, although of order (αsub(S)/π) 2 with respect to the leading quark annihilation, can give an appreciable contribution to the cross-section for Zsup(O)γ and even a larger one for the γγ production. (author)

Quantum gravitation. The Feynman path integral approach

International Nuclear Information System (INIS)

Hamber, Herbert W.

2009-01-01

The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals. These provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. The path integral method is suitable for both perturbative as well as non-perturbative studies, and is known to already provide a framework of choice for the theoretical investigation of non-abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman's formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. Later the lattice formulation of gravity is presented as an essential tool towards an understanding of key features of the non-perturbative vacuum. The book ends with a discussion of contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe. (orig.)

Calculation of the pulsed Feynman- and Rossi-alpha formulae with delayed neutrons

International Nuclear Information System (INIS)

Kitamura, Y.; Pazsit, I.; Wright, J.; Yamamoto, A.; Yamane, Y.

2005-01-01

In previous works, the authors have developed an effective solution technique for calculating the pulsed Feynman- and Rossi-alpha formulae. Through derivation of these formulae, it was shown that the technique can easily handle various pulse shapes of the pulsed neutron source. Furthermore, it was also shown that both the deterministic (i.e., synchronizing with the pulsing of neutron source) and stochastic (non-synchronizing) Feynman-alpha formulae can be obtained with this solution technique. However, for mathematical simplicity and the sake of insight, the formal derivation was performed in a model without delayed neutrons. In this paper, to demonstrate the robustness of the technique, the pulsed Feynman- and Rossi-alpha formulae were re-derived by taking one group of delayed neutrons into account. The results show that the advantages of this technique are retained even by inclusion of the delayed neutrons. Compact explicit formulae are derived for the Feynman- and Rossi-alpha methods for various pulse shapes and pulsing methods

Three gluon jets as a test of QCD

International Nuclear Information System (INIS)

Koller, K.; Walsh, T.F.

1977-10-01

As a test of quantum chromodynamics (QCD), we suggest looking for gluon jets in the decay of a heavy quark-antiquark bound state produced in e + e - -annihilation, Q anti Q → 3 gluons → 3 gluon jets. In particular, we point out that these events form a jet Dalitz plot, and we calculate the gluon or jet distributions (including the effect of polarized e + e - -beams). This process affords a test of the gluon spin. It is the analogue of two-jet angular distributions in e + e - %→ q anti q → 2 quark jets. We also estimate multiplicities and momentum distributions of hadrons in Q anti Q → 3 gluons → hadrons, using the recently discovered UPSILON (9.4) as an example. (orig.) [de

Transport coefficients for deeply inelastic scattering from the Feynman path integral method

International Nuclear Information System (INIS)

Brink, D.M.; Neto, J.; Weidenmueller, H.A.

1979-01-01

Friction and diffusion coefficients can be derived simply by combining statistical arguments with the Feynman path integral method. A transport equation for Feynman's influence functional is obtained, and transport coefficients are deduced from it. The expressions are discussed in the limits of weak, and of strong coupling. (Auth.)

Semirelativistic potential model for three-gluon glueballs

International Nuclear Information System (INIS)

Mathieu, Vincent; Semay, Claude; Silvestre-Brac, Bernard

2008-01-01

The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Our results are in good agreement with other approaches and lattice calculation for the odderon trajectory but differ strongly from lattice in the J +- sector. We propose a possible explanation for this problem.

The R{sup ∗}-operation for Feynman graphs with generic numerators

Energy Technology Data Exchange (ETDEWEB)

Herzog, Franz [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Ruijl, Ben [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Leiden University,Niels Bohrweg 1, 2333 CA Leiden (Netherlands)

2017-05-08

The R{sup ∗}-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R{sup ∗}-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional ϕ{sup 3} theory.

Solutions of the Wheeler-Feynman equations with discontinuous velocities.

Science.gov (United States)

de Souza, Daniel Câmara; De Luca, Jayme

2015-01-01

We generalize Wheeler-Feynman electrodynamics with a variational boundary value problem for continuous boundary segments that might include velocity discontinuity points. Critical-point orbits must satisfy the Euler-Lagrange equations of the action functional at most points, which are neutral differential delay equations (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann continuity conditions for the partial momenta and the partial energies. We study a special setup having the shortest time-separation between the (infinite-dimensional) boundary segments, for which case the critical-point orbit can be found using a two-point boundary problem for an ordinary differential equation. For this simplest setup, we prove that orbits can have discontinuous velocities. We construct a numerical method to solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann conditions and calculate some numerical orbits with discontinuous velocities. We also prove that the variational boundary value problem has a unique solution depending continuously on boundary data, if the continuous boundary segments have velocity discontinuities along a reduced local space.

Dynamical gluon mass in the instanton vacuum model

Science.gov (United States)

Musakhanov, M.; Egamberdiev, O.

2018-04-01

We consider the modifications of gluon properties in the instanton liquid model (ILM) for the QCD vacuum. Rescattering of gluons on instantons generates the dynamical momentum-dependent gluon mass Mg (q). First, we consider the case of a scalar gluon, no zero-mode problem occurs and its dynamical mass Ms (q) can be found. Using the typical phenomenological values of the average instanton size ρ = 1 / 3 fm and average inter-instanton distance R = 1 fm we get Ms (0) = 256 MeV. We then extend this approach to the real vector gluon with zero-modes carefully considered. We obtain the following expression Mg2 (q) = 2 Ms2 (q). This modification of the gluon in the instanton media will shed light on nonperturbative aspect on heavy quarkonium physics.

Feynman-Kac equations for reaction and diffusion processes

Science.gov (United States)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Systematic approximation of multi-scale Feynman integrals arXiv

CERN Document Server

Borowka, Sophia; Hulme, Daniel

An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman integrals, allowing for fast numerical evaluation. The results are valid in all kinematical regions, both above and below thresholds, up to in principle arbitrary orders in the dimensional regulator. The scope of the algorithm is demonstrated by presenting results for selected two-loop three-point and four-point integrals with an internal mass scale that appear in the two-loop amplitudes for Higgs+jet production.

Production and recombination of gluons

International Nuclear Information System (INIS)

Temiraliev, A.T.

2006-01-01

Full text: Nonlinear Markov process of parton production has been considered. The Kolmogorov equation is applied for the evolution equation based on the approximation of independent gluons production in every decay act. We introduced a 'crossing' parameter and used the combination relations to obtain nonlinear recombination equation for the evolution of gluon structure function. (author)

On the quantization and asymptotic freedom of Yang-Mills theory in the temporal gauge

International Nuclear Information System (INIS)

Frenkel, J.

1979-01-01

The relevance of the longitudinal gluons in the derivation of the Feynman rules in the temporal gauge is studied, via the canonical approach. It is then shown that these gluons are also fundamental for the asymptotic freedom of the Yang-Mills theory [pt

Statistical error estimation of the Feynman-α method using the bootstrap method

International Nuclear Information System (INIS)

Endo, Tomohiro; Yamamoto, Akio; Yagi, Takahiro; Pyeon, Cheol Ho

2016-01-01

Applicability of the bootstrap method is investigated to estimate the statistical error of the Feynman-α method, which is one of the subcritical measurement techniques on the basis of reactor noise analysis. In the Feynman-α method, the statistical error can be simply estimated from multiple measurements of reactor noise, however it requires additional measurement time to repeat the multiple times of measurements. Using a resampling technique called 'bootstrap method' standard deviation and confidence interval of measurement results obtained by the Feynman-α method can be estimated as the statistical error, using only a single measurement of reactor noise. In order to validate our proposed technique, we carried out a passive measurement of reactor noise without any external source, i.e. with only inherent neutron source by spontaneous fission and (α,n) reactions in nuclear fuels at the Kyoto University Criticality Assembly. Through the actual measurement, it is confirmed that the bootstrap method is applicable to approximately estimate the statistical error of measurement results obtained by the Feynman-α method. (author)

Feynman integrals and difference equations

International Nuclear Information System (INIS)

Moch, S.; Schneider, C.

2007-09-01

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

Lectures on differential equations for Feynman integrals

International Nuclear Information System (INIS)

Henn, Johannes M

2015-01-01

Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations (DE). These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to DE for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that is based on properties of the space–time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the DE. Finally, as an application of these ideas we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a DE. (topical review)

A recursive reduction of tensor Feynman integrals

International Nuclear Information System (INIS)

Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.

2009-07-01

We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)

A Feynman-Hellmann approach to the spin structure of hadrons

Energy Technology Data Exchange (ETDEWEB)

Chambers, A.J. [Adelaide Univ., SA (Australia). CSSM, Dept. of Physics; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe (Japan); Collaboration: CSSM and QCDSF/UKQCD Collaborations; and others

2014-05-15

We perform a N{sub f}=2+1 lattice QCD simulation to determine the quark spin fractions of hadrons using the Feynman-Hellmann theorem. By introducing an external spin operator to the fermion action, the matrix elements relevant for quark spin fractions are extracted from the linear response of the hadron energies. Simulations indicate that the Feynman-Hellmann method offers statistical precision that is comparable to the standard three-point function approach, with the added benefit that it is less susceptible to excited state contamination. This suggests that the Feynman-Hellmann technique offers a promising alternative for calculations of quark line disconnected contributions to hadronic matrix elements. At the SU(3)-flavour symmetry point, we find that the connected quark spin fractions are universally in the range 55-70% for vector mesons and octet and decuplet baryons. There is an indication that the amount of spin suppression is quite sensitive to the strength of SU(3) breaking.

The gluon structure of hadrons and nuclei from lattice QCD

Science.gov (United States)

Shanahan, Phiala

2018-03-01

I discuss recent lattice QCD studies of the gluon structure of hadrons and light nuclei. After very briefly highlighting new determinations of the gluon contributions to the nucleon's momentum and spin, presented by several collaborations over the last year, I describe first calculations of gluon generalised form factors. The generalised transversity gluon distributions are of particular interest since they are purely gluonic; they do not mix with quark distributions at leading twist. In light nuclei they moreover provide a clean signature of non-nucleonic gluon degrees of freedom, and I present the first evidence for such effects, based on lattice QCD calculations. The planned Electron-Ion Collider, designed to access gluon structure quantities, will have the capability to test this prediction, and measure a range of gluon observables including generalised gluon distributions and transverse momentum dependent gluon distributions, within the next decade.

The elusive gluon

International Nuclear Information System (INIS)

Chala, Mikael; Juknevich, Jose; Perez, Gilad

2014-11-01

We study the phenomenology of vector resonances in the context of natural composite Higgs models. A mild hierarchy between the fermionic partners and the vector resonances can be expected in these models based on the following arguments. Both direct and indirect (electroweak and flavor precision) constraints on fermionic partners are milder than the ones on spin one resonances. Also the naturalness pressure coming from the top partners is stronger than that induced by the gauge partners. This observation implies that the search strategy for vector resonances at the LHC needs to be modified. In particular, we point out the importance of heavy gluon decays (or other vector resonances) to top partner pairs that were overlooked in previous experimental searches at the LHC. These searches focused on simplified benchmark models in which the only new particle beyond the Standard Model was the heavy gluon. It turns out that, when kinematically allowed, such heavy-heavy decays make the heavy gluon elusive, and the bounds on its mass can be up to 2 TeV milder than in the simpler models considered so far for the LHC14. We discuss the origin of this difference and prospects for dedicated searches.

The elusive gluon

Energy Technology Data Exchange (ETDEWEB)

Chala, Mikael [Granada Univ. (Spain). CAFPE; Granada Univ. (Spain). Dept. de Fisica Teorica y del Cosmos; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Juknevich, Jose [International School for Advanced Studies, Trieste (Italy); Istituto Nazionale di Fisica Nucleare, Trieste (Italy); Perez, Gilad [Weizmann Institute of Science, Rehovot (Israel). Dept. of Particle Physics and Astrophysics; Santiago, Jose [Granada Univ. (Spain). CAFPE; Granada Univ. (Spain). Dept. de Fisica Teorica y del Cosmos; European Organization for Nuclear Research (CERN), Geneva (Switzerland)

2014-11-15

We study the phenomenology of vector resonances in the context of natural composite Higgs models. A mild hierarchy between the fermionic partners and the vector resonances can be expected in these models based on the following arguments. Both direct and indirect (electroweak and flavor precision) constraints on fermionic partners are milder than the ones on spin one resonances. Also the naturalness pressure coming from the top partners is stronger than that induced by the gauge partners. This observation implies that the search strategy for vector resonances at the LHC needs to be modified. In particular, we point out the importance of heavy gluon decays (or other vector resonances) to top partner pairs that were overlooked in previous experimental searches at the LHC. These searches focused on simplified benchmark models in which the only new particle beyond the Standard Model was the heavy gluon. It turns out that, when kinematically allowed, such heavy-heavy decays make the heavy gluon elusive, and the bounds on its mass can be up to 2 TeV milder than in the simpler models considered so far for the LHC14. We discuss the origin of this difference and prospects for dedicated searches.

The gluon structure of hadrons and nuclei from lattice QCD

Energy Technology Data Exchange (ETDEWEB)

Shanahan, Phiala A. [College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

2018-04-01

I discuss recent lattice QCD studies of the gluon structure of hadrons and light nuclei. After very briefly highlighting new determinations of the gluon contributions to the nucleon's momentum and spin, presented by several collaborations over the last year, I describe first calculations of gluon generalised form factors. The generalised transversity gluon distributions are of particular interest since they are purely gluonic; they do not mix with quark distributions at leading twist. In light nuclei they moreover provide a clean signature of non-nucleonic gluon degrees of freedom, and I present the first evidence for such effects, based on lattice QCD calculations. The planned Electron-Ion Collider, designed to access gluon structure quantities, will have the capability to test this prediction, and measure a range of gluon observables including generalised gluon distributions and transverse momentum dependent gluon distributions, within the next decade.

Selection of Photon Gluon Fusion Events in DIS

International Nuclear Information System (INIS)

Kowalik, K.; Rondio, E.; Sulej, R.; Zaremba, K.

2001-01-01

A selection of the Photon Gluon Fusion (PGF) process with light quarks for deep inelastic scattering events is presented. This process is directly sensitive to gluon polarization and our goal is to find out the most effective selection on a sample of events simulated for the SMC experiment. We compare two general multi-class classification methods - Bayes method and neural network with a conventional selection procedure. The neural network algorithm presented here is a modification of method belonging to the family of directional minimization algorithms. This method is convenient and effective for photon gluon fusion selection and determination of gluon polarization. Finally we present the estimation for precision of gluon polarization for neural network method. (author)

The very hot soup of quarks and gluons; La tres chaude soupe de quarks et de gluons

Energy Technology Data Exchange (ETDEWEB)

Ter Minassian, V.

2010-05-15

The Phenix collaboration at the RHIC collider (Usa) has measured directly, for the first time, the temperature just after 2 gold nuclei have collided. All the experimental conditions were taken to assure that the temperature measured was that of the quark-gluon plasma. The value of this temperature is 4000*10{sup 9} K, which is 1.20 as high as the theoretical temperature threshold for the existence of the quark-gluon plasma. It is a proof that the quark-gluon plasma can be created within the operating conditions of the RHIC. (A.C.)

Feynman integrals and difference equations

Energy Technology Data Exchange (ETDEWEB)

Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

2007-09-15

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

S-bases as a tool to solve reduction problems for Feynman integrals

International Nuclear Information System (INIS)

Smirnov, A.V.; Smirnov, V.A.

2006-01-01

We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a recently suggested reduction algorithm which uses Groebner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined

S-bases as a tool to solve reduction problems for Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Smirnov, A.V. [Scientific Research Computing Center of Moscow State University, Moscow 119992 (Russian Federation); Smirnov, V.A. [Nuclear Physics Institute of Moscow State University, Moscow 119992 (Russian Federation)

2006-10-15

We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a recently suggested reduction algorithm which uses Groebner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined.

Cuts of Feynman Integrals in Baikov representation

Energy Technology Data Exchange (ETDEWEB)

Frellesvig, Hjalte; Papadopoulos, Costas G. [Institute of Nuclear and Particle Physics, NCSR ‘Demokritos’,P.O. Box 60037, Agia Paraskevi, 15310 (Greece)

2017-04-13

Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in d dimensions. The information provided by these computations may be used to determine the class of functions needed to analytically express the full integrals.

Cuts of Feynman Integrals in Baikov representation

International Nuclear Information System (INIS)

Frellesvig, Hjalte; Papadopoulos, Costas G.

2017-01-01

Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in d dimensions. The information provided by these computations may be used to determine the class of functions needed to analytically express the full integrals.

Quadratic forms for Feynman-Kac semigroups

International Nuclear Information System (INIS)

Hibey, Joseph L.; Charalambous, Charalambos D.

2006-01-01

Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions

Equation of state of quasi-free gluon gas

International Nuclear Information System (INIS)

Chakrabarty, Somenath; Syam, Debapriyo

1993-01-01

The object of this work is to derive an equation of state for a system of gluons beyond the deconfining temperature (∼200 MeV) with phenomenological applications in mind. Our starting point is the relativistic virial theorem. We assume that the non-Abelian nature of QCD (especially the confirming gluon-gluon interaction), as far as the gluon gas is concerned, can be accounted for by postulating a bag pressure (B), while the residual interaction among the gluons can be treated as if the problem is Abelian. Near the 'critical' temperature the residual interactions are seen to play an important role. Also the Stefan-Boltzmann constant is required to be replaced by an effective constant having a somewhat smaller value. (Author)

Feynman and physics. Life and research of an exceptional man; Feynman und die Physik. Leben und Forschung eines aussergewoehnlichen Menschen

Energy Technology Data Exchange (ETDEWEB)

Resag, Joerg

2018-04-01

The life of Feynman is described together with his work on path integrals, quantum electrodynmaics, helium at low temperatures, the weak interaction, the quark model, and computer-calculation methods, and his contribution to the Manhattan project. (HSI)

Equivariance, Variational Principles, and the Feynman Integral

Directory of Open Access Journals (Sweden)

George Svetlichny

2008-03-01

Full Text Available We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in physics and their connection to Feynman's integral.

Confinement models for gluons

International Nuclear Information System (INIS)

Khadkikar, S.B.; Vinodkumar, P.C.

1987-04-01

Confinement model for gluons using a 'colour super current' is formulated. An attempt has been made to derive a suitable dielectric function corresponding to the current confinement model. A simple inhomogeneous dielectric confinement model for gluons is studied for comparison. The model Hamiltonians are second quantized and the glueball states are constructed. The spurious motion of the centre of confinement is accounted for. The results of the current confinement scheme are found to be in good agreement with the experimental candidates for glueballs. (author). 16 refs, 3 tabs

The Mixed Quark-Gluon Condensate from the Global Color Symmetry Model

Institute of Scientific and Technical Information of China (English)

ZONG Hong-Shi; PING Jia-Lun; LU Xiao-Fu; WANG Fan; ZHAO En-Guang

2002-01-01

The mixed quark-gluon condensate from the global color symmetry model is derived. It is shown that themixed quark-gluon condensate depends explicitly on the gluon propagator. This interesting feature may be regarded asan additional constraint on the model of gluon propagator. The values of the mixed quark-gluon condensate from someansatz for the gluon propagator are compared with those determined from QCD sum rules.

Feynman Integrals with Absorbing Boundaries

OpenAIRE

Marchewka, A.; Schuss, Z.

1997-01-01

We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined to the non-absorbing region. Trajectories that reach the absorbing wall are discounted from the population of the surviving trajectories with a certain weighting factor. Under the assumption that absorbed trajectories do not interfere with the surviving trajectories, we obtain a time dependent absorption law. Two examples are worked ...

A modern theory of random variation with applications in stochastic calculus, financial mathematics, and Feynman integration

CERN Document Server

Muldowney, Patrick

2012-01-01

A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. I...

Exploring the Nuclear Phase Diagram with Beam Energy Scans

International Nuclear Information System (INIS)

Horvat, Stephen

2017-01-01

The nuclear phase diagram is mapped using beam energy scans of relativistic heavy-ion collisions. This mapping is possible because different collision energies develop along different trajectories through the phase diagram. High energy collisions will evolve though a crossover phase transition according to lattice QCD, but lower collision energies may traverse a first order phase transition. There are hints for this first order phase transition and its critical endpoint, but further measurements and theoretical guidance is needed. In addition to mapping the phase transition, beam energy scans allow us to see if we can turn off the signatures of deconfinement. If an observable is a real signature for the formation of the deconfined state called quark-gluon plasma, then it should turn off at sufficiently low collision energies. In this summary talk I will show the current state of the field using beam energy scan results from RHIC and SPS, I will show where precise theoretical guidance is needed for understanding recent measurements, and I will motivate the need for more data and new measurements from FAIR, NICA, RHIC, and the SPS. (paper)

Confinement in Polyakov gauge and the QCD phase diagram

Energy Technology Data Exchange (ETDEWEB)

Marhauser, Marc Florian

2009-10-14

We investigate Quantum Chromodynamics (QCD) in the framework of the functional renormalisation group (fRG). Thereby describing the phase transition from the phase with confined quarks into the quark-gluon-plasma phase. We focus on a physical gauge in which the mechanism driving the phase transition is discernible. We find results compatible with lattice QCD data, as well as with functional methods applied in different gauges. The phase transition is of the expected order and we computed critical exponents. Extensions of the model are discussed. When investigating the QCD phase diagram, we compute the effects of dynamical quarks at finite density on the running of the gauge coupling. Additionally, we calculate how these affect the deconfinement phase transition, also, dynamical quarks allow for the inclusion of a finite chemical potential. Concluding the investigation of the phase diagram, we establish a relation between confinement and chiral symmetry breaking, which is tied to the dynamical generation of hadron masses. In the investigations, we often encounter scale dependent fields. We investigate a footing on which these can be dealt with in a uniform way. (orig.)

Gluon Bremsstrahlung in Weakly-Coupled Plasmas

International Nuclear Information System (INIS)

Arnold, Peter

2009-01-01

I report on some theoretical progress concerning the calculation of gluon bremsstrahlung for very high energy particles crossing a weakly-coupled quark-gluon plasma. (i) I advertise that two of the several formalisms used to study this problem, the BDMPS-Zakharov formalism and the AMY formalism (the latter used only for infinite, uniform media), can be made equivalent when appropriately formulated. (ii) A standard technique to simplify calculations is to expand in inverse powers of logarithms ln(E/T). I give an example where such expansions are found to work well for ω/T≥10 where ω is the bremsstrahlung gluon energy. (iii) Finally, I report on perturbative calculations of q.

Deduction of the in-medium gluon distribution from photon-gluon fusion processes in peripheral ultrarelativistic heavy-ion collisions

International Nuclear Information System (INIS)

Greiner, M.; Hofmann, C.; Schaefer, A.; Soff, G.

1994-08-01

The photon-gluon fusion process into a pair of heavy quarks is studied for peripheral Pb+Pb collisions at LHC energies. The double differential cross section with respect to the invariant mass and the rapidity of the produced quark pair at zero rapidity is directly proportional to the gluon distribution in the nuclear medium. Differential cross sections for the b-quark production lie well in the μbarn/GeV regime which will allow the deduction of the gluon distribution at low x. Rapidity cuts for the actual detectors are also considered. (orig.)

High energy evolution of soft gluon cascades

International Nuclear Information System (INIS)

Shuvaev, A.; Wallon, S.

2006-01-01

In this paper we derive an evolution equation for the gluon density in soft gluon cascades emitted from any colored source, in the leading logarithmic approximation of perturbative QCD. We show that this equation has the same form as the BFKL equation in the forward case. An explicit expression for the total cascade wavefunction involving an arbitrary number of soft gluons is obtained. Renormalization of the colored source wavefunction turns out to be responsible for the reggeization of the source. (orig.)

High energy evolution of soft gluon cascades

Energy Technology Data Exchange (ETDEWEB)

Shuvaev, A. [St. Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg district (Russian Federation); Wallon, S. [Universite Paris XI, Laboratoire de Physique Theorique, Orsay Cedex (France)

2006-04-15

In this paper we derive an evolution equation for the gluon density in soft gluon cascades emitted from any colored source, in the leading logarithmic approximation of perturbative QCD. We show that this equation has the same form as the BFKL equation in the forward case. An explicit expression for the total cascade wavefunction involving an arbitrary number of soft gluons is obtained. Renormalization of the colored source wavefunction turns out to be responsible for the reggeization of the source. (orig.)

The Errors of Feynman and Hibbs

Indian Academy of Sciences (India)

rors simply because he was so smart. He would write down equations that got to the gist of the difficult ... work at a level somewhat below Feynman's, these fac- tors and limits and so forth are not obvious, and their ... an interview with Hibbs in which he said he's working on a book to be titled Quantum Mechanics and Path In-.

Probing finite coarse-grained virtual Feynman histories with sequential weak values

Science.gov (United States)

Georgiev, Danko; Cohen, Eliahu

2018-05-01

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories.

Baryonic hybrids: Gluons as beads on strings between quarks

International Nuclear Information System (INIS)

Cornwall, John M.

2005-01-01

In this paper we analyze the ground state of the heavy-quark qqqG system using standard principles of quark confinement and massive constituent gluons as established in the center-vortex picture. The known string tension K F and approximately-known gluon mass M lead to a precise specification of the long-range nonrelativistic part of the potential binding the gluon to the quarks with no undetermined phenomenological parameters, in the limit of large interquark separation R. Our major tool (also used earlier by Simonov) is the use of proper-time methods to describe gluon propagation within the quark system, along with some elementary group theory describing the gluon Wilson-line as a composite of colocated q and q lines. We show that (aside from color-Coulomb and similar terms) the gluon potential energy in the presence of quarks is accurately described (for small gluon fluctuations) via attaching these three strings to the gluon, which in equilibrium sits at the Steiner point of the Y-shaped string network joining the three quarks. The gluon undergoes small harmonic fluctuations that slightly stretch these strings and quasiconfine the gluon to the neighborhood of the Steiner point. To describe nonrelativistic ground-state gluonic fluctuations at large R we use the Schroedinger equation, ignoring mixing with l=2 states. Available lattice data and real-world hybrids require consideration of R values small enough for significant relativistic corrections, which we apply using a variational principle for the relativistic harmonic-oscillator. We also consider the role of color-Coulomb contributions. In terms of interquark separations R, we find leading nonrelativistic large-R terms in the gluon excitation energy of the form ε(R)→M+ξ[K F /(MR)] 1/2 -ζα c /R where ξ,ζ are calculable numerical coefficients and α c ≅ 0.15 is the color-Coulomb qq coupling. When the gluon is relativistic, ε∼(K F /R) 1/3 . We get an acceptable fit to lattice data with M=500 Me

Bound states of quarks and gluons and hadronic transitions

International Nuclear Information System (INIS)

Castro, Antonio Soares de.

1990-05-01

A potential which incorporates the concepts of confinement and asymptotic freedom, previously utilized in the description of the spectroscopy of mesons and baryons, is extended to the gluon sector. The mass spectroscopy of glueballs and hybrids is analyzed considering only pairwise potentials and massive constituent gluons. The mass spectrum of the color octet two-gluon system is adopted as a suitable description of the intermediate states of hadronic transitions, within the framework of the multipole expansion for quantum chromodynamics. The spin-dependent effects in the gluonium spectrum, associated with the Coulombian potential, are calculated through the inverted first Born approximation for the gluon-gluon scattering. (author). 102 refs, 1 fig, 13 tabs

Le cours de physique de Feynman

CERN Document Server

Feynman, Richard; Sands, Matthew

L’ampleur du succès qu’a rencontré le « Cours de physique de Feynman » dès sa parution s’explique par son caractère fondamentalement novateur. Richard Feynman, qui fut professeur d’université dès l’âge de vingt-quatre ans, a exprimé dans ce cours, avant d’obtenir le prix Nobel de Physique, une vision expérimentale et extrêmement personnelle de l’enseignement de la physique. Cette vision a, depuis, remporté l’adhésion des physiciens du monde entier, faisant de cet ouvrage un grand classique. Ce cours en cinq volumes (Électromagnétisme 1 et 2, Mécanique 1 et 2, Mécanique quantique) s’adresse aux étudiants de tous niveaux qui y trouveront aussi bien les notions de base débarrassées de tout appareil mathématique inutile, que les avancées les plus modernes de cette science passionnante qu’est la physique. Cette nouvelle édition corrigée bénéficie d’une mise en page plus aérée pour un meilleur confort de lecture.

Soft-gluon resummation for high-pT inclusive-hadron production at COMPASS

International Nuclear Information System (INIS)

Pfeuffer, Melanie

2013-01-01

One of the experiments that may be used to probe the nucleon's gluon distribution is the fixed-target lepton scattering experiment COMPASS at CERN, where charged hadrons with high transverse momentum are observed. An aspect that makes the COMPASS experiment quite challenging for the theoretical calculation in perturbative QCD is its fixed-target regime. The hadron's transverse momentum is relatively large compared to the available center-of-mass energy. Thus the partonic process is close to the threshold, where all available partonic center-of-mass energy is just used to produce the high-transverse momentum parton that subsequently hadronizes into the observed hadron, and its recoiling counterpart. Additional real gluon radiation is strongly suppressed and therefore mostly constrained to the emission of soft and/or collinear gluons. This results in a strong imbalance between real and virtual gluon diagrams and the cancellation of infrared singularities leaves behind large logarithmic corrections to the leading order cross section. These logarithms are not only present in the next-to-leading (NLO) corrections, but appear also in all higher order corrections in its perturbation expansion. They dominate the cross section in the kinematic region close to the threshold and thus have to be taken into account order-by-order. A technique that addresses these logarithms is known as threshold resummation. The main goal of this work is to investigate the relevance of higher-order QCD corrections of the unpolarized photoproduction reaction in fixed-target scattering at COMPASS, where the hadron is produced at large transverse momentum. In particular the large logarithmic threshold corrections to the partonic cross sections are addressed, which are resummed to all orders at next-to-leading logarithmic (NLL) accuracy. As new technical ingredient to resummation, the rapidity dependence of the cross section in the resummed calculation is fully included in order to account for all

The Color Antisymmetric Ghost Propagator and One-Loop Vertex Renormalization

OpenAIRE

Furui, Sadataka

2007-01-01

The color matrix elements of the ghost triangle diagram that appears in the triple gluon vertex and the ghost-ghost-gluon triangle diagram that appears in the ghost-gluon-ghost vertex are calculated. The ghost-ghost-gluon triangle contains a loop consisting of two color diagonal ghosts and one gluon and a loop consisting of two color antisymmetric ghosts and one gluon. Consequently, the pQCD argument in the infrared region based on the one particle irreducible diagram should be modified. Impl...

