Sekihara, Takayasu
2016-01-01
For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For this purpose, we first show that the two-body wave function of the bound state corresponds to the residue of the off-shell scattering amplitude at the bound state pole. Then, we examine our scheme to extract the two-body wave function from the scattering amplitude in several schematic models. As a result, the two-body wave functions from the Lippmann--Schwinger equation coincides with that from the Schr\\"{o}dinger equation for an energy-independent interaction. Of special interest is that the two-body wave function from the scattering amplitude is automatically scaled; the norm of the two-body wave function, to which we refer as the compositeness, is unity for an energy-independent interaction, while the compositeness deviates from unity for an energy-dependent interaction, ...
Effective potential and off-shell two-body scattering amplitudes in the eikonal approximation
Energy Technology Data Exchange (ETDEWEB)
Bartnik, E.A.; Rek, Z.
1973-12-31
An effective potential is computed for 2-body elastic scattering with the experimental on-shell t-matrices as an input. Nonrelativistic elkonal approximation and locality together with spherical ial are assumed. The explicit form of potential for pp, pi /sup +/p, and pi /sup -/p in the energy range from 5 to 20 GeV is investigated. The half off-shell scattering amplitude is calculated in the potential model. In the position representation this amplitude is found to be asymmetric along the eikonal direction, and an interesting absorption interpretation of this fact is given. (auth)
Hagen, G; Vaagen, J S
2003-01-01
A generalized contour deformation method (GCDM) which combines complex rotation and translation in momentum space, is discussed. GCDM gives accurate results for bound, virtual (antibound), resonant and scattering states starting with a realistic nucleon-nucleon interaction. It provides a basis for full off-shell $t$-matrix calculations both for real and complex input energies. Results for both spectral structures and scattering amplitudes compare perfectly well with exact values for the separable Yamaguchi potential. Accurate calculation of virtual states in the Malfliet-Tjon and the realistic CD-Bonn nucleon-nucleon interactions are presented. GCDM is also a promising method for the computation of in-medium properties such as the resummation of particle-particle and particle-hole diagrams in infinite nuclear matter. Implications for in-medium scattering are discussed.
Protostring Scattering Amplitudes
Thorn, Charles B
2016-01-01
We calculate some tree level scattering amplitudes for a generalization of the protostring, which is a novel string model implied by the simplest string bit models. These bit models produce a lightcone worldsheet which supports $s$ integer moded Grassmann fields. In the generalization we supplement this Grassmann worldsheet system with $d=24-s$ transverse coordinate worldsheet fields. The protostring corresponds to $s=24$ and the bosonic string to $s=0$. The interaction vertex is a simple overlap with no operator insertions at the break/join point. Assuming that $s$ is even we calculate the multi-string scattering amplitudes by bosonizing the Grassmann fields, each pair equivalent to one compactified bosonic field, and applying Mandelstam's interacting string formalism to a system of $s/2$ compactified and $d$ uncompactified bosonic worldsheet fields. We obtain all amplitudes for open strings with no oscillator excitations and for closed strings with no oscillator excitations and zero winding number. We then ...
Protostring scattering amplitudes
Thorn, Charles B.
2016-11-01
We calculate some tree-level scattering amplitudes for a generalization of the protostring, which is a novel string model implied by the simplest string bit models. These bit models produce a light-cone world sheet which supports s integer moded Grassmann fields. In the generalization we supplement this Grassmann world-sheet system with d =24 -s transverse coordinate world-sheet fields. The protostring corresponds to s =24 and the bosonic string to s =0 . The interaction vertex is a simple overlap with no operator insertions at the break/join point. Assuming that s is even we calculate the multistring scattering amplitudes by bosonizing the Grassmann fields, each pair equivalent to one compactified bosonic field, and applying Mandelstam's interacting string formalism to a system of s /2 compactified and d uncompactified bosonic world-sheet fields. We obtain all amplitudes for open strings with no oscillator excitations and for closed strings with no oscillator excitations and zero winding number. We then study in detail some simple special cases. Multistring processes with maximal helicity violation have much simpler amplitudes. We also specialize to general four-string amplitudes and discuss their high energy behavior. Most of these models are not covariant under the full Lorentz group O (d +1 ,1 ). The exceptions are the bosonic string whose Lorentz group is O (25 ,1 ) and the protostring whose Lorentz group is O (1 ,1 ). The models in between only enjoy an O (1 ,1 )×O (d ) spacetime symmetry.
Two-body bound state problem and nonsingular scattering equations
Energy Technology Data Exchange (ETDEWEB)
Bartnik, E.A.; Haberzettl, H.; Sandhas, W.
1986-11-01
We present a new momentum space approach to the two-body problem in partial waves. In contrast to the usual momentum space approaches, we treat the bound state case with the help of an inhomogeneous integral equation which possesses solutions for all (negative) energies. The bound state energies and corresponding wave functions are identified by an additional condition. This procedure straightforwardly leads to a nonsingular formulation of the scattering problem in terms of essentially the same equation and thus unifies the descriptions of both energy regimes. We show that the properties of our momentum-space approach can be understood in terms of the so-called regular solution of the Schroedinger equation in position space. The unified description of the bound state and scattering energy regimes in terms of one single, real, and manifestly nonsingular equation allows us to construct an exact representation of the two-body off-shell T matrix in which all the bound state pole and scattering cut information is contained in one single separable term, the remainder being real, nonsingular, and vanishing half on-shell. Such a representation may be of considerable advantage as input in three-body Faddeev-type integral equations. We demonstrate the applicability of our method by calculating bound state and scattering data for the two-nucleon system with the s-wave Malfliet--Tjon III potential.
Scattering amplitudes in gauge theories
Henn, Johannes M
2014-01-01
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum ...
Separable approximation method for two-body relativistic scattering
Energy Technology Data Exchange (ETDEWEB)
Tandy, P.C.; Thaler, R.M.
1988-03-01
A method for defining a separable approximation to a given interaction within a two-body relativistic equation, such as the Bethe-Salpeter equation, is presented. The rank-N separable representation given here permits exact reproduction of the T matrix on the mass shell and half off the mass shell at N selected bound state and/or continuum values of the invariant mass. The method employed is a four-space generalization of the separable representation developed for Schroedinger interactions by Ernst, Shakin, and Thaler, supplemented by procedures for dealing with the relativistic spin structure in the case of Dirac particles.
Separable approximation method for two-body relativistic scattering
Tandy, P. C.; Thaler, R. M.
1988-03-01
A method for defining a separable approximation to a given interaction within a two-body relativistic equation, such as the Bethe-Salpeter equation, is presented. The rank-N separable representation given here permits exact reproduction of the T matrix on the mass shell and half off the mass shell at N selected bound state and/or continuum values of the invariant mass. The method employed is a four-space generalization of the separable representation developed for Schrödinger interactions by Ernst, Shakin, and Thaler, supplemented by procedures for dealing with the relativistic spin structure in the case of Dirac particles.
Two body scattering length of Yukawa model on a lattice
De Soto, F; Roiesnel, C; Boucaud, P; Leroy, J P; Pène, O; Boucaud, Ph.
2007-01-01
The extraction of scattering parameters from Euclidean simulations of a Yukawa model in a finite volume with periodic boundary conditions is analyzed both in non relativistic quantum mechanics and in quantum field theory.
Scattering Amplitudes in Gauge Theories
Schubert, Ulrich
2014-01-01
This thesis is focused on the development of new mathematical methods for computing multi-loop scattering amplitudes in gauge theories. In this work we combine, for the first time, the unitarity-based construction for integrands, and the recently introduced integrand-reduction through multivariate polynomial division. After discussing the generic features of this novel reduction algorithm, we will apply it to the one- and two-loop five-point amplitudes in ${\\cal N}=4$ sYM. The integrands of the multiple-cuts are generated from products of tree-level amplitudes within the super-amplitudes formalism. The corresponding expressions will be used for the analytic reconstruction of the polynomial residues. Their parametric form is known a priori, as derived by means of successive polynomial divisions using the Gr\\"obner basis associated to the on-shell denominators. The integrand reduction method will be exploited to investigate the color-kinematic duality for multi-loop ${\\cal N}=4$ sYM scattering amplitudes. Our a...
Renormalized two-body low-energy scattering
DEFF Research Database (Denmark)
Skibsted, Erik
For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension d≥3, we introduce a stationary scattering theory for Schrödinger operators which is regular at zero energy. In particular it is well defined at this energy, and we use it to...
Scattering amplitudes in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Henn, Johannes M. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Plefka, Jan C. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2014-03-01
First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.
Computing Maximally Supersymmetric Scattering Amplitudes
Stankowicz, James Michael, Jr.
This dissertation reviews work in computing N = 4 super-Yang--Mills (sYM) and N = 8 maximally supersymmetric gravity (mSUGRA) scattering amplitudes in D = 4 spacetime dimensions in novel ways. After a brief introduction and overview in Ch. 1, the various techniques used to construct amplitudes in the remainder of the dissertation are discussed in Ch. 2. This includes several new concepts such as d log and pure integrand bases, as well as how to construct the amplitude using exactly one kinematic point where it vanishes. Also included in this chapter is an outline of the Mathematica package on shell diagrams and numerics.m (osdn) that was developed for the computations herein. The rest of the dissertation is devoted to explicit examples. In Ch. 3, the starting point is tree-level sYM amplitudes that have integral representations with residues that obey amplitude relations. These residues are shown to have corresponding residue numerators that allow a double copy prescription that results in mSUGRA residues. In Ch. 4, the two-loop four-point sYM amplitude is constructed in several ways, showcasing many of the techniques of Ch. 2; this includes an example of how to use osdn. The two-loop five-point amplitude is also presented in a pure integrand representation with comments on how it was constructed from one homogeneous cut of the amplitude. On-going work on the two-loop n-point amplitude is presented at the end of Ch. 4. In Ch. 5, the three-loop four-point amplitude is presented in the d log representation and in the pure integrand representation. In Ch. 6, there are several examples of four- through seven-loop planar diagrams that illustrate how considerations of the singularity structure of the amplitude underpin dual-conformal invariance. Taken with the previous examples, this is additional evidence that the structure known to exist in the planar sector extends to the full theory. At the end of this chapter is a proof that all mSUGRA amplitudes have a pole at
Analysis of charmless two-body B decays in factorization-assisted topological-amplitude approach
Energy Technology Data Exchange (ETDEWEB)
Zhou, Si-Hong; Zhang, Qi-An; Lue, Cai-Dian [Institute of High Energy Physics, Beijing (China); University of Chinese Academy of Sciences, School of Physics, Beijing (China); Lyu, Wei-Ran [Renmin University of China, Physics Department, Beijing (China)
2017-02-15
We analyze charmless two-body non-leptonic B decays B → PP, PV under the framework of a factorization-assisted topological-amplitude approach, where P(V) denotes a light pseudoscalar (vector) meson. Compared with the conventional flavor diagram approach, we consider the flavor SU(3) breaking effect assisted by a factorization hypothesis for topological diagram amplitudes of different decay modes, factorizing out the corresponding decay constants and form factors. The non-perturbative parameters of topology diagram magnitudes χ and the strong phase φ are universal; they can be extracted by χ{sup 2} fit from current abundant experimental data of charmless B decays. The number of free parameters and the χ{sup 2} per degree of freedom are both reduced compared with previous analyses. With these best fitted parameters, we predict branching fractions and CP asymmetry parameters of nearly 100 B{sub u,d} and B{sub s} decay modes. The long-standing ππ and πK-CP puzzles are solved simultaneously. (orig.)
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Scattering Amplitudes via Algebraic Geometry Methods
DEFF Research Database (Denmark)
Søgaard, Mads
This thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without...... Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized...
Positivity of the real part of the forward scattering amplitude arXiv
Martin, André
We prove the general theorem that the real part of the forward two-body scattering amplitude is positive at sufficiently high energies if, above a certain energy, the total cross section increases monotonically to infinity at infinite energy.
One dimensional scattering of a two body interacting system by an infinite wall
Moro, A M; Gomez-Camacho, J
2010-01-01
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear systems. The scattering problem is solved exactly, for the case of a harmonic interaction between the fragments. The exact result is used to assess the validity of two different approximations to the scattering process. The adiabatic approximation, which considers that the relative co-ordinate is frozen during the scattering process, is found to be inadequate for this problem. The uncorrelated scattering approximation, which neglects the correlation between the fragments, gives results in accordance with the exact calculations when the scattering energy is high compared to the oscillator parameter.
Neutral weak-current two-body contributions in inclusive scattering from {sup 12}C
Energy Technology Data Exchange (ETDEWEB)
Lovato, Alessandro [ANL; Gandolfi, Stefano [LANL; Carlson, Joseph [LANL; Pieper, S. C. [ANL; Schiavilla, Rocco [JLAB, ODU
2014-05-01
An {\\it ab initio} calculation of the sum rules of the neutral weak response functions in $^{12}$C is reported, based on a realistic Hamiltonian, including two- and three-nucleon potentials, and on realistic currents, consisting of one- and two-body terms. We find that the sum rules of the response functions associated with the longitudinal and transverse components of the (space-like) neutral current are largest and that a significant portion ($\\simeq 30$\\%) of the calculated strength is due to two-body terms. This fact may have implications for the MiniBooNE and other neutrino quasi-elastic scattering data on nuclei.
Scattering Amplitudes via Algebraic Geometry Methods
Søgaard, Mads; Damgaard, Poul Henrik
This thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized unitarity cuts. We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed in terms of certain linear combinations of multivariate residues and elliptic integrals computed from products of ...
Neutron-deuteron scattering calculations with W-matrix representation of the two-body input
Energy Technology Data Exchange (ETDEWEB)
Bartnik, E.A.; Haberzettl, H.; Januschke, T.; Kerwath, U.; Sandhas, W.
1987-11-01
Employing the W-matrix representation of the partial-wave T matrix introduced by Bartnik, Haberzettl, and Sandhas, we show for the example of the Malfliet-Tjon potentials I and III that the single-term separable part of the W-matrix representation, when used as input in three-nucleon neutron-deuteron scattering calculations, is fully capable of reproducing the exact results obtained by Kloet and Tjon. This approximate two-body input not only satisfies the two-body off-shell unitarity relation but, moreover, it also contains a parameter which may be used in optimizing the three-body data. We present numerical evidence that there exists a variational (minimum) principle for the determination of the three-body binding energy which allows one to choose this parameter also in the absence of an exact reference calculation. Our results for neutron-deuteron scattering show that it is precisely this choice of the parameter which provides optimal scattering data. We conclude that the W-matrix approach, despite its simplicity, is a remarkably efficient tool for high-quality three-nucleon calculations.
Neutron-deuteron scattering calculations with W-matrix representation of the two-body input
Energy Technology Data Exchange (ETDEWEB)
Bartnik, E.A.; Haberzettl, H.; Januschke, T.; Kerwath, U.; Sandhas, W.
1987-05-01
Employing the W-matrix representation of the partial-wave T matrix introduced by Bartnik, Haberzettl, and Sandhas, we show for the example of the Malfliet-Tjon potentials I and III that the single-term separable part of the W-matrix representation, when used as input in three-nucleon neutron-deuteron scattering calculations, is fully capable of reproducing the exact results obtained by Kloet and Tjon. This approximate two-body input not only satisfies the two-body off-shell unitarity relation but, moreover, it also contains a parameter which may be used in optimizing the three-body data. We present numerical evidence that there exists a variational (minimum) principle for the determination of the three-body binding energy which allows one to choose this parameter also in the absence of an exact reference calculation. Our results for neutron-deuteron scattering show that it is precisely this choice of the parameter which provides optimal scattering data. We conclude that the W-matrix approach, despite its simplicity, is a remarkably efficient tool for high-quality three-nucleon calculations.
Induced two-body scattering resonances from a square-well potential with oscillating depth
Hudson Smith, D.
2016-03-01
In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism which does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the Bohr frequency for the transition to a two-atom bound state. The real part of the s-wave scattering length a has a resonance as a function of the oscillation frequency near the Bohr frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a which arises predominantly because the oscillating field converts atom pairs into molecules. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.
Scattering Amplitudes and Worldsheet Models of QFTs
CERN. Geneva
2016-01-01
I will describe recent progress on the study of scattering amplitudes via ambitwistor strings and the scattering equations. Ambitwistor strings are worldsheet models of quantum field theories, inspired by string theory. They naturally lead to a representation of amplitudes based on the scattering equations. While worldsheet models and related ideas have had a wide-ranging impact on the modern study of amplitudes, their direct application at loop level is a very recent success. I will show how a major difficulty in the loop-level story, the technicalities of higher-genus Riemann surfaces, can be avoided by turning the higher-genus surface into a nodal Riemann sphere, with the nodes representing the loop momenta. I will present new formulas for the one-loop integrands of gauge theory and gravity, with or without supersymmetry, and also some two-loop results.
Holographic corrections to meson scattering amplitudes
Energy Technology Data Exchange (ETDEWEB)
Armoni, Adi; Ireson, Edwin, E-mail: 746616@swansea.ac.uk
2017-06-15
We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature of such computations is explained, thanks to the well-understood nature of confining string backgrounds, and two different examples of the calculation in given backgrounds are used to illustrate the details. The effect we discover, whilst only qualitative, is re-obtainable in many such examples, in four-point but also higher point amplitudes.
Holographic Corrections to Meson Scattering Amplitudes
Armoni, Adi
2016-01-01
We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature of such computations is explained, thanks to the well-understood nature of confining string backgrounds, and two different examples of the calculation in given backgrounds are used to illustrate the details. The effect we discover, whilst only qualitative, is re-obtainable in many such examples, in four-point but also higher point amplitudes.
Three-particle scattering amplitudes from a finite volume formalism
Briceno, Raul A
2012-01-01
We present a quantization condition for the spectrum of a system composed of three identical bosons in a finite volume with periodic boundary conditions. This condition gives a relation between the finite volume spectrum and infinite volume scattering amplitudes. The quantization condition presented is an integral equation that in general must be solved numerically. However, for systems with an attractive two-body force that supports a two-body bound-state, a diboson, and for energies below the diboson breakup, the quantization condition reduces to the well-known Luscher formula with exponential corrections in volume that scale with the diboson binding momentum. To accurately determine infinite volume phase shifts, it is necessary to extrapolate the phase shifts obtained from the Luscher formula for the boson-diboson system to the infinite volume limit. For energies above the breakup threshold, or for systems with no two-body bound-state (with only scattering states and resonances) the Luscher formula gets po...
Gluon scattering amplitudes at strong coupling
Energy Technology Data Exchange (ETDEWEB)
Alday, Luis F. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands); Maldacena, Juan [School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 (United States)
2007-06-15
We describe how to compute planar gluon scattering amplitudes at strong coupling in N = 4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent. We introduce the gravity version of dimensional regularization to define finite quantities. The leading and subleading IR divergencies are characterized by two functions of the coupling that we compute at strong coupling. We compute also the full finite form for the four point amplitude and we find agreement with a recent ansatz by Bern, Dixon and Smirnov.
New structures in scattering amplitudes: A review
Benincasa, Paolo
2014-02-01
We review some recent developments in the understanding of field theories in the perturbative regime. In particular, we discuss the notions of analyticity, unitarity and locality, and therefore the singularity structure of scattering amplitudes in general interacting theories. We describe their tree-level structure and their on-shell representations, as well as the links between the tree-level structure itself and the structure of the loop amplitudes. Finally, we describe the on-shell diagrammatics recently proposed both on general grounds and in the remarkable example of planar supersymmetric theories.
Scattering amplitudes in open superstring theory
Energy Technology Data Exchange (ETDEWEB)
Schlotterer, Oliver
2011-07-15
The present thesis deals with the theme field of the scattering amplitudes in theories of open superstrings. Especially two different formalisms for the handling of superstrings are introduced and applied for the calaculation of tree-level amplitudes - the Ramond- Neveu-Schwarz (RNS) and the Pure-Spinor (PS) formalism. The RNS approach is proved as flexible in order to describe compactification of the initially ten flat space-time dimensions to four dimensions. We solve the technical problems, which result from the interacting basing world-sheet theory with conformal symmetry. This is used to calculate phenomenologically relevant scattering amplitudes of gluons and quarks as well as production rates of massive harmonic vibrations, which were already identified as virtual exchange particles on the massless level. In the case of a low string mass scale in the range of some Tev the string-specific signatures in parton collisions can be observed in the near future in the LHC experiment at CERN and indicated as first experimental proof of the string theory. THose string effects occur universally for a wide class of string ground states respectively internal geometries and represent an elegant way to avoid the so-called landscape problem of the string theory. A further theme complex in this thesis is based on the PS formalism, which allows a manifestly supersymmetric treatment of scattering amplitudes in ten space-time dimension with sixteen supercharges. We introduce a family of superfields, which occur in massless amplitudes of the open string and can be naturally identified with diagrams of three-valued knots. Thereby we reach not only a compact superspace representation of the n-point field-theory amplitude but can also write the complete superstring n-point amplitude as minimal linear combination of partial amplitudes of the field theory as well as hypergeometric functions. The latter carry the string effects and are analyzed from different perspectives, above all
New structures in scattering amplitudes: a review
Benincasa, Paolo
2013-01-01
We review some recent developments in the understanding of field theories in the perturbative regime. In particular, we discuss the notions of analyticity, unitarity and locality, and therefore the singularity structure of scattering amplitudes in general interacting theories. We describe their tree-level structure and their on-shell representations, as well as the links between the tree-level structure itself and the structure of the loop amplitudes. Finally, we describe the on-shell diagrammatics recently proposed both on general grounds and in the remarkable example of planar supersymmetric theories. This review is partially based on lectures given at: Dipartimento di Fisica and INFN, Universit\\`a di Bologna; Departamento de F{\\i}sica de Part{\\i}culas, Universidade de Santiago de Compostela; and as part of the program Strings@ar Lectures on Advanced Topics of High Energy Physics held at the IAFE
Integrable spin chains and scattering amplitudes
Energy Technology Data Exchange (ETDEWEB)
Bartels, J.; Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute (Russian Federation); Sankt-Peterburgskij Univ., St. Petersburg (Russian Federation)
2011-04-15
In this review we show that the multi-particle scattering amplitudes in N=4 SYM at large N{sub c} and in the multi-Regge kinematics for some physical regions have the high energy behavior appearing from the contribution of the Mandelstam cuts in the complex angular momentum plane of the corresponding t-channel partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon composite states in the adjoint representation of the gauge group SU(N{sub c}). In the leading logarithmic approximation (LLA) their contribution to the six point amplitude is in full agreement with the known two-loop result. The Hamiltonian for the Mandelstam states constructed from n gluons in LLA coincides with the local Hamiltonian of an integrable open spin chain. We construct the corresponding wave functions using the integrals of motion and the Baxter-Sklyanin approach. (orig.)
Analytic amplitude models for forward scattering
Kang, K; Ezhela, Vladimir V; Gauron, P; Kuyanov, Yu V; Lugovsky, S B; Nicolescu, Basarab; Tkachenko, N P; Kuyanov, Yu. V.