Free energy and plaquette expectation value for gluons on the lattice, in three dimensions

International Nuclear Information System (INIS)

Panagopoulos, H.; Skouroupathis, A.; Tsapalis, A.

2006-01-01

We calculate the perturbative value of the free energy in lattice QCD in three dimensions, up to three loops. Our calculation is performed using the Wilson formulation for gluons in SU(N) gauge theories. The free energy is directly related to the average plaquette. To carry out the calculation, we compute the coefficients involved in the perturbative expansion of the Free Energy up to three loops, using an automated set of procedures developed by us in Mathematica. The dependence on N is shown explicitly in our results. For purposes of comparison, we also present the individual contributions from every diagram. These have been obtained by means of two independent calculations, in order to cross check our results

Computer generation of integrands for Feynman parametric integrals

International Nuclear Information System (INIS)

Cvitanovic, Predrag

1973-01-01

TECO text editing language, available on PDP-10 computers, is used for the generation and simplification of Feynman integrals. This example shows that TECO can be a useful computational tool in complicated calculations where similar algebraic structures recur many times

Asymptotic behaviour of Feynman integrals

International Nuclear Information System (INIS)

Bergere, M.C.

1980-01-01

In these lecture notes, we describe how to obtain the asymptotic behaviour of Feynman amplitudes; this technique has been already applied in several cases, but the general solution for any kind of asymptotic behaviour has not yet been found. From the mathematical point of view, the problem to solve is close to the following problem: find the asymptotic expansion at large lambda of the integral ∫...∫ [dx] esup(-LambdaP[x]) where P[x] is a polynomial of several variables. (orig.)

Feynman path integrals - from the prodistribution definition to the calculation of glory scattering

International Nuclear Information System (INIS)

DeWitt-Morette, C.

1984-01-01

In these lectures I present a path integral calculation, starting from a global definition of Feynman path integrals and ending at a scattering cross section formula. Along the way I discuss some basic issues which had to be resolved to exploit the computational power of the proposed definition of Feynman integrals. I propose to compute the glory scattering of gravitational waves by black holes. (orig./HSI)

Soft Gluon Radiation off Heavy Quarks beyond Eikonal Approximation

International Nuclear Information System (INIS)

Mazumder, Surasree; Bhattacharyya, Trambak; Abir, Raktim

2016-01-01

We calculate the soft gluon radiation spectrum off heavy quarks (HQs) interacting with light quarks (LQs) beyond small angle scattering (eikonality) approximation and thus generalize the dead-cone formula of heavy quarks extensively used in the literatures of Quark-Gluon Plasma (QGP) phenomenology to the large scattering angle regime which may be important in the energy loss of energetic heavy quarks in the deconfined Quark-Gluon Plasma medium. In the proper limits, we reproduce all the relevant existing formulae for the gluon radiation distribution off energetic quarks, heavy or light, used in the QGP phenomenology.

Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD

International Nuclear Information System (INIS)

von Smekal, L.; Hauck, A.; Alkofer, R.

1997-01-01

A truncation scheme for the Dyson-Schwinger equations of Euclidean QCD in Landau gauge is presented. It implements the Slavnov-Taylor identities for the three-gluon and ghost-gluon vertices, whereas irreducible four-gluon couplings as well as the gluon-ghost and ghost-ghost scattering kernels are neglected. The infrared behavior of gluon and ghost propagators is obtained analytically: The gluon propagator vanishes for small momenta, whereas the ghost propagator diverges strongly. The numerical solutions are compared with recent lattice results. The running coupling approaches a fixed point, α c ≅9.5 , in the infrared. copyright 1997 The American Physical Society

Constituent gluon interpretation of glueballs and gluelumps

International Nuclear Information System (INIS)

Boulanger, N.; Buisseret, F.; Mathieu, V.; Semay, C.

2008-01-01

Arguments are given that support the interpretation of the lattice QCD glueball and gluelump spectra in terms of bound states of massless constituent gluons with helicity 1. In this scheme, we show that the mass hierarchy of the currently known gluelumps and glueballs is mainly due to the number of constituent gluons and can be understood within a simple flux tube model. It is also argued that the lattice QCD 0 +- glueball should be seen as a four-gluon bound state. We finally predict the mass of the 0 - state, not yet computed in lattice QCD. (orig.)

Feynman propagator in curved space-time

International Nuclear Information System (INIS)

Candelas, P.; Raine, D.J.

1977-01-01

The Wick rotation is generalized in a covariant manner so as to apply to curved manifolds in a way that is independent of the analytic properties of the manifold. This enables us to show that various methods for defining a Feynman propagator to be found in the literature are equivalent where they are applicable. We are also able to discuss the relation between certain regularization methods that have been employed

The gluon condensation at high energy hadron collisions

Energy Technology Data Exchange (ETDEWEB)

Zhu, Wei, E-mail: weizhu@mail.ecnu.edu.cn [Department of Physics, East China Normal University, Shanghai 200241 (China); Lan, Jiangshan [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China)

2017-03-15

We report that the saturation/CGC model of gluon distribution is unstable under action of the chaotic solution in a nonlinear QCD evolution equation, and it evolves to the distribution with a sharp peak at the critical momentum. We find that this gluon condensation is caused by a new kind of shadowing–antishadowing effects, and it leads to a series of unexpected effects in high energy hadron collisions including astrophysical events. For example, the extremely intense fluctuations in the transverse-momentum and rapidity distributions of the gluon jets present the gluon-jet bursts; a sudden increase of the proton–proton cross sections may fill the GZK suppression; the blocking QCD evolution will restrict the maximum available energy of the hadron–hadron colliders.

Gluon field distribution in baryons

International Nuclear Information System (INIS)

Bissey, F.; Cao, F-G.; Kitson, A.; Lasscock, B.G.; Leinweber, D.B.; Signal, A.I.; Williams, A.G.; Zanotti, J.M.

2005-01-01

Methods for revealing the distribution of gluon fields within the three-quark static-baryon potential are presented. In particular, we outline methods for studying the sensitivity of the source on the emerging vacuum response for the three-quark system. At the same time, we explore the possibility of revealing gluon-field distributions in three-quark systems in QCD without the use of gauge-dependent smoothing techniques. Renderings of flux tubes from a preliminary high-statistics study on a 12 3 x 24 lattice are presented

The three-gluon vertex of QCD

International Nuclear Information System (INIS)

Koller, K.; Zerwas, P.M.; Walsh, T.F.

1978-12-01

We show how the Q 2 evolution of gluon jets can be used to provide indirect but strong evidence for the 3 gluon vertex of QCD. We propose looking for this evolution in the QantiQ → 3G → hadrons decay of successive 1 3 S 1 quarkonium states. The results apply to other processes if G jets can be isolated. (orig.) [de

Feynman path integral formulation of quantum mechanics

International Nuclear Information System (INIS)

Mizrahi, M.M.

1975-01-01

The subject of this investigation is Feynman's path integral quantization scheme, which is a powerful global formalism with great intuitive appeal. It stems from the simple idea that a probability amplitude for a system to make a transition between two states is the ''sum'' of the amplitudes for all the possible ways the transition can take place

Quark and gluon jet properties in symmetric three-jet events

CERN Document Server

Buskulic, Damir; De Bonis, I; Décamp, D; Ghez, P; Goy, C; Lees, J P; Lucotte, A; Minard, M N; Odier, P; Pietrzyk, B; Chmeissani, M; Crespo, J M; Efthymiopoulos, I; Fernández, E; Fernández-Bosman, M; Garrido, L; Juste, A; Martínez, M; Orteu, S; Pacheco, A; Padilla, C; Palla, Fabrizio; Pascual, A; Perlas, J A; Riu, I; Sánchez, F; Teubert, F; Colaleo, A; Creanza, D; De Palma, M; Farilla, A; Gelao, G; Girone, M; Iaselli, Giuseppe; Maggi, G; Maggi, M; Marinelli, N; Natali, S; Nuzzo, S; Ranieri, A; Raso, G; Romano, F; Ruggieri, F; Selvaggi, G; Silvestris, L; Tempesta, P; Zito, G; Huang, X; Lin, J; Ouyang, Q; Wang, T; Xie, Y; Xu, R; Xue, S; Zhang, J; Zhang, L; Zhao, W; Alemany, R; Bazarko, A O; Bonvicini, G; Cattaneo, M; Comas, P; Coyle, P; Drevermann, H; Forty, Roger W; Frank, M; Hagelberg, R; Harvey, J; Jacobsen, R; Janot, P; Jost, B; Kneringer, E; Knobloch, J; Lehraus, Ivan; Martin, E B; Mato, P; Minten, Adolf G; Miquel, R; Mir, L M; Moneta, L; Oest, T; Palazzi, P; Pater, J R; Pusztaszeri, J F; Ranjard, F; Rensing, P E; Rolandi, Luigi; Schlatter, W D; Schmelling, M; Schneider, O; Tejessy, W; Tomalin, I R; Venturi, A; Wachsmuth, H W; Wildish, T; Witzeling, W; Wotschack, J; Ajaltouni, Ziad J; Barrès, A; Boyer, C; Falvard, A; Gay, P; Guicheney, C; Henrard, P; Jousset, J; Michel, B; Monteil, S; Montret, J C; Pallin, D; Perret, P; Podlyski, F; Proriol, J; Rossignol, J M; Fearnley, Tom; Hansen, J B; Hansen, J D; Hansen, J R; Hansen, P H; Nilsson, B S; Wäänänen, A; Kyriakis, A; Markou, C; Simopoulou, Errietta; Siotis, I; Vayaki, Anna; Zachariadou, K; Blondel, A; Bonneaud, G R; Brient, J C; Bourdon, P; Rougé, A; Rumpf, M; Tanaka, R; Valassi, Andrea; Verderi, M; Videau, H L; Candlin, D J; Parsons, M I; Focardi, E; Parrini, G; Corden, M; Delfino, M C; Georgiopoulos, C H; Jaffe, D E; Antonelli, A; Bencivenni, G; Bologna, G; Bossi, F; Campana, P; Capon, G; Chiarella, V; Felici, G; Laurelli, P; Mannocchi, G; Murtas, F; Murtas, G P; Passalacqua, L; Pepé-Altarelli, M; Curtis, L; Dorris, S J; Halley, A W; Knowles, I G; Lynch, J G; O'Shea, V; Raine, C; Reeves, P; Scarr, J M; Smith, K; Thompson, A S; Thomson, F; Thorn, S; Turnbull, R M; Becker, U; Braun, O; Geweniger, C; Graefe, G; Hanke, P; Hepp, V; Kluge, E E; Putzer, A; Rensch, B; Schmidt, M; Sommer, J; Stenzel, H; Tittel, K; Werner, S; Wunsch, M; Abbaneo, D; Beuselinck, R; Binnie, David M; Cameron, W; Colling, D J; Dornan, Peter J; Moutoussi, A; Nash, J; San Martin, G; Sedgbeer, J K; Stacey, A M; Dissertori, G; Girtler, P; Kuhn, D; Rudolph, G; Bowdery, C K; Brodbeck, T J; Colrain, P; Crawford, G; Finch, A J; Foster, F; Hughes, G; Sloan, Terence; Whelan, E P; Williams, M I; Galla, A; Greene, A M; Kleinknecht, K; Quast, G; Renk, B; Rohne, E; Sander, H G; Van Gemmeren, P; Zeitnitz, C; Aubert, Jean-Jacques; Bencheikh, A M; Benchouk, C; Bonissent, A; Bujosa, G; Calvet, D; Carr, J; Diaconu, C A; Etienne, F; Konstantinidis, N P; Nicod, D; Payre, P; Rousseau, D; Talby, M; Sadouki, A; Thulasidas, M; Trabelsi, K; Abt, I; Assmann, R W; Bauer, C; Blum, Walter; Brown, D; Dietl, H; Dydak, Friedrich; Ganis, G; Gotzhein, C; Jakobs, K; Kroha, H; Lütjens, G; Lutz, Gerhard; Männer, W; Moser, H G; Richter, R H; Rosado-Schlosser, A; Schael, S; Settles, Ronald; Seywerd, H C J; Saint-Denis, R; Wiedenmann, W; Wolf, G; Boucrot, J; Callot, O; Cordier, A; Davier, M; Duflot, L; Grivaz, J F; Heusse, P; Jacquet, M; Kim, D W; Le Diberder, F R; Lefrançois, J; Lutz, A M; Nikolic, I A; Park, H J; Park, I C; Schune, M H; Simion, S; Veillet, J J; Videau, I; Azzurri, P; Bagliesi, G; Batignani, G; Bettarini, S; Bozzi, C; Calderini, G; Carpinelli, M; Ciocci, M A; Ciulli, V; Dell'Orso, R; Fantechi, R; Ferrante, I; Foà, L; Forti, F; Giassi, A; Giorgi, M A; Gregorio, A; Ligabue, F; Lusiani, A; Marrocchesi, P S; Messineo, A; Rizzo, G; Sanguinetti, G; Sciabà, A; Spagnolo, P; Steinberger, Jack; Tenchini, Roberto; Tonelli, G; Vannini, C; Verdini, P G; Walsh, J; Betteridge, A P; Blair, G A; Bryant, L M; Cerutti, F; Chambers, J T; Gao, Y; Green, M G; Johnson, D L; Medcalf, T; Perrodo, P; Strong, J A; Von Wimmersperg-Töller, J H; Botterill, David R; Clifft, R W; Edgecock, T R; Haywood, S; Edwards, M; Maley, P; Norton, P R; Thompson, J C; Bloch-Devaux, B; Colas, P; Emery, S; Kozanecki, Witold; Lançon, E; Lemaire, M C; Locci, E; Marx, B; Pérez, P; Rander, J; Renardy, J F; Roussarie, A; Schuller, J P; Schwindling, J; Trabelsi, A; Vallage, B; Johnson, R P; Kim, H Y; Litke, A M; McNeil, M A; Taylor, G; Beddall, A; Booth, C N; Boswell, R; Brew, C A J; Cartwright, S L; Combley, F; Köksal, A; Letho, M; Newton, W M; Rankin, C; Reeve, J; Thompson, L F; Böhrer, A; Brandt, S; Cowan, G D; Feigl, E; Grupen, Claus; Lutters, G; Minguet-Rodríguez, J A; Rivera, F; Saraiva, P; Smolik, L; Stephan, F; Apollonio, M; Bosisio, L; Della Marina, R; Giannini, G; Gobbo, B; Musolino, G; Ragusa, F; Rothberg, J E; Wasserbaech, S R; Armstrong, S R; Bellantoni, L; Elmer, P; Feng, Z; Ferguson, D P S; Gao, Y S; González, S; Grahl, J; Greening, T C; Harton, J L; Hayes, O J; Hu, H; McNamara, P A; Nachtman, J M; Orejudos, W; Pan, Y B; Saadi, Y; Schmitt, M; Scott, I J; Sharma, V; Turk, J; Walsh, A M; Wu Sau Lan; Wu, X; Yamartino, J M; Zheng, M; Zobernig, G

1996-01-01

Quark and gluon jets with the same energy, 24GeV, are compared in symmetric three-jet configurations from hadronic Z decays observed by the ALEPH detector. Jets are defined using the Durham algorithm. Gluon jets are identified using an anti-tag on b jets, based on either a track impact parameter method or a high transverse momentum lepton tag. The comparison of gluon and mixed flavour quark jets shows that gluon jets have a softer fragmentation function, a larger angular width and a higher particle multiplicity. Evidence is also presented which shows that the corresponding differences between gluon and heavy flavour jets are significantly smaller.

A quantum formulation of the Feynman-Kac formula

International Nuclear Information System (INIS)

Accardi, L.

1981-01-01

The author discusses a formulation, in the general setting of W*- (or C*)-algebras, of the classical Feynman-Kac formula. The equivalence, in the commutative case, of the present formulation and the usual one is based on the identification between stochastic processes and local algebras. (Auth.)

The ε-form of the differential equations for Feynman integrals in the elliptic case

Science.gov (United States)

Adams, Luise; Weinzierl, Stefan

2018-06-01

Feynman integrals are easily solved if their system of differential equations is in ε-form. In this letter we show by the explicit example of the kite integral family that an ε-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The ε-form is obtained by a (non-algebraic) change of basis for the master integrals.

Quark-gluon plasma, and strangeness

International Nuclear Information System (INIS)

Rafelski, Johann; Letessier, Jean

2002-01-01

In order to recognize the new form of matter created at RHIC and SPS as the deconfined quark-gluon plasma state (QGP), we need to understand the expected properties of this phase near to the conditions of its formation and disintegration. Thus, we first develop a model of QGP considering the constrains arising from QCD properties and lattice results, and explore its properties. In the second part, we describe the kinetic theory of strangeness production in the QGP phase. We show that gluon fusion dominate and evaluate the degree of equilibration expected at RHIC

Holiday fun with soft gluons

CERN Multimedia

CERN. Geneva

2017-01-01

Emissions of soft gluons from energetic particles play an important role in collider processes. While the basic physics of soft emissions is simple, it gives rise to a variety of interesting and intricate phenomena (non-global logs, Glauber phases, super-leading logs, factorization breaking). After an introduction, I will review progress in resummation methods such as Soft-Collinear Effective Theory driven by a better understanding of soft emissions. I will also show some new results for computations of soft-gluon effects in gap-between-jets and isolation-cone cross sections.

Photon diffractive dissociation in deep inelastic scattering

International Nuclear Information System (INIS)

Wuesthoff, M.

1995-09-01

The cross section of the Photon Diffractive Dissociation in Deep Inelastic Scattering is calculated in the frame work of perturbative QCD. In the triple Regge region the BFKL-approximation is used to evaluate the leading contributions of the corresponding Feynman diagrams with a subsequent resummation in terms of integral equations. These equations are partly solved leading to an effective two to four gluons transition vertex. This exhibits remarkable properties like the total symmetry under the interchange of gluons, the conformal invariance and a simple colour structure. The presence of four interacting gluons in the t-channel does not support the simple triple Pomeron picture with solely a local vertex. A dimensional conservation law is found for zero momentum transfer with the consequence that a direct coupling of the three BFKL-singularities is absent. Another consequence is the dominance of small transverse momenta at the triple Pomeron vertex. Beyond the triple Regge limit a slightly different approach is used in which the diagrams are calculated with leading log(Q 2 ) accuracy. Higher twist contributions are neglected except for the longitudinal part of the cross section which dominates at small invariant masses M in accordance with QCD-predictions and measurements for the exclusive production of vector mesons. For the comparison with the recently measured Photon Diffractive Dissociation-data from H1 and ZEUS a model for the Pomeron is introduced based on the F 2 -data. In the spirit of the k t -factorization theorem this model is inserted in place of the BFKL-Pomeron. Considering the fact that this approach does not contain free parameters the agreement between the theoretical prediction and the data is found to be good. (orig.)

Worldline calculation of the three-gluon vertex

International Nuclear Information System (INIS)

Ahmadiniaz, N.; Schubert, C.

2012-01-01

The three-gluon vertex is a basic object of interest in nonabelian gauge theory. At the one-loop level, it has been calculated and analyzed by a number of authors. Here we use the worldline formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in terms of field strength tensors. We verify its equivalence with previously obtained representations, and explain the relation of its structure to the low-energy effective action. The sum rule found by Binger and Brodsky for the scalar, spinor and gluon loop contributions in the present approach relates to worldline supersymmetry.

The gluon Sivers asymmetry measurements at COMPASS

CERN Document Server

Szabelski, Adam

2018-01-01

The Sivers function describes the correlation between the transverse spin of a nucleon and the transverse motion of its partons. As such, a nonzero Sivers effect for gluons could be a signature of their nonzero orbital angular momentum inside the nucleon. COMPASS has collected data of semi-inclusive deep inelastic scattering by impinging 160 GeV/$c$ muons on transversely polarised proton and deuteron targets. The gluon Sivers asymmetry is extracted from a high-$p_T$ hadron pair sample with the use of monte carlo simulations and the a neural network approach. The results of a similar analysis for a Collins-like asymmetry for gluons will also be given.

The gluon Sivers asymmetry measurements at COMPASS

CERN Document Server

Szabelski, Adam

2017-01-01

The Sivers function describes the correlation between the transverse spin of a nucleon and the transverse motion of its partons. As such, a nonzero Sivers effect for gluons could be a signature of their nonzero orbital angular momentum inside the nucleon. COMPASS has collected data of semi-inclusive deep inelastic scattering by impinging 160 GeV/$c$ muons on transversely polarised proton and deuteron targets. The gluon Sivers asymmetry is extracted from a high-$p_T$ hadron pair sample with the use of monte carlo simulations and the a neural network approach. The results of a similar analysis for a Collins-like asymmetry for gluons will also be given.

A partial solution for Feynman's problem: A new derivation of the Weyl equation

Directory of Open Access Journals (Sweden)

Atsushi Inoue

2000-07-01

Full Text Available Associating classical mechanics to a system of partial differential equations, we give a procedure for Feynman-type quantization of a "Schrodinger-type equation with spin." Mathematically, we construct a "good parametrix" for the Weyl equation with an external electromagnetic field. Main ingredients are (i a new interpretation of the matrix structure using superanalysis and (ii another interpretation of the method of characteristics as a quantization procedure of Feynman type.

Gluon density in nuclei

International Nuclear Information System (INIS)

Ayala, A.L.

1996-01-01

In this talk we present our detailed study (theory and numbers) on the shadowing corrections to the gluon structure functions for nuclei. Starting from rather controversial information on the nucleon structure function which is originated by the recent HERA data, we develop the Glauber approach for the gluon density in a nucleus based on Mueller formula and estimate the value of the shadowing corrections in this case. Then we calculate the first corrections to the Glauber approach and show that these corrections are big. Based on this practical observation we suggest the new evolution equation which takes into account the shadowing corrections and solve it. We hope to convince you that the new evolution equation gives a good theoretical tool to treat the shadowing corrections for the gluons density in a nucleus and, therefore, it is able to provide the theoretically reliable initial conditions for the time evolution of the nucleus-nucleus cascade. The initial conditions should be fixed both theoretically and phenomenologically before to attack such complicated problems as the mixture of hard and soft processes in nucleus-nucleus interactions at high energy or the theoretically reliable approach to hadron or/and parton cascades for high energy nucleus-nucleus interaction. 35 refs., 24 figs., 1 tab

Semirelativistic potential model for low-lying three-gluon glueballs

International Nuclear Information System (INIS)

Mathieu, Vincent; Semay, Claude; Silvestre-Brac, Bernard

2006-01-01

The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Low-lying J PC states are computed and compared with recent lattice calculations. A good agreement is found for 1 -- and 3 -- states, but our model predicts a 2 -- state much higher in energy than the lattice result. The 0 -+ mass is also computed

Quark-gluon mixing in pseudoscalar and tensor mesons

International Nuclear Information System (INIS)

Eremyan, Sh.S.; Nazaryan, A.E.

1986-01-01

A mixing model of quark-antiquark ang gluonium states in η, η', i(1440) pseudoscalar and f, f', Θ(1690) tensor mesons is considered. Description of and predictions for 68 two-particle decays with these particles taking part in them are obtained. It is shown that i(1440) by 85% consists of gluonium and Θ(1690) is a pure gluonic state. The quark-gluon and gluon-gluon couplings in the pseudoscalar sector are obtained to be stronger as compared to the corresponding ones in the tensor case

Gluon and quark jets in a recursive model motivated by quantum chromodynamics

International Nuclear Information System (INIS)

Sukhatme, U.P.

1979-01-01

We compute observable quantities like the multiplicity and momentum distributions of hadrons in gluon and quark jets in the framework of a recursive cascade model, which is strongly motivated by the fundamental interactions of QCD. Fragmentation occurs via 3 types of breakups: quark → meson + quark, gluon → meson + gluon, gluon → quark + antiquark. In our model gluon jets are softer than quark jets. The ratio of gluon jet to quark jet multiplicity is found to be 2 asymptotically, but much less at lower energies. Some phenomenological consequences for γ decay are discussed. (orig.)

Towards the dynamical study of heavy-flavor quarks in the Quark-Gluon-Plasma

International Nuclear Information System (INIS)

Berrehrah, H; Bratkovskaya, E; Cassing, W; Gossiaux, P B; Aichelin, J

2014-01-01

Within the aim of a dynamical study of on- and off-shell heavy quarks Q in the quark gluon plasma (QGP) – as produced in relativistic nucleus-nucleus collisions – we study the heavy quark collisional scattering on partons of the QGP. The elastic cross sections σ q,g−Q are evaluated for perturbative partons (massless on-shell particles) and for dynamical quasi-particles (massive off-shell particles as described by the dynamical quasi-particles model D QPM ) using the leading order Born diagrams. We demonstrate that the finite width of the quasi-particles in the DQPM has little influence on the cross sections σ q,g−Q except close to thresholds. We, furthermore, calculate the heavy quark relaxation time as a function of temperature T within the different approaches using these cross sections

Shear and bulk viscosity of high-temperature gluon plasma

Science.gov (United States)

Zhang, Le; Hou, De-Fu

2018-05-01

We calculate the shear viscosity (η) and bulk viscosity (ζ) to entropy density (s) ratios η/s and ζ/s of a gluon plasma system in kinetic theory, including both the elastic {gg}≤ftrightarrow {gg} forward scattering and the inelastic soft gluon bremsstrahlung {gg}≤ftrightarrow {ggg} processes. Due to the suppressed contribution to η and ζ in the {gg}≤ftrightarrow {gg} forward scattering and the effective g≤ftrightarrow {gg} gluon splitting, Arnold, Moore and Yaffe (AMY) and Arnold, Dogan and Moore (ADM) have got the leading order computations for η and ζ in high-temperature QCD matter. In this paper, we calculate the correction to η and ζ in the soft gluon bremsstrahlung {gg}≤ftrightarrow {ggg} process with an analytic method. We find that the contribution of the collision term from the {gg}≤ftrightarrow {ggg} soft gluon bremsstrahlung process is just a small perturbation to the {gg}≤ftrightarrow {gg} scattering process and that the correction is at ∼5% level. Then, we obtain the bulk viscosity of the gluon plasma for the number-changing process. Furthermore, our leading-order result for bulk viscosity is the formula \\zeta \\propto \\tfrac{{α }s2{T}3}{ln}{α }s-1} in high-temperature gluon plasma. Supported by Ministry of Science and Technology of China (MSTC) under the “973” Project (2015CB856904(4)) and National Natural Science Foundation of China (11735007, 11521064)

How classical gluon fields generate odd azimuthal harmonics for the two-gluon correlation function in high-energy collisions

Science.gov (United States)

Kovchegov, Yuri V.; Skokov, Vladimir V.

2018-05-01

We show that, in the saturation/color glass condensate framework, odd azimuthal harmonics of the two-gluon correlation function with a long-range separation in rapidity are generated by the higher-order saturation corrections in the interactions with the projectile and the target. At the very least, the odd harmonics require three scatterings in the projectile and three scatterings in the target. We derive the leading-order expression for the two-gluon production cross section which generates odd harmonics: the expression includes all-order interactions with the target and three interactions with the projectile. We evaluate the obtained expression both analytically and numerically, confirming that the odd-harmonics contribution to the two-gluon production in the saturation framework is nonzero.

In search of the quark-gluon plasma

International Nuclear Information System (INIS)

Schutz, Y.; Delagrange, H.

2002-01-01

This article describes in a very pedagogical manner the ultimate state of matter when quarks are no longer confined in hadrons. This state is called quark and gluon plasma, its existence is suspected through 4 facts: 1) a quark and gluon plasma that has just been created from a high energy ion-collision is mainly made up of light quarks (up and down), then this plasma should evolve towards other quarks (particularly strange quarks) because of the Pauli exclusion principle. This fact has been experimentally confirmed: at the CERN accelerator physicists have detected a higher production of strange hadrons when the energy of the collision increases; 2) some particles like ρ 0 mesons, that are made up of 2 quarks, are massively produced in ion collisions, their mass has been measured at the moment of the collision and later in the quark and gluon plasma, 2 different values have been found so it confirms the theory that predicts that free quarks have a mass that decreases as energy increases; 3) J/Ψ mesons are made up of a charmed quark combined with its anti-quark, physicists have noticed that less J/Ψ mesons are detected when the energy of the collision rises, this result agrees with the fact that in quark gluon plasma where quarks are free and of different colours and flavors, it is highly unlikely that a charmed quark combines with its anti-quark to form a J/Ψ meson; and 4) the theory of the formation of quark gluon plasma predicts that its electromagnetic radiation has a thermal radiation specificity, physicists have studied the radiation spectra emitted in the core of a ion collision, they have shown that it is a thermal radiation and that the temperature of the emitter corresponds to the temperature of a quark gluon plasma. (A.C.)

The gluon contribution to polarised nucleon structure functions

International Nuclear Information System (INIS)

Ross, G.G.; Roberts, R.G.

1990-08-01

As with all parton distributions in quantum chromodynamics (QCD) the separation of polarised nucleon structure functions into gluon and quark contributions must be specified. We consider a definition of the gluon contribution to polarised nucleon structure functions based on exclusive processes which is explicitly gauge invariant, has no regularisation ambiguities, is insensitive to infrared singularities and can be related to other polarised scattering processes. We discuss the relationship of this gluon definition to others that have recently been used and to the estimates that have been made of the gluon contribution using current algebra and other methods. A quantitative analysis of the structure function g 1 (x,Q 2 ) for polarised deep inelastic scattering is carried out, with the aim of examining the importance of the gluon contribution. Using the positivity of parton distributions the magnitude of Δg(x,Q 2 ) is constrained by a realistic estimate of the unpolarised glue. With the appropriate choice of the hard scattering cross-section, Δσ γg , we find that even with a maximally polarised glue (for x > 0.1), some polarised strange quark contribution is still needed by the data of the EMC. (author)

The color antisymmetric ghost propagator and one-loop vertex renormalization

International Nuclear Information System (INIS)

Furui, Sadataka

2008-01-01

The color matrix elements of the ghost triangle diagram that appears in the triple gluon vertex and the ghost-ghost-gluon triangle diagram that appears in the ghost-gluon-ghost vertex are calculated. The ghost-ghost-gluon triangle contains a loop consisting of two color diagonal ghosts and one gluon and a loop consisting of two color antisymmetric ghosts and one gluon. Consequently, the pQCD argument in the infrared region based on the one particle irreducible diagram should be modified. Implications for the Kugo-Ojima color confinement and the QCD running coupling are discussed. (author)

Quark and gluon jet properties in symmetric three-jet events

Science.gov (United States)

Buskulic, D.; Casper, D.; de Bonis, I.; Decamp, D.; Ghez, P.; Goy, C.; Lees, J.-P.; Lucotte, A.; Minard, M.-N.; Odier, P.; Pietrzyk, B.; Chmeissani, M.; Crespo, J. M.; Efthymiopoulos, I.; Fernandez, E.; Fernandez-Bosman, M.; Garrido, Ll.; Juste, A.; Martinez, M.; Orteu, S.; Pacheco, A.; Padilla, C.; Palla, F.; Pascual, A.; Perlas, J. A.; Riu, I.; Sanchez, F.; Teubert, F.; Colaleo, A.; Creanza, D.; de Palma, M.; Farilla, A.; Gelao, G.; Girone, M.; Iaselli, G.; Maggi, G.; Maggi, M.; Marinelli, N.; Natali, S.; Nuzzo, S.; Ranieri, A.; Raso, G.; Romano, F.; Ruggieri, F.; Selvaggi, G.; Silvestris, L.; Tempesta, P.; Zito, G.; Huang, X.; Lin, J.; Ouyang, Q.; Wang, T.; Xie, Y.; Xu, R.; Xue, S.; Zhang, J.; Zhang, L.; Zhao, W.; Alemany, R.; Bazarko, A. O.; Bonvicini, G.; Cattaneo, M.; Comas, P.; Coyle, P.; Drevermann, H.; Forty, R. W.; Frank, M.; Hagelberg, R.; Harvey, J.; Jacobsen, R.; Janot, P.; Jost, B.; Kneringer, E.; Knobloch, J.; Lehraus, I.; Martin, E. B.; Mato, P.; Minten, A.; Miquel, R.; Mir, Ll. M.; Moneta, L.; Oest, T.; Palazzi, P.; Pater, J. R.; Pusztaszeri, J.-F.; Ranjard, F.; Rensing, P.; Rolandi, L.; Schlatter, D.; Schmelling, M.; Schneider, O.; Tejessy, W.; Tomalin, I. R.; Venturi, A.; Wachsmuth, H.; Wildish, T.; Witzeling, W.; Wotschack, J.; Ajaltouni, Z.; Barrès, A.; Boyer, C.; Falvard, A.; Gay, P.; Guicheney, C.; Henrard, P.; Jousset, J.; Michel, B.; Monteil, S.; Montret, J.-C.; Pallin, D.; Perret, P.; Podlyski, F.; Proriol, J.; Rossignol, J.-M.; Fearnley, T.; Hansen, J. B.; Hansen, J. D.; Hansen, J. R.; Hansen, P. H.; Nilsson, B. S.; Wäänänen, A.; Kyriakis, A.; Markou, C.; Simopoulou, E.; Siotis, I.; Vayaki, A.; Zachariadou, K.; Blondel, A.; Bonneaud, G.; Brient, J. C.; Bourdon, P.; Rougé, A.; Rumpf, M.; Tanaka, R.; Valassi, A.; Verderi, M.; Videau, H.; Candlin, D. J.; Parsons, M. I.; Focardi, E.; Parrini, G.; Corden, M.; Delfino, M.; Georgiopoulos, C.; Jaffe, D. E.; Antonelli, A.; Bencivenni, G.; Bologna, G.; Bossi, F.; Campana, P.; Capon, G.; Chiarella, V.; Felici, G.; Laurelli, P.; Mannocchi, G.; Murtas, F.; Murtas, G. P.; Passalacqua, L.; Pepe-Altarelli, M.; Curtis, L.; Dorris, S. J.; Halley, A. W.; Knowles, I. G.; Lynch, J. G.; O'Shea, V.; Raine, C.; Reeves, P.; Scarr, J. M.; Smith, K.; Thompson, A. S.; Thomson, F.; Thorn, S.; Turnbull, R. M.; Becker, U.; Braun, O.; Geweniger, C.; Graefe, G.; Hanke, P.; Hepp, V.; Kluge, E. E.; Putzer, A.; Rensch, B.; Schmidt, M.; Sommer, J.; Stenzel, H.; Tittel, K.; Werner, S.; Wunsch, M.; Abbaneo, D.; Beuselinck, R.; Binnie, D. M.; Cameron, W.; Colling, D. J.; Dornan, P. J.; Moutoussi, A.; Nash, J.; San Martin, G.; Sedgbeer, J. K.; Stacey, A. M.; Dissertori, G.; Girtler, P.; Kuhn, D.; Rudolph, G.; Bowdery, C. K.; Brodbeck, T. J.; Colrain, P.; Crawford, G.; Finch, A. J.; Foster, F.; Hughes, G.; Sloan, T.; Whelan, E. P.; Williams, M. I.; Galla, A.; Greene, A. M.; Kleinknecht, K.; Quast, G.; Renk, B.; Rohne, E.; Sander, H.-G.; van Gemmeren, P.; Zeitnitz, C.; Aubert, J. J.; Bencheikh, A. M.; Benchouk, C.; Bonissent, A.; Bujosa, G.; Calvet, D.; Carr, J.; Diaconu, C.; Etienne, F.; Konstantinidis, N.; Nicod, D.; Payre, P.; Rousseau, D.; Talby, M.; Sadouki, A.; Thulasidas, M.; Trabelsi, K.; Abt, I.; Assmann, R.; Bauer, C.; Blum, W.; Brown, D.; Dietl, H.; Dydak, F.; Ganis, G.; Gotzhein, C.; Jakobs, K.; Kroha, H.; Lütjens, G.; Lutz, G.; Männer, W.; Moser, H.-G.; Richter, R.; Rosado-Schlosser, A.; Schael, S.; Settles, R.; Seywerd, H.; Denis, R. St.; Wiedenmann, W.; Wolf, G.; Boucrot, J.; Callot, O.; Cordier, A.; Davier, M.; Duflot, L.; Grivaz, J.-F.; Heusse, Ph.; Jacquet, M.; Kim, D. W.; Le Diberder, F.; Lefrançois, J.; Lutz, A.-M.; Nikolic, I.; Park, H. J.; Park, I. C.; Schune, M.-H.; Simion, S.; Veillet, J.-J.; Videau, I.; Azzurri, P.; Bagliesi, G.; Batignani, G.; Bettarini, S.; Bozzi, C.; Calderini, G.; Carpinelli, M.; Ciocci, M. A.; Ciulli, V.; Dell'Orso, R.; Fantechi, R.; Ferrante, I.; Foà, L.; Forti, F.; Giassi, A.; Giorgi, M. A.; Gregorio, A.; Ligabue, F.; Lusiani, A.; Marrocchesi, P. S.; Messineo, A.; Rizzo, G.; Sanguinetti, G.; Sciabà, A.; Spagnolo, P.; Steinberger, J.; Tenchini, R.; Tonelli, G.; Vannini, C.; Verdini, P. G.; Walsh, J.; Betteridge, A. P.; Blair, G. A.; Bryant, L. M.; Cerutti, F.; Chambers, J. T.; Gao, Y.; Green, M. G.; Johnson, D. L.; Medcalf, T.; Perrodo, P.; Strong, J. A.; von Wimmersperg-Toeller, J. H.; Botterill, D. R.; Clifft, R. W.; Edgecock, T. R.; Haywood, S.; Edwards, M.; Maley, P.; Norton, P. R.; Thompson, J. C.; Bloch-Devaux, B.; Colas, P.; Emery, S.; Kozanecki, W.; Lançon, E.; Lemaire, M. C.; Locci, E.; Marx, B.; Perez, P.; Rander, J.; Renardy, J.-F.; Roussarie, A.; Schuller, J.-P.; Schwindling, J.; Trabelsi, A.; Vallage, B.; Johnson, R. P.; Kim, H. Y.; Litke, A. M.; McNeil, M. A.; Taylor, G.; Beddall, A.; Booth, C. N.; Boswell, R.; Brew, C. A. J.; Cartwright, S.; Combley, F.; Koksal, A.; Letho, M.; Newton, W. M.; Rankin, C.; Reeve, J.; Thompson, L. F.; Böhrer, A.; Brandt, S.; Cowan, G.; Feigl, E.; Grupen, C.; Lutters, G.; Minguet-Rodriguez, J.; Rivera, F.; Saraiva, P.; Smolik, L.; Stephan, F.; Apollonio, M.; Bosisio, L.; Della Marina, R.; Giannini, G.; Gobbo, B.; Musolino, G.; Ragusa, F.; Rothberg, J.; Wasserbaech, S.; Armstrong, S. R.; Bellantoni, L.; Elmer, P.; Feng, Z.; Ferguson, D. P. S.; Gao, Y. S.; González, S.; Grahl, J.; Greening, T. C.; Harton, J. L.; Hayes, O. J.; Hu, H.; McNamara, P. A.; Nachtman, J. M.; Orejudos, W.; Pan, Y. B.; Saadi, Y.; Schmitt, M.; Scott, I. J.; Sharma, V.; Turk, J. D.; Walsh, A. M.; Wu, Sau Lan; Wu, X.; Yamartino, J. M.; Zheng, M.; Zobernig, G.; Aleph Collaboration

1996-02-01

Quark and gluon jets with the same energy, 24 GeV, are compared in symmetric three-jet configurations from hadronic Z decays observed by the ALEPH detector. Jets are defined using the Durham algorithm. Gluon jets are identified using an anti-tag on b jets, based on a track impact parameter method. The comparison of gluon and mixed flavour quark jets shows that gluon jets have a softer fragmentation function, a larger angular width and a higher particle multiplicity, Evidence is presented which shows that the corresponding differences between gluon and b jets are significantly smaller. In a statistically limited comparison the multiplicity in c jets was found to be comparable with that observed for the jets of mixed quark flavour.

Picard-Fuchs equations of dimensionally regulated Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Zayadeh, Raphael

2013-12-15

This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is

Picard-Fuchs equations of dimensionally regulated Feynman integrals

International Nuclear Information System (INIS)

Zayadeh, Raphael

2013-12-01

This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is the two

Pembuatan Kakas Bantu untuk Mendeteksi Ketidaksesuaian Diagram Urutan (Sequence Diagram dengan Diagram Kasus Penggunaan (Use Case Diagram

Directory of Open Access Journals (Sweden)

Andrias Meisyal Yuwantoko

2017-03-01

Full Text Available Sebuah diagram urutan dibuat  berdasarkan alur yang ada pada deskripsi kasus penggunaan. Alur tersebut dire- presentasikan dalam  bentuk  interaksi antara aktor  dan  sistem. Pemeriksaan rancangan diagram urutan perlu dilakukan untuk mengetahui ketidaksesuaian urutan alur  kasus penggunaan dengan urutan pesan yang dikirimkan oleh objek-objek pada diagram urutan. Rancangan diagram yang sesuai merupakan kunci ketepatan (correctness implementasi  perangkat lunak. Namun, pemeriksaan ketidaksesuaian masih dilakukan secara manual. Hal ini menjadi masalah apabila sebuah proyek perangkat lunak memiliki banyak  rancangan diagram dan sumber daya manusia tidak  mencukupi. Pemeriksaan membutuhkan waktu yang lama dan memiliki dampak pada waktu pengembangan perangkat lunak. Penelitian ini mengusulkan pembuatan kakas bantu  untuk mendeteksi ketidaksesuaian diagram urutan dengan diagram kasus penggunaan. Ketidaksesuaian dilihat dari kemiripan semantik kalimat antara alur pada deskripsi kasus penggunaan dan triplet. Dari hasil pembuatan kakas bantu, kakas bantu yang dibuat dapat mendeteksi ketidaksesuaian diagram urutan dengan diagram kasus penggunaan. Kakas  bantu ini diharapkan tidak hanya membantu pemeriksaan rancangan diagram akan tetapi mempercepat waktu pengembangan perangkat lunak.

On the many-body foundation of the nuclear field theory

International Nuclear Information System (INIS)

Bes, D.R.; Dussel, G.G.; Liotta, R.J.; Perazzo, R.P.J.; Broglia, R.A.

1976-01-01

The equivalence between the description of the many-body finite nuclear system in terms of Feynman diagrams involving only the fermion degrees of freedom and of Feynman diagrams involving fermion and phonon degrees of freedom is proved for intermediate states in the case of a general two-body residual interaction. (Auth.)

Proton-proton elastic scattering with massive gluons

International Nuclear Information System (INIS)

Sauter, Werner K.; Ducati, M.B. Gay

2001-01-01

In this contribution different approaches to generate a gluon mass are discussed. More specially a recent result for the gluon propagator with a dynamical mass, proposal by Gorbar and Natale, is used in connection with the Landshoff-Nachtmann model for the Pomeron to describe the elastic differential cross section for pp scattering, with good agreement. (author)

Improving the simulation of quark and gluon jets with Herwig 7

Energy Technology Data Exchange (ETDEWEB)

Reichelt, Daniel [Technische Universitaet Dresden, Institut fuer Kern- und Teilchenphysik, Dresden (Germany); Richardson, Peter [CERN, Theory Department, Geneva (Switzerland); Durham University, Department of Physics, IPPP, Durham (United Kingdom); Siodmok, Andrzej [Polish Academy of Sciences, Institute of Nuclear Physics, Krakow (Poland)

2017-12-15

The properties of quark and gluon jets, and the differences between them, are increasingly important at the LHC. However, Monte Carlo event generators are normally tuned to data from e{sup +}e{sup -} collisions which are primarily sensitive to quark-initiated jets. In order to improve the description of gluon jets we make improvements to the perturbative and the non-perturbative modelling of gluon jets and include data with gluon-initiated jets in the tuning for the first time. The resultant tunes significantly improve the description of gluon jets and are now the default in Herwig 7.1. (orig.)

The unconfined quarks and gluons

International Nuclear Information System (INIS)

Abdus Salam

1977-01-01

The consequences of the lepton-hadron gauge unification hypothesis with unconfined quarks and gluons being the hall-mark are discussed. Quark and gluon decays into leptons are shown to provide a new source of multileptonic production in NN, νN and μN collisions. A theorem is stated and proved which highlights the differences between the dynamics of gauge versus non-gauge 1 - particles. Empirical manifestations of gauge coloured mesons are discussed. The question of exact confinement or not is concluded to be in the end an empirical one and must be settled in the laboratory

The LPM effect in sequential bremsstrahlung: 4-gluon vertices

Energy Technology Data Exchange (ETDEWEB)

Arnold, Peter; Chang, Han-Chih [Department of Physics, University of Virginia,382 McCormick Road, Charlottesville, Virginia 22904-4714 (United States); Iqbal, Shahin [National Centre for Physics, Quaid-i-Azam University Campus, Islamabad, 45320 (Pakistan)

2016-10-24

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper, we continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-gluon approximations. In particular, this paper completes the calculation of the rate for real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media; q̂ approximation; and large N{sub c}) by now including processes involving 4-gluon vertices.

From State Diagram to Class Diagram

DEFF Research Database (Denmark)

Borch, Ole; Madsen, Per Printz

2009-01-01

UML class diagram and Java source code are interrelated and Java code is a kind of interchange format. Working with UML state diagram in CASE tools, a corresponding xml file is maintained. Designing state diagrams is mostly performed manually using design patterns and coding templates - a time...... consuming process. This article demonstrates how to compile such a diagram into Java code and later, by reverse engineering, produce a class diagram. The process from state diagram via intermediate SAX parsed xml file to Apache Velocity generated Java code is described. The result is a fast reproducible...

Monte Carlo evidence for the gluon-chain model of QCD string formation

International Nuclear Information System (INIS)

Greensite, J.; San Francisco State Univ., CA

1988-08-01

The Monte Carlo method is used to calculate the overlaps string vertical stroken gluons>, where Ψ string [A] is the Yang-Mills wavefunctional due to a static quark-antiquark pair, and vertical stroken gluons > are orthogonal trial states containing n=0, 1, or 2 gluon operators multiplying the true ground state. The calculation is carried out for SU(2) lattice gauge theory in Coulomb gauge, in D=4 dimensions. It is found that the string state is dominated, at small qanti q separations, by the vacuum ('no-gluon') state, at larger separations by the 1-gluon state, and, at the largest separations attempted, the 2-gluon state begins to dominate. This behavior is in qualitative agreement with the gluon-chain model, which is a large-N colors motivated theory of QCD string formation. (orig.)

Contribution of t-channel photon-exchange diagrams to the amplitudes of the semihard photoproduction of C-odd neutral mesons

International Nuclear Information System (INIS)

Ivanov, D.Yu.

1996-01-01

The production of neutral pseudoscalar (π0,η,η') and tensor (a2,f2,f'2) mesons in high-energy γγ and γq collisions is considered in the semihard kinematical region. The reactions γq→Mq can be investigated at the HERA ep collider, and the two-photon processes can be accomplished at future photon colliders. In the lowest order of perturbative QCD and QED, the reactions in question are described by three-gluon and one-photon exchanges in the t-channel diagrams. It is shown that the one-photon-exchange contribution to the amplitudes of processes that are characterized by the largest cross sections (π0 and a2 production) is much smaller than the three-gluon-exchange contribution. However, the processes with the smallest cross sections (η' and f2 production) are dominated by photon-exchange contributions

Disconnected Diagrams in Lattice QCD

Science.gov (United States)

Gambhir, Arjun Singh

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements

Disconnected Diagrams in Lattice QCD

Energy Technology Data Exchange (ETDEWEB)

Gambhir, Arjun [College of William and Mary, Williamsburg, VA (United States)

2017-08-01

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements

Calculations in perturbative string field theory

International Nuclear Information System (INIS)

Thorn, C.B.

1987-01-01

The author discusses methods for evaluating the Feynman diagrams of string field theory, with particular emphasis on Witten's version of open string field theory. It is explained in some detail how the rules states by Giddings and Martinec for relating a given diagram to a Polyakov path integral emerge from the Feynman rules

Ward identities for amplitudes with reggeized gluons

International Nuclear Information System (INIS)

Bartles, J.; Vacca, G.P.

2012-05-01

Starting from the effective action of high energy QCD we derive Ward identities for Green's functions of reggeized gluons. They follow from the gauge invariance of the effective action, and allow to derive new representations of amplitudes containing physical particles as well as reggeized gluons. We explicitly demonstrate their validity for the BFKL kernel, and we present a new derivation of the kernel.

The SU(3) running coupling from lattice gluons

Energy Technology Data Exchange (ETDEWEB)

Parrinello, C. [Edinburgh Univ. (United Kingdom). Dept. of Phys. and Astron.; UKQCD Collaboration

1995-04-01

We provide numerical results for the running coupling in SU(3) Yang-Mills theory as determined from an analysis of lattice two and three-point gluon correlation functions. The coupling is evaluated directly, from first principles, by defining suitable renormalisation constants from the lattice triple gluon vertex and gluon propagator. For momenta larger than 2GeV, the coupling is found to run according to the 2-loop asymptotic formula. The influence of lattice artifacts on the results appears negligible within the precision of our measurements, although further work on this point is in progress. ((orig.)).

Remark on the solution of the Schroedinger equation for anharmonic oscillators via the Feynman path integral

International Nuclear Information System (INIS)

Rezende, J.

1983-01-01

We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)

Differences between quark and gluon jets at LEP1

CERN Document Server

Boutemeur, Madjid

1997-01-01

A report is ven here on the differences between quark and gluon initiated jets as measured in LEPl. Various measurements, agree qualitatively on the differences between quark and gluon jets. However a direct quantitative comparison among the measurements as well as comparisons between the measurements and analytical calculations are difficult. This is due to the dependence of the results on the selected event topologies and used jet finding algorithms. Topology dependence of the charged particle multiplicity in quark and gluon jets is studied by ALEPH and transverse momentum-like scales are proposed to account for it. OPAL produced the first quantitative test of QCD analytic prediction for the ratio of the mean particle multiplicity between gluon and quark jets valid, at least, for 39 GeV jets.

The structure of the gluon propagator

Energy Technology Data Exchange (ETDEWEB)

Leinweber, D.B.; Parrinello, C.; Skullerud, J.I.; Williams, A.G

1999-03-01

The gluon propagator has been calculated for quenched QCD in the Landau gauge at {beta} = 6.0 for volumes 16{sup 3} x 48 and 32{sup 3} x 64, and at {beta} 6.2 for volume 24{sup 3} x 48. The large volume and different lattice spacings allow us to identify and minimise finite volume and finite lattice spacing artefacts. We also study the tensor structure of the gluon propagator, confirming that it obeys the lattice Landau gauge condition.

EXPLORING THE POLARIZATION OF GLUONS IN THE NUCLEON.

Energy Technology Data Exchange (ETDEWEB)

STRATMANN,M.; VOGELSANG,W.

2007-10-22

We give an overview of the current status of investigations of the polarization of gluons in the nucleon. We describe some of the physics of the spin-dependent gluon parton distribution and its phenomenology in high-energy polarized hadronic scattering. We also review the recent experimental results.

Summing over Feynman histories by functional contour integration

International Nuclear Information System (INIS)

Garrison, J.C.; Wright, E.M.

1986-01-01

The authors show how complex paths can be consistently introduced into sums for Feynman histories by using the notion of functional contour integration. For a kappa-dimensional system specified by a potential with suitable analyticity properties, each coordinate axis is replaced by a copy of the complex plane, and at each instant of time a contour is chosen in each plane. This map from the time axis into the set of complex contours defines a functional contour. The family of contours labelled by time generates a (kappa+1)-dimensional submanifold of the (2kappa+1)-dimensional space defined by the cartesian product of the time axis and the coordinate planes. The complex Feynman paths lie on this submanifold. An application of this idea to systems described by absorptive potentials yields a simple derivation of the correct WKB result in terms of a complex path that extremalises the action. The method can also be applied to spherically symmetric potentials by using a partial wave expansion and restricting the contours appropriately. (author)

Bounds on the gluon mass from nucleon decay

Energy Technology Data Exchange (ETDEWEB)

Avila, M.A. [Universidad Autonoma del Estado de Morelos, Morelos (Mexico)

2001-04-01

Permanent confinement of quarks is assumed to hold in QCD. However, if the gluon has a small mass it is possible to produce-quarks in hadron decays, high-energy reactions or in the early-universe. This situation is modelled by a quark-diquark potential composed of a linear (or harmonic) plus a Yukawa term. We compare our prediction for the proton decay with the experimental lower bound on its life-time, and obtain an upper bound on the gluon mass. [Spanish] Se supone se cumple el confinamiento permanente de quarks en cromodinamica cuantica. Si el gluon tiene masa pequena es posible producir quarks libres en decaimiento hadronicos, reacciones de altas energias o en el universo temprano. Esta situacion es modelada por un potencial quark-diquark, compuesto de un termino lineal (o armonico) mas un termino Yukawa. Comparamos nuestra prediccion para el decaimiento del proton con la cota inferior experimental de su vida media y obtenemos una cota superior sobre la masa del gluon.

The hadron to quark/gluon transition

International Nuclear Information System (INIS)

Brown, G.E.; Bethe, H.A.; Pizzochero, P.M.

1991-01-01

In this paper we are concerned with the hadron to quark/gluon transition. We describe the equilibrium states of hadronic matter by a Hagedorn spectrum; introducing scaling masses, as dictated by the restoration of chiral invariance with increasing temperature, we show that in the chiral SU(2) f limit there is a maximum hadron temperature (T H ) max ≅ 128 MeV. Since the quark/gluon perturbative phase involves restoration of conformal invariance, we take the bag constant to be the conformal anomaly, i.e. the gluon condensate. The stability condition P QG > 0 for the pressure requires that there is a minimum temperature; we find (T QG ) min ≅ 172 MeV for SU(2) f . According to the simple Hagedorn model, there appears to be a region of temperature between (T H ) max and (T QG ) min in which no admissible equilibrium states exist. Since the two phases cannot exist at a common temperature, in this model there is no QCD phase transition. (orig.)

Gluon 2- and 3-Point Correlation Functions on the Lattice

OpenAIRE

Parrinello, Claudio

1993-01-01

I present some preliminary results, obtained in collaboration with C. Bernard and A. Soni, for the lattice evaluation of 2- and 3-point gluon correlation functions in momentum space, with emphasis on the amputated 3-gluon vertex function. The final goal of this approach is the study of the running QCD coupling constant as defined from the amputated 3-gluon vertex.

2- and 3-point gluon correlation functions on the lattice

Energy Technology Data Exchange (ETDEWEB)

Parrinello, C. (Dept. of Physics, Univ. of Edinburgh (United Kingdom))

1994-04-01

I present some preliminary results, obtained in collaboration with C. Bernard and A. Soni, for the lattice evaluation of 2- and 3-point gluon correlation functions in momentum space, with emphasis on the amputated 3-gluon vertex function. The final goal of this approach is the study of the running QCD coupling constant as defined from the amputated 3-gluon vertex. (orig.)

The gluon distribution at small x - a phenomenological analysis

International Nuclear Information System (INIS)

Harriman, P.N.; Martin, A.D.; Stirling, W.J.; Roberts, R.G.

1990-03-01

The size of the gluon distribution at small χ has important implications for phenomenology at future high energy hadron-hadron and lepton-hadron colliders. We extend a recent global parton distribution fit to investigate the constraints on the gluon from deep inelastic and prompt photon data. In particular, we estimate a band of allowed gluon distributions with qualitatively small-χ behaviour and study the implications of these on a variety of cross sections at high energy pp and ep colliders. (author)

Feynman path integral related to stochastic schroedinger equation

International Nuclear Information System (INIS)

Belavkin, V.P.; Smolyanov, O.G.

1998-01-01

The derivation of the Schroedinger equation describing the continuous measurement process is presented. The representation of the solution of the stochastic Schroedinger equation for continuous measurements is obtained by means of the Feynman path integral. The connection with the heuristic approach to the description of continuous measurements is considered. The connection with the Senon paradox is established [ru

Gluon bremsstrahlung and elastic scattering of hadrons

International Nuclear Information System (INIS)

Povh, B.

2001-01-01

The differential and the total cross sections in high energy hadron-proton interactions give a beautiful insight in the low Q 2 structure of the nucleon. The cross section is composed of two parts: a large energy independent part corresponding to the interaction of the valence quark with the target without gluon radiation and an energy dependent part caused by gluon bremsstrahlung. The gluons are located at small transverse distances of about 0.3 fm from the valence quarks. The model with two scales, the size of the hadron (R 2 ∼ 1 fm 2 ) and the size of the gluonic cloud (r 0 2 ∼ 0.1 fm 2 ), correctly predicts the total and the differential cross sections and the behaviour of diffractive dissociation in hadronic and deep inelastic events. (orig.)

Vertex of three and four gluons in the Yang-Mills theory

International Nuclear Information System (INIS)

Brandt, F.T.C.

1986-01-01

In a general covariant gauge, the structure of the three-point function with one and two external gluons on shell is studied. The contributions which result in the one-loop approximation are expressed in terms of simple functions containing collinear and soft singularities. Furthermore, the contributions asociated with the four-point vertex when all external gluons are on-sheel, are analysed. As an application of these results, the infrared structure of the gluon-gluon scattering amplitude, is studied. (author) [pt

[Identification of meridian-acupoint diagrams and meridian diagrams].

Science.gov (United States)

Shen, Wei-hong

2008-08-01

In acu-moxibustion literature, there are two kinds of diagrams, meridian-acupoint diagrams and meridian diagrams. Because they are very similar in outline, and people now have seldom seen the typical ancient meridian diagrams, meridian-acupoint diagrams have been being incorrectly considered to be the meridian diagrams for a long time. It results in confusion in acu-moxibustion academia. The present paper stresses its importance in academic research and introduces some methods for identifying them correctly. The key points for identification of meridian-acupoint diagrams and meridian diagrams are: the legend of diagrams and the drawing style of the ancient charts. In addition, the author makes a detailed explanation about some acu-moxibustion charts which are easily confused. In order to distinguish meridian-acupoint diagrams and meridian diagrams correctly, he or she shoulnd understand the diagrams' intrinsic information as much as possible and make a comprehensive analysis about them.

Heavy ion collisions, the quark-gluon plasma and antinucleon annihilation

International Nuclear Information System (INIS)

Sarma, Nataraja

1985-01-01

Studies in high energy physics have indicated that nucleon and mesons are composed of quarks confined in bags by the strong colours mediated by gluons. It is reasonably expected that at suitably high baryon density and temperature of the nucleus, these bags of nucleon and mesons fuse into a big bag of quarks or gluons i.e. hadronic matter undergoes transition to a quark-gluon phase. Two techniques to achieve this transition in a laboratory are: (1) collision of two heavy nuclei, and (2) annihilation of antinucleons and antinuclei in nuclear matter. Theoretical studies as well as experimental studies associated with the transition to quark-gluon phase are reviewed. (author)

The power counting theorem for Feynman integrals with massless propagators

International Nuclear Information System (INIS)

Lowenstein, J.H.