2002-01-01
We report on fits of a large class of analytic amplitude models for forward scattering against the comprehensive data for all available reactions. To differentiate the goodness of the fits of many possible parametrizations to a large sample of data, we developed and used a set of quantitative indicators measuring statistical quality of the fits over and beyond the typical criterion of the $\\Chi^2 /dof$. These indicators favor models with a universal $ log^2 s$ Pomeron term, which enables one to extend the fit down to $\\sqrt s = 4$ GeV.
New fixed points of the renormalisation group for two-body scattering
Energy Technology Data Exchange (ETDEWEB)
Birse, M.C. [The University of Manchester, Theoretical Physics Division, School of Physics and Astronomy, Manchester (United Kingdom); Epelbaum, E. [Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik II, Fakultaet fuer Physik und Astronomie, Bochum (Germany); Gegelia, J. [Juelich Center for Hadron Physics, Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik, Juelich (Germany); Tbilisi State University, Tbilisi (Georgia)
2016-02-15
We outline a separable matrix ansatz for the potentials in effective field theories of non-relativistic two-body systems with short-range interactions. We use this ansatz to construct new fixed points of the renormalisation-group equation for these potentials. New fixed points indicate a much richer structure than previously recognized in the RG flows of simple short-range potentials. (orig.)
The scattering amplitude for rationally extended shape invariant Eckart potentials
Energy Technology Data Exchange (ETDEWEB)
Yadav, Rajesh Kumar, E-mail: rajeshastrophysics@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India); Khare, Avinash, E-mail: khare@iiserpune.ac.in [Raja Ramanna Fellow, Indian Institute of Science Education and Research (IISER), Pune-411021 (India); Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India)
2015-01-23
Highlights: • Bound states of rationally extended Eckart potentials have been discussed. • These potentials exhibit extended shape invariant properties. • The potentials which are isospectral to the conventional Eckart potential are considered. • The scattering amplitude of these potentials has been obtained. • For a check, m=0 provide the scattering amplitude for the conventional potential. - Abstract: We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally extended potentials is calculated analytically for the generalized mth (m=1,2,3,...) case by considering the asymptotic behavior of the scattering state wave functions which are written in terms of some new polynomials related to the Jacobi polynomials. As expected, in the m=0 limit, this scattering amplitude goes over to the scattering amplitude for the conventional Eckart potential.
Miracles in Scattering Amplitudes: from QCD to Gravity
Energy Technology Data Exchange (ETDEWEB)
Volovich, Anastasia [Brown Univ., Providence, RI (United States)
2016-10-09
The goal of my research project "Miracles in Scattering Amplitudes: from QCD to Gravity" involves deepening our understanding of gauge and gravity theories by exploring hidden structures in scattering amplitudes and using these rich structures as much as possible to aid practical calculations.
Chiral closed strings: four massless states scattering amplitude
Leite, Marcelo M.; Siegel, Warren
2017-01-01
We compute the scattering amplitudes of four massless states for chiral (closed) bosonic and type II superstrings using the Kawai-Lewellen-Tye ( KLT ) factorization method. The amplitude in the chiral bosonic case is identical to a field theory amplitude corresponding to the spin-2 tachyon, massless gravitational sector and massive spin-2 tardyon states of the spectrum. Chiral type II superstrings amplitude only possess poles associated with the massless gravitational sector. We briefly discuss the extension of the calculation to heterotic superstrings.
Chiral Closed strings: Four massless states scattering amplitude
Leite, Marcelo M
2016-01-01
We compute the scattering amplitudes of four massless states for chiral (closed) bosonic and type II superstrings using the Kawai-Lewellen-Tye ($KLT$) factorization method. The amplitude in the chiral bosonic case is identical to a field theory amplitude corresponding to the spin-$2$ tachyon, massless gravitational sector and massive spin-2 tardyon states of the spectrum. Chiral type II superstrings amplitude only possess poles associated with the massless gravitational sector. We briefly discuss the extension of the calculation to heterotic superstrings.
Energy Technology Data Exchange (ETDEWEB)
Navelet-Noualhier, H. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1967-06-15
Helicity amplitudes are expressed via the spinor amplitudes in terms of the Joos invariant which have been shown by Williams to be free from kinematical singularities. This procedure allows to analyze the kinematical singularities of helicity amplitudes and separate them out, which results into the definition of regularized helicity amplitudes. A crossing matrix for helicity amplitudes, is written down, corresponding to the continuation path used to cross spinor amplitudes. We verify explicitly that the corresponding crossing matrix for regularized helicity amplitudes is uniform as it should be. Kinematical constraints which generalize, to the case of arbitrary spins and masses, relations which must hold between helicity amplitudes at some values of the energy variable in {pi}N {yields} {pi}N, {pi}{pi} {yields} NN-bar and NN-bar {yields} NN-bar reactions, appear as a consequence of the existence of poles in the crossing matrix between regularized helicity amplitudes. An english version of this work has been written with G. Cohen-Tannoudji and A. Morel and submitted for publication to Annals of Physics. (author) [French] Les amplitudes d'helicite pour une reaction a deux corps sont exprimees, par l'intermediaire des amplitudes spinorielles, en fonction d'amplitudes invariantes de Joos qui sont, comme l'a montre Williams, sans singularites cinematiques. Ce procede nous permet d'analyser puis d'eliminer les singularites cinematiques des amplitudes d'helicite. Ceci nous conduit a la definition d'amplitudes d'helicite 'regularisees'. Une relation de 'croisement' entre amplitudes d'helicite est ecrite; elle realise leur prolongement analytique le long du chemin utilise pour 'croiser' les amplitudes spinorielles. Nous verifions que les elements de la matrice de croisement entre amplitudes d'helicite 'regularisees' sont bien uniformes. Les contraintes cinematiques qui
Cluster functions and scattering amplitudes for six and seven points
Harrington, Thomas; Spradlin, Marcus
2017-07-01
Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the mathematics of cluster algebras. The power of the bootstrap program for amplitudes is inversely proportional to the size of the intersection between these physical and mathematical constraints: ideally we would like a list of constraints which determine scattering amplitudes uniquely. We explore this intersection quantitatively for two-loop six- and seven-point amplitudes by providing a complete taxonomy of the Gr(4, 6) and Gr(4, 7) cluster polylogarithm functions of [15] at weight 4.
Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
2011-11-01
This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field, even if our continually evolving understanding of the subject might soon render this compilation incomplete. Why the fascination with scattering amplitudes, which have attracted the imagination and dedicated effort of so many physicists? Part of it stems from the belief, supported now by numerous examples, that unexpected simplifications of otherwise apparently complicated calculations do not happen by accident. Instead they provide a strong motivation to seek out an underlying explanation. The insight thereby gained can subsequently be used to make the next class of seemingly impossible calculations not only possible, but in some cases even trivial. This two-pronged strategy of exploring and exploiting the structure of gauge theory amplitudes appeals to a wide audience from formal theorists interested in mathematical structure for the sake of its own beauty to more phenomenologically-minded physicists eager to speed up the next generation of analysis software. Understandably it is the maximally supersymmetric 𝒩 = 4 Yang-Mills theory (SYM) which has the simplest structure and has correspondingly received the most attention. Rarely in theoretical physics are we fortunate enough to encounter a toy model which is simple enough to be solved completely yet rich enough to possess interesting non-trivial structure while simultaneously, and most importantly, being applicable (even if only as a good approximation) to a wide range of 'real' systems. The canonical example in quantum mechanics is of course the harmonic
Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
DEFF Research Database (Denmark)
Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy
2014-01-01
We present evidence that loop amplitudes in maximally supersymmetric (N=4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N=4 SYM has only logarithmic ...... singularities and is free of any poles at infinity—properties closely related to uniform transcendentality and the UV finiteness of the theory. We also briefly comment on implications for maximal (N=8) supergravity theory (SUGRA)....
Lectures on scattering amplitudes via AdS/CFT
Energy Technology Data Exchange (ETDEWEB)
Alday, L.F. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University (Netherlands)
2008-08-05
We review recent progress on computing scattering amplitudes of planar N=4 super Yang-Mills at strong coupling by using the AdS/CFT duality. We consider in detail the scattering of four gluons and do explicit computations by using both, dimensional regularization and a cut-off in the radial direction. The later scheme is particularly appropriate for understanding the conformal properties of the amplitudes. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
On Triple-Cut of Scattering Amplitudes
Mastrolia, Pierpaolo
2007-01-01
It is analysed the triple-cut of one-loop amplitudes in dimensional regularisation within spinor-helicity representation. The triple-cut is defined as a difference of two double-cuts with the same particle content, and a same propagator carrying, respectively, causal and anti-causal prescription in each of the two cuts. That turns out into an effective tool for extracting the coefficients of the three-point functions (and higher-point ones) from one-loop-amplitudes. The phase-space integration is oversimplified by using residues theorem to perform the integration over the spinor variables, via the holomorphic anomaly, and a trivial integration on the Feynman parameter. The results are valid for arbitrary values of dimensions.
Scattering Amplitudes via Algebraic Geometry Methods
DEFF Research Database (Denmark)
Søgaard, Mads
unitarity cuts. We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed...... in terms of certain linear combinations of multivariate residues and elliptic integrals computed from products of tree-level amplitudes. Several explicit examples are provided...
Scattering amplitudes and BCFW recursion in twistor space
Mason, Lionel; Skinner, David
2010-01-01
Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for n-particle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N2MHV super-amplitude. We also give simple closed form formulae for the mathcal{N} = 8 supergravity recursion and the MHV and overline {text{MHV}} amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N k MHV, the amplitudes are given by 2 n - 4 integrals in the form of Hilbert transforms of a product of n - k - 2 purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in mathcal{N} = 4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan.
Scattering Amplitudes: The Most Perfect Microscopic Structures in the Universe
Energy Technology Data Exchange (ETDEWEB)
Dixon, Lance J.; /CERN /SLAC
2011-11-04
This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N = 4 super-Yang-Mills theory, as well as (super)gravity. I also provide a pedagogical introduction to some of the basic tools used to organize and illuminate the color and kinematic structure of amplitudes. This article is an invited review introducing a special issue of Journal of Physics A devoted to 'Scattering Amplitudes in Gauge Theories'.
EPR = ER, scattering amplitude and entanglement entropy change
Energy Technology Data Exchange (ETDEWEB)
Seki, Shigenori, E-mail: sigenori@hanyang.ac.kr [Research Institute for Natural Science, Hanyang University, Seoul 133-791 (Korea, Republic of); Sin, Sang-Jin, E-mail: sjsin@hanyang.ac.kr [Department of Physics, Hanyang University, Seoul 133-791 (Korea, Republic of)
2014-07-30
We study the causal structure of the minimal surface of the four-gluon scattering, and find a world-sheet wormhole parametrized by Mandelstam variables, thereby demonstrate the EPR = ER relation for gluon scattering. We also propose that scattering amplitude is the change of the entanglement entropy by generalizing the holographic entanglement entropy of Ryu–Takayanagi to the case where two regions are divided in space–time.
Cluster Functions and Scattering Amplitudes for Six and Seven Points
Harrington, Thomas
2015-01-01
Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the mathematics of cluster algebras. The power of the bootstrap program for amplitudes is inversely proportional to the size of the intersection between these physical and mathematical constraints: ideally we would like a list of constraints which determine scattering amplitudes uniquely. We explore this intersection quantitatively for two-loop six- and seven-point amplitudes by providing a complete taxonomy of the Gr(4,6) and Gr(4,7) cluster polylogarithm functions of arXiv:1401.6446 at weight 4.
Compact multigluonic scattering amplitudes with heavy scalars and fermions
Ferrario, P; Talavera, P; Ferrario, Paola; Rodrigo, German; Talavera, Pere
2006-01-01
Combining the Berends-Giele and on-shell recursion relations we obtain an extremely compact expression for the scattering amplitude of a complex scalar-antiscalar pair and an arbitrary number of positive helicity gluons. This is one of the basic building blocks for constructing other helicity configurations from recursion relations. We also show explicity that the all positive helicity gluons amplitude for heavy fermions is proportional to the scalar one, confirming in this way the recently advocated SUSY-like Ward identities relating both amplitudes.
Conformal higher spin scattering amplitudes from twistor space
Adamo, Tim; McLoughlin, Tristan
2016-01-01
We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point anti-MHV amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.
Effective Field Theories from Soft Limits of Scattering Amplitudes.
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-05
We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
Quantum Corrections to Scattering Amplitude in Conical Space-time
Shiraishi, Kiyoshi
2015-01-01
It is known that the vacuum polarization of zero-point field arises around a conical singularity generated by an infinite, straight cosmic string. In this paper we study quantum electromagnetic corrections to the gravitational Aharonov-Bohm effect around a cosmic string. We find the scattering amplitude from a conical defect for charged Klein-Gordon field.
The Appell function F1 and Regge string scattering amplitudes
Directory of Open Access Journals (Sweden)
Jen-Chi Lee
2014-12-01
Full Text Available We show that each 26D open bosonic Regge string scattering amplitude (RSSA can be expressed in terms of one single Appell function F1 in the Regge limit. This result enables us to derive infinite number of recurrence relations among RSSA at arbitrary mass levels, which are conjectured to be related to the known SL(5,C dynamical symmetry of F1. In addition, we show that these recurrence relations in the Regge limit can be systematically solved so that all RSSA can be expressed in terms of one amplitude. All these results are dual to high energy symmetries of fixed angle string scattering amplitudes discovered previously [4–8].
Fidelity amplitude of the scattering matrix in microwave cavities
Schäfer, R.; Gorin, T.; Seligman, T. H.; Stöckmann, H.-J.
2005-06-01
The concept of fidelity decay is discussed from the point of view of the scattering matrix, and the 'scattering fidelity' is introduced as the parametric cross-correlation of a given S-matrix element, taken in the time domain, normalized by the corresponding autocorrelation function. We show that for chaotic systems, this quantity represents the usual fidelity amplitude, if appropriate ensemble and/or energy averages are taken. We present a microwave experiment where the scattering fidelity is measured for an ensemble of chaotic systems. The results are in excellent agreement with random matrix theory for the standard fidelity amplitude. The only parameter, namely the perturbation strength, could be determined independently from level dynamics of the system, thus providing agreement between theory and experiment without any free fit parameter.
Fidelity amplitude of the scattering matrix in microwave cavities
Energy Technology Data Exchange (ETDEWEB)
Schaefer, R [Fachbereich Physik, Philipps-Universitaet Marburg, Renthof 5, D-35032 Marburg (Germany); Gorin, T [Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Str. 38, D-01187 Dresden (Germany); Seligman, T H [Centro de Ciencias FIsicas, Universidad Nacional Autonoma de Mexico, Campus Morelos, C. P. 62251, Cuernavaca, Morelos (Mexico); Stoeckmann, H-J [Fachbereich Physik, Philipps-Universitaet Marburg, Renthof 5, D-35032 Marburg (Germany)
2005-06-01
The concept of fidelity decay is discussed from the point of view of the scattering matrix, and the 'scattering fidelity' is introduced as the parametric cross-correlation of a given S-matrix element, taken in the time domain, normalized by the corresponding autocorrelation function. We show that for chaotic systems, this quantity represents the usual fidelity amplitude, if appropriate ensemble and/or energy averages are taken. We present a microwave experiment where the scattering fidelity is measured for an ensemble of chaotic systems. The results are in excellent agreement with random matrix theory for the standard fidelity amplitude. The only parameter, namely the perturbation strength, could be determined independently from level dynamics of the system, thus providing agreement between theory and experiment without any free fit parameter.
Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
Bianchi, Marco S; Mauri, Andrea; Penati, Silvia; Santambrogio, Alberto
2011-01-01
For N=6 superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scatteringa amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is a nontrivial evidence of the scattering amplitudes/Wilson loop duality in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in terms of the N=4 SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four-loop correction to the amplitude. We also discuss the dual conformal invariance of the two-loop result.
The Lauricella functions and exact string scattering amplitudes
Lai, Sheng-Hong; Lee, Jen-Chi; Yang, Yi
2016-11-01
We discover that the 26 D open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state can be expressed in terms of the D-type Lauricella functions with associated SL(K+3,C) symmetry. As a result, SSA and symmetries or relations among SSA of different string states at various limits calculated previously can be rederived. These include the linear relations first conjectured by Gross [1-5] and later corrected and proved in [6-12] in the hard scattering limit, the recurrence relations in the Regge scattering limit with associated SL(5,C) symmetry [24-26] and the extended recurrence relations in the nonrelativistic scattering limit with associated SL(4,C) symmetry [29] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.
The Lauricella Functions and Exact String Scattering Amplitudes
Lai, Sheng-Hong; Yang, Yi
2016-01-01
We discover that the 26D open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state can be expressed in terms of the D-type Lauricella functions with associated SL(K+3,C) symmetry. As a result, SSA and symmetries or relations among SSA of different string states at various limits calculated previously can be rederived. These include the linear relations first conjectured by Gross [1-3] and later corrected and proved in [4-9] in the hard scattering limit, the recurrence relations in the Regge scattering limit with associated SL(5,C) symmetry [19-21] and the extended recurrence relations in the nonrelativistic scattering limit with associated SL(4,C) symmetry [24] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.
Measuring the phase of the scattering amplitude with vortex beams
Ivanov, I P
2012-01-01
We show that colliding vortex beams instead of (approximate) plane waves can lead to a direct measurement of how the overall phase of the scattering amplitude changes with the scattering angle. Since the overall phase is inaccessible in a plane wave collision, this measurement would be of great importance for a number of topics in hadronic physics, for example, for meson production in the resonance region and for the physics of nucleon resonances. Although the required parameters of the vortex beams have not yet been achieved experimentally, they deserves further dedicated experimental research due to the high expected physics pay-off.
Scattering amplitude and bosonization duality in general Chern-Simons vector models
Yokoyama, Shuichi
2016-09-01
We present the exact large N calculus of four point functions in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine the two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, an unusual crossing relation and a non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to the Chern-Simons theory interacting with free fermions.
Harmonic R-matrices for scattering amplitudes and spectral regularization
Energy Technology Data Exchange (ETDEWEB)
Ferro, Livia; Plefka, Jan [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Lukowski, Tomasz [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik; Humboldt-Univ. Berlin (Germany). IRIS Adlershof; Meneghelli, Carlo [Hamburg Univ. (Germany). Fachbereich 11 - Mathematik; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Staudacher, Matthias [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany)
2012-12-15
Planar N=4 super Yang-Mills appears to be integrable. While this allows to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R-matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R-matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of non-integrable four-dimensional field theories.
Infrared singularities of scattering amplitudes in perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Becher, Thomas [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Neubert, Matthias [Johannes Gutenberg-Universitaet Mainz, Mainz (Germany)
2013-11-01
An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.
Harmonic R matrices for scattering amplitudes and spectral regularization.
Ferro, Livia; Łukowski, Tomasz; Meneghelli, Carlo; Plefka, Jan; Staudacher, Matthias
2013-03-22
Planar N = 4 supersymmetric Yang-Mills theory appears to be integrable. While this allows one to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R matrix of the integrable N = 4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of nonintegrable four-dimensional field theories.
Scattering amplitudes and Wilson loops in twistor space
Energy Technology Data Exchange (ETDEWEB)
Adamo, Tim; Mason, Lionel [Mathematical Institute, 24-29 St. Giles' , Oxford OX1 3LB (United Kingdom); Bullimore, Mathew [Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP (United Kingdom); Skinner, David, E-mail: adamo@maths.ox.ac.uk [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2 L 2Y5 (Canada)
2011-11-11
This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for N=4 super-Yang-Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally supersymmetric Yang-Mills theory. We start by deriving the MHV rules for gauge theory amplitudes from the twistor action in an axial gauge in twistor space, and show that this gives rise to the original momentum space version given by Cachazo, Svrcek and Witten. We then go on to obtain from these the construction of the momentum twistor space loop integrand using (planar) MHV rules and show how it arises as the expectation value of a holomorphic Wilson loop in twistor space. We explain the connection between the holomorphic Wilson loop and certain light-cone limits of correlation functions. We give a brief review of other ideas in connection with amplitudes in twistor space: twistor-strings, recursion in twistor space, the Grassmannian residue formula for leading singularities and amplitudes as polytopes. This paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Scattering amplitudes in gauge theories'. (review)
Advanced methods for scattering amplitudes in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Peraro, Tiziano
2014-09-24
We present new techniques for the evaluation of multi-loop scattering amplitudes and their application to gauge theories, with relevance to the Standard Model phenomenology. We define a mathematical framework for the multi-loop integrand reduction of arbitrary diagrams, and elaborate algebraic approaches, such as the Laurent expansion method, implemented in the software Ninja, and the multivariate polynomial division technique by means of Groebner bases.
Massive quark-gluon scattering amplitudes at tree level
Hall, Anthony
2008-01-01
Results for four-, five-, and six-parton tree amplitudes for massive quark-antiquark scattering with gluons are calculated using the recursion relations of Britto, Cachazo, Feng, and Witten. The required diagrams are generated using shifts of the momenta of a pair of massless legs to complex values. Checks verifying the calculations are described, and a simple formula for the shifted spinors of an internal gluon is presented.
Hadronic scattering amplitudes medium-energy constraints on asymptotic behaviour
Cudell, J R; Gauron, P; Kang, K; Kuyanov, Yu V; Lugovsky, S B; Nicolescu, Basarab; Tkachenko, N P; Kuyanov, Yu. V.
2002-01-01
We consider several classes of analytic parametrisations of hadronic scattering amplitudes, and compare their predictions to all available forward data (p p, pbar p, pi p, K p, gamma p, gamma gamma, Sigma p). Although these parametrisations are very close for sqrt(s) > 9 GeV, it turns out that they differ markedly at low energy, where a universal pomeron term ~log^2(s) enables one to extend the fit down to sqrt(s)=4 GeV.
Two-Loop Scattering Amplitudes from the Riemann Sphere
Geyer, Yvonne; Monteiro, Ricardo; Tourkine, Piotr
2016-01-01
The scattering equations give striking formulae for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the worldsheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the colour dependence, which includes non-planar contributions.
Two-loop scattering amplitudes from the Riemann sphere
Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo; Tourkine, Piotr
2016-12-01
The scattering equations give striking formulas for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor-string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the world sheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the color dependence, which includes nonplanar contributions.
EPR = ER and Scattering Amplitude as Entanglement Entropy Change
Seki, Shigenori
2014-01-01
Alday and Maldacena have found an exact minimal surface of open string world-sheet describing a gluon scattering. We study the causal structure of that minimal surface in AdS of position space, and find a world-sheet wormhole parametrized by Mandelstam variables. If we figure a gluon as an open string in AdS, the ribbon connecting the two strings always pass the world-sheet wormhole, demonstrating the EPR = ER for gluon scattering. Since entanglement is caused by an interaction, one can ask what is the relation between entanglement entropy and the scattering amplitude. We propose an answer by generalizing the holographic entanglement entropy (EE) of Ryu-Takayanagi to the case where two regions are divided in space-time and interpret the result as the change of EE.