2000-01-01

Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.)

Feynman and physics. Life and research of an exceptional man

International Nuclear Information System (INIS)

Resag, Joerg

2018-01-01

The life of Feynman is described together with his work on path integrals, quantum electrodynmaics, helium at low temperatures, the weak interaction, the quark model, and computer-calculation methods, and his contribution to the Manhattan project. (HSI)

Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method)

International Nuclear Information System (INIS)

Ceder, M.

2002-03-01

The Feynman-alpha method is used in traditional nuclear reactors to determine the subcritical reactivity of a system. The method is based on the measurement of the mean number and the variance of detector counts for different measurement times. The measurement is performed while a steady-state neutron flux is maintained in the reactor by an external neutron source, as a rule a radioactive source. From a plot of the variance-to-mean ratio as a function of measurement time ('gate length'), the reactivity can be determined by fitting the measured curve to the analytical solution. A new situation arises in the planned accelerator driven systems (ADS). An ADS will be run in a subcritical mode, and the steady flux will be maintained by an accelerator based source. Such a source has statistical properties that are different from those of a steady radioactive source. As one example, in a currently running European Community project for ADS research, the MUSE project, the source will be a periodically pulsed neutron generator. The theory of Feynman-alpha method needs to be extended to such nonstationary sources. There are two ways of performing and evaluating such pulsed source experiments. One is to synchronise the detector time gate start with the beginning of an incoming pulse. The Feynman-alpha method has been elaborated for such a case recently. The other method can be called stochastic pulsing. It means that there is no synchronisation between the detector time gate start and the source pulsing, i.e. the start of each measurement is chosen at a random time. The analytical solution to the Feynman-alpha formula from this latter method is the subject of this report. We have obtained an analytical Feynman-alpha formula for the case of stochastic pulsing by two different methods. One is completely based on the use of the symbolic algebra code Mathematica, whereas the other is based on complex function techniques. Closed form solutions could be obtained by both methods

Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method)

Energy Technology Data Exchange (ETDEWEB)

Ceder, M

2002-03-01

The Feynman-alpha method is used in traditional nuclear reactors to determine the subcritical reactivity of a system. The method is based on the measurement of the mean number and the variance of detector counts for different measurement times. The measurement is performed while a steady-state neutron flux is maintained in the reactor by an external neutron source, as a rule a radioactive source. From a plot of the variance-to-mean ratio as a function of measurement time ('gate length'), the reactivity can be determined by fitting the measured curve to the analytical solution. A new situation arises in the planned accelerator driven systems (ADS). An ADS will be run in a subcritical mode, and the steady flux will be maintained by an accelerator based source. Such a source has statistical properties that are different from those of a steady radioactive source. As one example, in a currently running European Community project for ADS research, the MUSE project, the source will be a periodically pulsed neutron generator. The theory of Feynman-alpha method needs to be extended to such nonstationary sources. There are two ways of performing and evaluating such pulsed source experiments. One is to synchronise the detector time gate start with the beginning of an incoming pulse. The Feynman-alpha method has been elaborated for such a case recently. The other method can be called stochastic pulsing. It means that there is no synchronisation between the detector time gate start and the source pulsing, i.e. the start of each measurement is chosen at a random time. The analytical solution to the Feynman-alpha formula from this latter method is the subject of this report. We have obtained an analytical Feynman-alpha formula for the case of stochastic pulsing by two different methods. One is completely based on the use of the symbolic algebra code Mathematica, whereas the other is based on complex function techniques. Closed form solutions could be obtained by both methods

Quantum cosmology based on discrete Feynman paths

International Nuclear Information System (INIS)

Chew, Geoffrey F.

2002-01-01

Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''

Derivation and analysis of the Feynman-alpha formula for deterministically pulsed sources

International Nuclear Information System (INIS)

Wright, J.; Pazsit, I.

2004-03-01

The purpose or this report is to give a detailed description of the calculation of the Feynman-alpha formula with deterministically pulsed sources. In contrast to previous calculations, Laplace transform and complex function methods are used to arrive at a compact solution in form of a Fourier series-like expansion. The advantage of this method is that it is capable to treat various pulse shapes. In particular, in addition to square- and Dirac delta pulses, a more realistic Gauss-shaped pulse is also considered here. The final solution of the modified variance-to-mean, that is the Feynman Y(t) function, can be quantitatively evaluated fast and with little computational effort. The analytical solutions obtained are then analysed quantitatively. The behaviour of the number or neutrons in the system is investigated in detail, together with the transient that follows the switching on of the source. An analysis of the behaviour of the Feynman Y(t) function was made with respect to the pulse width and repetition frequency. Lastly, the possibility of using me formulae for the extraction of the parameter alpha from a simulated measurement is also investigated

Destructive interferences results in bosons anti bunching: refining Feynman's argument

Science.gov (United States)

Marchewka, Avi; Granot, Er'el

2014-09-01

The effect of boson bunching is frequently mentioned and discussed in the literature. This effect is the manifestation of bosons tendency to "travel" in clusters. One of the core arguments for boson bunching was formulated by Feynman in his well-known lecture series and has been frequently used ever since. By comparing the scattering probabilities of two bosons and of two distinguishable particles, he concluded: "We have the result that it is twice as likely to find two identical Bose particles scattered into the same state as you would calculate assuming the particles were different" [R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics: Quantum mechanics (Addison-Wesley, 1965)]. This argument was rooted in the scientific community (see for example [C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (John Wiley & Sons, Paris, 1977); W. Pauli, Exclusion Principle and Quantum Mechanics, Nobel Lecture (1946)]), however, while this sentence is completely valid, as is proved in [C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (John Wiley & Sons, Paris, 1977)], it is not a synonym of bunching. In fact, as it is shown in this paper, wherever one of the wavefunctions has a zero, bosons can anti-bunch and fermions can bunch. It should be stressed that zeros in the wavefunctions are ubiquitous in Quantum Mechanics and therefore the effect should be common. Several scenarios are suggested to witness the effect.

High energy multi-gluon exchange amplitudes

International Nuclear Information System (INIS)

Jaroszewicz, T.

1980-11-01

We examine perturbative high energy n-gluon exchange amplitudes calculated in the Coulomb gauge. If n exceeds the minimum required by the t-channel quantum numbers, such amplitudes are non-leading in lns. We derive a closed system of coupled integral equations for the corresponding two-particle n-gluon vertices, obtained by summing the leading powers of ln(N μ psup(μ)), where psup(μ) is the incident momentum and Nsup(μ) the gauge-defining vector. Our equations are infra-red finite, provided the external particles are colour singlets. (author)

The power counting theorem for Feynman integrals with massless propagators

International Nuclear Information System (INIS)

Lowenstein, J.H.

1975-01-01

Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.) [de

Advanced computer algebra algorithms for the expansion of Feynman integrals

International Nuclear Information System (INIS)

Ablinger, Jakob; Round, Mark; Schneider, Carsten

2012-10-01

Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+ε-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.

Advanced computer algebra algorithms for the expansion of Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Round, Mark; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2012-10-15

Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+{epsilon}-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.

Forward gluon production in hadron-hadron scattering with Pomeron loops

International Nuclear Information System (INIS)

Iancu, E.

2006-01-01

We discuss new physical phenomena expected in particle production in hadron-hadron collisions at high energy, as a consequence of Pomerons loop effects in the evolution equations for the Color Glass Condensate. We focus on gluon production in asymmetric, 'dilute-dense', collisions: a dilute projectile scatters off a dense hadronic target, whose gluon distribution is highly evolved. This situation is representative for particle production in proton-proton collisions at forward rapidities (say, at LHC) and admits a dipole factorization similar to that of deep inelastic scattering (DIS). We show that at sufficiently large forward rapidities, where the Pomerons loop effects become important in the evolution of the target wavefunction, gluon production is dominated by 'black spots' (saturated gluon configurations) up to very large values of the transverse momentum, well above the average saturation momentum in the target. In this regime, the produced gluon spectrum exhibits diffusive scaling, so like DIS at sufficiently high energy. (authors)

Forward gluon production in hadron-hadron scattering with Pomeron loops

Energy Technology Data Exchange (ETDEWEB)

Iancu, E. [CEA Saclay, Service de Physique Th orique (DSM/SPhT), Unite de recherche associ e au CNRS (URA D2306), 91 - Gif-sur-Yvette (France). Direction des Sciences de la Matiere; Marquet, C.; Soyez, G. [CEA Saclay, Service de Physique Th orique (DSM/SPhT), Unite de recherche associ e au CNRS (URA D2306), 91 - Gif-sur-Yvette (France). Direction des Sciences de la Matiere; Liege Univ., Fundamental Theoretical Physics Group (Belgium)

2006-07-01

We discuss new physical phenomena expected in particle production in hadron-hadron collisions at high energy, as a consequence of Pomerons loop effects in the evolution equations for the Color Glass Condensate. We focus on gluon production in asymmetric, 'dilute-dense', collisions: a dilute projectile scatters off a dense hadronic target, whose gluon distribution is highly evolved. This situation is representative for particle production in proton-proton collisions at forward rapidities (say, at LHC) and admits a dipole factorization similar to that of deep inelastic scattering (DIS). We show that at sufficiently large forward rapidities, where the Pomerons loop effects become important in the evolution of the target wavefunction, gluon production is dominated by 'black spots' (saturated gluon configurations) up to very large values of the transverse momentum, well above the average saturation momentum in the target. In this regime, the produced gluon spectrum exhibits diffusive scaling, so like DIS at sufficiently high energy. (authors)

A new method for computing the quark-gluon vertex

International Nuclear Information System (INIS)

Aguilar, A C

2015-01-01

In this talk we present a new method for determining the nonperturbative quark-gluon vertex, which constitutes a crucial ingredient for a variety of theoretical and phenomenological studies. This new method relies heavily on the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. The longitudinal part of this latter quantity is fixed using the standard gauge technique, whereas the transverse is estimated with the help of the so-called transverse Ward identities. This method allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. Numerical results are presented for the form factors in three special kinematical configurations (soft gluon and quark symmetric limit, zero quark momentum), and compared with the corresponding lattice data. (paper)

Thermalization of mini-jets in a quark–gluon plasma

Energy Technology Data Exchange (ETDEWEB)

Iancu, Edmond, E-mail: edmond.iancu@cea.fr; Wu, Bin, E-mail: bin.wu.phys@gmail.com [Institut de Physique Théorique, CEA Saclay, CNRS UMR 3681, F-91191 Gif-sur-Yvette (France); Department of Physics, The Ohio State University, Columbus, OH 43210 (United States)

2016-12-15

We present the complete physical picture for the evolution of a high-energy jet propagating through a weakly-coupled quark-gluon plasma (QGP) by analytical and numerical investigation of thermalization of the soft components of the jet. Our results support the following physical picture: the leading particle emits a significant number of mini-jets which promptly evolve via multiple branching and thus degrade into a myriad of soft gluons, with energies of the order of the medium temperature T. Via elastic collisions with the medium constituents, these soft gluons relax to local thermal equilibrium with the plasma over a time scale which is considerably shorter than the typical lifetime of the mini-jet. The thermalized gluons form a tail which lags behind the hard components of the jet. Together with the background QGP, they behave hydrodynamically.

Solving differential equations for Feynman integrals by expansions near singular points

Science.gov (United States)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Quark and gluon propagators in the spherical bag model

Energy Technology Data Exchange (ETDEWEB)

Kulish, Yu V [AN Ukrainskoj SSR, Fiziko-Tekhnicheskij Inst., Kharkov

1983-12-01

The quark and gluon propagators in a spherical cavity have been obtained by summation of the quark field modes (J-1/2, J is the total moment) and gluon field modes (J=1). The requirements for the spatial components of the gluon propagator Gsub(ik)(x, x') and the quark propagator S(x, x') to be Green functions of the wave equations result in the coincidence of directions for anti x and anti x' vectors. Relations have been derived which allow verification of the self-consistency of approximations used to calculate dynamic values.

Quark and gluon propagators in the spherical bag model

International Nuclear Information System (INIS)

Kulish, Yu.V.

1983-01-01

The quark and gluon propagators in a spherical cavity have been obtained by summation of the quark field modes (J-1/2, J is the total moment) and gluon field modes (J=1). The requirements for the spatial components of the gluon propagator Gsub(ik)(x, x') and the quark propagator S(x, x') to be Green functions of the wave equations result in the coincidence of directions for anti x and anti x' vectors. Relations have been derived which allow verification of the self-consistency of approximations used to calculate dynamic values

High energy production of gluons in a quasi-multi-Regge kinematics

International Nuclear Information System (INIS)

Fadin, V.S.; Lipatov, L.N.

1989-01-01

Inelastic gluon-gluon scattering amplitudes in the Born approximation for the quasi-multi-Regge kinematics are calculated, starting with the Veneziano-type expression for the inelastic amplitude of the gluon-tachyon scattering with its subsequent simplification in the region of large energies and the Regge slope α'→0. Results obtained allow one to determine the high order corrections to the gluon Regge trajectory, the reggeon-particle vertices and to the integral kernel of the Bethe-Salpeter equation for the vacuum t-channel partial waves. 10 refs.; 7 figs

Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

International Nuclear Information System (INIS)

Tanimura, Shogo

1992-01-01

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs

Quark vs Gluon Jet Tagging at ATLAS

CERN Document Server

Rubbo, Francesco; The ATLAS collaboration

2017-01-01

Distinguishing quark-initiated from gluon-initiated jets is useful for many measurements and searches at the LHC. We present a quark-initiated versus gluon-initiated jet tagger from the ATLAS experiment using the number of reconstructed charged particles inside the jet. The measurement of the charged-particle multiplicity inside jets from Run 1 is used to derive uncertainties on the tagger performance for Run 2. With an efficiency of 60% to select quark-initiated jets, the efficiency to select gluon-initiated jets is between 10 and 20% across a wide range in jet pT up to 1.5 TeV with about an absolute 5% systematic uncertainty on the efficiencies. In addition, we also present preliminary studies on a tagger for the ATLAS experiment using the full radiation pattern inside a jet processed as images in deep neural network classifiers.

Quantum chromodynamics as effective theory of quarks and composite gluons

International Nuclear Information System (INIS)

Fuss, T.

2004-01-01

The dynamics of quarks is described by a nonperturbatively regularized NJL model which is canonically quantized and fulfil a probability interpretation. The quantum field theory of this model is formulated in a functional space. The wave functions of the quarks and gluons are calculated as eigenstates of Hard-Core equations and the gluons are considered as relativistic bound states of colored quark-antiquark pairs. The effective dynamics of the quarks and gluons is derived from weak mapping in functional space. This leads to the functional formulation of the phenomenological SU(3) local gauge invariant quark-gluon equations in temporal gauge. This means that the local gauge symmetry is a dynamical effect resulting from the quark model

Describing gluons at zero and finite temperature

International Nuclear Information System (INIS)

Maas, A.

2010-01-01

Any description of gluons requires a well-defined gauge. This is complicated non-perturbatively by Gribov copies. A possible method-independent gauge definition to resolve this problem is presented and afterwards used to study the properties of gluons at any temperature. It is found that only chromo-electric properties reflect the phase transition. From these the gauge-invariant phase transition temperature is determined for SU(2) and SU(3) Yang-Mills theory independently. (author)

Shadowing of gluons in perturbative QCD: A comparison of different models

International Nuclear Information System (INIS)

Jalilian-Marian, Jamal; Wang, Xin-Nian

2001-01-01

We investigate the different perturbative QCD-based models for nuclear shadowing of gluons. We show that, in the kinematic region appropriate to the BNL relativistic heavy ion collider experiment, all models give similar estimates for the magnitude of gluon shadowing. At scales relevant to CERN large hadron collider (LHC), there is a sizable difference between the predictions of the different models. However, the uncertainties in gluon shadowing coming from a different parametrization of the gluon distribution in nucleons, are larger than those due to different perturbative QCD models of gluon shadowing. We also investigate the effect of initial nonperturbative shadowing on the magnitude of perturbative shadowing and show that the magnitudes of perturbative and nonperturbative shadowing are comparable at RHIC but perturbative shadowing dominates over nonperturbative shadowing at smaller values of x reached at LHC

Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

Science.gov (United States)

Fan, Hong-yi; Xu, Xue-xiang

2009-06-01

By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

Quark and gluon condensate in vacuum

International Nuclear Information System (INIS)

Vajnshtejn, A.I.; Zakharov, V.I.; Shifman, M.A.

1979-01-01

The mechanism of quark confinement has been reviewed. The fact that coloured particles in a free state cannot be observed is connected with specific properties of vacuum in quantum chromodynamics. The basic hypothesis consists in the existence of vacuum fields, quark and gluon condensates, which affect the coloured objects. The vacuum transparent relative to noncharged ''white'' states serves as a source of the force acting upon the coloured particles. It has been a sucess to examine strictly the action of the vacuum fields on quarks when the distance between them is relatively small and the force of the vacuum fields on quarks is relatively small too. It is shown that the interaction with the vacuum fields manifests itself earlier than the forces connected with the gluon exchange do. It is assumed that the vacuum condensate of quarks and gluons and its relation to properties of resonances and to the bag model exist in reality. The dispersion sum rules are used for calculating masses and lepton widths of resonances

Soft gluon resummation in the infrared region and the Froissart bound

CERN Document Server

Pancheri, Giulia; Godbole, Rohini M; Srivastava, Yogendra N

2010-01-01

We describe the taming effect induced by soft gluon $k_t$-resummation on the rapid rise of QCD mini-jet contributions to the total cross-sections.This results from an eikonal model in which the rise of the total cross-section is due to mini-jet contribution. We perform the calculation with current Parton Density Functions (PDFs). The impact parameter distribution we use is obtained as the Fourier transform of the resummed $k_t$-distribution of soft gluons emitted from the initial state during the collision.The emission, which is energy dependent, destroys the initial collinearity of partons.In this model, the strong power-like rise due to the increasing number of low-x gluon collisions is tamed by the acollinearity induced by soft gluon kt-resummation down to zero gluon momenta. It explicitly links a singular soft gluon coupling in the infrared region to the behaviour dictated by the Froissart bound for the total cross-section. The model describes well both proton and photon processes at present accelerator e...

Linearly Polarized Gluons and the Higgs Transverse Momentum Distribution

NARCIS (Netherlands)

Boer, Daniel; den Dunnen, Wilco J.; Pisano, Cristian; Schlegel, Marc; Vogelsang, Werner

2012-01-01

We study how gluons carrying linear polarization inside an unpolarized hadron contribute to the transverse momentum distribution of Higgs bosons produced in hadronic collisions. They modify the distribution produced by unpolarized gluons in a characteristic way that could be used to determine

Gluon amplitudes as 2 d conformal correlators

Science.gov (United States)

Pasterski, Sabrina; Shao, Shu-Heng; Strominger, Andrew

2017-10-01

Recently, spin-one wave functions in four dimensions that are conformal primaries of the Lorentz group S L (2 ,C ) were constructed. We compute low-point, tree-level gluon scattering amplitudes in the space of these conformal primary wave functions. The answers have the same conformal covariance as correlators of spin-one primaries in a 2 d CFT. The Britto-Cachazo-Feng-Witten (BCFW) recursion relation between three- and four-point gluon amplitudes is recast into this conformal basis.

Identified particles in quark and gluon jets

CERN Document Server

Abreu, P; Adye, T; Ajinenko, I; Alekseev, G D; Alemany, R; Allport, P P; Almehed, S; Amaldi, Ugo; Amato, S; Andreazza, A; Andrieux, M L; Antilogus, P; Apel, W D; Åsman, B; Augustin, J E; Augustinus, A; Baillon, Paul; Bambade, P; Barão, F; Barbi, M S; Barbiellini, Guido; Bardin, Dimitri Yuri; Barker, G; Baroncelli, A; Bärring, O; Barrio, J A; Bartl, Walter; Bates, M J; Battaglia, Marco; Baubillier, M; Baudot, J; Becks, K H; Begalli, M; Beillière, P; Belokopytov, Yu A; Benvenuti, Alberto C; Berggren, M; Bertini, D; Bertrand, D; Besançon, M; Bianchi, F; Bigi, M; Bilenky, S M; Billoir, P; Bizouard, M A; Bloch, D; Blume, M; Bolognese, T; Bonesini, M; Bonivento, W; Booth, P S L; Bosio, C; Botner, O; Boudinov, E; Bouquet, B; Bourdarios, C; Bowcock, T J V; Bozzo, M; Branchini, P; Brand, K D; Brenke, T; Brenner, R A; Bricman, C; Brown, R C A; Brückman, P; Brunet, J M; Bugge, L; Buran, T; Burgsmüller, T; Buschmann, P; Cabrera, S; Caccia, M; Calvi, M; Camacho-Rozas, A J; Camporesi, T; Canale, V; Canepa, M; Cankocak, K; Cao, F; Carena, F; Carroll, L; Caso, Carlo; Castillo-Gimenez, M V; Cattai, A; Cavallo, F R; Chabaud, V; Charpentier, P; Chaussard, L; Checchia, P; Chelkov, G A; Chen, M; Chierici, R; Chliapnikov, P V; Chochula, P; Chorowicz, V; Chudoba, J; Cindro, V; Collins, P; Contri, R; Cortina, E; Cosme, G; Cossutti, F; Cowell, J H; Crawley, H B; Crennell, D J; Crosetti, G; Cuevas-Maestro, J; Czellar, S; Dahl-Jensen, Erik; Dahm, J; D'Almagne, B; Dam, M; Damgaard, G; Dauncey, P D; Davenport, Martyn; Da Silva, W; Defoix, C; Deghorain, A; Della Ricca, G; Delpierre, P A; Demaria, N; De Angelis, A; de Boer, Wim; De Brabandere, S; De Clercq, C; La Vaissière, C de; De Lotto, B; De Min, A; De Paula, L S; De Saint-Jean, C; Dijkstra, H; Di Ciaccio, Lucia; Di Diodato, A; Djama, F; Djannati, A; Dolbeau, J; Doroba, K; Dracos, M; Drees, J; Drees, K A; Dris, M; Durand, J D; Edsall, D M; Ehret, R; Eigen, G; Ekelöf, T J C; Ekspong, Gösta; Elsing, M; Engel, J P; Erzen, B; Espirito-Santo, M C; Falk, E; Fassouliotis, D; Feindt, Michael; Ferrer, A; Fichet, S; Filippas-Tassos, A; Firestone, A; Fischer, P A; Föth, H; Fokitis, E; Fontanelli, F; Formenti, F; Franek, B J; Frenkiel, P; Fries, D E C; Frodesen, A G; Frühwirth, R; Fulda-Quenzer, F; Fuster, J A; Galloni, A; Gamba, D; Gandelman, M; García, C; García, J; Gaspar, C; Gasparini, U; Gavillet, P; Gazis, E N; Gelé, D; Gerber, J P; Gerdyukov, L N; Gokieli, R; Golob, B; Gopal, Gian P; Gorn, L; Górski, M; Guz, Yu; Gracco, Valerio; Graziani, E; Green, C; Grefrath, A; Gris, P; Grosdidier, G; Grzelak, K; Gumenyuk, S A; Gunnarsson, P; Günther, M; Guy, J; Hahn, F; Hahn, S; Hajduk, Z; Hallgren, A; Hamacher, K; Harris, F J; Hedberg, V; Henriques, R P; Hernández, J J; Herquet, P; Herr, H; Hessing, T L; Heuser, J M; Higón, E; Hilke, Hans Jürgen; Hill, T S; Holmgren, S O; Holt, P J; Holthuizen, D J; Hoorelbeke, S; Houlden, M A; Hrubec, Josef; Huet, K; Hultqvist, K; Jackson, J N; Jacobsson, R; Jalocha, P; Janik, R; Jarlskog, C; Jarlskog, G; Jarry, P; Jean-Marie, B; Johansson, E K; Jönsson, L B; Jönsson, P E; Joram, Christian; Juillot, P; Kaiser, M; Kapusta, F; Karafasoulis, K; Karlsson, M; Karvelas, E; Katargin, A; Katsanevas, S; Katsoufis, E C; Keränen, R; Khokhlov, Yu A; Khomenko, B A; Khovanskii, N N; King, B J; Kjaer, N J; Klapp, O; Klein, H; Klovning, A; Kluit, P M; Köne, B; Kokkinias, P; Koratzinos, M; Korcyl, K; Kostyukhin, V; Kourkoumelis, C; Kuznetsov, O; Krammer, Manfred; Kreuter, C; Kronkvist, I J; Krumshtein, Z; Krupinski, W; Kubinec, P; Kucewicz, W; Kurvinen, K L; Lacasta, C; Laktineh, I; Lamsa, J; Lanceri, L; Lane, D W; Langefeld, P; Lapin, V; Laugier, J P; Lauhakangas, R; Leder, Gerhard; Ledroit, F; Lefébure, V; Legan, C K; Leitner, R; Lemonne, J; Lenzen, Georg; Lepeltier, V; Lesiak, T; Libby, J; Liko, D; Lindner, R; Lipniacka, A; Lippi, I; Lörstad, B; Loken, J G; López, J M; Loukas, D; Lutz, P; Lyons, L; MacNaughton, J N; Maehlum, G; Mahon, J R; Malmgren, T G M; Malychev, V; Mandl, F; Marco, J; Marco, R P; Maréchal, B; Margoni, M; Marin, J C; Mariotti, C; Markou, A; Martínez-Rivero, C; Martínez-Vidal, F; Martí i García, S; Masik, J; Matorras, F; Matteuzzi, C; Matthiae, Giorgio; Mazzucato, M; McCubbin, M L; McKay, R; McNulty, R; Medbo, J; Merk, M; Meroni, C; Meyer, S; Meyer, W T; Michelotto, M; Migliore, E; Mirabito, L; Mitaroff, Winfried A; Mjörnmark, U; Moa, T; Møller, R; Mönig, K; Monge, M R; Morettini, P; Müller, H; Münich, K; Mulders, M; Mundim, L M; Murray, W J; Muryn, B; Myatt, Gerald; Naraghi, F; Navarria, Francesco Luigi; Navas, S; Nawrocki, K; Negri, P; Neumann, W; Neumeister, N; Nicolaidou, R; Nielsen, B S; Nieuwenhuizen, M; Nikolaenko, V; Niss, P; Nomerotski, A; Normand, Ainsley; Novák, M; Oberschulte-Beckmann, W; Obraztsov, V F; Olshevskii, A G; Onofre, A; Orava, Risto; Österberg, K; Ouraou, A; Paganini, P; Paganoni, M; Pagès, P; Pain, R; Palka, H; Papadopoulou, T D; Papageorgiou, K; Pape, L; Parkes, C; Parodi, F; Passeri, A; Pegoraro, M; Peralta, L; Pernicka, Manfred; Perrotta, A; Petridou, C; Petrolini, A; Petrovykh, M; Phillips, H T; Piana, G; Pierre, F; Pimenta, M; Podobnik, T; Podobrin, O; Pol, M E; Polok, G; Poropat, P; Pozdnyakov, V; Privitera, P; Pukhaeva, N; Pullia, Antonio; Radojicic, D; Ragazzi, S; Rahmani, H; Rames, J; Ratoff, P N; Read, A L; Reale, M; Rebecchi, P; Redaelli, N G; Regler, Meinhard; Reid, D; Reinhardt, R; Renton, P B; Resvanis, L K; Richard, F; Richardson, J; Rídky, J; Rinaudo, G; Ripp, I; Romero, A; Roncagliolo, I; Ronchese, P; Roos, L; Rosenberg, E I; Roudeau, Patrick; Rovelli, T; Rückstuhl, W; Ruhlmann-Kleider, V; Ruiz, A; Rybicki, K; Rybin, A; Saarikko, H; Sacquin, Yu; Sadovskii, A; Sahr, O; Sajot, G; Salt, J; Sánchez, J; Sannino, M; Schimmelpfennig, M; Schneider, H; Schwickerath, U; Schyns, M A E; Sciolla, G; Scuri, F; Seager, P; Sedykh, Yu; Segar, A M; Seitz, A; Sekulin, R L; Serbelloni, L; Shellard, R C; Siegrist, P; Silvestre, R; Simonetti, S; Simonetto, F; Sissakian, A N; Sitár, B; Skaali, T B; Smadja, G; Smirnov, N; Smirnova, O G; Smith, G R; Sosnowski, R; Souza-Santos, D; Spassoff, Tz; Spiriti, E; Sponholz, P; Squarcia, S; Stampfer, D; Stanescu, C; Stanic, S; Stapnes, Steinar; Stavitski, I; Stevenson, K; Stocchi, A; Strauss, J; Strub, R; Stugu, B; Szczekowski, M; Szeptycka, M; Tabarelli de Fatis, T; Tavernet, J P; Chikilev, O G; Thomas, J; Tilquin, A; Timmermans, J; Tkatchev, L G; Todorov, T; Todorova, S; Toet, D Z; Tomaradze, A G; Tomé, B; Tonazzo, A; Tortora, L; Tranströmer, G; Treille, D; Tristram, G; Trombini, A; Troncon, C; Tsirou, A L; Turluer, M L; Tyapkin, I A; Tyndel, M; Tzamarias, S; Überschär, B; Ullaland, O; Uvarov, V; Valenti, G; Vallazza, E; Van der Velde, C; van Apeldoorn, G W; van Dam, P; Van Doninck, W K; Van Eldik, J; Van Lysebetten, A; Vassilopoulos, N; Vegni, G; Ventura, L; Venus, W A; Verbeure, F; Verlato, M; Vertogradov, L S; Vilanova, D; Vincent, P; Vitale, L; Vlasov, E; Vodopyanov, A S; Vrba, V; Wahlen, H; Walck, C; Weierstall, M; Weilhammer, Peter; Weiser, C; Wetherell, Alan M; Wicke, D; Wickens, J H; Wielers, M; Wilkinson, G R; Williams, W S C; Winter, M; Witek, M; Wlodek, T; Woschnagg, K; Yip, K; Yushchenko, O P; Zach, F; Zaitsev, A; Zalewska-Bak, A; Zalewski, Piotr; Zavrtanik, D; Zevgolatakos, E; Zimin, N I; Zito, M; Zontar, D; Zucchelli, G C; Zumerle, G

1997-01-01

A sample of about 1.4 million hadronic \\z decays, selected among the data recorded by the DELPHI detector at LEP during 1994, was used to measure for the first time the momentum spectra of \\kp, \\ko, \\p, \\l and their antiparticles in gluon and quark jets. As observed for inclusive charged particles, the production spectra of identified particles were found to be softer in gluon jets than in quark jets, with a higher total multiplicity.