Frederico, Tobias; Pace, Emanuele; Salme`, Giovanni
2010-01-01
The electromagnetic properties of the deuteron are investigated within a Light-Front Hamiltonian Dynamics framework, with a current operator that contains both one-body and two-body contributions. In this work, we are considering new two-body contributions, with a dynamical nature generated within a Yukawa model and a structure inspired by a recent analysis of the current operator, that acts on the three-dimensional valence component and fulfills the Ward-Takahashi identity. Preliminary results for the magnetic moment are shown.
Long-distance singularities in multi-leg scattering amplitudes
Gardi, Einan; Duhr, Claude
2016-01-01
We report on the recent completion of the three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes. This brings the state-of-the-art knowledge of long-distance singularities in multi-leg QCD amplitudes with any number of massless particles to three loops. The result displays some novel features: this is the first time non-dipole corrections appear, which directly correlate the colour and kinematic degrees of freedom of four coloured partons. We find that non-dipole corrections appear at three loops also for three coloured partons, but these are independent of the kinematics. The final result is remarkably simple when expressed in terms of single-valued harmonic polylogarithms, and it satisfies several non-trivial constraints. In particular, it is consistent with the high-energy limit behaviour and it satisfies the expected factorization properties in two-particle collinear limits.
Cluster algebras in Scattering Amplitudes with special 2D kinematics
Torres, Marcus A C
2013-01-01
We study the cluster algebra of the kinematic configuration space $Conf_n(\\mathbb{P}^3)$ of a n-particle scattering amplitude restricted to the special 2D kinematics. We found that the n-points two loop MHV remainder function found in special 2D kinematics depend on a selection of \\XX-coordinates that are part of a special structure of the cluster algebra related to snake triangulations of polygons. This structure forms a necklace of hypercubes beads in the corresponding Stasheff polytope. Furthermore in $n = 12$, the cluster algebra and the selection of \\XX-coordinates in special 2D kinematics replicates the cluster algebra and the selection of \\XX-coordinates of $n=6$ two loop MHV amplitude in 4D kinematics.
Analytic Amplitudes for Hadronic Forward Scattering COMPETE Update
Nicolescu, Basarab; Ezhela, Vladimir V; Gauron, P; Kang, K; Kuyanov, Yu V; Lugovsky, S B; Martynov, E S; Razuvaev, E A; Tkachenko, N P; Kuyanov, Yu. V.
2002-01-01
We consider several classes of analytic parametrizations of hadronic scattering amplitudes, and compare their predictions to all available forward data in hadron-hadron, gamma-p and gamma-gamma reactions. Although these parametrizations are very close for SQRTs larger than 9 GeV, it turns out that they differ markedly at low energy, where a universal Pomeron term like ln**2 s enables one to extend the fit down to SQRTs equal to 4 GeV. We present predictions on the total cross sections and on the ratio of the real part to the imaginary part of the elastic amplitude (RHO parameter) for present and future pp and antipp colliders, and on total cross sections for gamma-p into hadrons at cosmic-ray energies and for gamma-gamma into hadrons up to SQRTs equal to 1 TeV.
Du, Yi-Jian; Wu, Yong-Shi
2016-01-01
In this talk, we review our recent work on direct evaluation of tree-level MHV amplitudes by Cachazo-He-Yuan (CHY) formula. We also investigate the correspondence between solutions to scattering equations and amplitudes in four dimensions along this line. By substituting the MHV solution of scattering equations into the integrated CHY formula, we explicitly calculate the tree-level MHV amplitudes for four dimensional Yang-Mills theory and gravity. These results naturally reproduce the Parke-Taylor and Hodges formulas. In addition, we derive a new compact formula for tree-level single-trace MHV amplitudes in Einstein-Yang-Mills theory, which is equivalent to the known Selivanov-Bern-De Freitas-Wong (SBDW) formula. Other solutions do not contribute to the MHV amplitudes in Yang-Mills theory, gravity and Einstein-Yang-Mills theory. We further investigate the correspondence between solutions of scattering equation and helicity configurations beyond MHV and proposed a method for characterizing solutions of scatter...
Amplitude analysis of $\\bar{K}N$ scattering
Fernandez-Ramirez, Cesar
2016-01-01
We present the results of a coupled-channel model for $\\bar{K}N$ scattering in the resonance region. The model fulfills unitarity, has the correct analytical properties for the amplitudes and the partial waves have the right threshold behavior. The parameters of the model have been established by fitting single-energy partial waves up to $J=7/2$ and up to 2.15 GeV of center-of-mass energy. The $\\Lambda^*$ and $\\Sigma^*$ spectra has been obtained, providing a comprehensive picture of the $S=-1$ hyperon spectrum. We use the structure of the hyperon spectrum and Regge phenomenology to gain insight on the nature of the $\\Lambda(1405)$ resonances.
Improvement of the Calculation of Scattering Amplitudes with External Fermions
Chopin, E
1998-01-01
In this paper, we expose an improvement of a method for computing scattering amplitudes that include external fermions (with polarization) with the following features: the formulas are quite general and work for different kinematic configurations and different external masses, they are explicitely covariant, they do not depend on a specific representation of the Dirac matrices and they have a meaningful limit when the masses tend to 0. The results presented make use of some well known formulas describing the density matrices in terms of projection operators within a more general formalism. Since our formulas intend to be as general as possible, we also take into account the possibility of a transverse polarization for massless fermions.
Frederico, Tobias; Viviani, Michele
2011-01-01
The Nakanishi perturbative integral representation of the four-dimensional T-matrix is investigated in order to get a workable treatment for scattering states, solutions of the inhomogeneous Bethe-Salpeter Equation, in Minkowski space. The projection onto the null-plane of the four-dimensional inhomogeneous Bethe-Salpeter Equation plays a key role for devising an equation for the Nakanishi weight function (a real function), as in the homogeneous case that corresponds to bound states and it has been already studied within different frameworks. In this paper, the whole formal development is illustrated in detail and applied to a system, composed by two massive scalars interacting through the exchange of a massive scalar. The explicit expression of the scattering integral equations are also obtained in ladder approximation, and, as simple applications of our formalism, some limiting cases, like the zero-energy limit and the Wick-Cutkosky model in the continuum, are presented.
Off-shell scattering amplitudes in the double-logarithmic approximation
Ermolaev, B I; Olness, F; Troyan, S I
2005-01-01
When scattering amplitudes are calculated in the double-logarithmic approximation, it is possible to relate the double-logarithmic on-shell and off-shell amplitudes. Explicit relations are obtained for scattering amplitudes in QED, QCD, and the ElectroWeak Standard Model. The off-shell amplitudes are considered in the hard and the Regge kinematic limits. We compare our results in both the Feynman and Coulomb gauges.
Relativistic chiral representation of the \\pi N scattering amplitude
Alarcón, J M; Oller, J A; Alvarez-Ruso, L
2011-01-01
We have analyzed pion-nucleon scattering using the manifestly relativistic covariant frameworks of Infrared Regularization (IR) and Extended-On-Mass-Shell (EOMS) up to O(q^3) in the chiral expansion, where q is a generic small momentum. We describe the low-energy phase shifts with a similar quality as previously achieved with Heavy Baryon Chiral Perturbation Theory, being the EOMS description better than the IR one. The Goldberger-Treiman discrepancy is extracted from data of partial wave analyses using both schemes, obtaining an unacceptable large value for the case of IR due to the loop contribution. On the other hand, EOMS gives small values compatible with other phenomenological approaches. Finally, we have unitarized the amplitudes provided by both schemes to extend the range of our description obtaining a good agreement with the data up to energies of \\sqrt{s}\\approx 1.3 GeV for the EOMS scheme while IR can not go beyond energies of \\sqrt{s}\\approx 1.25 GeV due to the unphysical cut that this scheme int...
The Stoyanovsky-Ribault-Teschner Map and String Scattering Amplitudes
Giribet, G; Giribet, Gaston; Nakayama, Yu
2005-01-01
Recently, Ribault and Teschner pointed out the existence of a one-to-one correspondence between N-point correlation functions for the SL(2,C)_k/SU(2) WZNW model on the sphere and certain set of 2N-2-point correlation functions in Liouville field theory. This result is based on a seminal work by Stoyanovsky. Here, we discuss the implications of this correspondence focusing on its application to string theory on curved backgrounds. For instance, we analyze how the divergences corresponding to worldsheet instantons in AdS_3 can be understood as arising from the insertion of the dual screening operator in the Liouville theory side. We also study the pole structure of N-point functions in the 2D Euclidean black hole and its holographic meaning in terms of the Little String Theory. This enables us to interpret the correspondence between CFTs as encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering amplitudes violating the winding number conservation in those backgrounds and provide a formu...
Scattering amplitudes over finite fields and multivariate functional reconstruction
Peraro, Tiziano
2016-01-01
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topol...
Scattering amplitudes over finite fields and multivariate functional reconstruction
Peraro, Tiziano
2016-12-01
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.
Scattering amplitudes over finite fields and multivariate functional reconstruction
Energy Technology Data Exchange (ETDEWEB)
Peraro, Tiziano [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)
2016-12-07
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.
Recursion relations and scattering amplitudes in the light-front formalism
Cruz-Santiago, Christian A
2013-01-01
The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends-Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.
Irreducible tensor basis and general Fierz relations for Bhabha scattering like amplitudes
Liu, Tao
2016-01-01
We construct an irreducible s- and t-channel tensor basis for Bhabha scattering like amplitudes based on the properties of the underlying Lorentz symmetry in four space-time dimensions. In the given basis the calculation of amplitude contractions like the amplitude square reduces to the contraction of their corresponding coefficient tensors. Further the basis retains the full amplitude information and thus can be applied in off-shell cases. The general Fierz transformations which relate the s- and t-channel basis with each other are obtained. As an example for application we use the basis to calculate the tree-level Bhabha scattering amplitude.
Implementation of Recursion Relations in Gluon Scattering Amplitude Calculations in AdS4 /CFT3
Dokmetzoglou, Nikolaos; Kharel, Savan
2017-01-01
The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence is a duality between a theory of gravity in curved-space (AdS) and a conformally-invariant quantum field theory in flat-space (CFT). Scattering amplitudes are observables associated with the probability of the interaction of a given assembly of particles. Gluons, being the exchange particles associated with the strong nuclear force, which holds quarks together to form protons, are abundant byproducts of fundamental particle collisions. Thus, studying gluon scattering amplitudes is an effective way of deepening our understanding of these observables in AdS/CFT. Traditionally, Feynman diagrams have been used to calculate such scattering amplitudes. In this project, we use factorization properties and recursion relations to simplify these calculations. More specifically, we calculate multiple (different helicity combinations) four-point gluon scattering amplitudes in AdS4 /CFT3 (4-D AdS and 3-D CFT) as sums of products of three-point amplitudes. And then we calculate a five-point gluon scattering amplitude in AdS4 /CFT3 by decomposing it into a sum of products of these four-point and three-point amplitudes. Finally we comment on useful identities for checking these amplitudes. This work was supported by a Weinstein Davidson College Research Initiative Summer Research grant.
High-Energy String Scattering Amplitudes and Signless Stirling Number Identity
Directory of Open Access Journals (Sweden)
Jen-Chi Lee
2012-07-01
Full Text Available We give a complete proof of a set of identities (7 proposed recently from calculation of high-energy string scattering amplitudes. These identities allow one to extract ratios among high-energy string scattering amplitudes in the fixed angle regime from high-energy amplitudes in the Regge regime. The proof is based on a signless Stirling number identity in combinatorial theory. The results are valid for arbitrary real values L rather than only for L=0,1 proved previously. The identities for non-integer real value L were recently shown to be realized in high-energy compactified string scattering amplitudes [He S., Lee J.C., Yang Y., arXiv:1012.3158]. The parameter L is related to the mass level of an excited string state and can take non-integer values for Kaluza-Klein modes.
Maharana, Jnanadeva
2016-01-01
The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is adopted. The analyticity properties of the causal, the retarded and the advanced functions associated with the four point elastic amplitudes are studied. The analog of the Lehmann-Jost-Dyson representation is obtained in higher dimensional field theories. The generalized J-L-D representation is utilized to derive the t-plane analyticity property of the amplitude. The existence of an ellipse analogous to the Lehmann ellipse is demonstrated. Thus a fixed-t dispersion relation can be written down with finite number of subtractions due to the temperedness of the amplitudes. The domain of analyticity of scattering amplitude in $s$ and $t$ variables is extended by imposing unitarity constraints. A generalized version of Martin's theorem is derived to prove the existence of such a domai...
Eikonal fit to $pp$ and $\\bar{p}p$ scattering and the edge in the scattering amplitude
Block, Martin M; Ha, Phuoc; Halzen, Francis
2015-01-01
We make a detailed eikonal fit to current data on the total and elastic scattering cross sections, the ratios $\\rho$ of the real to the imaginary parts of the forward elastic scattering amplitudes, and the logarithmic slopes $B$ of the differential cross sections $d\\sigma/dt$ at $t=0$, for proton-proton and antiproton-proton scattering at center-of-mass energies $W$ from 5 GeV to 57 TeV. The fit allows us to investigate the structure of the eikonal amplitudes in detail, including the impact-parameter structure of the energy-independent edge in the scattering amplitude shown to exist by Block {\\em et al.} \\cite{edge}. We show that the edge region has an essentially fixed shape with a peak at approximately the "black disk" radius $R_{\\rm tot}=\\sqrt{\\sigma_{\\rm tot}/2\\pi}$ of the scattering amplitude, a constant width $t_{\\rm edge}\\approx 1$ fm, and migrates to larger impact parameters with increasing energy proportionally to $R_{\\rm tot}$. We comment on possible physical mechanisms which could lead to the edge....
Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2002-03-19
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.
Maharana, Jnanadeva
2017-01-01
The properties of the high energy behavior of the scattering amplitude of massive, neutral, and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik, and Zimmermann (LSZ) is adopted. The analyticity properties of the causal, the retarded, and the advanced functions associated with the four point elastic amplitudes are studied. The analog of the Lehmann-Jost-Dyson representation is obtained in higher dimensional field theories. The generalized J-L-D representation is utilized to derive the t-plane analyticity property of the amplitude. The existence of an ellipse analogous to the Lehmann ellipse is demonstrated. Thus a fixed-t dispersion relation can be written down with a finite number of subtractions due to the temperedness of the amplitudes. The domain of analyticity of scattering amplitude in s and t variables is extended by imposing unitarity constraints. A generalized version of Martin's theorem is derived to prove the existence of such a domain in D-dimensional field theories. It is shown that the amplitude can be expanded in a power series in t which converges for |" separators=" t | < R , R being s-independent. The positivity properties of absorptive amplitudes are derived to prove the t-plane analyticity of amplitude. In the extended analyticity domain dispersion relations are written with two subtractions. The bound on the total cross section is derived from LSZ axioms without any extra ad hoc assumptions.
High-energy two-body photoproduction
Salin, P
1974-01-01
Considers three aspects of two-body photoproduction reactions: vector meson production as a tool to investigate properties of diffractive reactions; the occurrence of a possible J=0 fixed pole in the Compton amplitude; and pseudoscalar meson photoproduction. (73 refs).
On the tree-level structure of scattering amplitudes of massless particles
Benincasa, Paolo; Conde, Eduardo
2011-11-01
We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their poles and zeroes. The latter determine the boundary term arising in the BCFW-representation when the amplitudes do not vanish as some momenta are taken to infinity along some complex direction. Specifically, such a boundary term can be expressed as a sum of products of two on-shell amplitudes with fewer external states and a factor dependent on the location of the relevant zeroes and poles. This allows us to recast the amplitudes to have the standard BCFW-structure, weighted by a simple factor dependent on a subset of zeroes and poles of the amplitudes. We further comment on the physical interpretation of the zeroes as a particular kinematic limit in the complexified momentum space. The main implication of the existence of such recursion relations is that the tree-level approximation of any consistent theory of massless particles can be fully determined just by the knowledge of the corresponding three-particle amplitudes.
Energy Technology Data Exchange (ETDEWEB)
Artemyev, A. V., E-mail: ante0226@gmail.com [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS - University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2015-06-15
In this paper, we study relativistic electron scattering by fast magnetosonic waves. We compare results of test particle simulations and the quasi-linear theory for different spectra of waves to investigate how a fine structure of the wave emission can influence electron resonant scattering. We show that for a realistically wide distribution of wave normal angles θ (i.e., when the dispersion δθ≥0.5{sup °}), relativistic electron scattering is similar for a wide wave spectrum and for a spectrum consisting in well-separated ion cyclotron harmonics. Comparisons of test particle simulations with quasi-linear theory show that for δθ>0.5{sup °}, the quasi-linear approximation describes resonant scattering correctly for a large enough plasma frequency. For a very narrow θ distribution (when δθ∼0.05{sup °}), however, the effect of a fine structure in the wave spectrum becomes important. In this case, quasi-linear theory clearly fails in describing accurately electron scattering by fast magnetosonic waves. We also study the effect of high wave amplitudes on relativistic electron scattering. For typical conditions in the earth's radiation belts, the quasi-linear approximation cannot accurately describe electron scattering for waves with averaged amplitudes >300 pT. We discuss various applications of the obtained results for modeling electron dynamics in the radiation belts and in the Earth's magnetotail.
Liu, Xiaodong
2017-08-01
A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functional decays like the bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functional continuously depends on the scattering amplitude, this further implies that the novel sampling method is extremely stable with respect to errors in the data. Different to the classical sampling method such as the linear sampling method or the factorization method, from the numerical point of view, the novel indicator takes its maximum near the boundary of the underlying target and decays like the bessel functions as the sampling points go away from the boundary. The numerical simulations also show that the proposed sampling method can deal with multiple multiscale case, even the different components are close to each other.
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2002-03-12
Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle-antiparticle amplitude. This process differs from conventional on-shell Mandelstam s,t,u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel nonperturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle-antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the nonrelativistic Coulomb problem, including the forward scattering singularity , the essential singularity in the phase, and the Bohr bound-state spectrum.
Meggiolaro, E
2005-01-01
We shall discuss about the infrared finitness and some analyticity properties of the loop-loop scattering amplitudes in gauge theories, when going from Minkowskian to Euclidean theory, and we shall see how they can be related to the still unsolved problem of the s-dependence of the hadron-hadron total cross-sections.
Scattering of gravitational radiation - Second order moments of the wave amplitude
Macquart, JP
2004-01-01
Gravitational radiation that propagates through an inhomogeneous mass distribution is subject to random gravitational tensing, or scattering, causing variations in the wave amplitude and temporal smearing of the signal. A statistical theory is constructed to treat these effects. The statistical prop
Yadav, Rajesh Kumar; Mandala, Bhabani Prasad
2013-01-01
We consider the recently discovered, one parameter family of exactly solvable shape invariant potentials which are isospectral to the generalized P\\"oschl-Teller potential. By explicitly considering the asymptotic behaviour of the Xm Jacobi polynomials associated with this system (m = 1, 2, 3, ...), the scattering amplitude for the one parameter family of potentials is calculated explicitly.
Energy Technology Data Exchange (ETDEWEB)
Lai, Sheng-Hong; Lee, Jen-Chi; Yang, Yi [Department of Electrophysics, National Chiao Tung University,1001 University Street, Hsinchu, ROC (China)
2016-05-31
We review and extend high energy four point string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s−t and t−u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one higher spin string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.
Lai, Sheng-Hong; Yang, Yi
2016-01-01
We review and extend high energy string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s-t and t-u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one leading trojectory string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.
Lai, Sheng-Hong; Lee, Jen-Chi; Yang, Yi
2016-05-01
We review and extend high energy four point string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s- t and t- u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one higher spin string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.
Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
Mastrolia, P; Reiter, T; Tramontano, F
2010-01-01
SAMURAI is a tool for the automated numerical evaluation of one-loop corrections to any scattering amplitudes within the dimensional-regularization scheme. It is based on the decomposition of the integrand according to the OPP-approach, extended to accommodate an implementation of the generalized d-dimensional unitarity-cuts technique, and uses a polynomial interpolation exploiting the Discrete Fourier Transform. SAMURAI can process integrands written either as numerator of Feynman diagrams or as product of tree-level amplitudes. We discuss some applications, among which the 6- and 8-photon scattering in QED, and the 6-quark scattering in QCD. SAMURAI has been implemented as a Fortran90 library, publicly available, and it could be a useful module for the systematic evaluation of the virtual corrections oriented towards automating next-to-leading order calculations relevant for the LHC phenomenology.
Scattering amplitudes of massive N =2 gauge theories in three dimensions
Agarwal, Abhishek; Lipstein, Arthur E.; Young, Donovan
2014-02-01
We study the scattering amplitudes of mass-deformed Chern-Simons theories and Yang-Mills-Chern-Simons theories with N =2 supersymmetry in three dimensions. In particular, we derive the on-shell supersymmetry algebras which underlie the scattering matrices of these theories. We then compute various 3 and 4-point on-shell tree-level amplitudes in these theories. For the mass-deformed Chern-Simons theory, odd-point amplitudes vanish and we find that all of the 4-point amplitudes can be encoded elegantly in superamplitudes. For the Yang-Mills-Chern-Simons theory, we obtain all of the 4-point tree-level amplitudes using a combination of perturbative techniques and algebraic constraints and we comment on difficulties related to computing amplitudes with external gauge fields using Feynman diagrams. Finally, we propose a Britto-Cachazo-Feng-Witten recursion relation for mass-deformed theories in three dimensions and discuss the applicability of this proposal to mass-deformed N =2 theories.
On the Tree-Level Structure of Scattering Amplitudes of Massless Particles
Benincasa, Paolo
2011-01-01
We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their poles and zeroes. The latter determine the boundary term arising in the BCFW-representation when the amplitudes do not vanish as some momenta are taken to infinity along some complex direction. Specifically, such a boundary term can be expressed as a sum of products of two on-shell amplitudes with fewer external states and a factor dependent on the location of the relevant zeroes and poles. This allows us to recast the amplitudes to have the standard BCFW-structure, weighted by a simple factor dependent on a subset of zeroes and poles of the amplitudes. We further comment on the physical interpretation of the zeroes as a particular kinematic limit in the complexified momentum space. The main implication of the existence of such recursion relations is that the tree-level appro...
The Exact SL(K+3,C) Symmetry of String Scattering Amplitudes
Lai, Sheng-Hong; Yang, Yi
2016-01-01
We discover that the 26D open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state can be expressed in terms of the D-type Lauricella functions with associated SL(K+3,C) symmetry. As a result, SSA and symmetries or relations among SSA of different string states at various limits calculated previously can be rederived. These include the linear relations conjectured by Gross [1-3] and proved in [4-9] in the hard scattering limit, the recurrence relations in the Regge scattering limit [14-16] and the extended recurrence relations in the nonrelativistic scattering limit [19] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.
The Inverse Amplitude Method in $\\pi\\pi$ Scattering in Chiral Perturbation Theory to Two Loops
Nieves, J; Ruiz-Arriola, E
2002-01-01
The inverse amplitude method is used to unitarize the two loop $\\pi\\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.
New dispersion relations in the description of $\\pi\\pi$ scattering amplitudes
Kaminski, R; Grynkiewicz, P; Peláez, J R; Ynduráin, F J
2009-01-01
We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the $\\pi\\pi$ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three $\\pi\\pi$ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for $\\pi\\pi$ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.