Huygens-Feynman-Fresnel principle as the basis of applied optics.

Science.gov (United States)

Gitin, Andrey V

2013-11-01

The main relationships of wave optics are derived from a combination of the Huygens-Fresnel principle and the Feynman integral over all paths. The stationary-phase approximation of the wave relations gives the correspondent relations from the point of view of geometrical optics.

χc charmonium - a tool to investigate gluon polarization

International Nuclear Information System (INIS)

Batunin, A.V.; Slabospitskij, S.R.

1986-01-01

Production of particles with a hidden charm Χ C in polarized parton beams (quarks or gluons) is studied. Parton polarization is shown to cause the changes of angular distributions of Χ C meson decay products, which allows one to investigate possible gluon polarization in hadrons

Infrared behaviour of three and four gluon vertices in Yang-Mills theory

International Nuclear Information System (INIS)

Brandt, F.T.; Frenkel, J.

1985-01-01

The structure of the 3-point function with one and two external gluons on-shell is studied in a general covariant gauge. The contributions which result in one loop approximation are expressed in terms of simple functions containing collinear and soft singularities. Furthermore, the contributions associated with the 4-point vertex when all external gluons are on-shell are analysed. As an application of these results, the infrared structure of gluon-gluon scattering amplitude is studied. (Author) [pt

Phenomenology of large Nc QCD

International Nuclear Information System (INIS)

Lebed, R.F.

1999-01-01

These lectures are designed to introduce the methods and results of large N c QCD in a presentation intended for nuclear and particle physicists alike. Beginning with definitions and motivations of the approach, we demonstrate that all quark and gluon Feynman diagrams are organized into classes based on powers of 1/N c . We then show that this result can be translated into definite statements about mesons and baryons containing arbitrary numbers of constituents. In the mesons, numerous well-known phenomenological properties follow as immediate consequences of simply counting powers of N c , while for the baryons, quantitative large N c analyses of masses and other properties are seen to agree with experiment, even when 'large' N c is set equal to its observed value of 3. Large N c reasoning is also used to explain some simple features of nuclear interactions. (author)

Phenomenology of large Nc QCD

International Nuclear Information System (INIS)

Richard Lebed

1998-01-01

These lectures are designed to introduce the methods and results of large N c QCD in a presentation intended for nuclear and particle physicists alike. Beginning with definitions and motivations of the approach, they demonstrate that all quark and gluon Feynman diagrams are organized into classes based on powers of 1/N c . They then show that this result can be translated into definite statements about mesons and baryons containing arbitrary numbers of constituents. In the mesons, numerous well-known phenomenological properties follow as immediate consequences of simply counting powers of N c , while for the baryons, quantitative large N c analyses of masses and other properties are seen to agree with experiment, even when ''large'' N c is set equal to its observed value of 3. Large N c reasoning is also used to explain some simple features of nuclear interactions

Structure functions and pair correlations of the quark-gluon plasma

International Nuclear Information System (INIS)

Thoma, Markus H.

2005-01-01

Recent experiments at RHIC and theoretical considerations indicate that the quark-gluon plasma, present in the fireball of relativistic heavy-ion collisions, might be in a liquid phase. The liquid state can be identified by characteristic correlation and structure functions. Here definitions of the structure functions and pair correlations of the quark-gluon plasma are presented as well as perturbative results. These definitions might be useful for verifying the quark-gluon-plasma liquid in QCD lattice calculations

Heavy Flavour Production as Probe of Gluon Sivers Function

International Nuclear Information System (INIS)

Godbole, Rohini M.; Kaushik, Abhiram; Misra, Anuradha; Rawoot, Vaibhav; Sonawane, Bipin

2017-01-01

Heavy flavour production like J/ψ and D-meson production in scattering of electrons/unpolarized protons off polarized proton target offer promising probes to investigate gluon Sivers function. In this talk, I will summarize our recent work on transverse single spin asymmetry in J/ψ-production and D-meson production in pp↑ scattering using a generalized parton model approach. We compare predictions obtained using different models of gluon Sivers function within this approach and then, taking into account the transverse momentum dependent evolution of the unpolarized parton distribution functions and gluon Sivers function, we study the effect of evolution on asymmetry. (author)

Infra-red ghost contribution to the gluon Green's functions

International Nuclear Information System (INIS)

Paccanoni, F.

1985-01-01

The Schwinger-Dyson equations for the ghost propagator and the ghost-ghost-gluon vertex function are studied in the Landau gauge. A confining infra-red singularity is assumed for the gluon propagator and a suitable approximation is devised for the solution of the integral equations. It is found that the bare values of the ghost propagator and coupling cannot be a consistent solution of either equation. It is determined a possible behaviour of the correction factor for the ghost propagator in the small-momentum limit and discussed the consistency of the approximation schemes for the gluon propagator that neglet Faddeev-Popov ghost

Dynamical instabilities in quark-gluon plasma with hard jet

International Nuclear Information System (INIS)

Pavlenko, O.P.

1990-01-01

The dynamical instabilities, whose development can be expected under the hard jet propagating through the quark-gluon plasma, are analyzed. The possible signals of the quark-gluon plasma formation in ultrarelativistic nuclear collisions connected with the development of the plasma-jet instabilities are discussed. 10 refs

Two theoretical treatments of the quark-gluon plasma

International Nuclear Information System (INIS)

Carrington, M.E.

1989-01-01

The study of the quark-gluon plasma is of direct relevance to questions about the confinement properties of QCD and the validity of the standard theory of QCD in a different physical regime. Part 1 of this work contains a brief discussion of the theoretical and numerical evidence for the existence of the quark-gluon plasma. In the next two sections, two different approaches are discussed. In Part 2, the problem is presented in the general framework of kinetic theory. A definition of the Wigner distribution operator is introduced for quarks and a set of kinetic equations are derived for the momentum moments of this operator. A Wigner distribution operator is defined for gluons and the momentum of this operator are calculated and related to physical quantities. In Part 3, a calculation of linear response functions in a hot gluon plasma is presented. Problems related to gauge invariance and to the definition of a thermal ensemble in the presence of unphysical degrees of freedom are discussed. Results in different gauges and with different ensembles are compared, and the implications of the results for plasma oscillations are discussed

Gluon contribution to the Sivers effect. COMPASS results on deuteron target

Directory of Open Access Journals (Sweden)

Szabelski Adam

2015-01-01

Full Text Available Sivers effect for gluons is connected to gluon orbital angular momentum which may be the missing part of the nucleon spin puzzle. We present a method of extraction of Sivers effect for gluons from COMPASS SIDIS data on transversely polarised target. In order to access the Sivers effect for gluons photon-gluon fusion (PGF process is used. To enhance the fraction of PGF in the sample high-pT hadron pair events are selected. The method is based on a assumption that there are 3 processes contributing to the muon-nucleon scattering: PGF, leading process and QCD Compton process. Then one performs a weighting procedure which enables to extract the asymmetries for the 3 contributing processes simultaneously. In order to do that a neural network trained by a Monte Carlo to assign to each event 3 probabilities corresponding to the 3 processes is needed. Finaly we show results of Sivers effect for gluons extraction on COMPASS data with transversely polarised deuteron target. APGFsinΦ2h–ΦS = −0.14 ± 0.15 (stat. at ‹XG› = 0.126.

On the application of gluon to heavy quarkonium fragmentation function

International Nuclear Information System (INIS)

Qi Wei; Wang Jianxiong

2007-01-01

We analyze the uncertainties induced by different definitions of the momentum fraction z in the application of gluon to heavy quarkonium fragmentation function. We numerically calculate the initial g→J/ψ fragmentation functions by using the non-covariant definitions of z with finite gluon momentum and find that these fragmentation functions have strong dependence on the gluon momentum k. As |k|→∞, these fragmentation functions approach to the fragmentation function in the light-cone definition. We find that when |k| is small (for instance in the typical energy scale (about 4-20GeV) of the gluon production at the hadron colliders, such as Tevatron and LHC), large uncertainty remains while the in-covariant definitions of z are employed in the application of the fragmentation functions. (authors)

Inclusive gluon production in deep inelastic scattering at high parton density

International Nuclear Information System (INIS)

Kovchegov, Yuri V.; Tuchin, Kirill

2002-01-01

We calculate the cross section of single inclusive gluon production in deep inelastic scattering at very high energies in the saturation regime, where the parton densities inside hadrons and nuclei are large and the evolution of structure functions with energy is nonlinear. The expression we obtain for the inclusive gluon production cross section is generated by this nonlinear evolution. We analyze the rapidity distribution of the produced gluons as well as their transverse momentum spectrum given by the derived expression for the inclusive cross section. We propose an ansatz for the multiplicity distribution of gluons produced in nuclear collisions which includes the effects of nonlinear evolution in both colliding nuclei

Feynman's path integrals and Bohm's particle paths

International Nuclear Information System (INIS)

Tumulka, Roderich

2005-01-01

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schroedinger's equation, which is half of the defining equations of Bohmian mechanics. I try to give a clear and concise description of the various aspects of the situation. (letters and comments)

Richard Feynman a life in science

CERN Document Server

Gribbin, John

1998-01-01

This text is a portrayal of one of the greatest scientists of the late 20th-century, which also provides a picture of the significant physics of the period. It combines personal anecdotes, writings and recollections with narrative. Richard Feynman's career included: war-time work on the atomic bomb at Los Alamos; a theory of quantum mechanics for which he won the Nobel prize; and major contributions to the sciences of gravity, nuclear physics and particle theory. In 1986, he was able to show that the Challenger disaster was due to the effect of cold on the booster rocket rubber sealings.

Improving the Simulation of Quark and Gluon Jets with Herwig 7 arXiv

CERN Document Server

Reichelt, Daniel; Siodmok, Andrzej

2017-12-16

The properties of quark and gluon jets, and the differences between them, are increasingly important at the LHC. However, Monte Carlo event generators are normally tuned to data from $e^+e^-$ collisions which are primarily sensitive to quark-initiated jets. In order to improve the description of gluon jets we make improvements to the perturbative and the non-perturbative modelling of gluon jets and include data with gluon-initiated jets in the tuning for the first time. The resultant tunes significantly improve the description of gluon jets and are now the default in Herwig 7.1.

A practical criterion of irreducibility of multi-loop Feynman integrals

International Nuclear Information System (INIS)

Baikov, P.A.

2006-01-01

A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable (with zero gradient) points of a specially constructed polynomial

Study of gluon condensates using the Bogolyubov transformation

International Nuclear Information System (INIS)

Iracane, Daniel

1985-01-01

We describe the ground state of non-perturbative QCD as a gluon condensate. In the framework of the Coulomb gauge Hamiltonian, we introduce an effective interaction between infrared gluons by removing high-momentum gluons. The Bogoliubov transformation provides us with our variational space. The minimisation over this Fock subspace leads to a non-perturbative vacuum and its excitations. The minimum functional space for a boson dynamic is a distribution set. We find two kinds of condensation. The first one occurs only for zero-momentum states and looks like the Bose Condensation. In the second one, the quasiparticle spectrum shows a finite gap and the vacuum is a superconducting state. We give constraints on the interaction so that the superconducting phase is more bounded than the Bose one. (author) [fr

The gluon Reggeization in perturbative QCD at NLO

Energy Technology Data Exchange (ETDEWEB)

Fadin, V.S. [Novosibirsk State Univ., Institute for Nuclear Physics (Russian Federation)

2005-07-01

The gluon Reggeization is one of the outstanding properties of QCD. It is extremely important for description of high energy processes. In particular, it appears as the basis of the BFKL approach to summation of the terms strengthened by powers of log(1/x). The hypothesis is extremely powerful, since all scattering amplitudes are expressed in terms of the gluon trajectory and several Reggeon vertices. Now the hypothesis is proved in NLA (next-to leading approximation). The proof is based on bootstrap relations. It is shown that an infinite number of these relations is reduced to several bootstrap conditions on the gluon trajectory and the Reggeon vertices. It is shown that fulfillment of these conditions means a proof of the Reggeization hypothesis. All bootstraps conditions are formulated explicitly and are proved to be fulfilled.

The quark beam function at two loops

International Nuclear Information System (INIS)

Gaunt, Jonathan R.; Stahlhofen, Maximilian; Tackmann, Frank J.

2014-01-01

In differential measurements at a hadron collider, collinear initial-state radiation is described by process-independent beam functions. They are the field-theoretic analog of initial-state parton showers. Depending on the measured observable they are differential in the virtuality and/or transverse momentum of the colliding partons in addition to their usual longitudinal momentum fractions. Perturbatively, the beam functions can be calculated by matching them onto standard quark and gluon parton distribution functions. We calculate the inclusive virtuality-dependent quark beam function at NNLO, which is relevant for any observables probing the virtuality of the incoming partons, including N-jettiness and beam thrust. For such observables, our results are an important ingredient in the resummation of large logarithms at N 3 LL order, and provide all contributions enhanced by collinear t-channel singularities at NNLO for quark-initiated processes in analytic form. We perform the calculation in both Feynman and axial gauge and use two different methods to evaluate the discontinuity in the two-loop Feynman diagrams, providing nontrivial checks of the calculation. As part of our results we reproduce the known two-loop QCD splitting functions and confirm at two loops that the virtuality-dependent beam and final-state jet functions have the same anomalous dimension.

Summaries of recent computer-assisted Feynam diagram calculations

International Nuclear Information System (INIS)

Mark Fischler

2001-01-01

The AIHENP Workshop series has traditionally included cutting edge work on automated computation of Feynman diagrams. The conveners of the Symbolic Problem Solving topic in this ACAT conference felt it would be useful to solicit presentations of brief summaries of the interesting recent calculations. Since this conference was the first in the series to be held in the Western Hemisphere, it was decided that the summaries would be solicited both from attendees and from researchers who could not attend the conference. This would represent a sampling of many of the key calculations being performed. The results were presented at the Poster session; contributions from ten researchers were displayed and posted on the web. Although the poster presentation, which can be viewed at conferences.fnal.gov/acat2000/ placed equal emphasis on results presented at the conference and other contributions, here we primarily discuss the latter, which do not appear in full form in these proceedings. This brief paper can't do full justice to each contribution; interested readers can find details of the work not presented at this conference in references (1), (2), (3), (4), (5), (6), (7)

Double soft theorem for perturbative gravity

OpenAIRE

Saha, Arnab

2016-01-01

Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.

Evidence of ghost suppression in gluon mass scale dynamics

Science.gov (United States)

Aguilar, A. C.; Binosi, D.; Figueiredo, C. T.; Papavassiliou, J.

2018-03-01

In this work we study the impact that the ghost sector of pure Yang-Mills theories may have on the generation of a dynamical gauge boson mass scale, which hinges on the appearance of massless poles in the fundamental vertices of the theory, and the subsequent realization of the well-known Schwinger mechanism. The process responsible for the formation of such structures is itself dynamical in nature, and is governed by a set of Bethe-Salpeter type of integral equations. While in previous studies the presence of massless poles was assumed to be exclusively associated with the background-gauge three-gluon vertex, in the present analysis we allow them to appear also in the corresponding ghost-gluon vertex. The full analysis of the resulting Bethe-Salpeter system reveals that the contribution of the poles associated with the ghost-gluon vertex are particularly suppressed, their sole discernible effect being a slight modification in the running of the gluon mass scale, for momenta larger than a few GeV. In addition, we examine the behavior of the (background-gauge) ghost-gluon vertex in the limit of vanishing ghost momentum, and derive the corresponding version of Taylor's theorem. These considerations, together with a suitable Ansatz, permit us the full reconstruction of the pole sector of the two vertices involved.

You err, Einstein.. Newton, Einstein, Heisenberg, and Feynman discuss quantum physics

International Nuclear Information System (INIS)

Fritzsch, Harald

2008-01-01

Harald Fritzsch and his star physicists Einstein, Heisenberg, and Feynman explain the central concept of nowadays physics, quantum mechanics, without it nothing goes in modern world. And the great Isaac newton puts the questions, which all would put

Regge behaviour of distribution functions and evolution of gluon ...

Indian Academy of Sciences (India)

work we solved DGLAP evolution equation for gluon distribution function at low-x in next-to-leading order (NLO) and the t and x-evolutions of gluon distribution function thus obtained have been compared with global MRST2004 and GRV98 parametrizations. In PQCD, since the higher-order terms in the leading logarithmic.

Orbit-averaged quantities, the classical Hellmann-Feynman theorem, and the magnetic flux enclosed by gyro-motion

Energy Technology Data Exchange (ETDEWEB)

Perkins, R. J., E-mail: rperkins@pppl.gov; Bellan, P. M. [Applied Physics and Materials Science, California Institute of Technology, Pasadena, California 91125 (United States)

2015-02-15

Action integrals are often used to average a system over fast oscillations and obtain reduced dynamics. It is not surprising, then, that action integrals play a central role in the Hellmann-Feynman theorem of classical mechanics, which furnishes the values of certain quantities averaged over one period of rapid oscillation. This paper revisits the classical Hellmann-Feynman theorem, rederiving it in connection to an analogous theorem involving the time-averaged evolution of canonical coordinates. We then apply a modified version of the Hellmann-Feynman theorem to obtain a new result: the magnetic flux enclosed by one period of gyro-motion of a charged particle in a non-uniform magnetic field. These results further demonstrate the utility of the action integral in regards to obtaining orbit-averaged quantities and the usefulness of this formalism in characterizing charged particle motion.

Gluon saturation and baryon stopping in the SPS, RHIC, and LHC energy regions

International Nuclear Information System (INIS)

Li Shuang; Feng Shengqin

2012-01-01

A new geometrical scaling method with a gluon saturation rapidity limit is proposed to study the gluon saturation feature of the central rapidity region of relativistic nuclear collisions. The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. We take advantage of the gluon saturation model with geometric scaling of the rapidity limit to investigate net baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions. Predictions for net baryon rapidity distributions, mean rapidity loss and gluon saturation feature in central Pb + Pb collisions at the LHC are made in this paper. (authors)

The PLUTO experiment at DORIS (DESY) and the discovery of the gluon (A recollection)

International Nuclear Information System (INIS)

Stella, Bruno R.; Meyer, Hans-Juergen

2010-08-01

With the aim of determining the contribution of the PLUTO experiment at the DORIS e + e - storage ring to the discovery of the gluon, as members of this former collaboration we have reconsidered all the scientific material produced by PLUTO in 1978 and the first half of 1979. It is clear that the experiment demonstrated the main decay of the Y(9.46 GeV) resonance to be mediated by 3 gluons, by providing evidence for the agreement of this hypothesis with average values and differential distributions of all possible experimental variables and by excluding all other possible alternative models. Moreover PLUTO measured in June 1979 the matrix element of the 3-gluon decay to be quantitatively as expected by QCD (even after hadronization) and, having checked the possibility to correctly trace the gluons' directions, demonstrated the spin 1 nature of the gluon by excluding spin 0 and spin 1/2. The hadronization of the gluon like a quark jet, hypothesized in the 3-gluon jet Monte Carlo simulation, was compatible with the topological data at this energy and was shown to be an approximation at 10% level for the multiplicity (∼ vertical stroke vertical stroke > -1 ); the right expected gluon fragmentation was needed for the inclusive distributions; this was the first experimental study of (identified) gluon jets. In the following measurements at the PETRA storage ring, these results were confirmed by PLUTO and by three contemporaneous experiments by evidencing at higher energies the gluon radiation (''bremsstrahlung''), the softer one, by jet broadening, and the hard one, by the emission of (now clearly visible) gluon jets by quarks. The gluon's spin 1 particle nature was also confirmed. The PLUTO results on Y decays had been confirmed both by contemporaneous experiments at DORIS (partially) and later (also partially) were confirmed by more sophisticated detectors. (orig.)

Convergence theorems for renormalized Feynman integrals with zero-mass propagators

International Nuclear Information System (INIS)

Lowenstein, J.H.

1976-01-01

A general momentum-space subtraction procedure is proposed for the removal of both ultraviolet and infrared divergences of Feynman integrals. Convergence theorems are proved which allow one to define time-ordered Green functions, as tempered distributions for a wide class of theories with zero-mass propagators. (orig.) [de

Automatic calculation of Feynman amplitude - GRACE/CHANEL

International Nuclear Information System (INIS)

Kurihara, Yoshimasa

1992-01-01

To investigate feasibility of physics at TeV energy region, cross sections from Feynman amplitudes have to be calculated for processes with multi-particle final state. Event generation and detector simulation must also be carried out to determine a detector design and a requirement of necessary luminosity. The JLC (Japan Linear Collider) working group has developed useful software and hardware tools for above purposes. An overview of the tools developed for the physics study at the JLC is given in this report. (author) 7 refs.; 2 figs

Energy dependence of the differences between the quark and gluon jet fragmentation

CERN Document Server

Abreu, P; Adye, T; Agasi, E; Ajinenko, I; Aleksan, Roy; Alekseev, G D; Alemany, R; Allport, P P; Almehed, S; Alvsvaag, S J; Amaldi, Ugo; Amato, S; Andreazza, A; Andrieux, M L; Antilogus, P; Apel, W D; Arnoud, Y; Åsman, B; Augustin, J E; Augustinus, A; Baillon, Paul; Bambade, P; Barão, F; Barate, R; Bardin, Dimitri Yuri; Baroncelli, A; Bärring, O; Barrio, J A; Bartl, Walter; Bates, M J; Battaglia, Marco; Baubillier, M; Baudot, J; Becks, K H; Begalli, M; Beillière, P; Belokopytov, Yu A; Belous, K S; Benvenuti, Alberto C; Berggren, M; Bertrand, D; Bianchi, F; Bigi, M; Bilenky, S M; Billoir, P; Bloch, D; Blume, M; Blyth, S; Bolognese, T; Bonesini, M; Bonivento, W; Booth, P S L; Borisov, G; Bosio, C; Bosworth, S; Botner, O; Bouquet, B; Bourdarios, C; Bowcock, T J V; Bozzo, M; Branchini, P; Brand, K D; Brenke, T; Brenner, R A; Bricman, C; Brillault, L; Brown, R C A; Brückman, P; Brunet, J M; Bugge, L; Buran, T; Burgsmüller, T; Buschmann, P; Buys, A; Cabrera, S; Caccia, M; Calvi, M; Camacho-Rozas, A J; Camporesi, T; Canale, V; Canepa, M; Cankocak, K; Cao, F; Carena, F; Carrilho, P; Carroll, L; Caso, Carlo; Castillo-Gimenez, M V; Cattai, A; Cavallo, F R; Cerrito, L; Chabaud, V; Charpentier, P; Chaussard, L; Chauveau, J; Checchia, P; Chelkov, G A; Chen, M; Chierici, R; Chliapnikov, P V; Chochula, P; Chorowicz, V; Chudoba, J; Cindro, V; Collins, P; Contreras, J L; Contri, R; Cortina, E; Cosme, G; Cossutti, F; Crawley, H B; Crennell, D J; Crosetti, G; Cuevas-Maestro, J; Czellar, S; Dahl-Jensen, Erik; Dahm, J; D'Almagne, B; Dam, M; Damgaard, G; Dauncey, P D; Davenport, Martyn; Da Silva, W; Defoix, C; Deghorain, A; Della Ricca, G; Delpierre, P A; Demaria, N; De Angelis, A; de Boer, Wim; De Brabandere, S; De Clercq, C; La Vaissière, C de; De Lotto, B; De Min, A; De Paula, L S; De Saint-Jean, C; Dijkstra, H; Di Ciaccio, Lucia; Djama, F; Dolbeau, J; Dönszelmann, M; Doroba, K; Dracos, M; Drees, J; Drees, K A; Dris, M; Dufour, Y; Dupont, F; Edsall, D M; Ehret, R; Eigen, G; Ekelöf, T J C; Ekspong, Gösta; Elsing, M; Engel, J P; Ershaidat, N; Erzen, B; Espirito-Santo, M C; Falk, E; Fassouliotis, D; Feindt, Michael; Ferrer, A; Filippas-Tassos, A; Firestone, A; Fischer, P A; Föth, H; Fokitis, E; Fontanelli, F; Formenti, F; Franek, B J; Frenkiel, P; Fries, D E C; Frodesen, A G; Frühwirth, R; Fulda-Quenzer, F; Fuster, J A; Galloni, A; Gamba, D; Gandelman, M; García, C; García, J; Gaspar, C; Gasparini, U; Gavillet, P; Gazis, E N; Gelé, D; Gerber, J P; Gerdyukov, L N; Gibbs, M; Gokieli, R; Golob, B; Gopal, Gian P; Gorn, L; Górski, M; Guz, Yu; Gracco, Valerio; Graziani, E; Grosdidier, G; Grzelak, K; Gumenyuk, S A; Gunnarsson, P; Günther, M; Guy, J; Hahn, F; Hahn, S; Hallgren, A; Hamacher, K; Hao, W; Harris, F J; Hedberg, V; Henriques, R P; Hernández, J J; Herquet, P; Herr, H; Hessing, T L; Higón, E; Hilke, Hans Jürgen; Hill, T S; Holmgren, S O; Holt, P J; Holthuizen, D J; Hoorelbeke, S; Houlden, M A; Hrubec, Josef; Huet, K; Hultqvist, K; Jackson, J N; Jacobsson, R; Jalocha, P; Janik, R; Jarlskog, C; Jarlskog, G; Jarry, P; Jean-Marie, B; Johansson, E K; Jönsson, L B; Jönsson, P E; Joram, Christian; Juillot, P; Kaiser, M; Kapusta, F; Karafasoulis, K; Karlsson, M; Karvelas, E; Katsanevas, S; Katsoufis, E C; Keränen, R; Khomenko, B A; Khovanskii, N N; King, B J; Kjaer, N J; Klapp, O; Klein, H; Klovning, A; Kluit, P M; Köne, B; Kokkinias, P; Koratzinos, M; Korcyl, K; Kostyukhin, V; Kourkoumelis, C; Kuznetsov, O; Kramer, P H; Krammer, Manfred; Kreuter, C; Kronkvist, I J; Krumshtein, Z; Krupinski, W; Kubinec, P; Kucewicz, W; Kurvinen, K L; Lacasta, C; Laktineh, I; Lamblot, S; Lamsa, J; Lanceri, L; Lane, D W; Langefeld, P; Lapin, V; Last, I; Laugier, J P; Lauhakangas, R; Leder, Gerhard; Ledroit, F; Lefébure, V; Legan, C K; Leitner, R; Lemoigne, Y; Lemonne, J; Lenzen, Georg; Lepeltier, V; Lesiak, T; Lindner, R; Lipniacka, A; Lippi, I; Lörstad, B; Loken, J G; López, J M; López-Aguera, M A; Loukas, D; Lutz, P; Lyons, L; MacNaughton, J N; Maehlum, G; Malychev, V; Mandl, F; Marco, J; Maréchal, B; Margoni, M; Marin, J C; Mariotti, C; Markou, A; Maron, T; Martínez-Rivero, C; Martínez-Vidal, F; Martí i García, S; Masik, J; Matorras, F; Matteuzzi, C; Matthiae, Giorgio; Mazzucato, M; McCubbin, M L; McKay, R; McNulty, R; Medbo, J; Meroni, C; Meyer, S; Meyer, W T; Michelotto, M; Migliore, E; Mirabito, L; Mitaroff, Winfried A; Mjörnmark, U; Moa, T; Møller, R; Mönig, K; Monge, M R; Morettini, P; Müller, H; Mundim, L M; Murray, W J; Muryn, B; Myatt, Gerald; Naraghi, F; Navarria, Francesco Luigi; Navas, S; Nawrocki, K; Negri, P; Neumann, W; Neumeister, N; Nicolaidou, R; Nielsen, B S; Nieuwenhuizen, M; Nikolaenko, V; Niss, P; Nomerotski, A; Normand, Ainsley; Oberschulte-Beckmann, W; Obraztsov, V F; Olshevskii, A G; Onofre, A; Orava, Risto; Österberg, K; Ouraou, A; Paganini, P; Paganoni, M; Pagès, P; Palka, H; Papadopoulou, T D; Papageorgiou, K; Pape, L; Parkes, C; Parodi, F; Passeri, A; Pegoraro, M; Peralta, L; Pernegger, H; Pernicka, Manfred; Perrotta, A; Petridou, C; Petrolini, A; Petrovykh, M; Phillips, H T; Piana, G; Pierre, F; Pimenta, M; Pindo, M; Plaszczynski, S; Podobrin, O; Pol, M E; Polok, G; Poropat, P; Pozdnyakov, V; Prest, M; Privitera, P; Pukhaeva, N; Pullia, Antonio; Radojicic, D; Ragazzi, S; Rahmani, H; Rames, J; Ratoff, P N; Read, A L; Reale, M; Rebecchi, P; Redaelli, N G; Regler, Meinhard; Reid, D; Renton, P B; Resvanis, L K; Richard, F; Richardson, J; Rídky, J; Rinaudo, G; Ripp, I; Romero, A; Roncagliolo, I; Ronchese, P; Roos, L; Rosenberg, E I; Rosso, E; Roudeau, Patrick; Rovelli, T; Rückstuhl, W; Ruhlmann-Kleider, V; Ruiz, A; Saarikko, H; Sacquin, Yu; Sadovskii, A; Sajot, G; Salt, J; Sánchez, J; Sannino, M; Schimmelpfennig, M; Schneider, H; Schwickerath, U; Schyns, M A E; Sciolla, G; Scuri, F; Seager, P; Sedykh, Yu; Segar, A M; Seitz, A; Sekulin, R L; Shellard, R C; Siccama, I; Siegrist, P; Simonetti, S; Simonetto, F; Sissakian, A N; Sitár, B; Skaali, T B; Smadja, G; Smirnov, N; Smirnova, O G; Smith, G R; Sosnowski, R; Souza-Santos, D; Spassoff, Tz; Spiriti, E; Sponholz, P; Squarcia, S; Stanescu, C; Stapnes, Steinar; Stavitski, I; Stichelbaut, F; Stocchi, A; Strauss, J; Strub, R; Stugu, B; Szczekowski, M; Szeptycka, M; Tabarelli de Fatis, T; Tavernet, J P; Chikilev, O G; Tilquin, A; Timmermans, J; Tkatchev, L G; Todorov, T; Toet, D Z; Tomaradze, A G; Tomé, B; Tonazzo, A; Tortora, L; Tranströmer, G; Treille, D; Trischuk, W; Tristram, G; Trombini, A; Troncon, C; Tsirou, A L; Turluer, M L; Tyapkin, I A; Tyndel, M; Tzamarias, S; Überschär, B; Ullaland, O; Uvarov, V; Valenti, G; Vallazza, E; Van der Velde, C; van Apeldoorn, G W; van Dam, P; Van Doninck, W K; Van Eldik, J; Vassilopoulos, N; Vegni, G; Ventura, L; Venus, W A; Verbeure, F; Verlato, M; Vertogradov, L S; Vilanova, D; Vincent, P; Vitale, L; Vlasov, E; Vodopyanov, A S; Vrba, V; Wahlen, H; Walck, C; Waldner, F; Weierstall, M; Weilhammer, Peter; Weiser, C; Wetherell, Alan M; Wicke, D; Wickens, J H; Wielers, M; Wilkinson, G R; Williams, W S C; Winter, M; Witek, M; Woschnagg, K; Yip, K; Yushchenko, O P; Zach, F; Zaitsev, A; Zalewska-Bak, A; Zalewski, Piotr; Zavrtanik, D; Zevgolatakos, E; Zimin, N I; Zito, M; Zontar, D; Zuberi, R; Zucchelli, G C; Zumerle, G; Charpentier, Ph; Gavillet, Ph; Jarlskog, Ch; Papadopoulou, Th D

1996-01-01

Three jet events arising from decays of the Z boson, collected by the DELPHI detector, were used to measure differences in quark and gluon fragmentation. Gluon jets were anti-tagged by identifying b quark jets. Unbiased quark jets came from events with two jets plus one photon. Quark and gluon jet properties in different energy ranges were compared for the first time within the same detector. Quark and gluon jets of nearly the same energy in symmetric three jet event topologies were also compared. Using three independent methods, the average value of the ratio of the mean charged multiplicities of gluon and quark jets is \\[ =1.241\\pm 0.015\\ (stat.) \\pm 0.025\\ (syst.). \\] Gluon jets are broader and produce fragments with a softer energy spectrum than quark jets of equivalent energy. The string effect has been observed in fully symmetric three jet events. The measured ratio R_{\\gamma} of the charged particle flow in the q\\overline{q} inter-jet region of the q\\bar{q}g and q\\bar{q}\\gamma samples agrees with the p...