Smooth interpolation between orear-and fixed angle scaling behaviour of the scattering amplitude
Bugrij, A. I.; Chikovani, Z. E.; Jenkovsky, L. L.
1980-03-01
A unified picture of both soft and hard hadronic collisions is suggested. The basis idea is to use Regge trajectories of the type 10052_2005_Article_BF01477306_TeX2GIFE1.gif α (t) = α (0) - γ ln (1 + β sqrt {t_0 - t} ) in dual models with Mandelstam analyticity. The idea is applied to elastic proton-proton scattering to derive kinematical boundaries of the asymptotic (Regge- t R and scaling- S sc., t sc.) regimes, to fix the angular dependence in the scaling-and the t-dependence in the Regge domain of the scattering amplitude and to interpolate between the two asymptotic domains.
Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
Yang, Gang
2007-01-01
Following the recent proposal of Alday and Maldacena to obtain the strong coupling scattering amplitude in N=4 SYM via AdS/CFT, we point out that a unique solution can be obtained by imposing all the Virasoro constraints. In the case of four-gluon scattering, this solution is identical to the Alday-Maldacena solution, which is in accordance with the ansatz of Bern, Dixon and Smirnov. This also solves the moduli space problem of the four-point solution in a recent paper of Mironov, Morozov and...
Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge
Lee, Taejin
2017-01-01
We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field...
Grassmannians for scattering amplitudes in 4d $\\mathcal{N}=4$ SYM and 3d ABJM
Elvang, Henriette; Keeler, Cynthia; Lam, Thomas; Olson, Timothy M; Roland, Samuel B; Speyer, David E
2014-01-01
Scattering amplitudes in 4d $\\mathcal{N}=4$ super Yang-Mills theory (SYM) can be described by Grassmannian contour integrals whose form depends on whether the external data is encoded in momentum space, twistor space, or momentum twistor space. After a pedagogical review, we present a new, streamlined proof of the equivalence of the three integral formulations. A similar strategy allows us to derive a new Grassmannian integral for 3d $\\mathcal{N}=6$ ABJM theory amplitudes in momentum twistor space: it is a contour integral in an orthogonal Grassmannian with the novel property that the internal metric depends on the external data. The result can be viewed as a central step towards developing an amplituhedron formulation for ABJM amplitudes. Various properties of Grassmannian integrals are examined, including boundary properties, pole structure, and a homological interpretation of the global residue theorems for $\\mathcal{N}=4$ SYM.
Gryniuk, Oleksii; Hagelstein, Franziska; Pascalutsa, Vladimir
2016-08-01
The forward Compton scattering off the proton is determined by substituting the empirical total photoabsorption cross sections into dispersive sum rules. In addition to the spin-independent amplitude evaluated previously [Phys. Rev. D 92, 074031 (2015)], we obtain the spin-dependent amplitude over a broad energy range. The two amplitudes contain all the information about the forward CS process and we hence can reconstruct the observables. The results are compared with predictions of chiral perturbation theory where available. The low-energy expansion of the spin-dependent Compton scattering amplitude yields the Gerasimov-Drell-Hearn (GDH) sum rule and relations for the forward spin polarizabilities (FSPs) of the proton. Our evaluation provides an empirical verification of the GDH sum rule for the proton and yields empirical values of the proton FSPs. For the GDH integral, we obtain 204.5 (21.4 ) μ b , in agreement with the sum rule prediction: 204.784481 (4 ) μ b . For the FSPs, we obtain γ0=-92.9 (10.5 )×10-6 fm4 and γ0¯=48.4 (8.2 )×10-6 fm6, improving on the accuracy of previous evaluations.
Evaluation of the forward Compton scattering off protons: I. Spin-independent amplitude
Gryniuk, Oleksii; Pascalutsa, Vladimir
2015-01-01
We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections. We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section, and evaluate the various spin-independent sum rules using these fits. For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): $\\alpha_{E1}+\\beta_{M1}=(14.0\\pm 0.20)\\times 10^{-4}\\,\\mathrm{fm}^3$. An analogous sum rule involving the quadrupole polarizabilities is evaluated here too. The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). We also remark on sum rules for the elastic component of polarizabilities.
Evaluation of the forward Compton scattering off protons: Spin-independent amplitude
Gryniuk, Oleksii; Hagelstein, Franziska; Pascalutsa, Vladimir
2015-10-01
We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections. We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section and evaluate the various spin-independent sum rules using these fits. For the sum of proton electric and magnetic dipole polarizabilities governed by the Baldin sum rule, we obtain the following average (between the two fits): αE 1+βM 1=14.0 (2 )×1 0-4 fm3 . An analogous sum rule involving the quadrupole polarizabilities of the proton is evaluated too. The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). We remark on sum rules for the elastic component of polarizabilities.
Role of Möbius constants and scattering functions in Cachazo-He-Yuan scalar amplitudes
Lam, C. S.; Yao, York-Peng
2016-05-01
The integration over the Möbius variables leading to the Cachazo-He-Yuan double-color n -point massless scalar amplitude are carried out one integral at a time. Möbius invariance dictates the final amplitude to be independent of the three Möbius constants σr,σs,σt, but their choice affects integrations and the intermediate results. The effect of the Möbius constants, which will be held finite but otherwise arbitrary, the two sets of colors, and the scattering functions on each integration is investigated. A general systematic way to carry out the n -3 integrations is explained, each exposing one of the n -3 propagators of a single Feynman diagram. Two detailed examples are shown to illustrate the procedure, one a five-point amplitude, and the other a nine-point amplitude. Our procedure does not generate intermediate spurious poles, in contrast to what is common by choosing Möbius constants at 0, 1, and ∞ .
Ishida, M; Ishida, Muneyuki; Ishida, Shin
2003-01-01
In our talk at Nihon university symposium, we have argued that the pipi / Kpi production amplitudes F generally have different structures from those of the pipi / Kpi scattering amplitudes T from a viewpoint of generalized S matrix on the right bases, reflecting the quark-physical picture of strong interactions, and that F should be analyzed independently from T. Here we discuss the miscellaneous topics related with this argument: The conventional analyses by K matrix method, which necessarily lead to the common phases and structures through both T and F, are based on improper application of elastic unitarity to the production processes. Recent criticisms on the method of analyses of J/psi -> omega pipi and D+ -> K- pi+ pi+, which led to the existence of sigma and kappa, respectively, are also based on improper application of elastic unitarity.
Positivity, Grassmannian Geometry and Simplex-like Structures of Scattering Amplitudes
Rao, Junjie
2016-01-01
This article revisits and elaborates the significant role of positive geometry of momentum twistor Grassmannian for planar N=4 SYM scattering amplitudes. First we establish the fundamentals of positive Grassmannian geometry for tree amplitudes. Then we formulate this subject around these four major facets: 1. Deriving the tree and 1-loop BCFW recursion relations solely from positivity, after introducing the simple building blocks called positive components. 2. Applying Grassmannian geometry and Plucker coordinates to determine the signs of N2MHV homological identities. Most of the signs are in fact the secret incarnation of the simple 6-term NMHV identity. 3. Deriving the stacking positivity relation, which is powerful for parameterizing the matrix representative in terms of positive variables, of a given Grassmannian geometric configuration. 4. Introducing a highly refined formalism for tree BCFW recursion relation, which reveals its two-fold simplex-like structures. First, the BCFW contour in terms of (redu...
A laboratory study of low-mode internal tide scattering by finite-amplitude topography
Peacock, Thomas; Didelle, Henri; Viboud, Samuel; Dauxois, Thierry
2015-01-01
We present the first laboratory experimental results concerning the scattering of a low-mode internal tide by a gaussian topography. Experiments performed at the Coriolis Platform in Grenoble used a recently-conceived internal wave generator as a means of producing a high-quality mode-1 wave field. The evolution of the wave field in the absence and presence of a supercritical Gaussian was studied by performing spatiotemporal modal decompositions of velocity field data obtained using Particle Image Velocimetry (PIV). The results support predictions that large-amplitude supercritical topography produces significant reflection of the internal tide and transfer of energy from low to high modes.
Nonplanar on-shell diagrams and leading singularities of scattering amplitudes
Chen, Baoyi; Chen, Gang; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan
2017-02-01
Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable.
Nonplanar on-shell diagrams and leading singularities of scattering amplitudes
Energy Technology Data Exchange (ETDEWEB)
Chen, Baoyi; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan [Nanjing University, Department of Physics, Nanjing (China); Chen, Gang [Zhejiang Normal University, Department of Physics, Jinhua, Zhejiang (China); Nanjing University, Department of Physics, Nanjing (China)
2017-02-15
Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable. (orig.)
Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity
Energy Technology Data Exchange (ETDEWEB)
Hohberger, H.
2006-10-16
We consider scattering in R{sup n}, n{>=}2, described by the Schroedinger operator P(h)=-h{sup 2}{delta}+V, where V is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as h{yields}0 of the scattering amplitude f({omega}{sub -},{omega}{sub +};{lambda},h) ({omega}{sub +}{ne}{omega}{sub -}) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity. (orig.)
Pion-nucleon amplitude near threshold the sigma-term and scattering lengths beyond few loops
Kondratyuk, S
2002-01-01
The pion-nucleon amplitude is considered in the vicinity of the elastic scattering threshold within a relativistic dynamical model dressing the $\\pi N N$ and $\\pi N \\Delta$ vertices self-consistently with an infinite number of meson loops. The dressing is formulated as solution of a system of coupled integral equations incorporating unitarity, crossing symmetry and analyticity constraints. The calculated scattering lengths and the sigma-term agree with recent data analyses. In this model multiple loops are significant both below and at threshold. The contribution of the $\\Delta$ resonance is discussed, including effects of its dressing. A comparison with the approaches of chiral perturbation theory and the Bethe-Salpeter equation is outlined.
4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
Cheung, Clifford; Sundrum, Raman
2016-01-01
We reformulate the scattering amplitudes of 4D flat space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D flat space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg soft factors of gauge theory and gravity. In general, the massless (A)dS modes are 3D Chern-Simons gauge fields describing the soft, single helicity sectors o...
Esmaeili, Mostafa; Motagh, Mahdi
2016-07-01
Time-series analysis of Synthetic Aperture Radar (SAR) data using the two techniques of Small BAseline Subset (SBAS) and Persistent Scatterer Interferometric SAR (PSInSAR) extends the capability of conventional interferometry technique for deformation monitoring and mitigating many of its limitations. Using dual/quad polarized data provides us with an additional source of information to improve further the capability of InSAR time-series analysis. In this paper we use dual-polarized data and combine the Amplitude Dispersion Index (ADI) optimization of pixels with phase stability criterion for PSInSAR analysis. ADI optimization is performed by using Simulated Annealing algorithm to increase the number of Persistent Scatterer Candidate (PSC). The phase stability of PSCs is then measured using their temporal coherence to select the final sets of pixels for deformation analysis. We evaluate the method for a dataset comprising of 17 dual polarization SAR data (HH/VV) acquired by TerraSAR-X data from July 2013 to January 2014 over a subsidence area in Iran and compare the effectiveness of the method for both agricultural and urban regions. The results reveal that using optimum scattering mechanism decreases the ADI values in urban and non-urban regions. As compared to single-pol data the use of optimized polarization increases initially the number of PSCs by about three times and improves the final PS density by about 50%, in particular in regions with high rate of deformation which suffer from losing phase stability over the time. The classification of PS pixels based on their optimum scattering mechanism revealed that the dominant scattering mechanism of the PS pixels in the urban area is double-bounce while for the non-urban regions (ground surfaces and farmlands) it is mostly single-bounce mechanism.
Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
Chiodaroli, Marco; Johansson, Henrik; Roiban, Radu
2015-01-01
We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which th...
Kovalenko, V N; Vechernin, V V; Diatchenko, D V
2015-01-01
Recently, fine experimental data on the behavior of elastic scattering cross section in the region of the diffraction peak and the first diffraction minimum was obtained by the TOTEM experiment for 7 TeV pp collisions at the LHC [1, 2]. The first restrictions on pp scattering amplitude imposed by this data were discussed in [3, 4]. In the present work we present the systematic analysis of the problem in the framework of quasi-eikonal Regge approach [5, 6] taking into account the unitarity condition. We show that although in this approach one can describe the general features of the pp scattering such as the total elastic and inelastic cross sections, the slope of diffraction cone and the multiplicity density at mid-rapidities [7], nevertheless the behavior of pp elastic differential cross section in the vicinity of the first diffraction minimum measured by the TOTEM experiment at LHC [1, 2] can not be reproduced under any parameter values at standard assumptions of the model. Physically one can say that in qu...
A unitarity analysis on the I=2 $d$ wave $\\pi\\pi$ scattering amplitude
Wang, J; Zheng, H Q; Wang, Jian-jun
2005-01-01
We study $d$ wave $\\pi\\pi$ scattering phase shift using a proper unitarization approach. It is verified that the $f_2(1270)$ resonance corresponds to a twin pole structure: one on the second sheet, another one on the third sheet. Also we find fair agreement on $f_2(1270)$ pole's mass and width between our results and the PDG values. Besides, our analysis reveals the existence of a virtual state in this channel. Its pole location is determined by fitting experimental data and it is found to be in good agreement with the prediction from chiral perturbation theory. Our analysis demonstrates that partial wave amplitudes calculated in chiral perturbation theory are reliable in the small $|s|$ region, contrary to some unitarization models.
4D scattering amplitudes and asymptotic symmetries from 2D CFT
Cheung, Clifford; de la Fuente, Anton; Sundrum, Raman
2017-01-01
We reformulate the scattering amplitudes of 4D flat space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D flat space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg soft factors of gauge theory and gravity. In general, the massless (A)dS modes are 3D Chern-Simons gauge fields describing the soft, single helicity sectors of 4D gauge theory and gravity. Consistent with the topological nature of Chern-Simons theory, Aharonov-Bohm effects record the "tracks" of hard particles in the soft radiation, leading to a simple characterization of gauge and gravitational memories. Soft particle exchanges between hard processes define the Kac-Moody level and Virasoro central charge, which are thereby related to the 4D gauge coupling and gravitational strength in units of an infrared cutoff. Finally, we discuss a toy model for black hole horizons via a restriction to the Rindler region.
Subharmonic scattering of phospholipid-shell microbubbles at low acoustic pressure amplitudes.
Frinking, Peter J A; Brochot, Jean; Arditi, Marcel
2010-08-01
Subharmonic scattering of phospholipid-shell microbubbles excited at relatively low acoustic pressure amplitudes (<30 kPa) has been associated with echo responses from compression-only bubbles having initial surface tension values close to zero. In this work, the relation between sbharmonics and compression-only behavior of phospholipid-shell microbubbles was investigated, experimentally and by simulation, as a function of the initial surface tension by applying ambient overpressures of 0 and 180 mmHg. The microbubbles were excited using a 64-cycle transmit burst with a center frequency of 4 MHz and peak-negative pressure amplitudes ranging from 20 of 150 kPa. In these conditions, an increase in subharmonic response of 28.9 dB (P < 0.05) was measured at 50 kPa after applying an overpressure of 180 mmHg. Simulations using the Marmottant model, taking into account the effect of ambient overpressure on bubble size and initial surface tension, confirmed the relation between subharmonics observed in the pressure-time curves and compression-only behavior observed in the radius-time curves. The trend of an increase in subharmonic response as a function of ambient overpressure, i.e., as a function of the initial surface tension, was predicted by the model. Subharmonics present in the echo responses of phospholipid-shell microbubbles excited at low acoustic pressure amplitudes are indeed related to the echo responses from compression-only bubbles. The increase in subharmonics as a function of ambient overpressure may be exploited for improving methods for noninvasive pressure measurement in heart cavities or big vessels in the human body.
Yang, Shin Nan
2011-01-01
A simple heuristic argument to understand the existence of branch points in the unphysical sheet for pi-N scattering amplitude is presented. It is based on a hypothesis that the singularity structure of the pi-N scattering amplitude is a smooth varying function of the pion mass. We find that, in general, multiple poles structure of a resonance is a direct mathematical consequence when additional Riemann surface is included in the study and the two-pole structure found to correspond to the Roper resonance is a good example.
Institute of Scientific and Technical Information of China (English)
Itsuki Banno; Kazumi Fujima
2007-01-01
A determinantal formula is developed for direct evaluation of transition amplitude without solving the wave equation in a one-dimensional potential scattering system. Our formulation is based on the principle that a desired quantity can be extracted from the wave operator, which is the master operator maintaining all the information of the system. This principle is tested in a simplified system, I.e., in a one-dimensional potential scattering system. We are now developing a formula for direct evaluation of near-field amplitude to design a system, in which local Geld enhancement is desired.
Burov, V. A.; Morozov, S. A.
2001-11-01
Wave scattering by a point-like inhomogeneity, i.e., a strong inhomogeneity with infinitesimal dimensions, is described. This type of inhomogeneity model is used in investigating the point-spread functions of different algorithms and systems. Two approaches are used to derive the rigorous relationship between the amplitude and phase of a signal scattered by a point-like acoustic inhomogeneity. The first approach is based on a Marchenko-type equation. The second approach uses the scattering by a scatterer whose size decreases simultaneously with an increase in its contrast. It is shown that the retarded and advanced waves are scattered differently despite the relationship between the phases of the corresponding scattered waves.
Elastic Scattering of Low Energy Pions by Nuclei and the In-Medium Isovector πN Amplitude
Friedman, E.; Bauer, M.; Breitschopf, J.; Clement, H.; Denz, H.; Doroshkevich, E.; Erhardt, A.; Hofman, G. J.; Kritchman, S.; Meier, R.; Wagner, G. J.; Yaari, G.
2006-07-01
Measurements of elastic scattering of 21.5 MeV π± by Si, Ca, Ni and Zr were made using a single arm magnetic spectrometer and absolute calibration was made by parallel measurements of Coulomb scattering of muons. Optical model fits to the data reveal the `anomalous' s-wave repulsion known from pionic atoms. Introducing a chiral-motivated density dependence of the isovector scattering amplitude, and considering the energy dependence of the free πN interaction greatly improve fits to the data and remove the `anomaly'.
Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
Hatsuda, Yasuyuki; Satoh, Yuji; Suzuki, Junji
2014-01-01
We study the six-point gluon scattering amplitudes in N=4 super Yang-Mills theory at strong coupling based on the twisted Z_4-symmetric integrable model. The lattice regularization allows us to derive the associated thermodynamic Bethe ansatz (TBA) equations as well as the functional relations among the Q-/T-/Y-functions. The quantum Wronskian relation for the Q-/T-functions plays an important role in determining a series of the expansion coefficients of the T-/Y-functions around the UV limit, including the dependence on the twist parameter. Studying the CFT limit of the TBA equations, we derive the leading analytic expansion of the remainder function for the general kinematics around the limit where the dual Wilson loops become regular-polygonal. We also compare the rescaled remainder functions at strong coupling with those at two, three and four loops, and find that they are close to each other along the trajectories parameterized by the scale parameter of the integrable model.
Probing phase of a scattering amplitude beyond the plane-wave approximation
Karlovets, Dmitry V
2016-01-01
Within a plane-wave approach, a number of scattering events in a generic collision process is insensitive to an overall complex phase of a transition amplitude, although this phase is extremely important for a number of problems, especially in hadronic physics at the LHC energies. In reality, however, the particles are better described as localized wave packets with the mean momenta $p$, their uncertainties $\\sigma$, and here we show that the observables grow dependent upon this phase if one lays aside the simplified plane-wave model. A relative contribution of the phase to the cross section is generally attenuated by a small factor $\\sigma^2/p^2 \\ll 1$, making its experimental measurement a rather challenging task. We discuss two methods for probing how this phase changes with the transferred momentum $t$, either by colliding two beams at a non-zero impact-parameter (say, $pp \\rightarrow X$) or by employing the states with the non-trivial wave functions, for instance, vortex particles carrying orbital angula...
Na, Seong-Won; Kallivokas, Loukas F.
2008-03-01
In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a two-dimensional homogeneous acoustic host, in terms of a partial-differential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush-Kuhn-Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1-4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle’s backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency- and wave-direction spaces through a sequence of problems. We report numerical results for sound-hard objects with shapes ranging from circles, to penny- and kite-shaped, including obstacles with arbitrarily shaped non-convex boundaries.
Elastic scattering of low energy pions by nuclei and the in-medium isovector pi N amplitude
Friedman, E; Breitschopf, J; Clement, H; Denz, H; Doroshkevich, E; Erhardt, A; Hofman, G J; Kritchman, S; Meier, R; Wagner, G J; Yaari, G
2005-01-01
Measurements of elastic scattering of 21.5 MeV pi+ and pi- by Si, Ca, Ni and Zr were made using a single arm magnetic spectrometer. Absolute calibration was made by parallel measurements of Coulomb scattering of muons. Parameters of a pion-nucleus optical potential were obtained from fits to all eight angular distributions put together. The `anomalous' s-wave repulsion known from pionic atoms is clearly observed and could be removed by introducing a chiral-motivated density dependence of the isovector scattering amplitude, which also greatly improved the fits to the data. The empirical energy dependence of the isoscalar amplitude also improves the fits to the data but, contrary to what is found with pionic atoms, on its own is incapable of removing the anomaly.
High Energy Asymptotics of the Scattering Amplitude for the Schrödinger Equation
Indian Academy of Sciences (India)
D Yafaev
2002-02-01
We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover, the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables.
DEFF Research Database (Denmark)
Schwahn, D.; Mortensen, K.; Janssen, S.
1994-01-01
The critical behavior of a polymer blend was measured by small-angle neutron scattering above and below the critical temperature T-c, i.e., outside and inside the unstable region. The critical exponents and the amplitudes of the susceptibility and the correlation length were determined. For T > T......-c the critical exponents gamma and nu are consistent with the renormalization-group predictions. Below T-c, however, deviations from the expected values were observed. Also experimental critical amplitude ratios (20-30)% smaller than predicted were found....
Detecting the amplitude mode of strongly interacting lattice bosons by Bragg scattering.
Bissbort, Ulf; Götze, Sören; Li, Yongqiang; Heinze, Jannes; Krauser, Jasper S; Weinberg, Malte; Becker, Christoph; Sengstock, Klaus; Hofstetter, Walter
2011-05-20
We report the first detection of the Higgs-type amplitude mode using Bragg spectroscopy in a strongly interacting condensate of ultracold atoms in an optical lattice. By the comparison of our experimental data with a spatially resolved, time-dependent bosonic Gutzwiller calculation, we obtain good quantitative agreement. This allows for a clear identification of the amplitude mode, showing that it can be detected with full momentum resolution by going beyond the linear response regime. A systematic shift of the sound and amplitude modes' resonance frequencies due to the finite Bragg beam intensity is observed.
Study of ambiguities in $\\pi^-p\\to \\Lambda K^0$ scattering amplitudes
Anisovich, A V; Klempt, E; Nikonov, V A; Sarantsev, A V; Thoma, U; Wunderlich, Y
2013-01-01
Amplitudes for the reaction $\\pi^-p\\to \\Lambda K^0$ are reconstructed from data on the differential cross section $d\\sigma/d\\Omega$, the recoil polarization $P$, and on the spin rotation parameter $\\beta$. At low energies, no data on $\\beta$ exist, resulting in ambiguities. An approximation using $S$ and $P$ waves leads only to a fair description of the data on $d\\sigma/d\\Omega$ and $P$; in this case, there are two sets of amplitudes. Including $D$ waves, the data on $d\\sigma/d\\Omega$ and $P$ are well reproduced by the fit but now, there are several distinct solutions which describe the data with identical precision. In the range where the spin rotation parameter $\\beta$ was measured, a full and unambiguous reconstruction of the partial wave amplitudes is possible. The energy-independent amplitudes are compared to the energy dependent amplitudes which resulted from a coupled channel fit (BnGa2011-02) to a large data set including both pion and photo-induced reactions. Significant deviations are observed. Cons...
Recursion relations for graviton scattering amplitudes from Bose symmetry and bonus scaling laws
McGady, David A.; Rodina, Laurentiu
2015-05-01
Modern on-shell S -matrix methods may dramatically improve our understanding of perturbative quantum gravity, but current foundations of on-shell techniques for general relativity still rely on off-shell Feynman diagram analysis. Here, we complete the fully on-shell proof of Schuster and Toro J. High Energy Phys. 06 (2009) 079] that the recursion relations of Britto, Cachazo, Feng, and Witten (BCFW) apply to relativity tree amplitudes. We do so by showing that the surprising requirement of "bonus" z-2 scaling under a BCFW shift directly follows from Bose symmetry. Moreover, we show that amplitudes in generic theories subjected to BCFW deformations of identical particles necessarily scale as zeven. When applied to the color ordered expansions of Yang-Mills, this directly implies the improved behavior under nonadjacent gluon shifts. Using the same analysis, three-dimensional gravity amplitudes scale as z-4, compared to the z-1 behavior for conformal Chern-Simons matter theory.
A new method for calculating the Glauber multiple scattering amplitude of composite particles
Zhang, Yu-Shun; Hu, Su-Fen; Yang, Chao-Yun; Liu, Ji-Feng
1997-11-01
The method for calculating the scattering of composite particles with several kinds of constituent is studied. The formulae are derived and the method for sorting all Glauber expansion terms into several classes is given. The method of the integration is different from that of Lin and co-workers (Lin Z J et al 1991 J. Phys. G: Nucl. Part. Phys. 17 1159) and its analytical expressions are introduced. We calculate the D - D, P - P, P - 0954-3899/23/11/005/img7 and 0954-3899/23/11/005/img8 - P elastic scatterings. These results are compared with the data.
Directory of Open Access Journals (Sweden)
L. A. Mayoral-Astorga
2016-04-01
Full Text Available We have studied numerically the diffraction of a surface plasmon polariton (SPP when it encounters a wide multi-wavelength slit in conducting films. As a jump process a SPP is excited beyond the slit by wave scattering at the second slit edge. The exciting radiation is produced when the incident SPP collapses at the first slit edge. We have found that the transmitted SPP supports inherent and unavoidable interference with grazing scattered radiation; the spatial modulation extends to the fields in the diffraction region where a series of low intensity spots arises. We demonstrate that the SPP generated on the second slab depends on the frequency but not on the wave vector of the collapsed SPP; a SPP is transmitted even when the two metals forming the slit are different. The numerical results were obtained using the Finite Difference Time Domain (FDTD method with a grid size λ/100.
Energy Technology Data Exchange (ETDEWEB)
Mayoral-Astorga, L. A.; Gaspar-Armenta, J. A.; Ramos-Mendieta, F. [Departamento de Investigación en Física, Universidad de Sonora, Apartado Postal 5-088, Hermosillo, Sonora, 83190 México (Mexico)
2016-04-15
We have studied numerically the diffraction of a surface plasmon polariton (SPP) when it encounters a wide multi-wavelength slit in conducting films. As a jump process a SPP is excited beyond the slit by wave scattering at the second slit edge. The exciting radiation is produced when the incident SPP collapses at the first slit edge. We have found that the transmitted SPP supports inherent and unavoidable interference with grazing scattered radiation; the spatial modulation extends to the fields in the diffraction region where a series of low intensity spots arises. We demonstrate that the SPP generated on the second slab depends on the frequency but not on the wave vector of the collapsed SPP; a SPP is transmitted even when the two metals forming the slit are different. The numerical results were obtained using the Finite Difference Time Domain (FDTD) method with a grid size λ/100.
Quasielastic neutron scattering study of large amplitude motions in molecular systems
Energy Technology Data Exchange (ETDEWEB)
Bee, M. [Univ. J. Fourier - Grenoble 1, Lab. de Spectrometrie Physique, Saint-Martin d`Heres (France)
1996-12-31
This lecture aims at giving some illustrations of the use of Incoherent Quasielastic Neutron Scattering in the investigation of motions of atoms or molecules in phases with dynamical disorder. The general incoherent scattering function is first recalled. Then the Elastic Incoherent Structure Factor is introduced. It is shown how its determination permits to deduce a particular dynamical model. Long-range translational diffusion is illustrated by some experiments carried out with liquids or with different chemical species intercalated in porous media. Examples of rotational motions are provided by solid phases where an orientational disorder of the molecules exists. The jump model is the most commonly used and yields simple scattering laws which can be easily handled. Highly disordered crystals require a description in terms of the isotropic rotational diffusion model. Many of the present studies are concerned with rather complicated systems. Considerable help is obtained either by using selectively deuterated samples or by carrying out measurements with semi-oriented samples. (author) 5 figs., 14 refs.
Loginov, A Y
2002-01-01
Bethe-Salpeter equation for the massive particles with spin 1 is considered. The scattering amplitude decomposition of the particles with spin 1 by relativistic tensors is derived. The transformation coefficients from helicity amplitudes to invariant functions is found. The integral equations system for invariant functions is obtained and partial decomposition of this system is performed. Equivalent system of the integral equation for the partial helicity amplitudes is presented.
Ishikawa, S; Iseri, Y
2001-01-01
In the neutron-deuteron scattering, four total cross sections are shown to form a complete set for the determination of the imaginary parts of the forward amplitudes because of the optical theorem. The amplitudes are decomposed into scalar and tensor ones in the spin space. Contributions of three-nucleon forces (3NF) to these amplitudes are studied, by the Faddeev calculation, which predicts significant tensor effects of the 3NF.
Yang, Shin Nan
2014-01-01
A simple heuristic argument to understand the existence of complex branch points in the $\\pi N$ scattering amplitude is presented. It is based on a hypothesis that the singularity structure of the $\\pi N$ scattering amplitude is a smooth varying function of the pion mass. We then show that the two-pole structure found to correspond to the Roper resonance could just a simple direct mathematical consequence of including additional Riemann surface in the analysis. Our study indicates that it is always possible to have multiple poles, either two or four etc., in different Riemann sheet, to be associated with a resonance. The poles in all Riemann sheets should be looked for to determine whether the two-pole feature of the Roper resonance $N^*(1440)$ is a manifestation of the "exact degeneracy" discussed here but masked by numerical indeterminacy, or an "accidental" one. The determination of the multiplicity of a pole could provide some information of the analytical structure of the numerator of the pole term, as t...
Schabinger, Robert M
2011-01-01
In this paper we discuss in detail computational methods and new results for one-loop virtual corrections to N = 4 super Yang-Mills scattering amplitudes calculated to all orders in epsilon, the dimensional regularization parameter. It is often the case that one-loop gauge theory computations are carried out to order epsilon^0, since higher order in epsilon contributions vanish in the small epsilon limit. We will show, however, that the higher order contributions are actually quite useful. In the context of maximally supersymmetric Yang-Mills, we consider two examples in detail to illustrate our point. First we will concentrate on computations with gluonic external states and argue that N = 4 supersymmetry implies a simple relation between all-orders-in-epsilon one-loop N = 4 super Yang-Mills amplitudes and the first and second stringy corrections to analogous tree-level superstring amplitudes. For our second example we will derive a new result for the all-orders-in-epsilon one-loop superamplitude for planar ...
Geometric scaling behavior of the scattering amplitude for DIS with nuclei
Energy Technology Data Exchange (ETDEWEB)
Kormilitzin, Andrey, E-mail: andreyk1@post.tau.ac.il [Department of Particle Physics, School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978 (Israel); Levin, Eugene, E-mail: leving@post.tau.ac.il [Department of Particle Physics, School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978 (Israel); Departamento de Fisica, Centro de Estudios Subatomicos, Universidad Tecnica Federico Santa Maria, and Centro Cientifico-Tecnologico de Valparaiso, Casilla 110-V, Valparaiso (Chile); Tapia, Sebastian, E-mail: trockut@gmail.com [Departamento de Fisica, Centro de Estudios Subatomicos, Universidad Tecnica Federico Santa Maria, and Centro Cientifico-Tecnologico de Valparaiso, Casilla 110-V, Valparaiso (Chile)
2011-12-15
The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky-Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran-Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at x{sub A}=1/mR{sub A} given by the solution to Balitsky-Kovchegov equation, leads to the geometric scaling behavior. The McLerran-Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory.
The in-medium isovector pi N amplitude from low energy pion scattering
Friedman, E; Breitschopf, J; Clement, H; Denz, H; Doroshkevich, E; Erhardt, A; Hofman, G J; Meier, R; Wagner, G J; Yaari, G
2004-01-01
Differential cross sections for elastic scattering of 21.5 MeV positive and negative pions by Si, Ca, Ni and Zr have been measured as part of a study of the pion-nucleus potential across threshold. The `anomalous' repulsion in the s-wave term was observed, as is the case with pionic atoms. The extra repulsion can be accounted for by a chiral-motivated model where the pion decay constant is modified in the medium. Unlike in pionic atoms, the anomaly cannot be removed by merely introducing an empirical on-shell energy dependence.
In-medium isovector piN amplitude from low-energy pion scattering.
Friedman, E; Bauer, M; Breitschopf, J; Clement, H; Denz, H; Doroshkevich, E; Erhardt, A; Hofman, G J; Meier, R; Wagner, G J; Yaari, G
2004-09-17
Differential cross sections for elastic scattering of 21.5 MeV positive and negative pions by Si, Ca, Ni, and Zr have been measured as part of a study of the pion-nucleus potential across the threshold. The "anomalous" repulsion in the s-wave term was observed, as is the case with pionic atoms. The extra repulsion can be accounted for by a chiral-motivated model where the pion decay constant is modified in the medium. Unlike in pionic atoms, the anomaly cannot be removed by merely introducing an empirical on-shell energy dependence.
The in-medium isovector pi N amplitude from low energy pion scattering
Friedman, E; Bauer, M.; Breitschopf, J.; H. Clement; Denz, H; Doroshkevich, E.; Erhardt, A.; Hofman, G. J.; Meier, R.; Wagner, G. J.; Yaari, G
2004-01-01
Differential cross sections for elastic scattering of 21.5 MeV positive and negative pions by Si, Ca, Ni and Zr have been measured as part of a study of the pion-nucleus potential across threshold. The `anomalous' repulsion in the s-wave term was observed, as is the case with pionic atoms. The extra repulsion can be accounted for by a chiral-motivated model where the pion decay constant is modified in the medium. Unlike in pionic atoms, the anomaly cannot be removed by merely introducing an e...
In-Medium Isovector πN Amplitude from Low-Energy Pion Scattering
Friedman, E.; Bauer, M.; Breitschopf, J.; Clement, H.; Denz, H.; Doroshkevich, E.; Erhardt, A.; Hofman, G. J.; Meier, R.; Wagner, G. J.; Yaari, G.
2004-09-01
Differential cross sections for elastic scattering of 21.5MeV positive and negative pions by Si, Ca, Ni, and Zr have been measured as part of a study of the pion-nucleus potential across the threshold. The “anomalous” repulsion in the s-wave term was observed, as is the case with pionic atoms. The extra repulsion can be accounted for by a chiral-motivated model where the pion decay constant is modified in the medium. Unlike in pionic atoms, the anomaly cannot be removed by merely introducing an empirical on-shell energy dependence.
MHV amplitude for 3->3 gluon scattering in Regge limit
Bartels, J; Prygarin, A
2010-01-01
We calculate corrections to the BDS formula for the six-particle planar MHV amplitude for the gluon transition 3->3 in the multi-Regge kinematics for the physical region, in which the Regge pole ansatz is not valid. The remainder function at two loops is obtained by an analytic continuation of the expression derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region described by the Mandelstam singularity exchange in the crossing channel. It contains both the imaginary and real contributions being in agreement with the BFKL predictions. The real part of the three loop expression is found from a dispersion-like all-loop formula for the remainder function in the multi-Regge kinematics derived by one of the authors. We also make a prediction for the all-loop real part of the remainder function multiplied by the BDS phase, which can be accessible through calculations in the regime of the strong coupling constant.
Two-body threshold spectral analysis, the critical case
DEFF Research Database (Denmark)
Skibsted, Erik; Wang, Xue Ping
We study in dimension $d\\geq2$ low-energy spectral and scattering asymptotics for two-body $d$-dimensional Schrödinger operators with a radially symmetric potential falling off like $-\\gamma r^{-2},\\;\\gamma>0$. We consider angular momentum sectors, labelled by $l=0,1,\\dots$, for which $\\gamma...
Hatefi, Ehsan
2015-01-01
From the world-sheet point of view we compute all three, four and five point BPS and non-BPS scattering amplitudes of type IIA and IIB superstring theory. All these mixed S-matrix elements including a closed string Ramond-Ramond (RR) in the bulk and a scalar/gauge or tachyons (in both non-BPS and brane anti brane formalism) in their all different pictures with RR in the asymmetric and symmetric pictures have been carried out. We have also shown that in asymmetric pictures various equations must be kept fixed. More importantly, by direct calculations on upper half plane, it is realized that some of the equations (that must be held) of BPS branes can not be necessarily applied to non-BPS amplitudes. We also derive the S-Matrix elements of $$ and clarify the fact that in the presence of the scalar field and RR, the terms carrying momentum of RR in transverse directions play important rule in the entire form of the S-matrix and their presence is needed in order to have gauge invariance for the entire S-matrix ele...
Energy Technology Data Exchange (ETDEWEB)
Nicolescu, Basarab [LPNHE, Unite de Recherche des Universites Paris 6 et Paris 7, associee au CNRS, Theory Group, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2004-07-01
We consider several classes of analytic parametrizations of hadronic scattering amplitudes (the COMPETE analysis), and compare their predictions to all available forward data (pp, {pi}p, Kp, {gamma}p, {gamma}{gamma}, {sigma}p). Although these parametrizations are very close for {radical}s {>=} 9 GeV, it turns out that they differ markedly at low energy, where a universal Pomeron term {approx} ln{sup 2} s enables one to extend the fit down to {radical}s = 4 GeV. We present predictions on the total cross sections and on the ratio of the real part to the imaginary part of the elastic amplitude ({rho} parameter) for present and future pp colliders, and on total cross sections for {gamma}p {yields} hadrons at cosmic-ray energies and for it{gamma}{gamma} {yields} hadrons up to {radical}s = 1 TeV. The ln{sup 2} s behaviour of total cross sections, first obtained by Heisenberg 50 years ago, receives now increased interest both on phenomenological and theoretical levels. We present a modification of the Heisenberg's model in connection with the presence of glueballs and we show that it leads to a realistic description of all existing hadron total cross-sections data, in agreement with the COMPETE analysis.
Bartels, Jochen; Lipatov, Lev
2013-01-01
We investigate the analytic structure of the $2\\to5$ scattering amplitude in the planar limit of $\\mathcal{N}=4$ SYM in multi-Regge kinematics in all physical regions. We demonstrate the close connection between Regge pole and Regge cut contributions: in a selected class of kinematic regions (Mandelstam regions) the usual factorizing Regge pole formula develops unphysical singularities which have to be absorbed and compensated by Regge cut contributions. This leads, in the corrections to the BDS formula, to conformal invariant 'renormalized' Regge pole expressions in the remainder function. We compute these renormalized Regge poles for the $2\\to5$ scattering amplitude.
Energy Technology Data Exchange (ETDEWEB)
Bartels, Jochen; Kormilitzin, Andrey [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Lipatov, Lev [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; St. Petersburg Nuclear Physics Institute, St. Petersburg (Russian Federation)
2013-11-15
We investigate the analytic structure of the 2 {yields} 5 scattering amplitude in the planar limit of N=4 SYM in multi-Regge kinematics in all physical regions. We demonstrate the close connection between Regge pole and Regge cut contributions: in a selected class of kinematic regions (Mandelstam regions) the usual factorizing Regge pole formula develops unphysical singularities which have to be absorbed and compensated by Regge cut contributions. This leads, in the corrections to the BDS formula, to conformal invariant 'renormalized' Regge pole expressions in the remainder function. We compute these renormalized Regge poles for the 2 {yields} 5 scattering amplitude.
Titantah, J. T.; Lamoen, D.; Schowalter, M.; Rosenauer, A.
2010-02-01
The atomic scattering amplitudes of the various atoms of the systems Ga1-xInxAs, GaAs1-xNx and InAs1-xNx are calculated using the density functional theory (DFT) approach. The scattering amplitudes of N, Ga, As and In in the model systems are compared with the frequently used Doyle and Turner values. Deviation from the latter values is found for small scattering vectors (sMASAs) for small scattering vectors (sMASAs are exploited within zero pressure classical Metropolis Monte Carlo (MC), finite temperature calculations to investigate the effect of quantum well size on the electron {002} structure factor (SF) of Ga1-xInxAs quantum wells.
Fioravanti, D; Fioravanti, Davide; Rossi, Marco
2005-01-01
Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\\it disordered regime}, thus paralleling similar results by Kl\\"umper \\cite{KLU}, achieved through a different technique in the {\\it antiferroelectric regime}. In terms of the counting function we obtain the usual physical quantities, like the energy and the transfer matrix (eigenvalues). Then, we introduce a double scaling limit which appears to describe the sine-Gordon theory on cylindrical geometry, so generalising famous results in the plane by Luther \\cite{LUT} and Johnson et al. \\cite{JKM}. Furthermore, after extending the nonlinear integral equation to excitations, we derive scattering amplitudes involving solitons/antisolitons first, and bound states later. The latter case comes out as manifestly related to the Deformed Virasoro Algebra of Shiraishi et al. \\cite{SKAO}. Although this nonlinear integral equations framework was contrived to deal with finite geometries, we prove it to be e...
Energy Technology Data Exchange (ETDEWEB)
Rubinstein, R.
1991-08-01
We have measured {rho}, the ratio of the real to the imaginary part of {bar p}p forward elastic scattering amplitude, at {radical}s = 1.8 TeV. Our result, {rho} = 0.140 {plus minus} 0.069, is consistent with the expected value, and thus no new physics is required. 10 refs., 2 figs.
Two-Body Relaxation in Cosmological Simulations
Binney, J; Binney, James; Knebe, Alexander
2002-01-01
The importance of two-body relaxation in cosmological simulations is explored with simulations in which there are two species of particles. The cases of mass ratio sqrt(2):1 and 4:1 are investigated. Simulations are run with both a fixed softening length and adaptive softening using the publicly available codes GADGET and MLAPM, respectively. The effects of two-body relaxation are detected in both the density profiles of halos and the mass function of halos. The effects are more pronounced with a fixed softening length, but even in this case they are not so large as to suggest that results obtained with one mass species are significantly affected by two-body relaxation. The simulations that use adaptive softening are slightly less affected by two-body relaxation and produce slightly higher central densities in the largest halos. They run about three times faster than the simulations that use a fixed softening length.
Energy Technology Data Exchange (ETDEWEB)
Du, Yi-Jian [Center for Theoretical Physics, School of Physics and Technology, Wuhan University,299 Bayi Road, Wuhan 430072 (China); Teng, Fei [Department of Physics and Astronomy, University of Utah,115 South 1400 East, Salt Lake City, UT 84112 (United States); Wu, Yong-Shi [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, Shanghai 200433 (China); Department of Physics and Astronomy, University of Utah,115 South 1400 East, Salt Lake City, UT 84112 (United States)
2016-11-15
In this paper we define, independent of theories, two discriminant matrices involving a solution to the scattering equations in four dimensions, the ranks of which are used to divide the solution set into a disjoint union of subsets. We further demonstrate, entirely within the Cachazo-He-Yuan formalism, that each subset of solutions gives nonzero contribution to tree-level N{sup k}MHV gauge/gravity amplitudes only for a specific value of k. Thus the solutions can be characterized by the rank of their discriminant matrices, which in turn determines the value of k of the N{sup k}MHV amplitudes a solution can support. As another application of the technique developed, we show analytically that in Einstein-Yang-Mills theory, if all gluons have the same helicity, the tree-level single-trace amplitudes must vanish.
Du, Yi-Jian; Wu, Yong-Shi
2016-01-01
In this paper, we define two discriminant matrices involving a solution to the scattering equations in four dimensions, the ranks of which are used to divide the solution set into a disjoint union of subsets. We further demonstrate that each subset of solutions gives nonzero contribution to tree-level $\\text{N}^{k}\\text{MHV}$ gauge/gravity amplitudes only for a specific value of $k$, using the Cachazo-He-Yuan formalism. Thus the solutions can be characterized by the rank of their discriminant matrices, which in turn determines the value of $k$ of the $\\text{N}^{k} \\text{MHV}$ amplitudes a solution can support. As another application of the technique developed, we show analytically that in Einstein-Yang-Mills theory, if all gluons have the same helicity, the tree-level single-trace amplitudes must vanish.
Gao, Tian-You; Peng, Shi-Guo; Jiang, Kaijun
2015-04-01
We theoretically study two atoms with p -wave interaction in a one-dimensional waveguide, investigating how the transverse anisotropy of the confinement affects the two-body state, especially the properties of the resonance. For a bound-state solution, we find there are a total of three two-body bound states due to the richness of the orbital magnetic quantum number of the p -wave interaction, while only one bound state is supported by the s -wave interaction. Two of them become nondegenerate due to the breaking of the rotation symmetry under a transversely anisotropic confinement. For a scattering solution, the effective one-dimensional scattering amplitude and scattering length are derived. We find the position of the p -wave confinement-induced resonance shifts apparently versus the transverse anisotropy. In addition, a two-channel mechanism for the confinement-induced resonance in a one-dimensional waveguide is generalized to the p -wave interaction, which was previously proposed only for the s -wave interaction. All our calculations are based on the parametrization of the 40K-atom experiments and can thus be confirmed in future experiments.
Lee, Jen-Chi
2014-01-01
We calculate quantum mechanical scattering problems for multi-indexed extensions of soliton potential by Darboux transformations in terms of pseudo virtual wavefunctions. As an application, we calculate infinite set of higher integer KdV solitons by the inverse scattering transform method of KdV equation.
The pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV
Pelaez, J R
2016-01-01
In this work we provide simple and precise parameterizations of the existing $\\pi K$ scattering data from threshold up to 1.6 GeV, which are constrained to satisfy forward dispersion relations as well as three additional threshold sum rules. We also provide phenomenological values of the threshold parameters and of the resonance poles that appear in elastic scattering.