Feynman rules of quantum chromodynamics inside a hadron

International Nuclear Information System (INIS)

Lee, T.D.

1979-01-01

We start from quantum chromodynamics in a finite volume of linear size L and examine its color-dielectric constant kappa/sub L/, especially the limit kappa/sub infinity/ as L → infinity. By choosing as our standard kappa/sub L/ = 1 when L = some hadron size R, we conclude that kappa/sub infinity/ must be -2 α where α is the fine-structure constant of QCD inside the hadron. A permanent quark confinement corresponds to the limit kappa/sub infinity/ = 0. The hadrons are viewed as small domain structures (with color-dielectric constant = 1) immersed in a perfect, or nearly perfect, color-dia-electric medium, which is the vacuum. The Feynman rules of QCD inside the hadron are derived; they are found to depend on the color-dielectric constant kappa/sub infinity/ of the vacuum that lies outside. We show that, when kappa/sub infinity/ → 0, the mass of any color-nonsinglet state becomes infinity, but for color-singlet states their masses and scattering amplitudes remain finite. These new Feynman rules also depend on the hadron size R. Only at high energy and large four-momentum transfer can such R dependence be neglected and, for color-singlet states, these new rules be reduced to the usual ones

Quark-Gluon Plasma

CERN Document Server

1990-01-01

This volume contains 14 review articles on the theory and phenomenology of the creation and diagnosis of quark-gluon plasma. They are written by active investigators of in the various research topics, which range from the QCD foundation through transport theory and thermalization models to the examination of possible signatures. The monograph should be useful not only to the experienced researchers in the subject but also to newcomers.

Effects of gluon radiation in hadronic collisions

International Nuclear Information System (INIS)

Gustafson, Goesta.

1989-10-01

In this talk I discuss effects of gluon emission in soft collisions, the so-called 'soft radiation' in the Fritjof model. It is seen e.g. that the pT in the fragmentation regions, the seagull effect, increases with energy in fair agreement with experiments. I also discuss the content of strange and heavier quarks in high-pT gluon jets. Within the dipole scheme for QCD cascades on finds a larger production of heavier quarks than in previous approaches. Qualitative agreement with data is obtained for the K/π ratio and D meson production

Non-perturbative power corrections to ghost and gluon propagators

International Nuclear Information System (INIS)

Boucaud, Philippe; Leroy, Jean-Pierre; Yaouanc, Alain Le; Lokhov, Alexey; Micheli, Jacques; Pene, Olivier; RodrIguez-Quintero, Jose; Roiesnel, Claude

2006-01-01

We study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ( ≅ 270MeV) of Λ M-barS-bar than the one obtained from the propagators separately( ≅ 320MeV). This argues in favour of significant non-perturbative ∼ 1/q 2 power corrections in the ghost and gluon propagators. We check the self-consistency of the method

Transverse momentum of gluons in ep-scattering at HERA

International Nuclear Information System (INIS)

Cholewa, A.

2005-11-01

A Monte Carlo analysis of the phase space of hard interacting gluons in ep-scattering is presented. The event generator CASCADE is used in combination with the program HZTOOL to identify the accessible regions of phase space of present HERA measurements. A map of the k t -x g -plane is presented to show that in the region -3≤log g ≤-1 transverse gluon momenta of up to k t >or sim 20 GeV are accessible to HERA measurements. Furthermore the observables x γ and the transverse jet energy E T are found to be highly sensitive to the transverse momentum and the longitudinal momentum fraction of gluons. (orig.) (orig.)

Neural network classification of quark and gluon jets

International Nuclear Information System (INIS)

Graham, M.A.; Jones, L.M.; Herbin, S.

1995-01-01

We demonstrate that there are characteristics common to quark jets and to gluon jets regardless of the interaction that produced them. The classification technique we use depends on the mass of the jet as well as the center-of-mass energy of the hard subprocess that produces the jet. In addition, we present the quark-gluon separability results of an artificial neural network trained on three-jet e + e - events at the Z 0 mass, using a back-propagation algorithm. The inputs to the network are the longitudinal momenta of the leading hadrons in the jet. We tested the network with quark and gluon jets from both e + e - →3 jets and bar pp→2 jets. Finally, we compare the performance of the artificial neural network with the results of making well chosen physical cuts

Gluon asymmetries in the leptoproduction of J/Ψ

International Nuclear Information System (INIS)

Godbole, R.M.; Gupta, S.; Sridhar, K.

1990-07-01

We study J/Ψ production, in deep inelastic scattering experiments with polarised beams and polarised targets. The spin asymmetries are seen to depend strongly on the particular form of the spin dependent gluon distributions used. Therefore, it should be possible in these experiments, to discriminate between different parametrizations of polarised gluon distributions, and hence between the distinctly different physical pictures of the proton spin underlying these parametrizations. (author). 18 refs, 4 figs, 1 tab

Transverse gluon contributions to the thermal static potential of heavy quarkonium

International Nuclear Information System (INIS)

Zhu, Jia-Qing; Li, Yun-De

2015-01-01

The transverse gluon contributions to the thermal static potentials of heavy quarkonia in isotropic medium are studied. Using the resummation of the damping rates method developed by Hou and Li, the infrared divergence that appeared in the effective potential calculations of transverse gluon is avoided. The comparisons between the transverse and the longitudinal contributions for heavy quarkonia are discussed. The results show that the dissociation scales of quarkonia in thermal medium are decreased by the transverse gluon contributions

Where and how the quark-gluon matter should be searched for?

International Nuclear Information System (INIS)

Strugalski, Z.

1997-01-01

The experimentally based answers are presented to the questions: 1) Where and how the quark-gluon matter should be searched for? 2) How to create objects of highly excited quark-gluon matter? 3) How to study the phase transitions in excited quark-gluon matter? In the argumentation, experimental information has been used about hadron passages through layers of intranuclear matter, about mechanisms of hadron-nucleus and nucleus-nucleus collisions, and about energy transfer from hadronic projectiles to target nuclei

GRACE with FORM

International Nuclear Information System (INIS)

Fujimoto, J.; Ishikawa, T.; Kato, K.; Kaneko, T.; Nakazawa, N..; Shimizu, Y.; Vermaseren, J.; Yasui, Y.

2006-01-01

A new version of GRACE/1-loop, a system for the automatic calculation of 1-loop Feynman diagrams, has been developed after the replacement of its symbolic manipulation engine from REDUCE to FORM. This enables us the efficient memory management that is essential for the handling of a tremendous number of Feynman diagrams, so that the performance of GRACE/1-loop is significantly improved as demonstrated in the text

Differences between quark and gluon jets as seen at LEP

International Nuclear Information System (INIS)

Tasevsky, M.

2001-01-01

The differences between quark and gluon jets are studied using LEP results on jet widths, scale dependent multiplicities, ratios of multiplicities, slopes and curvatures and fragmentation functions. It is emphasized that the observed differences stem primarily from the different quark and gluon colour factors

Accessing the distribution of linearly polarized gluons in unpolarized hadrons

NARCIS (Netherlands)

Boer, Daniël; Brodsky, Stanley J.; Mulders, Piet J.; Pisano, Cristian

2011-01-01

Gluons inside unpolarized hadrons can be linearly polarized provided they have a nonzero transverse momentum. The simplest and theoretically safest way to probe this distribution of linearly polarized gluons is through cos(2 phi) asymmetries in heavy quark pair or dijet production in electron-hadron

Differences between Quark and Gluon jets as seen at LEP

CERN Document Server

Tasevsky, Marek

2001-01-01

The differences between quark and gluon jets are studied using LEP results on jet widths, scale dependent multiplicities, ratios of multiplicities, slopes and curvatures and fragmentation functions. It is emphasized that the observed differences stem primarily from the different quark and gluon colour factors.

Introduction to quantum chromo transport theory for quark-gluon plasmas

International Nuclear Information System (INIS)

Gyulassy, M.; Elze, H.Th.; Iwazaki, A.; Vasak, D.

1986-08-01

Upcoming heavy ion experiments at the AGS and SPS are aimed at producing and diagnosing a primordial form of matter, the quark-gluon plasma. In these lectures some recent developments on formulating a quantum transport theory for quark-gluon plasmas are introduced. 46 refs

Quark-Gluon Plasma Signatures

CERN Document Server

Vogt, Ramona

1998-01-01

Aspects of quark-gluon plasma signatures that can be measured by CMS are discussed. First the initial conditions of the system from minijet production are introduced, including shadowing effects. Color screening of the Upsilon family is then presented, followed by energy loss effects on charm and bottom hadrons, high Pt jets and global observables.

Experimental properties of gluon and quark jets from a point source

CERN Document Server

Abbiendi, G.; Alexander, G.; Allison, John; Altekamp, N.; Anderson, K.J.; Anderson, S.; Arcelli, S.; Asai, S.; Ashby, S.F.; Axen, D.; Azuelos, G.; Ball, A.H.; Barberio, E.; Barlow, Roger J.; Batley, J.R.; Baumann, S.; Bechtluft, J.; Behnke, T.; Bell, Kenneth Watson; Bella, G.; Bellerive, A.; Bentvelsen, S.; Bethke, S.; Betts, S.; Biebel, O.; Biguzzi, A.; Blobel, V.; Bloodworth, I.J.; Bock, P.; Bohme, J.; Bonacorsi, D.; Boutemeur, M.; Braibant, S.; Bright-Thomas, P.; Brigliadori, L.; Brown, Robert M.; Burckhart, H.J.; Capiluppi, P.; Carnegie, R.K.; Carter, A.A.; Carter, J.R.; Chang, C.Y.; Charlton, David G.; Chrisman, D.; Ciocca, C.; Clarke, P.E.L.; Clay, E.; Cohen, I.; Conboy, J.E.; Cooke, O.C.; Couyoumtzelis, C.; Coxe, R.L.; Cuffiani, M.; Dado, S.; Dallavalle, G.Marco; Davis, R.; De Jong, S.; de Roeck, A.; Dervan, P.; Desch, K.; Dienes, B.; Dixit, M.S.; Dubbert, J.; Duchovni, E.; Duckeck, G.; Duerdoth, I.P.; Estabrooks, P.G.; Etzion, E.; Fabbri, F.; Fanfani, A.; Fanti, M.; Faust, A.A.; Fiedler, F.; Fierro, M.; Fleck, I.; Folman, R.; Frey, A.; Furtjes, A.; Futyan, D.I.; Gagnon, P.; Gary, J.W.; Gascon, J.; Gascon-Shotkin, S.M.; Gaycken, G.; Geich-Gimbel, C.; Giacomelli, G.; Giacomelli, P.; Gibson, V.; Gibson, W.R.; Gingrich, D.M.; Glenzinski, D.; Goldberg, J.; Gorn, W.; Grandi, C.; Graham, K.; Gross, E.; Grunhaus, J.; Gruwe, M.; Hanson, G.G.; Hansroul, M.; Hapke, M.; Harder, K.; Harel, A.; Hargrove, C.K.; Hauschild, M.; Hawkes, C.M.; Hawkings, R.; Hemingway, R.J.; Herndon, M.; Herten, G.; Heuer, R.D.; Hildreth, M.D.; Hill, J.C.; Hobson, P.R.; Hoch, M.; Hocker, James Andrew; Hoffman, Kara Dion; Homer, R.J.; Honma, A.K.; Horvath, D.; Hossain, K.R.; Howard, R.; Huntemeyer, P.; Igo-Kemenes, P.; Imrie, D.C.; Ishii, K.; Jacob, F.R.; Jawahery, A.; Jeremie, H.; Jimack, M.; Jones, C.R.; Jovanovic, P.; Junk, T.R.; Kanzaki, J.; Karlen, D.; Kartvelishvili, V.; Kawagoe, K.; Kawamoto, T.; Kayal, P.I.; Keeler, R.K.; Kellogg, R.G.; Kennedy, B.W.; Kim, D.H.; Klier, A.; Kobayashi, T.; Kobel, M.; Kokott, T.P.; Kolrep, M.; Komamiya, S.; Kowalewski, Robert V.; Kress, T.; Krieger, P.; von Krogh, J.; Kuhl, T.; Kyberd, P.; Lafferty, G.D.; Landsman, H.; Lanske, D.; Lauber, J.; Lautenschlager, S.R.; Lawson, I.; Layter, J.G.; Lee, A.M.; Lellouch, D.; Letts, J.; Levinson, L.; Liebisch, R.; List, B.; Littlewood, C.; Lloyd, A.W.; Lloyd, S.L.; Loebinger, F.K.; Long, G.D.; Losty, M.J.; Lu, J.; Ludwig, J.; Lui, D.; Macchiolo, A.; Macpherson, A.; Mader, W.; Mannelli, M.; Marcellini, S.; Markopoulos, C.; Martin, A.J.; Martin, J.P.; Martinez, G.; Mashimo, T.; Mattig, Peter; McDonald, W.John; McKenna, J.; Mckigney, E.A.; McMahon, T.J.; McPherson, R.A.; Meijers, F.; Menke, S.; Merritt, F.S.; Mes, H.; Meyer, J.; Michelini, A.; Mihara, S.; Mikenberg, G.; Miller, D.J.; Mir, R.; Mohr, W.; Montanari, A.; Mori, T.; Nagai, K.; Nakamura, I.; Neal, H.A.; Nisius, R.; O'Neale, S.W.; Oakham, F.G.; Odorici, F.; Ogren, H.O.; Oreglia, M.J.; Orito, S.; Palinkas, J.; Pasztor, G.; Pater, J.R.; Patrick, G.N.; Patt, J.; Perez-Ochoa, R.; Petzold, S.; Pfeifenschneider, P.; Pilcher, J.E.; Pinfold, J.; Plane, David E.; Poffenberger, P.; Poli, B.; Polok, J.; Przybycien, M.; Rembser, C.; Rick, H.; Robertson, S.; Robins, S.A.; Rodning, N.; Roney, J.M.; Rosati, S.; Roscoe, K.; Rossi, A.M.; Rozen, Y.; Runge, K.; Runolfsson, O.; Rust, D.R.; Sachs, K.; Saeki, T.; Sahr, O.; Sang, W.M.; Sarkisian, E.K.G.; Sbarra, C.; Schaile, A.D.; Schaile, O.; Scharff-Hansen, P.; Schieck, J.; Schmitt, S.; Schoning, A.; Schroder, Matthias; Schumacher, M.; Schwick, C.; Scott, W.G.; Seuster, R.; Shears, T.G.; Shen, B.C.; Shepherd-Themistocleous, C.H.; Sherwood, P.; Siroli, G.P.; Sittler, A.; Skuja, A.; Smith, A.M.; Snow, G.A.; Sobie, R.; Soldner-Rembold, S.; Spagnolo, S.; Sproston, M.; Stahl, A.; Stephens, K.; Steuerer, J.; Stoll, K.; Strom, David M.; Strohmer, R.; Surrow, B.; Talbot, S.D.; Taras, P.; Tarem, S.; Teuscher, R.; Thiergen, M.; Thomas, J.; Thomson, M.A.; Torrence, E.; Towers, S.; Trigger, I.; Trocsanyi, Z.; Tsur, E.; Turcot, A.S.; Turner-Watson, M.F.; Ueda, I.; Van Kooten, Rick J.; Vannerem, P.; Verzocchi, M.; Voss, H.; Wackerle, F.; Wagner, A.; Ward, C.P.; Ward, D.R.; Watkins, P.M.; Watson, A.T.; Watson, N.K.; Wells, P.S.; Wermes, N.; White, J.S.; Wilson, G.W.; Wilson, J.A.; Wyatt, T.R.; Yamashita, S.; Yekutieli, G.; Zacek, V.; Zer-Zion, D.

1999-01-01

Gluon jets are identified in hadronic Z0 decays as all the particles in a hemisphere opposite to a hemisphere containing two tagged quark jets. Gluon jets defined in this manner are equivalent to gluon jets produced from a color singlet point source and thus correspond to the definition employed for most theoretical calculations. In a separate stage of the analysis, we select quark jets in a manner to correspond to calculations, as the particles in hemispheres of flavor tagged light quark (uds) events. We present the distributions of rapidity, scaled energy, the logarithm of the momentum, and transverse momentum with respect to the jet axes, for charged particles in these gluon and quark jets. We also examine the charged particle multiplicity distributions of the jets in restricted intervals of rapidity. For soft particles at large transverse momentum, we observe the charged particle multiplicity ratio of gluon to quark jets to be 2.29 +- 0.09 +- 0.15 in agreement with the prediction that this ratio should ap...

Monte Carlo study on the properties of gluon and quark jets

CERN Document Server

Kun Shi Zhang; Mei Ling Yu; Lian Shou Liu

2002-01-01

The 3-jet events produced in e/sup +/e/sup -/ collisions at 91.2 GeV have been studied using Monte Carlo method. After applying two angular cuts the three angles between the jets are used to identify the individual jet in 3-jet events. The energy distributions of the three jets, the mean particle multiplicities, mean transverse momenta of the three jets in equal energy bins and their distributions have been analyzed. Comparing with the corresponding results from the quark jets in 2-jet events, a simple method to select gluon and quark jets from 3-jet events is obtained. The properties of the gluon and quark jets being selected using the introduced method are in qualitative agreement with the expectations of perturbative QCD. The ratio of the mean multiplicity between quark and gluon jets, /sub gluon///sub quark/, has been calculated. The results, again, agree with the experimental results from SLD, OPAL, ALEPH, and DELPHI Collaborations, indicating that the method proposed to select gluon and quark jets from ...

Rapidity evolution of gluon TMD from low to moderate x

International Nuclear Information System (INIS)

Balitsky, I.

2016-01-01

I discuss how the rapidity evolution of gluon transverse momentum dependent distribution (TMD) changes from nonlinear evolution at small x << 1 to linear evolution at moderate x ∼ 1. I have described the rapidity evolution of gluon TMD in the whole range of Bjorken x B and the whole range of transverse momentum. It should be emphasized that with our definition of rapidity cutoff the leading-order matrix elements of TMD operators are UV-finite so the rapidity evolution is the only evolution and it describes all the dynamics of gluon TMDs in the leading-log approximation

Multiplicity distributions of gluon and quark jets and tests of QCD analytic predictions

CERN Document Server

Ackerstaff, K; Allison, J; Altekamp, N; Anderson, K J; Anderson, S; Arcelli, S; Asai, S; Axen, D A; Azuelos, Georges; Ball, A H; Barberio, E; Barlow, R J; Bartoldus, R; Batley, J Richard; Baumann, S; Bechtluft, J; Beeston, C; Behnke, T; Bell, A N; Bell, K W; Bella, G; Bentvelsen, Stanislaus Cornelius Maria; Bethke, Siegfried; Biebel, O; Biguzzi, A; Bird, S D; Blobel, Volker; Bloodworth, Ian J; Bloomer, J E; Bobinski, M; Bock, P; Bonacorsi, D; Boutemeur, M; Bouwens, B T; Braibant, S; Brigliadori, L; Brown, R M; Burckhart, Helfried J; Burgard, C; Bürgin, R; Capiluppi, P; Carnegie, R K; Carter, A A; Carter, J R; Chang, C Y; Charlton, D G; Chrisman, D; Clarke, P E L; Cohen, I; Conboy, J E; Cooke, O C; Cuffiani, M; Dado, S; Dallapiccola, C; Dallavalle, G M; Davis, R; De Jong, S; del Pozo, L A; Desch, Klaus; Dienes, B; Dixit, M S; do Couto e Silva, E; Doucet, M; Duchovni, E; Duckeck, G; Duerdoth, I P; Eatough, D; Edwards, J E G; Estabrooks, P G; Evans, H G; Evans, M; Fabbri, Franco Luigi; Fanti, M; Faust, A A; Fiedler, F; Fierro, M; Fischer, H M; Fleck, I; Folman, R; Fong, D G; Foucher, M; Fürtjes, A; Futyan, D I; Gagnon, P; Gary, J W; Gascon, J; Gascon-Shotkin, S M; Geddes, N I; Geich-Gimbel, C; Geralis, T; Giacomelli, G; Giacomelli, P; Giacomelli, R; Gibson, V; Gibson, W R; Gingrich, D M; Glenzinski, D A; Goldberg, J; Goodrick, M J; Gorn, W; Grandi, C; Gross, E; Grunhaus, Jacob; Gruwé, M; Hajdu, C; Hanson, G G; Hansroul, M; Hapke, M; Hargrove, C K; Hart, P A; Hartmann, C; Hauschild, M; Hawkes, C M; Hawkings, R; Hemingway, Richard J; Herndon, M; Herten, G; Heuer, R D; Hildreth, M D; Hill, J C; Hillier, S J; Hobson, P R; Homer, R James; Honma, A K; Horváth, D; Hossain, K R; Howard, R; Hüntemeyer, P; Hutchcroft, D E; Igo-Kemenes, P; Imrie, D C; Ingram, M R; Ishii, K; Jawahery, A; Jeffreys, P W; Jeremie, H; Jimack, Martin Paul; Joly, A; Jones, C R; Jones, G; Jones, M; Jost, U; Jovanovic, P; Junk, T R; Karlen, D A; Kartvelishvili, V G; Kawagoe, K; Kawamoto, T; Kayal, P I; Keeler, Richard K; Kellogg, R G; Kennedy, B W; Kirk, J; Klier, A; Kluth, S; Kobayashi, T; Kobel, M; Koetke, D S; Kokott, T P; Kolrep, M; Komamiya, S; Kress, T; Krieger, P; Von Krogh, J; Kyberd, P; Lafferty, G D; Lahmann, R; Lai, W P; Lanske, D; Lauber, J; Lautenschlager, S R; Layter, J G; Lazic, D; Lee, A M; Lefebvre, E; Lellouch, Daniel; Letts, J; Levinson, L; Lloyd, S L; Loebinger, F K; Long, G D; Losty, Michael J; Ludwig, J; Macchiolo, A; MacPherson, A L; Mannelli, M; Marcellini, S; Markus, C; Martin, A J; Martin, J P; Martínez, G; Mashimo, T; Mättig, P; McDonald, W J; McKenna, J A; McKigney, E A; McMahon, T J; McPherson, R A; Meijers, F; Menke, S; Merritt, F S; Mes, H; Meyer, J; Michelini, Aldo; Mikenberg, G; Miller, D J; Mincer, A; Mir, R; Mohr, W; Montanari, A; Mori, T; Morii, M; Müller, U; Mihara, S; Nagai, K; Nakamura, I; Neal, H A; Nellen, B; Nisius, R; O'Neale, S W; Oakham, F G; Odorici, F; Ögren, H O; Oh, A; Oldershaw, N J; Oreglia, M J; Orito, S; Pálinkás, J; Pásztor, G; Pater, J R; Patrick, G N; Patt, J; Pearce, M J; Pérez-Ochoa, R; Petzold, S; Pfeifenschneider, P; Pilcher, J E; Pinfold, J L; Plane, D E; Poffenberger, P R; Poli, B; Posthaus, A; Rees, D L; Rigby, D; Robertson, S; Robins, S A; Rodning, N L; Roney, J M; Rooke, A M; Ros, E; Rossi, A M; Routenburg, P; Rozen, Y; Runge, K; Runólfsson, O; Ruppel, U; Rust, D R; Rylko, R; Sachs, K; Saeki, T; Sarkisyan-Grinbaum, E; Sbarra, C; Schaile, A D; Schaile, O; Scharf, F; Scharff-Hansen, P; Schenk, P; Schieck, J; Schleper, P; Schmitt, B; Schmitt, S; Schöning, A; Schröder, M; Schultz-Coulon, H C; Schumacher, M; Schwick, C; Scott, W G; Shears, T G; Shen, B C; Shepherd-Themistocleous, C H; Sherwood, P; Siroli, G P; Sittler, A; Skillman, A; Skuja, A; Smith, A M; Snow, G A; Sobie, Randall J; Söldner-Rembold, S; Springer, R W; Sproston, M; Stephens, K; Steuerer, J; Stockhausen, B; Stoll, K; Strom, D; Szymanski, P; Tafirout, R; Talbot, S D; Tanaka, S; Taras, P; Tarem, S; Teuscher, R; Thiergen, M; Thomson, M A; Von Törne, E; Towers, S; Trigger, I; Trócsányi, Z L; Tsur, E; Turcot, A S; Turner-Watson, M F; Utzat, P; Van Kooten, R; Verzocchi, M; Vikas, P; Vokurka, E H; Voss, H; Wäckerle, F; Wagner, A; Ward, C P; Ward, D R; Watkins, P M; Watson, A T; Watson, N K; Wells, P S; Wermes, N; White, J S; Wilkens, B; Wilson, G W; Wilson, J A; Wolf, G; Wyatt, T R; Yamashita, S; Yekutieli, G; Zacek, V; Zer-Zion, D

1999-01-01

Gluon jets are identified in e+e- hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon jets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The charged particle multiplicity distribution of the gluon jets is presented, and is analyzed for its mean, dispersion, skew, and curtosis values, and for its factorial and cumulant moments. The results are compared to the analogous results found for a sample of light quark (uds) jets, also defined inclusively. We observe differences between the mean, skew and curtosis values of gluon and quark jets, but not between their dispersions. The cumulant moment results are compared to the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observe...

A power counting theorem for Feynman integrals on the lattice

International Nuclear Information System (INIS)

Reisz, T.

1988-01-01

A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)

The PLUTO experiment at DORIS (DESY) and the discovery of the gluon (A recollection)

Energy Technology Data Exchange (ETDEWEB)

Stella, Bruno R. [Rome-3 Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Rome (Italy); Meyer, Hans-Juergen

2010-08-15

With the aim of determining the contribution of the PLUTO experiment at the DORIS e{sup +}e{sup -} storage ring to the discovery of the gluon, as members of this former collaboration we have reconsidered all the scientific material produced by PLUTO in 1978 and the first half of 1979. It is clear that the experiment demonstrated the main decay of the Y(9.46 GeV) resonance to be mediated by 3 gluons, by providing evidence for the agreement of this hypothesis with average values and differential distributions of all possible experimental variables and by excluding all other possible alternative models. Moreover PLUTO measured in June 1979 the matrix element of the 3-gluon decay to be quantitatively as expected by QCD (even after hadronization) and, having checked the possibility to correctly trace the gluons' directions, demonstrated the spin 1 nature of the gluon by excluding spin 0 and spin 1/2. The hadronization of the gluon like a quark jet, hypothesized in the 3-gluon jet Monte Carlo simulation, was compatible with the topological data at this energy and was shown to be an approximation at 10% level for the multiplicity ({approx} < p {sub vertical} {sub stroke} {sub vertical} {sub stroke} {sub >}{sup -1}); the right expected gluon fragmentation was needed for the inclusive distributions; this was the first experimental study of (identified) gluon jets. In the following measurements at the PETRA storage ring, these results were confirmed by PLUTO and by three contemporaneous experiments by evidencing at higher energies the gluon radiation (''bremsstrahlung''), the softer one, by jet broadening, and the hard one, by the emission of (now clearly visible) gluon jets by quarks. The gluon's spin 1 particle nature was also confirmed. The PLUTO results on Y decays had been confirmed both by contemporaneous experiments at DORIS (partially) and later (also partially) were confirmed by more sophisticated detectors. (orig.)