Fukutake, Naoki
2016-03-01
Coherent Raman scattering microspectroscopy, which includes coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS) microspectroscopy, permits label-free hyperspectral imaging. We report the theoretical study of the phase-shift effect of the impulse response function on the spectral and image-forming properties of coherent Raman scattering microspectroscopy. We show that the spectrum and image are influenced by not only the NA of objective for excitation (NA(ex)) but also that for signal collection (NA(col)), in association with the phase-shift effect. We discuss that, under the condition NA(ex)≠NA(col), both the spectrum and the image become deformed by the phase-shift effect, which can be applied to the direct measurement of the imaginary part of the nonlinear susceptibility in CARS spectroscopy. We point out that, even in SRS microscopy, the nonresonant background can contribute to the image formation and cause the artifact in the image.
Elastic scattering of low energy pions by nuclei and the in-medium isovector pi N amplitude
Friedman, E; Bauer, M.; Breitschopf, J.; H. Clement; Denz, H; Doroshkevich, E.; Erhardt, A.; Hofman, G. J.; Kritchman, S.; Meier, R.; Wagner, G. J.; Yaari, G
2005-01-01
Measurements of elastic scattering of 21.5 MeV pi+ and pi- by Si, Ca, Ni and Zr were made using a single arm magnetic spectrometer. Absolute calibration was made by parallel measurements of Coulomb scattering of muons. Parameters of a pion-nucleus optical potential were obtained from fits to all eight angular distributions put together. The `anomalous' s-wave repulsion known from pionic atoms is clearly observed and could be removed by introducing a chiral-motivated density dependence of the ...
Titantah, J. T.; Lamoen, D.; Schowalter, M.; Rosenauer, A.
2009-04-01
The modified atomic scattering amplitudes (MASAs) of mixed Ga1-xInxAs, GaAs1-xNx, and InAs1-xNx are calculated using the density functional theory approach and the results are compared with those of the binary counterparts. The MASAs of N, Ga, As, and In for various scattering vectors in various chemical environments and in the zinc-blende structure are compared with the frequently used Doyle and Turner values. Deviation from the Doyle and Turner results is found for small scattering vectors (s MASAs are found to be sensitive to the orientation of the scattering vector and on the chemical environment. The chemical environment sensitive MASAs are used within zero pressure classical Metropolis Monte Carlo, finite temperature calculations to investigate the effect of well size on the electron 002 and 220 structure factors (SFs). The implications of the use of the 002 (200) spot for the quantification of nanostructured Ga1-xInxAs systems are examined while the 220 SF across the well is evaluated and is found to be very sensitive to the in-plane static displacements.
Exact two-body solutions and quantum defect theory of two-dimensional dipolar quantum gas
Jie, Jianwen; Qi, Ran
2016-10-01
In this paper, we provide the two-body exact solutions of the two-dimensional (2D) Schrödinger equation with isotropic +/- 1/{r}3 interactions. An analytic quantum defect theory is constructed based on these solutions and it is applied to investigate the scattering properties as well as two-body bound states of an ultracold polar molecules confined in a quasi-2D geometry. Interestingly, we find that for the attractive case, the scattering resonance happens simultaneously in all partial waves, which has not been observed in other systems. The effect of this feature on the scattering phase shift across such resonances is also illustrated.
Djuraev, S K; Kuterbekov, K A; Strigina, S B
2002-01-01
We derive the formulas connecting the ratio of the total cross-sections sigma sub e sub l / sigma sub t and the ratio of the total cross-section to the diffraction cone slope parameter sigma sub t / b with the ratios of the real and imaginary parts of the scattering forward amplitude. The semiquantitative consideration is done. It is shown that the results become better due to the more precise calculation of the diffraction cone slope parameter and to the influence of the parameter c>1. Comparison with the experimental data on pp- and pp-bar-interaction shows better agreement in a wide range of energies sq root s = 5 / 546 GeV. It is important to note that the relations obtained lead to a large value of the ratio of the real part of the scattering forward amplitude to its imaginary part at sq root s = 546 GeV comparing to the values given by many theoretical models and the calculations by the dispersion relations.
Cherkas, S L
2001-01-01
T-violating P-even magnetism is considered. The magnetism arises from the T-violating P-conserving vertex of a spin 1/2 particle interaction with the electromagnetic field. The vertex varnishes for a particle on the mass shell. Considering the particle interaction with a point electric charge we have obtained the T-violating P-even spin dependent potential which is inversely proportional to the cubed distance from the charge. The matrix element of this potential is zero for particle states on the mass shell, nevertheless, the potential contributes to the T-odd P-even neutron forward elastic scattering amplitude by a deformed nucleus with spin S>1/2. The contribution arises if we take into account incident neutron plane wave distortion by the strong neutron interaction with the nucleus.
Energy Technology Data Exchange (ETDEWEB)
Hatefi, Ehsan [Queen Mary University of London, Centre for Research in String Theory, School of Physics and Astronomy, London (United Kingdom); University of the Witwatersrand, Wits, National Institute for Theoretical Physics, School of Physics, Mandelstam Institute for Theoretical Physics, Johannesburg (South Africa); Institute des Hautes Etudes Scientifiques, Bures-sur-Yvette (France)
2015-11-15
From the world-sheet point of view we compute three, four and five point BPS and non-BPS scattering amplitudes of type IIA and IIB superstring theory. All these mixed S-matrix elements including a Ramond-Ramond closed string (RR) in the bulk and a scalar/gauge or tachyons with all different pictures (including an RR in asymmetric and symmetric pictures) have been carried out. We have also shown that in asymmetric pictures various equations must be kept fixed. More importantly, by direct calculations on the upper half plane, it is realised that some of the equations (which must be true) for BPS branes cannot be necessarily applied to non-BPS amplitudes. We also derive the S-matrix elements of left angle V{sub C}{sup -2}V{sub φ}{sup 0}V{sub A}{sup 0}V{sub T}{sup 0} right angle and clarify the fact that in the presence of the scalar field and an RR, the terms carrying momentum of an RR in the transverse directions play an important role in the entire form of the S-matrix and their presence is needed in order to have gauge invariance for the entire S-matrix elements of type IIA (IIB) superstring theory. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Hatefi, Ehsan, E-mail: ehsanhatefi@gmail.com [Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, E1 4NS, London (United Kingdom); National Institute for Theoretical Physics, School of Physics, Mandelstam Institute for Theoretical Physics, University of the Witwatersrand, Wits, 2050, Johannesburg (South Africa); Institute des Hautes Etudes Scientifiques, 91440, Bures-sur-Yvette (France)
2015-10-31
From the world-sheet point of view we compute three, four and five point BPS and non-BPS scattering amplitudes of type IIA and IIB superstring theory. All these mixed S-matrix elements including a Ramond–Ramond closed string (RR) in the bulk and a scalar/gauge or tachyons with all different pictures (including an RR in asymmetric and symmetric pictures) have been carried out. We have also shown that in asymmetric pictures various equations must be kept fixed. More importantly, by direct calculations on the upper half plane, it is realised that some of the equations (which must be true) for BPS branes cannot be necessarily applied to non-BPS amplitudes. We also derive the S-matrix elements of 〈V{sub C}{sup -2}V{sub ϕ}{sup 0}V{sub A}{sup 0}V{sub T}{sup 0}〉 and clarify the fact that in the presence of the scalar field and an RR, the terms carrying momentum of an RR in the transverse directions play an important role in the entire form of the S-matrix and their presence is needed in order to have gauge invariance for the entire S-matrix elements of type IIA (IIB) superstring theory.
Martín, R García-; Peláez, J R; de Elvira, J Ruiz; Ynduráin, F J
2011-01-01
We improve our description of pion-pion scattering data by imposing additional requirements to our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of Forward Dispersion Relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy Kl4 decay results, including their isospin violation correction, and we have removed some cont...
Gryniuk, Oleksii
2016-01-01
We provide an updated analysis of the forward $J/\\psi$-p scattering amplitude, relating its imaginary part to $\\gamma p \\to J/\\psi p$ and $\\gamma p \\to c \\bar c X$ cross section data, and calculating its real part through a once-subtracted dispersion relation. From a global fit to both differential and total cross section data, we extract a value for the spin-averaged $J/\\psi$-p s-wave scattering length $a_{\\psi p} = 0.046 \\pm 0.005$ fm, which can be translated into a $J/\\psi$ binding energy in nuclear matter of $B_\\psi = 2.7 \\pm 0.3$ MeV. We estimate the forward-backward asymmetry to the $\\gamma p \\to e^- e^+ p$ process around the $J/\\psi$ resonance, which results from interchanging the leptons in the interference between the $J/\\psi$ production and the Bethe-Heitler mechanisms. We show that to good approximation this asymmetry depends linearly on $a_{\\psi p}$, and can reach values around -25% for forthcoming $J/\\psi$ threshold production experiments at Jefferson Lab. Its measurement can thus provide a very ...
Energy Technology Data Exchange (ETDEWEB)
Titantah, J T; Lamoen, D [EMAT, Universiteit Antwerpen, Groenenborgerlaan 171, 2020 Antwerpen (Belgium); Schowalter, M; Rosenauer, A, E-mail: john.titantah@ua.ac.b [Institut fuer Festkoerperphysik, Universitaet Bremen, D 28359 Bremen (Germany)
2010-02-01
The atomic scattering amplitudes of the various atoms of the systems Ga{sub 1-x}In{sub x}As, GaAs{sub 1-x}N{sub x} and InAs{sub 1-x}N{sub x} are calculated using the density functional theory (DFT) approach. The scattering amplitudes of N, Ga, As and In in the model systems are compared with the frequently used Doyle and Turner values. Deviation from the latter values is found for small scattering vectors (s<0.3A{sup -1}) and for these scattering vectors dependence on the orientation of the scattering vector and the chemical environment is reported. We suggest a parametrization of these modified scattering amplitudes (MASAs) for small scattering vectors (s<1.0A{sup -1}). The MASAs are exploited within zero pressure classical Metropolis Monte Carlo (MC), finite temperature calculations to investigate the effect of quantum well size on the electron {l_brace}002{r_brace} structure factor (SF) of Ga{sub 1-x}In{sub x}As quantum wells.
On gravitational interactions between two bodies
Szybka, Sebastian J
2014-01-01
Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only empirically determinable. We do not know if such a theory exists. Moreover, if it exists, there seems to be no reason for it to be comprehensible for the human mind. On the other hand, as pointed out in Wigner's famous paper, human mathematics is unbelievably successful in natural science. This seeming paradox may be mitigated by assuming that the mathematical structure of physical reality has many `layers'. As time goes by, physicists discover new theories that correspond to the physical reality on the deeper and deeper level. In this essay, I will take a narrow approach and discuss the mathematical structure behind a single physical phenomenon - gravitational interaction between two bodies. The main aim of this essay is to put some recent developments of this topic in a ...
Baryshevsky, V G
2005-01-01
In the present paper the equations for the spin evolution of a particle in a storage ring are analyzed considering contributions from the tensor electric and magnetic polarizabilities of the particle. Study of spin rotation and birefringence effect for a particle in a high energy storage ring provides for measurement as the real part of the coherent elastic zero-angle scattering amplitude as well as tensor electric and magnetic polarizabilities. We proposed the method for measurement the real part of the elastic coherent zero-angle scattering amplitude of particles and nuclei in a storage ring by the paramagnetic resonance in the periodical in time nuclear pseudoelectric and pseudomagnetic fields.
Mathematical aspects of scattering amplitudes
Duhr, Claude
2014-01-01
In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and discuss introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equations among polylogarithms.
Mathematical aspects of scattering amplitudes
Duhr, Claude
2014-01-01
In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and discuss introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equati...
Mathematical Aspects of Scattering Amplitudes
Duhr, Claude
In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equations among polylogarithms.
Penante, Brenda
2016-01-01
Planar maximally supersymmetric Yang-Mills theory (N=4 SYM) is a special quantum field theory. A few of its remarkable features are conformal symmetry at the quantum level, evidence of integrability and, moreover, it is a prime example of the AdS/CFT duality. Triggered by Witten's twistor string theory, the past 15 years have witnessed enormous progress in reformulating this theory to make as many of these special features manifest, from the choice of convenient variables to recursion relations that allowed new mathematical structures to appear, like the Grassmannian. These methods are collectively referred to as on-shell methods. The ultimate hope is that, by understanding N=4 SYM in depth, one can learn about other, more realistic quantum field theories. The overarching theme of this thesis is the investigation of how on-shell methods can aid the computation of quantities other than scattering amplitudes. In this spirit we study form factors and correlation functions, said to be partially and completely off...
Schowalter, M; Müller, K; Rosenauer, A
2012-01-01
Modified atomic scattering amplitudes (MASAs), taking into account the redistribution of charge due to bonds, and the respective correction factors considering the effect of static atomic displacements were computed for the chemically sensitive 002 reflection for ternary III-V and II-VI semiconductors. MASAs were derived from computations within the density functional theory formalism. Binary eight-atom unit cells were strained according to each strain state s (thin, intermediate, thick and fully relaxed electron microscopic specimen) and each concentration (x = 0, …, 1 in 0.01 steps), where the lattice parameters for composition x in strain state s were calculated using continuum elasticity theory. The concentration dependence was derived by computing MASAs for each of these binary cells. Correction factors for static atomic displacements were computed from relaxed atom positions by generating 50 × 50 × 50 supercells using the lattice parameter of the eight-atom unit cells. Atoms were randomly distributed according to the required composition. Polynomials were fitted to the composition dependence of the MASAs and the correction factors for the different strain states. Fit parameters are given in the paper.
Energy Technology Data Exchange (ETDEWEB)
Devereux, M.J.
1979-05-01
Elastic pion scattering from /sup 9/Be, /sup 28/Si, /sup 58/Ni, and /sup 208/Pb at 162 MeV is analyzed and compared with an optical model theory which incorporates a pion--nucleon range. Excellent fits to the data are obtained in all but one case. The fitted values of the pion--nucleon range, as well as other fitted values are listed. 108 references.
Two-body dissipation effects on synthesis of superheavy elements
Tohyama, M
2015-01-01
To investigate the two-body dissipation effects on the synthesis of superheavy elements, we calculate low-energy collisions of the $N=50$ isotones ($^{82}$Ge, $^{84}$Se, $^{86}$Kr and $^{88}$Sr) on $^{208}$Pb using the time-dependent density-matrix theory (TDDM). TDDM is an extension of the time-dependent Hartree-Fock (TDHF) theory and can determine the time evolution of one-body and two-body density matrices. Thus TDDM describes both one-body and two-body dissipation of collective energies. It is shown that the two-body dissipation may increase fusion cross sections and enhance the synthesis of superheavy elements.
Two-body physics in the Su-Schrieffer-Heeger model
Di Liberto, M.; Recati, A.; Carusotto, I.; Menotti, C.
2016-12-01
We consider two interacting bosons in a dimerized Su-Schrieffer-Heeger (SSH) lattice. We identify a rich variety of two-body states. In particular, for open boundary conditions and moderate interactions, edge bound states (EBS) are present even for the dimerization that does not sustain single-particle edge states. Moreover, for large values of the interactions, we find a breaking of the standard bulk-boundary correspondence. Based on the mapping of two interacting particles in one dimension onto a single particle in two dimensions, we propose an experimentally realistic coupled optical fibers setup as quantum simulator of the two-body SSH model. This setup is able to highlight the localization properties of the states as well as the presence of a resonant scattering mechanism provided by a bound state that crosses the scattering continuum, revealing the closed-channel population in real time and real space.
Renormalization of the Spin-dependent WIMP scattering off nuclei
Divari, P C
2013-01-01
We study the amplitude for the spin-dependent WIMP scattering off nuclei by including the leading long-range two-body currents in the most important isovector contribution. We show that such effects are essentially independent of the target nucleus and, as a result, they can be treated as a mere renormalization of the effective nucleon cross section or, equivalently, of the corresponding effective coupling with values around 25%.
Taylor, Tomasz R.
2017-05-01
This a pedagogical introduction to scattering amplitudes in gauge theories. It proceeds from Dirac equation and Weyl fermions to the two pivot points of current developments: the recursion relations of Britto, Cachazo, Feng and Witten, and the unitarity cut method pioneered by Bern, Dixon, Dunbar and Kosower. In ten lectures, it covers the basic elements of on-shell methods.
Energy Technology Data Exchange (ETDEWEB)
Amos, N.A.; Avila, C.; Baker, W.F.; Bertani, M.; Block, M.M.; Dimitroyannis, D.A.; Eartly, D.P.; Ellsworth, R.W.; Giacomelli, G.; Gomez, B.; Goodman, J.A.; Guss, C.M.; Lennox, A.J.; Mondardini, M.R.; Negret, J.P.; Orear, J.; Pruss, S.M.; Rubinstein, R.; Sadr, S.; Sanabria, J.C.; Shukla, S.; Spagnoli, M.; Veronesi, I.; Zucchelli, S. (Fermi National Accelerator Laboratory, Batavia, Illinoiss 60510 (United States) Universita di Bologna and Istituto Nazionale di Fisica Nucleare, Bologna (Italy) Italy Northwestern University, Evanston, Illinois 60201 (United States) University of Maryland, College Park, Maryland 20742 (United States) George Mason University, Fairfax, Virginia 22030 (United States) Cornell University, Ithaca, New York 14853 (United States)); (E-710 Collaboration)
1992-04-20
We have measured {rho}, the ratio of the real to the imaginary part of the {ital {bar p}p} forward elastic-scattering amplitude, at {radical}{ital s} =1.8 TeV. Our result, {rho}=0.140{plus minus}0.069, is compared with extrapolations from lower-energy data based on dispersion relations, and with the UA4 value at {radical}{ital s} =546 GeV.
Calculating Rayleigh scattering amplitudes from 100 eV to 10 MeV. [100 eV to 10 MeV
Energy Technology Data Exchange (ETDEWEB)
Parker, J.C.; Reynaud, G.W.; Botto, D.J.; Pratt, R.H.
1979-05-01
An attempt is made to explain how to calculate the contribution to elastic photon-atom scattering due to Rayleigh scattering (the scattering off bound electrons) in the photon energy range 100 eV less than or equal to W less than or equal to 10 MeV. All intermediate calculations are described, including the calculation of the potential, bound state wave functions, matrix elements, and final cross sections. 12 references. (JFP)
The Sharma-Parthasarathy stochastic two-body problem
Energy Technology Data Exchange (ETDEWEB)
Cresson, J. [LMAP/Université de Pau, 64013 Pau (France); SYRTE/Observatoire de Paris, 75014 Paris (France); Pierret, F. [SYRTE/Observatoire de Paris, 75014 Paris (France); Puig, B. [IPRA/Université de Pau, 64013 Pau (France)
2015-03-15
We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.
The Sharma-Parthasarathy stochastic two-body problem
Cresson, J.; Pierret, F.; Puig, B.
2015-03-01
We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in ["Dynamics of a stochastically perturbed two-body problem," Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.
Multinucleon Ejection Model for Two Body Current Neutrino Interactions
Energy Technology Data Exchange (ETDEWEB)
Sobczyk, Jan T.; /Fermilab
2012-06-01
A model is proposed to describe nucleons ejected from a nucleus as a result of two-body-current neutrino interactions. The model can be easily implemented in Monte Carlo neutrino event generators. Various possibilities to measure the two-body-current contribution are discussed. The model can help identify genuine charge current quasielastic events and allow for a better determination of the systematic error on neutrino energy reconstruction in neutrino oscillation experiments.
Charmless hadronic two-body decays of Bs mesons
Chen, Yaw-Hwang; Cheng, Hai-Yang; Tseng, B.
1999-04-01
Two-body charmless nonleptonic decays of the Bs meson are studied within the framework of generalized factorization in which factorization is applied to the tree level matrix elements while the effective Wilson coefficients are μ and renormalization scheme independent, and nonfactorizable effects are parametrized in terms of Neffc(LL) and Neffc(LR), the effective numbers of colors arising from (V-A)(V-A) and (V-A)(V+A) four-quark operators, respectively. Branching ratios of Bs-->PP,PV,VV decays (P: pseudoscalar meson, V: vector meson) are calculated as a function of Neffc(LR) with two different considerations for Neffc(LL): (a) Neffc(LL) being fixed at the value of 2 and (b) Neffc(LL)=Neffc(LR). Tree and penguin transitions are classified into six different classes. We find the following. (i) The electroweak penguin contributions account for about 85% [for Neffc(LL)=2] of the decay rates of Bs-->ηπ, η'π, ηρ, η'ρ, φπ, φρ, which receive contributions only from tree and electroweak penguin diagrams; a measurement of them will provide a clean determination of the electroweak penguin coefficient a9. (ii) Electroweak penguin corrections to Bs-->ωη('),φη,ωφ,K(*)φ,φφ are in general as significant as QCD penguin effects and even play a dominant role; their decay rates depend strongly on Neffc(LR). (iii) The branching ratio of Bs-->ηη', the analogue of Bd-->η'K, is of order 2×10-5, which is only slightly larger than that of η'η',K*+ρ-,K+K-,K0K¯0 decay modes. (iv) The contribution from the η' charm content is important for Bs-->η'η', but less significant for Bs-->ηη'. (v) The decay rates for the final states K+(*)K-(*) follow the pattern Γ(B¯s-->K+K-)>Γ(B¯s-->K+K*-)>~Γ(B¯s-->K*+K*-)>Γ(B¯s-->K+*K-) and likewise for K0(*)K¯0(*), as a consequence of various interference effects between the penguin amplitudes governed by the effective QCD penguin coefficients a4 and a6.
CHY formula and MHV amplitudes
Du, Yi-jian; Wu, Yong-shi
2016-01-01
In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl support the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes. This is achieved by developing techniques, in a manifestly M\\"obius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other $(n-3)!-1$ solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes.
CP Violating Polarization Asymmetry in Charmless Two-Body Decays of Beauty Baryons
He, Min; Li, Guan-Nan
2015-01-01
Several baryons containing a heavy b-quark, the b-baryons, have been discovered. The charmless two-body decays of b-baryons can provide a new platform for CP violating studies in a similar way as charmless two-body decays of B-meson. In b-baryon decays there are new CP violating observable related to baryon polarization. We show that in the flavor $SU(3)$ limit there exist relations involve different combinations of the decay amplitudes compared with those in CP violating rate asymmetry. These new relations therefore provide interesting tests for the mechanism of CP in the standard model (SM) and flavor $SU(3)$ symmetry. Future data from LHCb can test these relations.
Periods and Superstring Amplitudes
Stieberger, S
2016-01-01
Scattering amplitudes which describe the interaction of physical states play an important role in determining physical observables. In string theory the physical states are given by vibrations of open and closed strings and their interactions are described (at the leading order in perturbation theory) by a world-sheet given by the topology of a disk or sphere, respectively. Formally, for scattering of N strings this leads to N-3-dimensional iterated real integrals along the compactified real axis or N-3-dimensional complex sphere integrals, respectively. As a consequence the physical observables are described by periods on M_{0,N} - the moduli space of Riemann spheres of N ordered marked points. The mathematical structure of these string amplitudes share many recent advances in arithmetic algebraic geometry and number theory like multiple zeta values, single-valued multiple zeta values, Drinfeld, Deligne associators, Hopf algebra and Lie algebra structures related to Grothendiecks Galois theory. We review the...
Sensitivity analysis of random two-body interactions
Johnson, Calvin W
2010-01-01
The input to the configuration-interaction shell model includes many dozens or hundreds of independent two-body matrix elements. Previous studies have shown that when fitting to experimental low-lying spectra, the greatest sensitivity is to only a few linear combinations of matrix elements. Here we consider interactions drawn from the two-body random ensemble, or TBRE, and find that the low-lying spectra are also most sensitive to only a few linear combinations of two-body matrix elements, in a fashion nearly indistinguishable from an interaction empirically fit to data. We find in particular the spectra for both the random and empirical interactions are sensitive to similar matrix elements, which we analyze using monopole and contact interactions.
Pion-nucleon scattering in the P11 channel
Morioka, S.; Afnan, I. R.
1982-09-01
We present a parametrization of the π-N interaction in the P11 channel in which the amplitude is the sum of a pole part and a non-pole part (t=tpole+tnp) and satisfies two-body unitarity. Here tpole has both the nucleon propagator and the πNN vertex dressed. The final amplitude fits the scattering length and low energy π-N phase shifts (Tlabπ<300 MeV). We study the effect of a resonance in tnp on the phase shifts, πNN coupling constant, and the off-shell behavior of the amplitude. NUCLEAR REACTIONS πN scattering in P11 channel, renormalization, resonance effect.
Wave Function Structure in Two-Body Random Matrix Ensembles
Kaplan, L; Kaplan, Lev; Papenbrock, Thomas
2000-01-01
We study the structure of eigenstates in two-body interaction random matrix ensembles and find significant deviations from random matrix theory expectations. The deviations are most prominent in the tails of the spectral density and indicate localization of the eigenstates in Fock space. Using ideas related to scar theory we derive an analytical formula that relates fluctuations in wave function intensities to fluctuations of the two-body interaction matrix elements. Numerical results for many-body fermion systems agree well with the theoretical predictions.
Compositeness of the Delta(1232) resonance in pi N scattering
Sekihara, Takayasu; Yamagata-Sekihara, Junko; Yasui, Shigehiro
2015-01-01
We evaluate the $\\pi N$ compositeness of the $\\Delta (1232)$ resonance so as to clarify the internal structure of $\\Delta (1232)$ in terms of the $\\pi N$ component. Here the compositeness is defined as contributions from two-body wave functions to the normalization of the total wave function and is extracted from the $\\pi N$ scattering amplitude. In this study we employ the chiral unitary approach with the interaction up to the next-to-leading order plus a bare $\\Delta$ term in chiral perturbation theory and describe $\\Delta (1232)$ in an elastic $\\pi N$ scattering. Fitting the $\\pi N$ scattering amplitude to the solution of the partial wave analysis, we obtain a large real part of the $\\pi N$ compositeness for $\\Delta (1232)$ comparable to unity and non-negligible imaginary part as well, with which we reconfirm the result in the previous study on the $\\pi N$ compositeness for $\\Delta (1232)$.
Two-body quantum mechanical problem on spheres
2005-01-01
The quantum mechanical two-body problem with a central interaction on the sphere ${\\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.
Stochastic perturbation of the two-body problem
Jacky, Cresson; Bénédicte, Puig
2014-01-01
We study the impact of a stochastic perturbation on the classical two-body problem in particular concerning the preservation of first integrals and the Hamiltonian structure. Numerical simulations are performed which illustrate the dynamical behavior of the osculating elements as the semi-major axis, the eccentricity and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.
Stochastic perturbation of the two-body problem
Cresson, J.; Pierret, F.; Puig, B.
2013-11-01
We study the impact of a stochastic perturbation on the classical two-body problem in particular concerning the preservation of first integrals and the Hamiltonian structure. Numerical simulations are performed which illustrate the dynamical behavior of the osculating elements as the semi-major axis, the eccentricity and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.
Exact phase space functional for two-body systems
Gracia-Bondía, José M
2010-01-01
The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently be obtained by minimizing the ground-state energy.
On the change of density of states in two-body interactions
Gao, Bo
2016-01-01
We derive a general relation in two-body scattering theory that more directly relates the change of density of states (DDOS) due to interaction to the shape of the potential. The relation allows us to infer certain global properties of the DDOS from the global properties of the potential. In particular, we show that DDOS is negative at all energies and for all partial waves, for potentials that are more repulsive than $+1/r^2$ everywhere. This behavior represents a different class of global properties of DDOS from that described by the Levinson's theorem.
Separation of Potentials in the Two-Body Problem
Vasilyev, Andrey
2012-01-01
In contrast to the well-known solution of the two-body problem through the use of the concept of reduced mass, a solution is proposed involving separation of potentials. It is shown that each of the two point bodies moves in its own stationary potential well generated by the other body, and the magnitudes of these potentials are calculated. It is shown also that for each body separately the energy and the angular momentum laws are valid. The knowledge of the potentials in which the bodies are moving permits calculation of the trajectories of each body without resorting to the reduced mass. Key words: mechanics, two-body problem, gravitational potential, virial theorem.
Atlas2bgeneral: Two-body resonance calculator
Gallardo, Tabaré
2016-07-01
For a massless test particle and given a planetary system, Atlas2bgeneral calculates all resonances in a given range of semimajor axes with all the planets taken one by one. Planets are assumed in fixed circular and coplanar orbits and the test particle with arbitrary orbit. A sample input data file to calculate the two-body resonances is available for use with the Fortran77 source code.
Classical and Quantum Two-Body Problem in General Relativity
Maheshwari, Amar; Todorov, Ivan
2016-01-01
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different `Schwarzschild radii'. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.
Positive Amplitudes In The Amplituhedron
Arkani-Hamed, Nima; Trnka, Jaroslav
2014-01-01
The all-loop integrand for scattering amplitudes in planar N = 4 SYM is determined by an "amplitude form" with logarithmic singularities on the boundary of the amplituhedron. In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron. The statement is sensibly formulated thanks to the natural "bosonization" of the superamplitude associated with the amplituhedron geometry. However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian. The surprising positivity of the form suggests the existence of a "dual amplituhedron" formulation where this feature would be made obvious. We also suggest that the positivity is associated with an extended picture of amplituhedron geometry, with the amplituhedron sitting...
Ader, J P
1974-01-01
In the paper, dealing with high-energy quasi-two-body or multiparticle production, the authors focus on what can be learned about exchanged naturality amplitudes from final polarization measurements with polarized or unpolarized beam amd/or target. The separation of t- channel (boson exchange) and u-channel (baryon exchange) exchanges into components of natural and unnatural parity and the measure of naturality interferences are extensively studied in all cases which are now or will be soon available with present experimental techniques. Special attention is paid to the transversity amplitudes which are shown to be always naturality conserving. (19 refs).
Two-body bound states in quantum electrodynamics. [Rate
Energy Technology Data Exchange (ETDEWEB)
Lepage, G.P.
1978-07-01
Novel formulations of the two-body bound state problem in quantum field theory are examined. While equal in rigor, these have several calculational advantages over the traditional Bethe-Salpeter formalism. In particular there exist exact solutions of the bound state equations for a Coulomb-like interaction in quantum electrodynamics. The corrections to such zeroth-order solutions can be systematically computed in a simple perturbation theory. These methods are illustrated by computing corrections to the orthopositronium decay rate and to the ground state splittings in positronium and muonium.
Covariant Hamiltonian for the electromagnetic two-body problem
De Luca, Jayme
2005-09-01
We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem.
Two-body bound states & the Bethe-Salpeter equation
Energy Technology Data Exchange (ETDEWEB)
Pichowsky, M. [Argonne National Lab., IL (United States); Kennedy, M. [Univ. of New Hampshire, Durham, NH (United States). Physics Dept.; Strickland, M. [Duke Univ., Durham, NC (United States)
1995-01-18
The Bethe-Salpeter formalism is used to study two-body bound states within a scalar theory: two scalar fields interacting via the exchange of a third massless scalar field. The Schwinger-Dyson equation is derived using functional and diagrammatic techniques, and the Bethe-Salpeter equation is obtained in an analogous way, showing it to be a two-particle generalization of the Schwinger-Dyson equation. The authors also present a numerical method for solving the Bethe-Salpeter equation without three-dimensional reduction. The ground and first excited state masses and wavefunctions are computed within the ladder approximation and space-like form factors are calculated.
Role of three-body unitarity in. pi. -N scattering
Energy Technology Data Exchange (ETDEWEB)
Afnan, I.R.; Pearce, B.C.
1987-02-01
We consider the amplitude for ..pi..-N scattering within the framework of a Lagrangian of the form suggested by the cloudy bag model with volume coupling. By first exposing two-body, and then three-body unitarity, we derive a set of integral equations that couple the ..pi..N to the ..pi pi..N channel. These equations satisfy two- and three-body unitarity, and can be used to describe ..pi..-N scattering both below and above the threshold for pion production. Below this threshold, the equations have the form of the Lippmann-Schwinger equation with the new feature that in the potential, the vertices in the pole diagram are undressed, while those in the crossed diagram are dressed. This feature allows for the proper description of the P/sub 11/ amplitude.
Effective Field Theory Description of Two-Body Resonance States
Balalhabashi, Jaber
2017-01-01
The quantum-mechanical scattering of two particles around a resonance state appears in many areas of physics, for example in cold atoms near narrow, low-lying Feshbach resonances. We construct) an EFT that describes such scattering with contact, derivative interactions. We demonstrate that a careful choice of leading- and next-to-leading-order terms in an effective Lagrangian gives rise to a systematic expansion of the T matrix around the resonance, with controlled error estimates. We compare phase shifts and pole positions with those of a toy model. We are extending our EFT to include Coulomb interactions with the goal of describing nuclear resonances, such as those appearing in the scattering of alpha particles. This material is based upon work supported in part by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Award Number DE-FG02-04ER41338.
Nonleptonic two-body Bc-meson decays
Naimuddin, Sk.; Kar, Susmita; Priyadarsini, M.; Barik, N.; Dash, P. C.
2012-11-01
We study the exclusive nonleptonic two-body Bc decays within factorization approximation, in the framework of the relativistic independent quark model based on a confining potential in the scalar-vector harmonic form. The relevant weak form factors and branching ratios for different decay modes (Bc→PP,PV,VP) are predicted in reasonable agreement with other quark model predictions. We find that the dominant contribution to the Bc-meson lifetime comes from the Cabibbo-Kobayashi-Masakawa favored c¯→s¯, d¯ decay modes, and the most promising modes are found to be Bc-→B¯s0π-, Bc-→B¯s0ρ- and Bc-→B¯s⋆0π- with predicted branching ratios of 12.01, 9.96, and 8.61%, respectively, which might be easily detected at the hadron collider in the near future.
Two-body Dirac equation approach to the deuteron
Energy Technology Data Exchange (ETDEWEB)
Galeao, A.P.; Castilho A, J.A.; Ferreira, P. Leal
1996-06-01
The two-body Dirac (Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the J{sup {pi}} = 1{sup +} state contains four independent radial functions which satisfy a system of four coupled differential equations of firs order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant. The present treatment differs from the more conventional ones in that non-relativistic reductions up to the order c{sup -2} are not used. (author). 20 refs., 1 fig., 2 tabs.
Visualized kinematics code for two-body nuclear reactions
Lee, E. J.; Chae, K. Y.
2016-05-01
The one or few nucleon transfer reaction has been a great tool for investigating the single-particle properties of a nucleus. Both stable and exotic beams are utilized to study transfer reactions in normal and inverse kinematics, respectively. Because many energy levels of the heavy recoil from the two-body nuclear reaction can be populated by using a single beam energy, identifying each populated state, which is not often trivial owing to high level-density of the nucleus, is essential. For identification of the energy levels, a visualized kinematics code called VISKIN has been developed by utilizing the Java programming language. The development procedure, usage, and application of the VISKIN is reported.
A search for two body muon decay signals
Bayes, R; Davydov, Yu I; Depommier, P; Faszer, W; Fujiwara, M C; Gagliardi, C A; Gaponenko, A; Gill, D R; Grossheim, A; Gumplinger, P; Hasinoff, M D; Henderson, R S; Hillairet, A; Hu, J; Koetke, D D; MacDonald, R P; Marshall, G M; Mathie, E L; Mischke, R E; Olchanski, K; Olin, A; Openshaw, R; Poutissou, J -M; Poutissou, R; Selivanov, V; Sheffer, G; Shin, B; Stanislaus, T D S; Tacik, R; Tribble, R E
2014-01-01
Lepton family number violation is tested by searching for $\\mu^+\\to e^+X^0$ decays among the 5.8$\\times 10^8$ positive muon decay events analyzed by the TWIST collaboration. Limits are set on the production of both massless and massive $X^0$ bosons. The large angular acceptance of this experiment allows limits to be placed on anisotropic $\\mu^+\\to e^+X^0$ decays, which can arise from interactions violating both lepton flavor and parity conservation. Branching ratio limits of order $10^{-5}$\\ are obtained for boson masses of 10 - 80 MeV/c$^2$ and different asymmetries. For lighter bosons the asymmetry dependence is much stronger and the branching ratio limit varies up to $5.8 \\times 10^{-5}$. This is the first study that explicitly evaluates the limits for anisotropic two body muon decays.
Orbit Determination with the two-body Integrals. II
Gronchi, Giovanni F; Dimare, Linda
2011-01-01
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for this problem, that we can solve using the powerful tools of computational Algebra. An algorithm to decide if the linkage of two short arcs is successful, i.e. if they belong to the same observed body, is proposed and tested numerically. In this paper we continue the research started in [Gronchi, Dimare, Milani, 'Orbit determination with the two-body intergrals', CMDA (2010) 107/3, 299-318], where the angular momentum and the energy integrals were used. A suitable component of the Laplace-Lenz vector in place of the energy turns out to be convenient, in fact the degree of the resulting system is reduced to less than half.
Loschmidt echoes in two-body random matrix ensembles
Pižorn, Iztok; Prosen, Tomaž; Seligman, Thomas H.
2007-07-01
Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting, e.g., from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the unperturbed Hamiltonian, while the off-diagonal terms constitute the perturbation that distorts the echo. We give the linear response solution for this problem in a random matrix framework. While the ensemble average shows no surprising behavior, we find that the typical ensemble member as represented by the median displays a very slow fidelity decay known as “freeze.” Numerical calculations confirm this result and show that the ground state even on average displays the freeze. This may contribute to explanation of the “unreasonable” success of mean field theories.
Micromagnetic simulation of two-body magnetic nanoparticles
Li, Fei; Lu, Jincheng; Yang, Yu; Lu, Xiaofeng; Tang, Rujun; Sun, Z. Z.
2017-05-01
Field-induced magnetization dynamics was investigated in a system of two magnetic nanoparticles with uniaxial anisotropies and magnetostatic interaction. By using the micromagnetic simulation, ultralow switching field strength was found when the separation distance between the two particles reaches a critical small value on nanometer scale in the perpendicular configuration where the anisotropic axes of the two particles are perpendicular to the separation line. The switching field increases sharply when the separation is away from the critical distance. The same results were observed when varying the radius of particles. The micromagnetic results are consistent with the previous theoretical prediction where dipolar interaction between two single-domain magnetic particles was considered. Our present simulations offered further proofs and possibilities for the low-power applications of information storage as the two-body magnetic nanoparticles could be implemented as a composite information bit.
Nonsinglet pentagons and NMHV amplitudes
Directory of Open Access Journals (Sweden)
A.V. Belitsky
2015-07-01
Full Text Available Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respect to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to four-loop order.
Improving the Volume Dependence of Two-Body Binding Energies Calculated with Lattice QCD
Davoudi, Zohreh
2011-01-01
Volume modifications to the binding of two-body systems in large cubic volumes of extent L depend upon the total momentum and exponentially upon the ratio of L to the size of the boosted system. Recent work by Bour et al determined the momentum dependence of the leading volume modifications to nonrelativistic systems with periodic boundary conditions imposed on the single-particle wavefunctions, enabling them to numerically determine the scattering of such bound states using a low-energy effective field theory and Luschers finite-volume method. The calculation of bound nuclear systems directly from QCD using Lattice QCD has begun, and it is important to reduce the systematic uncertainty introduced into such calculations by the finite spatial extent of the gauge-field configurations. We extend the work of Bour et al from nonrelativistic quantum mechanics to quantum field theory by generalizing the work of Luscher and of Gottlieb and Rummukainen to boosted two-body bound states. The volume modifications to bind...
Exploring the Spin Structure of the Proton with Two-Body Partonic Scattering at RHIC
Sowinski, J
2007-01-01
The STAR collaboration at the Relativistic Heavy Ion Collider is using polarized proton beams at sqrt{s} = 200 GeV to study the spin structure of the proton. The first results for the double spin helicity dependence of inclusive jet production are presented along with projections for additional data taken in 2005 and 2006. When fully analyzed these data sets should place strong constraints on the possible contribution of gluonic spin to the proton spin as expressed by Delta G. Future studies using 2-jet or photon-jet coincidences to map out the gluon spin distribution vs. the gluon's momentum fraction of the proton are discussed.
S=--1 Meson-Baryon Scattering in Coupled Channel Unitarized Chiral Perturbation Theory
García-Recio, C; Ruiz-Arriola, E; Vacas, M J V
2003-01-01
The $s-$wave meson-baryon scattering amplitude is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four two-body channels have been considered: $\\bar K N$, $\\pi \\Sigma $, $\\eta \\Lambda $, $ K \\Xi$. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behaviour is parameterized in terms of low energy constants, which outnumber those assumed in previous works and provide a better fit to the data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths of the $\\Lambda (1405)$ and $\\Lambda(1670)$ resonances which compare well with accepted numbers.
S=-1 meson-baryon scattering in coupled-channel unitarized Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Garcia-Recio, C.; Nieves, J.; Ruiz Arriola, E. [Departamento de Fisica Moderna, Universidad de Granada, E-18071, Granada (Spain); Vicente Vacas, M. [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Ap. Correos 22085, E-46071, Valencia (Spain)
2003-11-01
The s-wave meson-baryon scattering amplitude is analyzed for the strangeness S=-1 and isospin I=0 sector in a Bethe-Salpeter coupled-channel formalism incorporating Chiral Symmetry. Four two-body channels have been considered: anti K N, {pi}{sigma}, {eta}{lambda}, K {xi}. The needed two-particle irreducible matrix amplitude is taken from lowest-order Chiral Perturbation Theory in a relativistic formalism. Off-shell behaviour is parameterized in terms of low-energy constants, which outnumber those assumed in previous works and provide a better fit to the data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determines masses and widths of the {lambda}(1405) and {lambda}(1670) resonances which compare well with accepted numbers. (orig.)
Descotes-Genon, S
2003-01-01
We study the radiative decay B -> gamma l nu_l in the framework of QCD factorization. We demonstrate explicitly that, in the heavy-quark limit and at one-loop order in perturbation theory, the amplitude does factorize, i.e. that it can be written as a convolution of a perturbatively calculable hard-scattering amplitude with the (non-perturbative) light-cone distribution amplitude of the B-meson. We evaluate the hard-scattering amplitude at one-loop order and verify that the large logarithms are those expected from a study of the b->u transition in the Soft-Collinear Effective Theory. Assuming that this is also the case at higher orders, we resum the large logarithms and perform an exploratory phenomenological analysis. The questions addressed in this study are also relevant for the applications of the QCD factorization formalism to two-body non-leptonic B-decays, in particular to the component of the amplitude arising from hard spectator interactions.
Smallness of tree-dominated charmless two-body baryonic B decay rates
Cheng, Hai-Yang; Chua, Chun-Khiang
2015-02-01
The long-awaited baryonic B decay B¯0→p p ¯ was recently observed by LHCb with a branching fraction of order 1 0-8. All the earlier model predictions are too large compared with experiment. In this work, we point out that for a given tree operator Oi, the contribution from its Fiertz transformed operator, an effect often missed in the literature, tends to cancel the internal W -emission amplitude induced from Oi. The wave function of low-lying baryons is symmetric in momenta and the quark flavor with the same chirality but antisymmetric in color indices. Using these symmetry properties and the chiral structure of weak interactions, we find that half of the Feynman diagrams responsible for internal W emission cancel. Since this feature holds in the charmless modes but not in the charmful ones, we advocate that the partial cancellation accounts for the smallness of the tree-dominated charmless two-body baryonic B decays. This also explains why most previous model calculations predicted too large rates as the above consideration was not taken into account. Finally, we emphasize that, contrary to the claim in the literature, the internal W -emission tree amplitude should be proportional to the Wilson coefficient c1+c2 rather than c1-c2.
Effect of Tensor Range in Nuclear Two-Body Problems
Feshbach, H.; Schwinger, J.; Harr, J. A.
1949-11-01
The interaction between neutron and proton in the triplet state is investigated, a wide variation in the values of both central and tensor ranges are included; the per cent D state in the deuteron and the effective triplet range have been computed; the results are applied tot he discussion of the magnetic moment of the deuteron, the photoelectric disintegration of the deuteron, and neutron-proton scattering.
Strong Two--Body Decays of Light Mesons
Ricken, R; Merten, D; Metsch, B C; Ricken, Ralf; Koll, Matthias; Merten, Dirk; Metsch, Bernard C.
2003-01-01
In this paper, we present results on strong two-body decay widths of light $q\\bar q$ mesons calculated in a covariant quark model. The model is based on the Bethe-Salpeter equation in its instantaneous approximation and has already been used for computing the complete meson mass spectrum and many electroweak decay observables. Our approach relies on the use of a phenomenological confinement potential with an appropriate spinorial Dirac structure and 't Hooft's instanton--induced interaction as a residual force for pseudoscalar and scalar mesons. The transition matrix element for the decay of one initial meson into two final mesons is evaluated in lowest order by considering conventional decays via quark loops as well as Zweig rule violating instanton--induced decays generated by the six--quark vertex of 't Hooft's interaction; the latter mechanism only contributes if all mesons in the decay have zero total angular momentum. We show that the interference of both decay mechanisms plays an important role in the ...
Material loss in two-body collisions during planet formation
Werner, J.; Schäfer, C.; Maindl, T. I.; Burger, C.; Speith, R.
2016-02-01
During the formation process of a terrestrial planet, a planetary embryo does not only accrete smaller dust particles but also suffers collisions with larger planetesimals. When simulating these collisions, most N-body codes treat them as perfect merging events, i.e. the resulting body's mass is the sum of the previous ones. In our work, we aim to determine whether this assumption is a justified simplification, specifically focusing on bodies containing volatile elements, such as water. To analyze this, we have developed a new Smooth Particle Hydrodynamics (SPH) code that includes elasto-plastic dynamics, a damage model for brittle materials and self gravity. It makes use of the Compute Unified Device Architecture (CUDA) and runs on modern GPU architectures which allows for higher resolution in less calculation time. This enables us to take a precise look at two-body collisions and determine the amount of both transferred and ejected mass according to specific parameters such as mass ratio of impactor and target, porosity, impact velocity, impact angle and water distribution.