Flavour equilibration studies of quark-gluon plasma with non-zero ...

Indian Academy of Sciences (India)

Abstract. Flavour equilibration for a thermally equilibrated but chemically non- equilibrated quark-gluon plasma is presented. Flavour equilibration is studied enforcing baryon number conservation. In addition to the usual processes like single additional gluon production gg ⇌ ggg and its reverse and quark–antiquark pair ...

Quark and gluon tagging in dijet mass resonance search

CERN Document Server

Kellermann, Edgar

2013-01-01

Several models beyond the Standard Model predict new phenomena in particle physics, which would appear as resonant signals in dijet mass distributions. An example for such a resonance is the excited quark q, which is a consequence of Compositeness Models postulating that quarks and leptons are build by more fundamental particles. The main signature of an excited quark would be a dijet event, originated from the radiation of a gluon from the original excited quark when going back to its non-excited state, leading to a quark and a gluon in the final state (with a branching ratio of 83%) . Other examples are the heavy vector bosonsW0 decaying to two quarks and colour octet scalar S8 decaying to two gluons.

Analysis of the proton longitudinal structure function from the gluon distribution function

International Nuclear Information System (INIS)

Boroun, G.R.; Rezaei, B.

2012-01-01

We make a critical, next-to-leading order, study of the relationship between the longitudinal structure function F L and the gluon distribution proposed in Cooper-Sarkar et al. (Z. Phys. C 39:281, 1988; Acta Phys. Pol. B 34:2911 2003), which is frequently used to extract the gluon distribution from the proton longitudinal structure function at small x. The gluon density is obtained by expanding at particular choices of the point of expansion and compared with the hard Pomeron behavior for the gluon density. Comparisons with H1 data are made and predictions for the proposed best approach are also provided. (orig.)

Dilepton production from quark gluon plasma using non-equilibrium thermodynamics

International Nuclear Information System (INIS)

Sinha, B.

1984-01-01

The importance of the approach phase to the thermodynamic equilibrium has been investigated for dilepton production from quark-gluon plasma - an effective temperature for the quarks as Brounian particle in a heat bath of gluons has been suggested. The spectrum for low invariant mass is, as a consequence, sharper

Gluon condensate from lattice caculations: SU(3) pure gauge theory

International Nuclear Information System (INIS)

Kripfganz, J.

1981-01-01

A short distance expansion of Wilson loops is used to define and isolate vacuum expectation values of composite gluon operators. It is applied to available lattice Monte Carlo data for SU(3) pure gauge theory. The value obtained for the gluon condensate is consistent with the ITEP estimate. (author)

Dynamics of high momentum transfer processes

International Nuclear Information System (INIS)

Efremov, A.V.

1977-01-01

The high momentum transfer processes are considered in terms of field theory of quarks interacting through scalar or pseudoscalar gluons. This approach is based on an algorithm involving the consideration of the Feynman diagram asymptotical behaviour and its summation. The Parton model and quark counting power are an approximation of not too high momentum transfer when anti g 2 (q 2 )ln(-q 2 /Λ) 2 -invariant charge, Λ-boundary parameter. The violation of scaling beyond this region depends on the character of charge renormalization and is of the same kind as in the Wilson expansion approach. Scaling in this region is suppressed by anti g 4 factor for high psub(UPSILON) hadroproduction and wide angle elastic scattering, and by anti g 2 factor for inclusive lepton production and wide angle electro- and photoproduction. Parameter Λ is controlled by hadron masses and can be essential for not too high psub(UPSILON)

Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators

International Nuclear Information System (INIS)

Jefferies, Brian; Johnson, Gerald W.; Nielsen, Lance

2007-01-01

The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A 1 ,..., A n and associated continuous Borel probability measures μ 1 , ?, μ n on [0,1]. Fix A 1 ,..., A n . Then each choice of an n-tuple (μ 1 ,...,μ n ) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A 1 , ..., A n are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi

Multiplicity distributions of gluon and quark jets and tests of QCD analytic predictions

Science.gov (United States)

OPAL Collaboration; Ackerstaff, K.; et al.

Gluon jets are identified in e+e^- hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon jets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The charged particle multiplicity distribution of the gluon jets is presented, and is analyzed for its mean, dispersion, skew, and curtosis values, and for its factorial and cumulant moments. The results are compared to the analogous results found for a sample of light quark (uds) jets, also defined inclusively. We observe differences between the mean, skew and curtosis values of gluon and quark jets, but not between their dispersions. The cumulant moment results are compared to the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observed to provide a much improved description of the data compared to a next-to-leading order calculation without energy conservation. There is agreement between the data and calculations for the ratios of the cumulant moments between gluon and quark jets.

The hard gluon component of the QCD Pomeron

International Nuclear Information System (INIS)

White, A.R.

1996-01-01

The authors argue that deep-inelastic diffractive scaling provides fundamental insight into the QCD Pomeron. The logarithmic scaling violations seen experimentally are in conflict with the scale-invariance of the BFKL Pomeron and with phenomenological two-gluon models. Instead the Pomeron appears as a single gluon at short-distances, indicating the appearance of a Super-Critical phase of Reggeon Field Theory. That the color compensation takes place at a longer distance is consistent with the Pomeron carrying odd color charge parity

Nielsen's identity and gluon condensation at finite temperature

International Nuclear Information System (INIS)

Skalozub, V.V.

1992-11-01

The gauge dependence problem of the gluon field zero component condensate, A 0 =const, is investigated in finite temperature SU(3) gluodynamics. The two-loop effective action W(A 0 ,ξ) is recalculated in the background R ξ gauge. The obtained result somewhat differs from that of other authors. By straightforward calculation it is shown that W(A 0 ,ξ) satisfies the Nielsen (the Ward type) identity. Thus, the gauge invariance of the gluon condensation phenomenon is proved. (author). 14 refs

Probing sea quarks and gluons: the electron-ion collider project

International Nuclear Information System (INIS)

Horn, T.

2014-01-01

A future Electron-Ion Collider (EIC) would be the world's first polarized electron-proton collider, and the world's first e-A collider, and would seek the QCD foundation of nucleons and nuclei in terms of the sea quarks and gluons, matching to these valence quark studies. The EIC will provide a versatile range of kinematics and beam polarization, as well as beam species, to allow for mapping the spin and spatial structure of the quark sea and gluons, to discover the collective effects of gluons in atomic nuclei, and to understand the emergence of hadronic matter from color charge. (authors)

Algorithmic implementation of particle-particle ladder diagram approximation to study strongly-correlated metals and semiconductors

Science.gov (United States)

Prayogi, A.; Majidi, M. A.

2017-07-01

In condensed-matter physics, strongly-correlated systems refer to materials that exhibit variety of fascinating properties and ordered phases, depending on temperature, doping, and other factors. Such unique properties most notably arise due to strong electron-electron interactions, and in some cases due to interactions involving other quasiparticles as well. Electronic correlation effects are non-trivial that one may need a sufficiently accurate approximation technique with quite heavy computation, such as Quantum Monte-Carlo, in order to capture particular material properties arising from such effects. Meanwhile, less accurate techniques may come with lower numerical cost, but the ability to capture particular properties may highly depend on the choice of approximation. Among the many-body techniques derivable from Feynman diagrams, we aim to formulate algorithmic implementation of the Ladder Diagram approximation to capture the effects of electron-electron interactions. We wish to investigate how these correlation effects influence the temperature-dependent properties of strongly-correlated metals and semiconductors. As we are interested to study the temperature-dependent properties of the system, the Ladder diagram method needs to be applied in Matsubara frequency domain to obtain the self-consistent self-energy. However, at the end we would also need to compute the dynamical properties like density of states (DOS) and optical conductivity that are defined in the real frequency domain. For this purpose, we need to perform the analytic continuation procedure. At the end of this study, we will test the technique by observing the occurrence of metal-insulator transition in strongly-correlated metals, and renormalization of the band gap in strongly-correlated semiconductors.

T -matrix approach to quark-gluon plasma

Science.gov (United States)

Liu, Shuai Y. F.; Rapp, Ralf

2018-03-01

A self-consistent thermodynamic T -matrix approach is deployed to study the microscopic properties of the quark-gluon plasma (QGP), encompassing both light- and heavy-parton degrees of freedom in a unified framework. The starting point is a relativistic effective Hamiltonian with a universal color force. The input in-medium potential is quantitatively constrained by computing the heavy-quark (HQ) free energy from the static T -matrix and fitting it to pertinent lattice-QCD (lQCD) data. The corresponding T -matrix is then applied to compute the equation of state (EoS) of the QGP in a two-particle irreducible formalism, including the full off-shell properties of the selfconsistent single-parton spectral functions and their two-body interaction. In particular, the skeleton diagram functional is fully resummed to account for emerging bound and scattering states as the critical temperature is approached from above. We find that the solution satisfying three sets of lQCD data (EoS, HQ free energy, and quarkonium correlator ratios) is not unique. As limiting cases we discuss a weakly coupled solution, which features color potentials close to the free energy, relatively sharp quasiparticle spectral functions and weak hadronic resonances near Tc, and a strongly coupled solution with a strong color potential (much larger than the free energy), resulting in broad nonquasiparticle parton spectral functions and strong hadronic resonance states which dominate the EoS when approaching Tc.

The Feynman integrand as a white noise distribution beyond perturbation theory

International Nuclear Information System (INIS)

Grothaus, Martin; Vogel, Anna

2008-01-01

In this note the concepts of path integrals and techniques how to construct them are presented. Here we concentrate on a White Noise approach. Combining White Noise techniques with a generalized time-dependent Doss' formula Feynman integrands are constructed as white noise distributions beyond perturbation theory

Fragmentation of quarks and gluons

International Nuclear Information System (INIS)

Soeding, P.

1983-10-01

The author presents a review about quark and gluon jets. He describes the particle contents of the different types of jets. Finally he considers the hadronization mechanism with special regards to three-jet events in e + e - annihilation and hadronization in nuclear matter. (HSI)

Quark versus Gluon Jet Tagging Using Jet Images with the ATLAS Detector

CERN Document Server

The ATLAS collaboration

2017-01-01

Distinguishing quark-initiated from gluon-initiated jets is useful for many measurements and searches at the LHC. This note presents a jet tagger for distinguishing quark-initiated from gluon-initiated jets, which uses the full radiation pattern inside a jet processed as an image in a deep neural network classifier. The study is conducted using simulated dijet events in $\\sqrt{s}$=13 TeV pp collisions with the ATLAS detector. Across a wide range of quark jet identification efficiencies, the neural network tagger achieves a gluon jet rejection that is comparable to or better than the performance of the jet width and track multiplicity observables conventionally used for quark-versus-gluon jet tagging.

Foundations for relativistic quantum theory. I. Feynman's operator calculus and the Dyson conjectures

International Nuclear Information System (INIS)

Gill, Tepper L.; Zachary, W.W.

2002-01-01

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman's path integral, and to prove Dyson's first conjecture that the divergences are in part due to a violation of Heisenberg's uncertainly relations

Bogoliubov condensation of gluons and spontaneous gauge symmetry breaking in QCD

International Nuclear Information System (INIS)

Pervushin, V.N.; Roepke, G.; Volkov, M.K.; Blaschke, D.; Pavel, H.P.; Litvin, A.

1995-08-01

The ''squeezed'' representation of commutation relations for gluon fields in QCD is formulated as the mathematical tool for the description of the gluon condensate. We first consider λφ 4 theory and show that the ''squeezed'' Bogoliubov condensate can lead to the spontaneous appearance of a mass. Using the ''squeezed'' representation, we show that in the non-Abelian theory spontaneous gauge symmetry breaking (SGSB) and the appearance of a constituent mass of gluons can be described. We construct a projector onto the oscillator - like variables, for which the ''squeezed'' representation is valid, by using the formal solution of the Gauss equation instead of fixing a gauge. We discuss the effects of the SGSB and present as an application of the approach the calculation of the gluon mass from the difference of the η' and the η - meson masses. (author). 27 refs

Quark-gluon plasma 2

CERN Document Server

1995-01-01

This is a sequel to the review volume Quark-Gluon Plasma. There are 13 articles contributed by leading investigators in the field, covering a wide range of topics about the theoretical approach to the subject. These contributions are timely reviews of nearly all the actively pursued problems, written in a pedagogical style suitable for beginners as well as experienced researchers.

Theory of Feynman-alpha technique with masking window for accelerator-driven systems

International Nuclear Information System (INIS)

Kitamura, Yasunori; Misawa, Tsuyoshi

2017-01-01

Highlights: • A theory of the modified Feynman-alpha technique for the ADS was developed. • The experimental conditions under which this technique works were discussed. • It is expected this technique is applied to the subcriticality monitor for the ADS. - Abstract: Recently, a modified Feynman-alpha technique for the subcritical system driven by periodically triggered neutron bursts was developed. One of the main features of this technique is utilization of a simple formula that is advantageous in evaluating the subcriticality. However, owing to the absence of the theory of this technique, this feature has not been fully investigated yet. In the present study, a theory of this technique is provided. Furthermore, the experimental conditions under which the simple formula works are discussed to apply this technique to the subcriticality monitor for the accelerator-driven system.

Muoproduction of J/ψ and the gluon distribution of the nucleon

International Nuclear Information System (INIS)

Ashman, J.; Combley, F.; Salmon, D.; Wheeler, S.; Bee, C.P.; Brown, S.C.; Court, G.; Francis, D.; Gabathuler, E.; Gamet, R.; Hayman, P.; Holt, J.R.; Jones, T.; Matthews, M.; Wimpenny, S.J.; Coignet, G.; Toth, J.; Urban, L.; Drees, J.; Edwards, A.W.; Hamacher, K.; Korzen, B.; Kruener, U.; Moenig, K.; Pavel, N.; Peschel, H.; Nassalski, J.; Sandacz, A.; Windmolders, R.; Ernst, T.; Landgraf, U.; Schroeder, T.; Stier, H.E.; Stock, J.; Wallucks, W.

1992-01-01

Measurements are presented of the inclusive distributions of the J/ψ meson produced by muons of energy 200 GeV from an ammonia target. The gluon distribution of the nucleon has been derived from the data in the range 0.04< x<0.36 using a technique based on the colour singlet model. An arbitrary normalisation factor is required to obtain a reasonable integral of the gluon distribution. Some comments are made on the use of J/ψ production by virtual photons to extract the gluon distribution at HERA. (orig.)

Low-energy behavior of gluons and gravitons from gauge invariance

DEFF Research Database (Denmark)

di Vecchia, Paolo; Bern, Zvi; Davies, Scott

2014-01-01

We show that at tree level, on-shell gauge invariance can be used to fully determine the first subleading soft-gluon behavior and the first two subleading soft-graviton behaviors. Our proofs of the behaviors for n-gluon and n-graviton tree amplitudes are valid in D dimensions and are similar to Low...

QED the strange theory of light and matter

CERN Document Server

Feynman, Richard Phillips

2006-01-01

Celebrated for his brilliantly quirky insights into the physical world, Nobel laureate Richard Feynman also possessed an extraordinary talent for explaining difficult concepts to the general public. Here Feynman provides a classic and definitive introduction to QED (namely quantum electrodynamics), that part of quantum field theory describing the interactions of light with charged particles. Using everyday language, spatial concepts, visualizations, and his renowned ""Feynman diagrams"" instead of advanced mathematics, Feynman clearly and humorously communicates both the substance and spiri

Two-gluon emission and interference in a thin QCD medium: insights into jet formation

International Nuclear Information System (INIS)

Casalderrey-Solana, Jorge; Pablos, Daniel; Tywoniuk, Konrad

2016-01-01

In heavy-ion collisions, an abundant production of high-energy QCD jets allows to study how these multiparticle sprays are modified as they pass through the quark-gluon plasma. In order to shed new light on this process, we compute the inclusive two-gluon rate off a hard quark propagating through a color deconfined medium at first order in medium opacity. We explicitly impose an energy ordering of the two emitted gluons, such that the “hard” gluon can be thought of as belonging to the jet substructure while the other is a “soft” emission (which can be collinear or medium-induced). Our analysis focusses on two specific limits that clarify the modification of the additional angle- and formation time-ordering of splittings. In one limit, the formation time of the “hard” gluon is short compared to the “soft” gluon formation time, leading to a probabilistic formula for production of and subsequent radiation off a quark-gluon antenna. In the other limit, the ordering of formation is reverted, which automatically leads to the fact that the jet substructure is resolved by the medium. We observe in this case a characteristic delay: the jet radiates as one color current (quark) up to the formation of the “hard” gluon, at which point we observe the onset of radiation of the new color current (gluon). Within our kinematic constraints, our computation supports a picture in which the in-medium jet dynamics are described as a collection of subsequent antennas which are resolved by the medium according to their transverse extent.

Self-consistent one-gluon exchange in soliton bag models

International Nuclear Information System (INIS)

Dodd, L.R.; Adelaide Univ.; Williams, A.G.

1988-01-01

The treatment of soliton bag models as two-point boundary value problems is extended to include self-consistent one-gluon exchange interactions. The colour-magnetic contribution to the nucleon-delta mass splitting is calculated self-consistently in the mean-field, one-gluon-exchange approximation for the Friedberg-Lee and Nielsen-Patkos models. Small glueball mass parameters (m GB ∝ 500 MeV) are favoured. Comparisons with previous calculations are made. (orig.)

Phenomenological Evidence for Gluon Depletion in pA Collisions

OpenAIRE

Hwa, R. C.; Pisut, J.; Pisutova, N.

2000-01-01

The data of J/psi suppression at large x_F in pA collisions are used to infer the existence of gluon depletion as the projectile proton traverses the nucleus. The modification of the gluon distribution is studied by use of a convolution equation whose non-perturbative splitting function is determined phenomenologically. The depletion factor at x_1=0.8 is found to be about 25% at A=100.

Quark Loop Effects on Dressed Gluon Propagator in Framework of Global Color Symmetry Model

Institute of Scientific and Technical Information of China (English)

ZONG Hong-Shi; SUN Wei-Min

2006-01-01

Based on the global color symmetry model (GCM), a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one should use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.

Multiplicity distributions of gluon and quark jets and a test of QCD analytic calculations

International Nuclear Information System (INIS)

Gary, J. William

1999-01-01

Gluon jets are identified in e + e - hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon jets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The mean and first few higher moments of the gluon jet charged particle multiplicity distribution are compared to the analogous results found for light quark (uds) jets, also defined inclusively. Large differences are observed between the mean, skew and curtosis values of the gluon and quark jets, but not between their dispersions. The cumulant factorial moments of the distributions are also measured, and are used to test the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observed to provide a much improved description of the separated gluon and quark jet cumulant moments compared to a next-to-leading order calculation without energy conservation. There is good quantitative agreement between the data and calculations for the ratios of the cumulant moments between gluon and quark jets. The data sample used is the LEP-1 sample of the OPAL experiment at LEP

Multiplicity distributions of gluon and quark jets and a test of QCD analytic calculations

Energy Technology Data Exchange (ETDEWEB)

Gary, J. William

1999-03-01

Gluon jets are identified in e{sup +}e{sup -} hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon jets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The mean and first few higher moments of the gluon jet charged particle multiplicity distribution are compared to the analogous results found for light quark (uds) jets, also defined inclusively. Large differences are observed between the mean, skew and curtosis values of the gluon and quark jets, but not between their dispersions. The cumulant factorial moments of the distributions are also measured, and are used to test the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observed to provide a much improved description of the separated gluon and quark jet cumulant moments compared to a next-to-leading order calculation without energy conservation. There is good quantitative agreement between the data and calculations for the ratios of the cumulant moments between gluon and quark jets. The data sample used is the LEP-1 sample of the OPAL experiment at LEP.

Multiplicity distributions of gluon and quark jets and a test of QCD analytic calculations

Energy Technology Data Exchange (ETDEWEB)

Gary, J.W. [California Univ., Riverside, CA (United States). Dept. of Physics

1999-03-01

Gluon jets are identified in e{sup +}e{sup -} hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon jets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The mean and first few higher moments of the gluon jet charged particle multiplicity distribution are compared to the analogous results found for light quark (uds) jets, also defined inclusively. Large differences are observed between the mean, skew and curtosis values of the gluon and quark jets, but not between their dispersions. The cumulant factorial moments of the distributions are also measured, and are used to test the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observed to provide a much improved description of the separated gluon and quark jet cumulant moments compared to a next-to-leading order calculation without energy conservation. There is good quantitative agreement between the data and calculations for the ratios of the cumulant moments between gluon and quark jets. The data sample used is the LEP-1 sample of the OPAL experiment at LEP. (orig.) 6 refs.

Multiplicity distributions of gluon and quark jets and a test of QCD analytic calculations

International Nuclear Information System (INIS)

Gary, J.W.

1999-01-01

Gluon jets are identified in e + e - hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon jets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The mean and first few higher moments of the gluon jet charged particle multiplicity distribution are compared to the analogous results found for light quark (uds) jets, also defined inclusively. Large differences are observed between the mean, skew and curtosis values of the gluon and quark jets, but not between their dispersions. The cumulant factorial moments of the distributions are also measured, and are used to test the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observed to provide a much improved description of the separated gluon and quark jet cumulant moments compared to a next-to-leading order calculation without energy conservation. There is good quantitative agreement between the data and calculations for the ratios of the cumulant moments between gluon and quark jets. The data sample used is the LEP-1 sample of the OPAL experiment at LEP. (orig.)

Multiplicity distributions of gluon and quark jets and a test of QCD analytic calculations

Science.gov (United States)

Gary, J. William

1999-03-01

Gluon jets are identified in e +e - hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon hets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The mean and first few higher moments of the gluon jet charged particle multiplicity distribution are compared to the analogous results found for light quark (uds) jets, also defined inclusively. Large differences are observed between the mean, skew and curtosis values of the gluon and quark jets, but not between their dispersions. The cumulant factorial moments of the distributions are also measured, and are used to test the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observed to provide a much improved description of the separated gluon and quark jet cumulant moments compared to a next-to-leading order calculation without energy conservation. There is good quantitative agreement between the data and calculations for the ratios of the cumulant moments between gluon and quark jets. The data sample used is the LEP-1 sample of the OPAL experiment at LEP.

Feynman's thesis: A new approach to quantum theory

International Nuclear Information System (INIS)

Das, Ashok

2007-01-01

It is not usual for someone to write a book on someone else's Ph.D. thesis, but then Feynman was not a usual physicist. He was without doubt one of the most original physicists of the twentieth century, who has strongly influenced the developments in quantum field theory through his many ingenious contributions. Path integral approach to quantum theories is one such contribution which pervades almost all areas of physics. What is astonishing is that he developed this idea as a graduate student for his Ph.D. thesis which has been printed, for the first time, in the present book along with two other related articles. The early developments in quantum theory, by Heisenberg and Schroedinger, were based on the Hamiltonian formulation, where one starts with the Hamiltonian description of a classical system and then promotes the classical observables to noncommuting quantum operators. However, Dirac had already stressed in an article in 1932 (this article is also reproduced in the present book) that the Lagrangian is more fundamental than the Hamiltonian, at least from the point of view of relativistic invariance and he wondered how the Lagrangian may enter into the quantum description. He had developed this idea through his 'transformation matrix' theory and had even hinted on how the action of the classical theory may enter such a description. However, although the brief paper by Dirac contained the basic essential ideas, it did not fully develop the idea of a Lagrangian description in detail in the functional language. Feynman, on the other hand, was interested in the electromagnetic interactions of the electron from a completely different point of view rooted in a theory involving action-at-a-distance. His theory (along with John Wheeler) did not have a Hamiltonian description and, in order to quantize such a theory, he needed an alternative formulation of quantum mechanics. When the article by Dirac was brought to his attention, he immediately realized what he was

Bose–Einstein condensation and thermalization of the quark–gluon plasma

International Nuclear Information System (INIS)

Blaizot, Jean-Paul; Gelis, François; Liao, Jinfeng; McLerran, Larry; Venugopalan, Raju

2012-01-01

In ultra-relativistic heavy ion collisions, the matter formed shortly after the collision is a dense, out of equilibrium, system of gluons characterized by a semi-hard momentum scale Q s . Simple power counting arguments indicate that this system is over-occupied: the gluon occupation number is parametrically large when compared to a system in thermal equilibrium with the same energy density. On short time scales, soft elastic scattering tends to drive the system toward the formation of a Bose–Einstein condensate that contains a large fraction of the gluons while contributing little to the energy density. The lifetime and existence of this condensate depends on whether inelastic processes, that occur on the same time scale as elastic processes, preferably increase or decrease the number of gluons. During this overpopulated stage, and all the way to thermalization, the system behaves as a strongly interacting fluid, even though the elementary coupling constant is small. Finally, we argue that while complete isotropization may never be reached, the system may yet evolve for a long time with a fixed anisotropy between average longitudinal and transverse momenta.

Eleven lectures on the physics of the quark-gluon plasma

International Nuclear Information System (INIS)

McLerran, L.

1984-10-01

These lectures are intended to be an introduction to the physics of the quark-gluon plasma, and were presented at a workshop on The Physics of the Quark-Gluon Plasma held at Hua-Zhong Normal University in Wuhan, People's Republic of China in September, 1983. The lectures cover perturbation theory of the plasma at high temperature as well as the non-perturbative methods and results of lattice gauge theory computations. Physical models of the confinement-deconfinement phase transition and the modes of chiral symmetry breaking are presented. The possibility that a quark-gluon plasma might be produced in ultra-relativistic nuclear collisions is analyzed. Separate entries were prepared for the data base for the eleven lectures

On the classical Maxwell-Lorentz electrodynamics, the electron inertia problem, and the Feynman proper time paradigm

International Nuclear Information System (INIS)

Prykarpatsky, A.K.; Bogolubov, J.R.

2016-01-01

The classical Maxwell electromagnetic field and the Lorentz-type force equations are rederived in the framework of the Feynman proper time paradigm and the related vacuum field theory approach. The classical Ampere law origin is rederived, and its relationship with the Feynman proper time paradigm is discussed. The electron inertia problem is analyzed in detail within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle of stochastic electrodynamics. The modified Abraham-Lorentz damping radiation force is derived and the electromagnetic electron mass origin is argued

The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory

Directory of Open Access Journals (Sweden)

Claude Semay

2015-01-01

Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.

Gluon structure function for deeply inelastic scattering with nucleus in QCD

Energy Technology Data Exchange (ETDEWEB)

Ayala Filho, Alvaro L; Ducati, M.B. Gay [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil). Inst. de Fisica; Levin, Eugene [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); [Petersburg Nuclear Physics Institute, Gatchina (Russian Federation). Theory Dept.

1995-06-01

In this talk we present the first calculation of the gluon structure function for nucleus in QCD. We discuss the Glauber formula for the gluon structure function and the violation of this simple approach that we anticipate in QCD. (author). 10 refs, 4 figs.

Strangeness Production in a Chemically Equilibrating Quark-Gluon Plasma

Institute of Scientific and Technical Information of China (English)

HE Ze-Jun; LONG Jia-Li; MA Yu-Gang; MA Guo-Liang

2004-01-01

@@ We study the strangeness of a chemically equilibrating quark-gluon plasma at finite baryon density based on the and will accelerate with the change of the initial system from a chemically non-equilibrated to an equilibrated system. We also find that the calculated strangeness is very different from the one in the thermodynamic equilibrium system. This study may be helpful to understand the formation of quark-gluon plasma via a chemically non-equilibrated evolution framework.

Relation between Feynman Cycles and Off-Diagonal Long-Range Order

International Nuclear Information System (INIS)

Ueltschi, Daniel

2006-01-01

The usual order parameter for Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate

Application of FIRE for the calculation of photon matrix elements

Indian Academy of Sciences (India)

to evaluate the two-loop Feynman diagrams for the photon matrix element of the ... sum of scalar Feynman integrals to a linear combination of a few master integrals. .... Then, FIRE is used to express these scalar integrals as a linear combi-.

Feynman propagator for a particle with arbitrary spin

International Nuclear Information System (INIS)

Huang Shi-Zhong; Zhang Peng-Fei; Ruan Tu-Nan; Zhu Yu-Can; Zheng Zhi-Peng

2005-01-01

Based on the solution to the Rarita-Schwinger equations, a direct derivation of the projection operator and propagator for a particle with arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin; the general commutation rules and Feynman propagator for a free particle of any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, 4 are provided. (orig.)

Regularization of the light-cone gauge gluon propagator singularities using sub-gauge conditions

Energy Technology Data Exchange (ETDEWEB)

Chirilli, Giovanni A.; Kovchegov, Yuri V.; Wertepny, Douglas E. [Department of Physics, The Ohio State University,191 W Woodruff Ave, Columbus, OH 43210 (United States)

2015-12-21

Perturbative QCD calculations in the light-cone gauge have long suffered from the ambiguity associated with the regularization of the poles in the gluon propagator. In this work we study sub-gauge conditions within the light-cone gauge corresponding to several known ways of regulating the gluon propagator. Using the functional integral calculation of the gluon propagator, we rederive the known sub-gauge conditions for the θ-function gauges and identify the sub-gauge condition for the principal value (PV) regularization of the gluon propagator’s light-cone poles. The obtained sub-gauge condition for the PV case is further verified by a sample calculation of the classical Yang-Mills field of two collinear ultrarelativistic point color charges. Our method does not allow one to construct a sub-gauge condition corresponding to the well-known Mandelstam-Leibbrandt prescription for regulating the gluon propagator poles.

First measurement of the Sivers asymmetry for gluons using SIDIS data

Directory of Open Access Journals (Sweden)

C. Adolph

2017-09-01

Full Text Available The Sivers function describes the correlation between the transverse spin of a nucleon and the transverse motion of its partons. For quarks, it was studied in previous measurements of the azimuthal asymmetry of hadrons produced in semi-inclusive deep inelastic scattering of leptons off transversely polarised nucleon targets, and it was found to be non-zero. In this letter the evaluation of the Sivers asymmetry for gluons is presented. The contribution of the photon–gluon fusion subprocess is enhanced by requiring two high transverse-momentum hadrons. The analysis method is based on a Monte Carlo simulation that includes three hard processes: photon–gluon fusion, QCD Compton scattering and the leading-order virtual-photon absorption process. The Sivers asymmetries of the three processes are simultaneously extracted using the LEPTO event generator and a neural network approach. The method is applied to samples of events containing at least two hadrons with large transverse momentum from the COMPASS data taken with a 160 GeV/c muon beam scattered off transversely polarised deuterons and protons. With a significance of about two standard deviations, a negative value is obtained for the gluon Sivers asymmetry. The result of a similar analysis for a Collins-like asymmetry for gluons is consistent with zero.

"New Tools for Forecasting Old Physics at the LHC"

CERN Document Server

CERN. Geneva

2011-01-01

For the LHC to uncover many types of new physics, the "old physics" produced by the Standard Model must be understood very well. For decades, the central theoretical tool for this job was the Feynman diagram expansion. However, Feynman diagrams are just too slow, even on fast computers, to allow adequate precision for complicated LHC events with many jets in the final state. Such events are already visible in the initial LHC data. Over the past few years, alternative methods to Feynman diagrams have come to fruition. These new "on-shell" methods are based on the old principles of unitarity and factorization. They can be much more efficient because they exploit the underlying simplicity of scattering amplitudes, and recycle lower-loop information. I will describe how and why these methods work, and present some of the recent state-of-the-art results that have been obtained with them.

Diagram Size vs. Layout Flaws: Understanding Quality Factors of UML Diagrams

DEFF Research Database (Denmark)

Störrle, Harald

2016-01-01

, though, is our third goal of extending our analysis aspects of diagram quality. Method: We improve our definition of diagram size and add a (provisional) definition of diagram quality as the number of topographic layout flaws. We apply these metrics on 60 diagrams of the five most commonly used types...... of UML diagram. We carefully analyze the structure of our diagram samples to ensure representativeness. We correlate diagram size and layout quality with modeler performance data obtained in previous experiments. The data set is the largest of its kind (n-156). Results: We replicate earlier findings......, and extend them to two new diagram types. We provide an improved definition of diagram size, and provide a definition of topographic layout quality, which is one more step towards a comprehensive definition of diagram quality as such. Both metrics are shown to be objectively applicable. We quantify...

Closure of the gauge algebra, generalized Lie equations and Feynman rules

International Nuclear Information System (INIS)

Batalin, I.A.

1984-01-01

A method is given by which an open gauge algebra can always be closed and even made abelian. As a preliminary the generalized Lie equations for the open group are obtained. The Feynman rules for gauge theories with open algebras are derived by reducing the gauge theory to a non-gauge one. (orig.)

Quark and gluon fragmentation in high energy e+e- annihilation

International Nuclear Information System (INIS)

Saxon, D.H.

1986-07-01

The paper on quark and gluon fragmentation in high energy e + e - annihilation is based on lectures given at the International School of High Energy Physics, Yugoslavia, 1986. Fragmentation Models, charged particle multiplicity, Bose-Einstein correlations, single particle inclusive distributions, hadrons in jets, leading particle effects, baryon production, comparison of quark and gluon jets, and the string effect, are all discussed. (UK)

Experimental study of rapidity gaps in gluon jets

CERN Document Server

Gary, J W

2003-01-01

Gluon jets are selected from hadronic Z/sup 0/ decay events produced in e/sup +/e/sup -/ annihilations, collected with the OPAL detector at LEP. A subsample of these jets is identified which exhibit a large gap in the rapidity distribution of particles within the jet. These jets are observed to demonstrate a high degree of sensitivity to the presence of color reconnection, i.e. higher order QCD processes affecting the underlying color structure. We test two QCD Monte Carlo programs which implement color reconnection: one in the Ariadne Monte Carlo and the other by Rathsman in the Pythia Monte Carlo. We find these models can describe our gluon jet measurements only if very large values are used for the cutoff parameters which serve to terminate the parton showers, and conclude that color reconnection as implemented in these models is disfavored. Further, we use our data on gluon jets with a rapidity gap to search for glueball-like objects in the leading part of those jets. We do not find any clear evidence for...

Axiomatic derivation of Feynman rules and related topics

International Nuclear Information System (INIS)

Dorfmeister, G.K.

1992-01-01

Previous results in axiomatic field theory by Steinmann and Epstein-Glaser establish the existence of the retarded and time ordered Green's functions in every order of perturbation. To connect these Green's functions with the ones calculated in canonical field theories via the Feynman rules, one has to consistently build them not just for every order of perturbation but for each specific graph. (open-quotes Consisentlyclose quotes means here that the Green functions associated with two open-quotes smallclose quotes graphs build up to the Green's functions of the open-quotes bigclose quotes graph formed by connecting the two open-quotes smallclose quotes ones). This paper shows that this can indeed be done; that in this sense the Feynman rules of perturbative Lagrangian field theory can be derived from the abstract, but physically very basic, principles of axiomatic field theory. All results hold only for massive field theories. The LSZ formalism, to the best knowledge of the author, has so far not been modified to admit mass zero fields. To make the representation simpler and more transparent, the author restricts the discussion to a single component, scalar Φ 4 interaction which is a part of the Standard Model of Particle Physics. Motivated by its role in particle physics, the author complements the perturbative study of Φ 4 -theory by reviewing the status of non-perturbative solutions to the theory in the final chapter

Hellmann–Feynman connection for the relative Fisher information

Energy Technology Data Exchange (ETDEWEB)

Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com [Systems Research Corporation, Aundh, Pune 411007 (India); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [IFLP, National University La Plata & National Research (CONICET) C. C., 727 1900, La Plata (Argentina)

2015-08-15

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS link and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.

Initial conditions of non-equilibrium quark-gluon plasma evolution

International Nuclear Information System (INIS)

Shmatov, S.V.

2002-01-01

In accordance with the hydrodynamic Bjorken limit, the initial energy density and temperature for a chemical non-equilibrium quark-gluon system formed in the heavy ion collisions at the LHC are computed. The dependence of this value on the type of colliding nuclei and the collision impact parameter is studied. The principle possibility of the non-equilibrium quark-gluon plasma (QGP) formation in the light nuclei collisions is shown. The life time of QGP is calculated. (author)

Transport quasiparticles and transverse interactions in quark-gluon plasmas

International Nuclear Information System (INIS)

Baym, Gordon

1996-01-01

Calculations of the properties of interacting quark-gluon plasmas are beset by infrared divergences associated with the fact that magnetic interactions, i.e., those occurring through exchange of transverse gluons, are, in the absence of a 'magnetic mass''in QCD, not screened. In this lecture we discuss the effects of magnetic interactions on the transport coefficients and the quasiparticle structure of quark-gluon plasmas. We describe how inclusion of dynamical screening effects - corresponding to Landau damping of the virtual quanta exchanged - leads to finite transport scattering rates. In the weak coupling limit, dynamical screening effects dominate over a magnetic mass. We illustrate the breakdown of the quasi particle structure of degenerate plasmas caused by long-ranged magnetic interactions, describe the structure of fermion quasiparticles in hot relativistic plasmas, and touch briefly on the problem of the lifetime of quasiparticle in the presence of long-ranged magnetic interactions. (author)

Low-momentum ghost dressing function and the gluon mass

International Nuclear Information System (INIS)

Boucaud, Ph.; Leroy, J. P.; Le Yaouanc, A.; Micheli, J.; Pene, O.; Gomez, M. E.; Rodriguez-Quintero, J.

2010-01-01

We study the low-momentum ghost propagator Dyson-Schwinger equation in the Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. Then, regular Dyson-Schwinger equation solutions (the zero-momentum ghost dressing function not diverging) appear to emerge, and we show the ghost propagator to be described by an asymptotic expression reliable up to the order O(q 2 ). That expression, depending on the gluon mass and the zero-momentum Taylor-scheme effective charge, is proven to fit pretty well some low-momentum ghost propagator data [I. L. Bogolubsky, E. M. Ilgenfritz, M. Muller-Preussker, and A. Sternbeck, Phys. Lett. B 676, 69 (2009); Proc. Sci., LAT2007 (2007) 290] from big-volume lattice simulations where the so-called ''simulated annealing algorithm'' is applied to fix the Landau gauge.

An introduction to quark-gluon plasma and high energy heavy ion collisions

International Nuclear Information System (INIS)

McLerran, L.

1987-01-01

The quark-gluon plasma, and how it might be produced in ultra-relativistic nuclear collisions is reviewed. I briefly introduce the quark-gluon plasma, and what we might learn from studying it. I then discuss what has been learned from the recent results from the CERN oxygen run. I then attempt to address the issue of whether A = 16 and E = 200 GeV are sufficient to make a quark-gluon plasma. I discuss strangeness and charm production as well as electromagnetic probes of the plasma

Numerical estimates of the evolution of quark and gluon populations inside QCD jets

International Nuclear Information System (INIS)

Garetto, M.

1980-01-01

The system of first order differential equations for the probabilities of producing nsub(g) gluons and nsub(q) quarks in a single gluon or quark jet are solved numerically for a convenient choice of the parameters A, A-tilde, B. Relevant branching ratios as the evolution parameter Y increases are shown. The different behaviour of the distributions in the quark- and in the gluon-jet is discussed. (author)

Experimental properties of gluon and quark jets from a point source

International Nuclear Information System (INIS)

Abbiendi, G.; Ackerstaff, K.; Alexander, G.

1999-01-01

Gluon jets are identified in hadronic Z 0 decays as all the particles in a hemisphere opposite to a hemisphere containing two tagged quark jets. Gluon jets defined in this manner are equivalent to gluon jets produced from a color singlet point source and thus correspond to the definition employed for most theoretical calculations. In a separate stage of the analysis, we select quark jets in a manner to correspond to calculations, as the particles in hemispheres of flavor tagged light quark (uds) events. We present the distributions of rapidity, scaled energy, the logarithm of the momentum, and transverse momentum with respect to the jet axes, for charged particles in these gluon and quark jets. We also examine the charged particle multiplicity distributions of the jets in restricted intervals of rapidity. For soft particles at large p T , we observe the charged particle multiplicity ratio of gluon to quark jets to be 2.29±0.09(stat.)±0.15(syst.), in agreement with the prediction that this ratio should approximately equal the ratio of QCD color factors, C A /C F =2.25. The intervals used to define soft particles and large p T for this result, p T < 3.0 GeV/c, are motivated by the predictions of the Herwig Monte Carlo multihadronic event generator. Additionally, our gluon jet data allow a sensitive test of the phenomenon of non-leading QCD terms known as color reconnection. We test the model of color reconnection implemented in the Ariadne Monte Carlo multihadronic event generator and find it to be disfavored by our data. (orig.)

Gluon condensation and modelling of quark confinement in QCD-motivated Nambu-Jona-Lasinio model

International Nuclear Information System (INIS)

Bel'kov, A.A.; Ebert, D.; Emel'yanenko, A.V.

1992-01-01

The possibility of modelling of a quark propagator without poles realizing quark confinement is considered on the basis of a nonperturbative gluon propagator including gluon condensation and a dynamical gluon mass. The property of spontaneous chiral symmetry breaking is retained providing us with a reasonable pattern of low-lying meson properties. 2 figs.; 1 tab

The Feynman fluid analogy in e+e- annihilation

International Nuclear Information System (INIS)

Hegyi, S.; Krasznovszky, S.

1990-07-01

An analysis of the charged particle multiplicity distributions observed in e + e - annihilation is given using the generalized Feynman fluid analogy of multiparticle production. Only the two-and three-particle integrated correlation functions are included into the scheme. It is shown that the model correctly describes the available experimental data from the TASSO and HRS collaborations. Some properties of the fluid of the analogy are computed and a prediction is made for the multiplicity distribution at √s = 91 GeV. (author) 19 refs.; 5 figs.; 1 tab

Extended Hellmann-Feynman theorem for degenerate eigenstates

Science.gov (United States)

Zhang, G. P.; George, Thomas F.

2004-04-01

In a previous paper, we reported a failure of the traditional Hellmann-Feynman theorem (HFT) for degenerate eigenstates. This has generated enormous interest among different groups. In four independent papers by Fernandez, by Balawender, Hola, and March, by Vatsya, and by Alon and Cederbaum, an elegant method to solve the problem was devised. The main idea is that one has to construct and diagonalize the force matrix for the degenerate case, and only the eigenforces are well defined. We believe this is an important extension to HFT. Using our previous example for an energy level of fivefold degeneracy, we find that those eigenforces correctly reflect the symmetry of the molecule.

Certain exclusive processes in QCD taking into account two-gluon states

International Nuclear Information System (INIS)

Baier, V.N.; Grozin, A.G.

1982-01-01

The wave functions and evolution equations for mesons are classified completely taking into account two-gluon states and then are compared to the Altarelli-Parisi evolution equations. The form factors of completely neutral mesons and the probabilities for exclusive decays of quarkonium states are found taking into account two-gluon states

Mechanism of J/PSI production: determining gluon distributions

International Nuclear Information System (INIS)

Nandi, S.; Schneider, H.R.

1978-01-01

Assuming a generalised Drell-Yan type mechanism for hadronic PSI-production, the relative importance of the different possible contributions is estimated from the data. We find that about 80% of the pp → PSI X cross-section is due to gluons. Therefore, these data give some information on the gluon distribution G(x) in the proton. Assuming xG(x) approximately (1-x)sup(n), data restrict n to 4... 6, in agreement with dimensional counting rules. The energy dependence of sigma(anti p p → PSI X)/sigma(pp → PSIX) is predicted. (orig.) [de

Gluon gas viscosity in nonperturbative region

International Nuclear Information System (INIS)

Il'in, S.V.; Mogilevskij, O.A.; Smolyanskij, S.A.; Zinov'ev, G.M.

1992-01-01

Using the Green-Kubo-type formulae and the cutoff model motivated by Monte Carlo lattice gluodynamics simulations we find the temperature behaviour of shear viscosity of gluon gas in the region of deconfinement phase transition. 22 refs.; 1 fig. (author)

Roundhouse Diagrams.

Science.gov (United States)

Ward, Robin E.; Wandersee, James

2000-01-01

Students must understand key concepts through reasoning, searching out related concepts, and making connections within multiple systems to learn science. The Roundhouse diagram was developed to be a concise, holistic, graphic representation of a science topic, process, or activity. Includes sample Roundhouse diagrams, a diagram checklist, and…

Plaquette expectation value and gluon condensate in three dimensions

CERN Document Server

Hietanen, A; Laine, Mikko; Rummukainen, K; Schröder, Y

2005-01-01

In three dimensions, the gluon condensate of pure SU(3) gauge theory has ultraviolet divergences up to 4-loop level only. By subtracting the corresponding terms from lattice measurements of the plaquette expectation value and extrapolating to the continuum limit, we extract the finite part of the gluon condensate in lattice regularization. Through a change of regularization scheme to MSbar and (inverse) dimensional reduction, this result would determine the first non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure.

The dependence of J/ψ-nucleon inelastic cross section on the Feynman variable

International Nuclear Information System (INIS)

Duan Chungui; Liu Na; Miao Wendan

2011-01-01

By means of two typical sets of nuclear parton distribution functions, meanwhile taking account of the energy loss of the beam proton and the nuclear absorption of the charmonium states traversing the nuclear matter in the uniform framework of the Glauber model, a leading order phenomenological analysis is given in the color evaporation model of the E866 experimental data on J/ψ production differential cross section ratios R Fe/Be (x F ). It is shown that the energy loss effect of beam proton on R Fe/Be (x F ) is more important than the nuclear effects on parton distribution functions in the high Feynman variable x F region. It is found that the J/ψ-nucleon inelastic cross section depends on the Feynman variable x F and increases linearly with x F in the region x F > 0.2. (authors)

Infrared divergences of Green functions and renormalization in massless theories. 2

International Nuclear Information System (INIS)

Anikin, S.A.; Zav'yalova, O.I.; Karchev, N.I.

1981-01-01

General theorems are proved concerning the infrared finiteness of Green functions in theories including massless particles. Considerations are based on α-representation of Feynman diagrams. Necessory conditions are considered for proving theorems in the case of diagrams with massive lines. Under certain conditions the contribution of the considered sections into the Feynman amplitude is shown to be free from infrared divergences, but only for those subgraphs which involve all the massive lines and contain all the outer vertexes in one affinity component

Perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential: Two-loop corrections

Science.gov (United States)

Maelger, J.; Reinosa, U.; Serreau, J.

2018-04-01

We extend a previous investigation [U. Reinosa et al., Phys. Rev. D 92, 025021 (2015), 10.1103/PhysRevD.92.025021] of the QCD phase diagram with heavy quarks in the context of background field methods by including the two-loop corrections to the background field effective potential. The nonperturbative dynamics in the pure-gauge sector is modeled by a phenomenological gluon mass term in the Landau-DeWitt gauge-fixed action, which results in an improved perturbative expansion. We investigate the phase diagram at nonzero temperature and (real or imaginary) chemical potential. Two-loop corrections yield an improved agreement with lattice data as compared to the leading-order results. We also compare with the results of nonperturbative continuum approaches. We further study the equation of state as well as the thermodynamic stability of the system at two-loop order. Finally, using simple thermodynamic arguments, we show that the behavior of the Polyakov loops as functions of the chemical potential complies with their interpretation in terms of quark and antiquark free energies.

Dark-matter bound states from Feynman diagrams

NARCIS (Netherlands)

Petraki, K.; Postma, M.; Wiechers, M.

2015-01-01

If dark matter couples directly to a light force mediator, then it may form bound states in the early universe and in the non-relativistic environment of haloes today. In this work, we establish a field-theoretic framework for the computation of bound-state formation cross-sections, de-excitation

DIANA, a program for Feynman Diagram Evaluation

OpenAIRE

Tentyukov, M.; Fleischer, J.

1999-01-01

Comment: LaTeX, 5 pages, no figures; talk given at 6th International Workshop on Software Engineering, Artificial Intelligence, Neural Nets, Genetic Algorithms, Symbolic Algebra, Automatic Calculation (AIHENP 99), Heraklion, Crete, Greece, 12-16 April, 1999

Safety- barrier diagrams

DEFF Research Database (Denmark)

Duijm, Nijs Jan

2008-01-01

Safety-barrier diagrams and the related so-called 'bow-tie' diagrams have become popular methods in risk analysis. This paper describes the syntax and principles for constructing consistent and valid safety-barrier diagrams. The relation of safety-barrier diagrams to other methods such as fault...... trees and Bayesian networks is discussed. A simple method for quantification of safety-barrier diagrams is proposed. It is concluded that safety-barrier diagrams provide a useful framework for an electronic data structure that integrates information from risk analysis with operational safety management....

Virtual two-loop corrections to Bhabha scattering

International Nuclear Information System (INIS)

Bjoerkevoll, K.S.

1992-03-01

The author has developed methods for the calculation of contributions from six ladder-like diagrams to Bhabha scattering. The leading terms both for separate diagrams and for the sum of the gauge-invariant set of all diagrams have been calculated. The study has been limited to contributions from Feynman diagrams without real photons, and all calculations have been done with s>> |t| >>m 2 , where s is the center of mass energy squared, t is the square of the transferred four-momentum, and m is the electron mass. For the separate diagrams the results depend upon how λ 2 is related to s, |t| and m 2 , whereas the leading term of the sum of the six diagrams is the same in the cases that have been considered. The methods described should be valuable for calculations of contributions from other Feynman diagrams, in particular QED corrections to Bhabha scattering or pair production at small angles. 23 refs., 5 figs., 5 tabs

Non-perturbative inputs for gluon distributions in the hadrons

International Nuclear Information System (INIS)

Ermolaev, B.I.; Troyan, S.I.

2017-01-01

Description of hadronic reactions at high energies is conventionally done in the framework of QCD factorization. All factorization convolutions comprise non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct inputs for the gluon-hadron scattering amplitudes in the forward kinematics and, using the optical theorem, convert them into inputs for gluon distributions in the hadrons, embracing the cases of polarized and unpolarized hadrons. In the first place, we formulate mathematical criteria which any model for the inputs should obey and then suggest a model satisfying those criteria. This model is based on a simple reasoning: after emitting an active parton off the hadron, the remaining set of spectators becomes unstable and therefore it can be described through factors of the resonance type, so we call it the resonance model. We use it to obtain non-perturbative inputs for gluon distributions in unpolarized and polarized hadrons for all available types of QCD factorization: basic, K_T-and collinear factorizations. (orig.)

Soft probes of the quark gluon plasma in ATLAS

CERN Document Server

Wozniak, K W; The ATLAS collaboration

2014-01-01

Measurements of low-$p_{T}$ (< 5 GeV) particle production have provided valuable insight on the production and evolution of the quark-gluon plasma in Pb+Pb collisions at the LHC. In particular, measurements of elliptic and higher order collective flow imprinted on the azimuthal angle distributions of low-$p_{T}$ particles directly probe the strongly-coupled dynamics of the quark gluon plasma and test hydrodynamic model descriptions of its evolution. The large acceptance of detectors like ATLAS have made it possible to measure flow event-by-event and to determine the correlations between different harmonics. Recent measurements of low-$p_{T}$ particle production and multi-particle correlations in proton-lead collisions have shown features similar to the collective flow observed in Pb+Pb collisions. Results will be presented from a variety of single and multi-particle measurements in Pb+Pb and proton-Pb collisions that probe the collective dynamics of the quark gluon plasma and possibly provide evidence for ...

Non-perturbative inputs for gluon distributions in the hadrons

Energy Technology Data Exchange (ETDEWEB)

Ermolaev, B.I. [Ioffe Physico-Technical Institute, Saint Petersburg (Russian Federation); Troyan, S.I. [St. Petersburg Institute of Nuclear Physics, Gatchina (Russian Federation)

2017-03-15

Description of hadronic reactions at high energies is conventionally done in the framework of QCD factorization. All factorization convolutions comprise non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct inputs for the gluon-hadron scattering amplitudes in the forward kinematics and, using the optical theorem, convert them into inputs for gluon distributions in the hadrons, embracing the cases of polarized and unpolarized hadrons. In the first place, we formulate mathematical criteria which any model for the inputs should obey and then suggest a model satisfying those criteria. This model is based on a simple reasoning: after emitting an active parton off the hadron, the remaining set of spectators becomes unstable and therefore it can be described through factors of the resonance type, so we call it the resonance model. We use it to obtain non-perturbative inputs for gluon distributions in unpolarized and polarized hadrons for all available types of QCD factorization: basic, K{sub T}-and collinear factorizations. (orig.)

Phenomenology of gluon TMDs at NNLL

NARCIS (Netherlands)

Garcia, M.

2015-01-01

All the leading-Twist (un)polarized gluon transverse momentum dependent parton distribution functions have the same evolution, once they are properly defined in order to cancel spurious rapidity divergences. Currently known perturbative ingredients can be used to resum large logarithms up to

Parton-parton scattering at two-loops

International Nuclear Information System (INIS)

Tejeda Yeomans, M.E.

2001-01-01

Abstract We present an algorithm for the calculation of scalar and tensor one- and two-loop integrals that contribute to the virtual corrections of 2 → 2 partonic scattering. First, the tensor integrals are related to scalar integrals that contain an irreducible propagator-like structure in the numerator. Then, we use Integration by Parts and Lorentz Invariance recurrence relations to build a general system of equations that enables the reduction of any scalar integral (with and without structure in the numerator) to a basis set of master integrals. Their expansions in ε = 2 - D/2 have already been calculated and we present a summary of the techniques that have been used to this end, as well as a compilation of the expansions we need in the different physical regions. We then apply this algorithm to the direct evaluation of the Feynman diagrams contributing to the O(α s 4 ) one- and two-loop matrix-elements for massless like and unlike quark-quark, quark-gluon and gluon-gluon scattering. The analytic expressions we provide are regularised in Convensional Dimensional Regularisation and renormalised in the MS-bar scheme. Finally, we show that the structure of the infrared divergences agrees with that predicted by the application of Catani's formalism to the analysis of each partonic scattering process. The results presented in this thesis provide the complete calculation of the one- and two-loop matrix-elements for 2 → 2 processes needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders. (author)

Recursive Neural Networks in Quark/Gluon Tagging

CERN Multimedia

CERN. Geneva

2018-01-01

Vidyo contribution Based on the natural tree-like structure of jet sequential clustering, the recursive neural networks (RecNNs) embed jet clustering history recursively as in natural language processing. We explore the performance of RecNN in quark/gluon discrimination. The results show that RecNNs work better than the baseline BDT by a few percent in gluon rejection at the working point of 50\\% quark acceptance. We also experimented on some relevant aspects which might influence the performance of networks. It shows that even only particle flow identification as input feature without any extra information on momentum or angular position is already giving a fairly good result, which indicates that most of the information for q/g discrimination is already included in the tree-structure itself.

Quarks and gluons in hadrons and nuclei

International Nuclear Information System (INIS)

Close, F.E.

1989-12-01

These lectures discuss the particle-nuclear interface -- a general introduction to the ideas and application of colored quarks in nuclear physics, color, the Pauli principle, and spin flavor correlations -- this lecture shows how the magnetic moments of hadrons relate to the underlying color degree of freedom, and the proton's spin -- a quark model perspective. This lecture reviews recent excitement which has led some to claim that in deep inelastic polarized lepton scattering very little of the spin of a polarized proton is due to its quarks. This lecture discusses the distribution functions of quarks and gluons in nucleons and nuclei, and how knowledge of these is necessary before some quark-gluon plasma searches can be analyzed. 56 refs., 2 figs

The three-point function in split dimensional regularization in the Coulomb gauge

CERN Document Server

Leibbrandt, G

1998-01-01

We use a gauge-invariant regularization procedure, called ``split dimensional regularization'', to evaluate the quark self-energy $\\Sigma (p)$ and quark-quark-gluon vertex function $\\Lambda_\\mu (p^\\prime,p)$ in the Coulomb gauge, $\\vec{\\bigtriangledown}\\cdot\\vec{A}^a = 0$. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, $\\omega$ and $\\sigma$, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are nonlocal. It is further argued that the standard one-loop BRST identity relating $\\Sigma$ and $\\Lambda_\\mu$, should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of nonlocal Coulomb integrals, both $\\Sigma$ and $\\Lambda_\\...

Introduction to soft-collinear effective theory

CERN Document Server

Becher, Thomas; Ferroglia, Andrea

2015-01-01

Among resummation techniques for perturbative QCD in the context of collider and flavor physics, soft-collinear effective theory (SCET) has emerged as both a powerful and versatile tool, having been applied to a large variety of processes, from B-meson decays to jet production at the LHC.  This book provides a concise, pedagogical introduction to this technique. It discusses the expansion of Feynman diagrams around the high-energy limit, followed by the explicit construction of the effective Lagrangian - first for a scalar theory, then for QCD. The underlying concepts are illustrated with the quark vector form factor at large momentum transfer, and the formalism is applied to compute soft-gluon resummation and to perform transverse-momentum resummation for the Drell-Yan process utilizing renormalization group evolution in SCET. Finally, the infrared structure of n-point gauge-theory amplitudes is analyzed by relating them to effective-theory operators. This text is suitable for graduate students and non-spe...

From the Dyson-Schwinger to the Transport Equation in the Background Field Gauge of QCD

CERN Document Server

Wang, Q; Stöcker, H; Greiner, W

2003-01-01

The non-equilibrium quantum field dynamics is usually described in the closed-time-path formalism. The initial state correlations are introduced into the generating functional by non-local source terms. We propose a functional approach to the Dyson-Schwinger equation, which treats the non-local and local source terms in the same way. In this approach, the generating functional is formulated for the connected Green functions and one-particle-irreducible vertices. The great advantages of our approach over the widely used two-particle-irreducible method are that it is much simpler and that it is easy to implement the procedure in a computer program to automatically generate the Feynman diagrams for a given process. The method is then applied to a pure gluon plasma to derive the gauge-covariant transport equation from the Dyson-Schwinger equation in the background covariant gauge. We discuss the structure of the kinetic equation and show its relationship with the classical one. We derive the gauge-covariant colli...

Specific features of the REDUCE system and calculation of QCD Feynman graphs

International Nuclear Information System (INIS)

Dulyan, L.S.

1990-01-01

The ways and methods used in calculation of one class of the QCD Feynman graphs with the help of the REDUCE system are described. It is shown how by introducing new constructions and operations the user could avoid difficulties connected with specific restrictions and features of the REDUCE system

Study of high-transverse momentum quark and gluon jet fragmentation

International Nuclear Information System (INIS)

Ghez, P.

1986-09-01

The fragmentation properties of high-transverse momentum jets are investigated using new data from the ISR and the SPS collider. Effects from gluon radiation are clearly demonstrated by comparison with a state-of-the-art model including QCD parton cascade evolution and string hadronization, which gives in general good agreement with the data. Differences between quark and gluon jets are discussed as well as Q 2 -dependent scaling violation effects