Two-body relaxation in modified Newtonian dynamics
Ciotti, L
2004-01-01
A naive extension to MOND of the standard computation of the two-body relaxation time Tb implies that Tb is comparable to the crossing time regardless of the number N of stars in the system. This computation is questionable in view of the non-linearity of MOND's field equation. A non-standard approach to the calculation of Tb is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case we find that in the deep-MOND regime Tbb scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in g...
Automating QCD amplitudes with on-shell methods
Badger, Simon
2016-01-01
We review some of the modern approaches to scattering amplitude computations in QCD and their application to precision LHC phenomenology. We emphasise the usefulness of momentum twistor variables in parameterising general amplitudes.
On the soft limit of tree-level string amplitudes
Bianchi, Massimo
2016-01-01
We study the soft behavior of string scattering amplitudes at three level with massless and massive external insertions, relying on different techniques to compute 4-points amplitudes respectively with open or closed strings.
Soft behavior of string amplitudes with external massive states
Guerrieri, Andrea L
2015-01-01
We briefly discuss the soft behavior of scattering amplitudes both in string and quantum field theory. In particular we show a general argument about the validity of soft theorems for open superstring amplitudes and list some of our recent results.
Quasi-two-body decays $B\\to K\\rho\\to K\\pi\\pi$ in perturbative QCD approach
Wang, Wen-Fei
2016-01-01
We analyze the quasi-two-body decays $B\\to K\\rho\\to K\\pi\\pi$ in the perturbative QCD (PQCD) approach, in which final-state interactions between the pions in the resonant regions associated with the $P$-wave states $\\rho(770)$ and $\\rho^\\prime(1450)$ are factorized into two-pion distribution amplitudes. Adopting experimental inputs for the time-like pion form factors involved in two-pion distribution amplitudes, we calculate branching ratios and direct $CP$ asymmetries of the $B\\to K\\rho(770),K\\rho^\\prime(1450)\\to K\\pi\\pi$ modes. It is shown that agreement of theoretical results with data can be achieved, through which Gegenbauer moments of the $P$-wave two-pion distribution amplitudes are determined. The consistency between the three-body and two-body analyses of the $B\\to K\\rho(770)\\to K\\pi\\pi$ decays supports the PQCD factorization framework for exclusive hadronic $B$ meson decays.
Two-Body Reactions at Large Transverse Momentum
2002-01-01
Large-angle exclusive reactions are studied, in particular elastic scattering and @*p annihilations into @p|+@p|- and K|+K|-. In a previous geometry, the 90|0 c.m. region was covered. The present geometry covers the -t range from about 1 to 8 (GeV/c)|2. The aim is to tie these two regions together and attem understading of large-angle scattering up to our highest energies. \\\\ \\\\ The experiment uses a 1 m liquid H^2 target surrounded by scintillator and lead sandwiches for vetoing neutral and charged particles missing the acceptance. An aerogel Cerenkov counter in the recoil arm can be used to veto charged pions above 0.8 GeV/c. Otherwise the events are selected as previously with fast coincidence matrices using pulses from arrays of scintillator counters. Identification of particles is carried out with threshold Cerenkov counters and iron calorimeters. MWPC's are used to establish the trajectories of the particles.
Softness and Amplitudes' Positivity for Spinning Particles
Bellazzini, Brando
2016-01-01
We derive positivity bounds for scattering amplitudes of particles with arbitrary spin using unitarity, analyticity and crossing symmetry. The bounds imply the positivity of certain low-energy coefficients of the effective action that controls the dynamics of the light degrees of freedom. We show that low-energy amplitudes strictly softer than $O(p^4)$ do not admit unitary ultraviolet completions unless the theory is free. This enforces a bound on the energy growth of scattering amplitudes in the region of validity of the effective theory. We discuss explicit examples including the Goldstino from spontaneous supersymmetry breaking, and the theory of a spin-1/2 fermion with a shift symmetry.
Gauge and Gravity Amplitude Relations
Carrasco, John Joseph M
2015-01-01
In these lectures I talk about simplifications and universalities found in scattering amplitudes for gauge and gravity theories. In contrast to Ward identities, which are understood to arise from familiar symmetries of the classical action, these structures are currently only understood in terms of graphical organizational principles, such as the gauge-theoretic color-kinematics duality and the gravitational double-copy structure, for local representations of multi-loop S-matrix elements. These graphical principles make manifest new relationships in and between gauge and gravity scattering amplitudes. My lectures will focus on arriving at such graphical organizations for generic theories with examples presented from maximal supersymmetry, and their use in unitarity-based multi-loop integrand construction.
Infrared singularities in QCD amplitudes
Gardi, Einan
2009-01-01
We review recent progress in determining the infrared singularity structure of on-shell scattering amplitudes in massless gauge theories. We present a simple ansatz where soft singularities of any scattering amplitude of massless partons, to any loop order, are written as a sum over colour dipoles, governed by the cusp anomalous dimension. We explain how this formula was obtained, as the simplest solution to a newly-derived set of equations constraining the singularity structure to all orders. We emphasize the physical ideas underlying this derivation: the factorization of soft and collinear modes, the special properties of soft gluon interactions, and the notion of the cusp anomaly. Finally, we briefly discuss potential multi-loop contributions going beyond the sum-over-dipoles formula, which cannot be excluded at present.
Gao, Bo
2017-04-01
We derive a general relation in two-body scattering theory that more directly relates the change of density of states (DDOS) due to interaction to the shape of the potential. The relation allows us to infer certain global properties of the DDOS from the global properties of the potential. In particular, we show that DDOS is negative at all energies and for all partial waves, for potentials that are more repulsive than +1 /r2 everywhere. This behavior represents a different class of global properties of DDOS from that described by the Levinson's theorem.
Mirazita, M; Rossi, P; De Sanctis, E; Adams, G; Ambrozewicz, P; Anciant, E; Anghinolfi, M; Asavapibhop, B; Audit, G; Avakian, H; Bagdasaryan, H; Ball, J P; Barrow, S; Battaglieri, M; Beard, K; Bektasoglu, M; Bellis, M; Benmouna, N; Berman, B L; Bertozzi, W; Bianchi, N; Biselli, A S; Boiarinov, S; Bonner, B E; Bouchigny, S; Bradford, R; Branford, D; Briscoe, W J; Brooks, W K; Burkert, V D; Butuceanu, C; Calarco, J R; Carman, D S; Carnahan, B; Chen, S; Cole, P L; Cords, D; Corvisiero, P; Crabb, D; Crannell, H; Cummings, J P; De Vita, R; Degtyarenko, P V; Denizli, H; Dennis, L; Deppman, A; Dharmawardane, K V; Dhuga, K S; Djalali, C; Dodge, G E; Doughty, D C; Dragovitsch, P; Dugger, M; Dytman, S; Dzyubak, O P; Egiyan, H; Egiyan, K S; Elouadrhiri, L; Empl, A; Eugenio, P; Fatemi, R; Feuerbach, R J; Ficenec, J; Forest, T A; Funsten, H; Gai, M; Gavalian, G; Gilad, S; Gilfoyle, G P; Giovanetti, K L; Gordon, C I O; Griffioen, K; Guidal, M; Guillo, M R; Guo, L; Gyurjyan, V; Hadjidakis, C; Hakobyan, R S; Hardie, J; Heddle, D; Hersman, F W; Hicks, K; Hicks, R S; Holtrop, M; Hu, J; Hyde-Wright, C E; Ilieva, Y; Ito, M M; Jenkins, D; Joo, K; Kellie, J D; Khandaker, M; Kim, K Y; Kim, K; Kim, W; Klein, A; Klein, F J; Klimenko, A V; Klusman, M; Kossov, M; Kramer, L H; Kühn, J; Kuhn, S E; Lachniet, J; Laget, J M; Lawrence, D; Ji Li; Lima, A C S; Livingston, K; Lukashin, K; Manak, J J; Marchand, C; McAleer, S; McCarthy, J; McNabb, J W C; Mecking, B A; Mehrabyan, S S; Melone, J J; Mestayer, M D; Meyer, C A; Mikhailov, K; Miskimen, R; Mokeev, V; Morand, L; Morrow, S A; Muccifora, V; Müller, J; Mutchler, G S; Napolitano, J; Nasseripour, R; Niccolai, S; Niculescu, G; Niculescu, I; Niczyporuk, B B; Niyazov, R A; Nozar, M; O'Brien, J T; O'Rielly, G V; Osipenko, M; Ostrovidov, A I; Park, K; Pasyuk, E A; Peterson, G; Philips, S A; Pivnyuk, N; Pocanic, D; Pogorelko, O I; Polli, E; Pozdniakov, S; Preedom, B M; Price, J W; Prok, Y; Protopopescu, D; Qin, L M; Raue, B A; Riccardi, G; Ricco, G; Ripani, M; Ritchie, B G; Rosner, G; Rowntree, D; Rubin, P D; Sabatie, F; Salgado, C; Santoro, J P; Sapunenko, V; Schumacher, R A; Serov, V S; Sharabyan, Yu G; Shaw, J; Simionatto, S; Skabelin, A V; Smith, E S; Smith, L C; Sober, D I; Spraker, M; Stavinsky, A V; Stepanyan, S; Stokes, B; Stoler, P; Strakovsky, I I; Strauch, S; Taiuti, M; Taylor, S; Tedeschi, D J; Thoma, U; Thompson, R; Tkabladze, A; Todor, L; Tur, C; Ungaro, M; Vineyard, M F; Vlassov, A V; Wang, K; Weinstein, L B; Weller, H; Weygand, D P; Whisnant, C S; Wolin, E; Wood, M H; Yegneswaran, A; Yun, J; Zhang, B; Zhou, Z
2004-01-01
Nearly complete angular distributions of the two-body deuteron photodisintegration differential cross section have been measured using the CLAS detector and the tagged photon beam at JLab. The data cover photon energies between 0.5 and 3.0 GeV and center-of-mass proton scattering angles 10-160 degrees. The data show a persistent forward-backward angle asymmetry over the explored energy range, and are well-described by the non-perturbative Quark Gluon String Model.
Mirazita, M.; Ronchetti, F.; Rossi, P.; de Sanctis, E.; Adams, G.; Ambrozewicz, P.; Anciant, E.; Anghinolfi, M.; Asavapibhop, B.; Audit, G.; Avakian, H.; Bagdasaryan, H.; Ball, J. P.; Barrow, S.; Battaglieri, M.; Beard, K.; Bektasoglu, M.; Bellis, M.; Benmouna, N.; Berman, B. L.; Bertozzi, W.; Bianchi, N.; Biselli, A. S.; Boiarinov, S.; Bonner, B. E.; Bouchigny, S.; Bradford, R.; Branford, D.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Butuceanu, C.; Calarco, J. R.; Carman, D. S.; Carnahan, B.; Chen, S.; Cole, P. L.; Cords, D.; Corvisiero, P.; Crabb, D.; Crannell, H.; Cummings, J. P.; de Vita, R.; Degtyarenko, P. V.; Denizli, H.; Dennis, L.; Deppman, A.; Dharmawardane, K. V.; Dhuga, K. S.; Djalali, C.; Dodge, G. E.; Doughty, D.; Dragovitsch, P.; Dugger, M.; Dytman, S.; Dzyubak, O. P.; Egiyan, H.; Egiyan, K. S.; Elouadrhiri, L.; Empl, A.; Eugenio, P.; Fatemi, R.; Feuerbach, R. J.; Ficenec, J.; Forest, T. A.; Funsten, H.; Gai, M.; Gavalian, G.; Gilad, S.; Gilfoyle, G. P.; Giovanetti, K. L.; Gordon, C. I.; Griffioen, K.; Guidal, M.; Guillo, M.; Guo, L.; Gyurjyan, V.; Hadjidakis, C.; Hakobyan, R. S.; Hardie, J.; Heddle, D.; Hersman, F. W.; Hicks, K.; Hicks, R. S.; Holtrop, M.; Hu, J.; Hyde-Wright, C. E.; Ilieva, Y.; Ito, M. M.; Jenkins, D.; Joo, K.; Kellie, J. D.; Khandaker, M.; Kim, K. Y.; Kim, K.; Kim, W.; Klein, A.; Klein, F. J.; Klimenko, A. V.; Klusman, M.; Kossov, M.; Kramer, L. H.; Kuhn, J.; Kuhn, S. E.; Kuhn, J.; Lachniet, J.; Laget, J. M.; Lawrence, D.; Li, Ji; Lima, A. C.; Livingston, K.; Lukashin, K.; Manak, J. J.; Marchand, C.; McAleer, S.; McCarthy, J.; McNabb, J. W.; Mecking, B. A.; Mehrabyan, S.; Melone, J. J.; Mestayer, M. D.; Meyer, C. A.; Mikhailov, K.; Miskimen, R.; Mokeev, V.; Morand, L.; Morrow, S. A.; Muccifora, V.; Mueller, J.; Mutchler, G. S.; Napolitano, J.; Nasseripour, R.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Niczyporuk, B. B.; Niyazov, R. A.; Nozar, M.; O'Brien, J. T.; O'Rielly, G. V.; Osipenko, M.; Ostrovidov, A.; Park, K.; Pasyuk, E.; Peterson, G.; Philips, S. A.; Pivnyuk, N.; Pocanic, D.; Pogorelko, O.; Polli, E.; Pozdniakov, S.; Preedom, B. M.; Price, J. W.; Prok, Y.; Protopopescu, D.; Qin, L. M.; Raue, B. A.; Riccardi, G.; Ricco, G.; Ripani, M.; Ritchie, B. G.; Rosner, G.; Rowntree, D.; Rubin, P. D.; Sabatié, F.; Salgado, C.; Santoro, J. P.; Sapunenko, V.; Schumacher, R. A.; Serov, V. S.; Sharabian, Y. G.; Shaw, J.; Simionatto, S.; Skabelin, A. V.; Smith, E. S.; Smith, L. C.; Sober, D. I.; Spraker, M.; Stavinsky, A.; Stepanyan, S.; Stokes, B.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Taiuti, M.; Taylor, S.; Tedeschi, D. J.; Thoma, U.; Thompson, R.; Tkabladze, A.; Todor, L.; Tur, C.; Ungaro, M.; Vineyard, M. F.; Vlassov, A. V.; Wang, K.; Weinstein, L. B.; Weller, H.; Weygand, D. P.; Whisnant, C. S.; Wolin, E.; Wood, M. H.; Yegneswaran, A.; Yun, J.; Zhang, B.; Zhou, Z.
2004-07-01
Nearly complete angular distributions of the two-body deuteron photodisintegration differential cross section have been measured using the CEBAF Large Acceptance Spectrometer detector and the tagged photon beam at the Thomas Jefferson National Accelerator Facility. The data cover photon energies between 0.5 and 3.0 GeV and center-of-mass proton scattering angles 10° 160° . The data show a persistent forward-backward angle asymmetry over the explored energy range, and are well described by the nonperturbative quark gluon string model.
DVCS amplitude with kinematical twist-3 terms
Radyushkin, A V
2000-01-01
We compute the amplitude of deeply virtual Compton scattering (DVCS) using the calculus of QCD string operators in coordinate representation. To restore the electromagnetic gauge invariance (transversality) of the twist-2 amplitude we include the operators of twist-3 which appear as total derivatives of twist-2 operators. Our results are equivalent to a Wandzura-Wilczek approximation for twist-3 skewed parton distributions. We find that this approximation gives a finite result for the amplitude of a longitudinally polarized virtual photon, while the amplitude for transverse polarization is divergent, i.e., factorization breaks down in this term.
One-loop triple collinear splitting amplitudes in QCD
Badger, Simon; Peraro, Tiziano
2015-01-01
We study the factorisation properties of one-loop scattering amplitudes in the triple collinear limit and extract the universal splitting amplitudes for processes initiated by a gluon. The splitting amplitudes are derived from the analytic Higgs plus four partons amplitudes. We present compact results for primitive helicity splitting amplitudes making use of super-symmetric decompositions. The universality of the collinear factorisation is checked numerically against the full colour six parton squared matrix elements.
On the smallness of Tree-dominated Charmless Two-body Baryonic $B$ Decay Rates
Cheng, Hai-Yang
2014-01-01
The long awaited baryonic $B$ decay $\\bar B{}^0\\to p\\bar p$ was recently observed by LHCb with a branching fraction of order $10^{-8}$. All the earlier model predictions are too large compared with experiment. In this work, we point out that for a given tree operator $O_i$, the contribution from its Fiertz transformed operator, an effect often missed in the literature, tends to cancel the internal $W$-emission amplitude induced from $O_i$. The wave function of low-lying baryons are symmetric in momenta and the quark flavor with the same chirality, but antisymmetric in color indices. Using these symmetry properties and the chiral structure of weak interactions, we find that half of the Feynman diagrams responsible for internal $W$-emission cancel. Since this feature holds in the charmless modes but not in the charmful ones, we advocate that the partial cancellation accounts for the smallness of the tree-dominated charmless two-body baryonic $B$ decays. This also explains why most previous model calculations pr...
Two-body and three-body contacts for identical Bosons near unitarity.
Smith, D Hudson; Braaten, Eric; Kang, Daekyoung; Platter, Lucas
2014-03-21
In a recent experiment with ultracold trapped Rb85 atoms, Makotyn et al. studied a quantum-degenerate Bose gas in the unitary limit where its scattering length is infinitely large. We show that the observed momentum distributions are compatible with a universal relation that expresses the high-momentum tail in terms of the two-body contact C2 and the three-body contact C3. We determine the contact densities for the unitary Bose gas with number density n to be C2 ≈ 20 n(4/3) and C3 ≈ 2n(5/3). We also show that the observed atom loss rate is compatible with that from 3-atom inelastic collisions, which gives a contribution proportional to C3, but the loss rate is not compatible with that from 2-atom inelastic collisions, which gives a contribution proportional to C2. We point out that the contacts C2 and C3 could be measured independently by using the virial theorem near and at unitarity, respectively.
Role of three-body unitarity in π-N scattering
Afnan, I. R.; Pearce, B. C.
1987-02-01
We consider the amplitude for π-N scattering within the framework of a Lagrangian of the form suggested by the cloudy bag model with volume coupling. By first exposing two-body, and then three-body unitarity, we derive a set of integral equations that couple the πN to the ππN channel. These equations satisfy two- and three-body unitarity, and can be used to describe π-N scattering both below and above the threshold for pion production. Below this threshold, the equations have the form of the Lippmann-Schwinger equation with the new feature that in the potential, the vertices in the pole diagram are undressed, while those in the crossed diagram are dressed. This feature allows for the proper description of the P11 amplitude.
Pion-nucleon scattering in the P/sub 11/ channel
Energy Technology Data Exchange (ETDEWEB)
Morioka, S.; Afnan, I.R.
1982-09-01
We present a parametrization of the ..pi..-N interaction in the P/sub 11/ channel in which the amplitude is the sum of a pole part and a non-pole part (t = t/sub pole/+t/sub np/) and satisfies two-body unitarity. Here t/sub pole/ has both the nucleon propagator and the ..pi..NN vertex dressed. The final amplitude fits the scattering length and low energy ..pi..-N phase shifts (T/sub ..pi..//sup lab/<300 MeV). We study the effect of a resonance in t/sub np/ on the phase shifts, ..pi..NN coupling constant and the off-shell behavior of the amplitude.
Analytic representations of Yang-Mills amplitudes
Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.; Feng, Bo
2016-12-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space-fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Möbius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is the foundations of a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Analytic Representations of Yang-Mills Amplitudes
Bjerrum-Bohr, N E J; Damgaard, Poul H; Feng, Bo
2016-01-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Mobius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization
Huber, Tobias; Li, Xin-Qiang
2016-01-01
We evaluate in the framework of QCD factorization the two-loop vertex corrections to the decays $\\bar{B}_{(s)}\\to D_{(s)}^{(\\ast)+} \\, L^-$ and $\\Lambda_b \\to \\Lambda_c^+ \\, L^-$, where $L$ is a light meson from the set $\\{\\pi,\\rho,K^{(\\ast)},a_1\\}$. These decays are paradigms of the QCD factorization approach since only the colour-allowed tree amplitude contributes at leading power. Hence they are sensitive to the size of power corrections once their leading-power perturbative expansion is under control. Here we compute the two-loop ${\\cal O}(\\alpha_s^2)$ correction to the leading-power hard scattering kernels, and give the results for the convoluted kernels almost completely analytically. Our newly computed contribution amounts to a positive shift of the magnitude of the tree amplitude by $\\sim 2$\\%. We then perform an extensive phenomenological analysis to NNLO in QCD factorization, using the most recent values for non-perturbative input parameters. Given the fact that the NNLO perturbative correction and ...
A global analysis of two-body D to VP decays within the framework of flavor symmetry
Cheng, Hai-Yang; Kuo, An-Li
2016-01-01
Two-body charmed meson decays $D\\to VP$ are studied within the framework of the diagrammatic approach. Under flavor SU(3) symmetry, all the flavor amplitude sizes and their associated strong phases are extracted by performing a $\\chi^2$ fit. Thanks to the recent measurement of $D_s^+\\to\\pi^+\\rho^0$, the magnitudes and the strong phases of the $W$-annihilation amplitudes $A_{P,V}$ have been extracted for the first time. As a consequence, the branching fractions of all the $D\\to VP$ decays are predicted, especially those modes that could not be predicted previously due to the unknown $A_{P,V}$. Our working assumption, the flavor SU(3) symmetry, is tested by comparing our predictions with experiment for the singly and doubly Cabibbo-suppressed decay modes based on the flavor amplitudes extracted from the Cabibbo-favored decays using the current data. The predictions for the doubly Cabibbo-suppressed channels are in good agreement with the data, while those for the singly Cabibbo-suppressed decay modes are seen t...
Hidden simplicity of gauge theory amplitudes
Energy Technology Data Exchange (ETDEWEB)
Drummond, J M, E-mail: drummond@lapp.in2p3.f [LAPTH, Universite de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux, Cedex (France)
2010-11-07
These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the Britto, Cachzo, Feng and Witten (BCFW) recursion relations we solve the tree-level S-matrix in N=4 super Yang-Mills theory and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.
Hidden simplicity of gauge theory amplitudes
Drummond, J. M.
2010-11-01
These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the Britto, Cachzo, Feng and Witten (BCFW) recursion relations we solve the tree-level S-matrix in \\ {N}=4 super Yang-Mills theory and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.
Polynomial structures in one-loop amplitudes
Britto, R.; Feng, B.; Yang, G.
2008-01-01
A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2epsilon)-dimensional master integrals; these formulas
Holographic corrections to the Veneziano amplitude
Armoni, Adi; Ireson, Edwin
2017-08-01
We propose a holographic computation of the 2 → 2 meson scattering in a curved string background, dual to a QCD-like theory. We recover the Veneziano amplitude and compute a perturbative correction due to the background curvature. The result implies a small deviation from a linear trajectory, which is a requirement of the UV regime of QCD.
A Model for High Energy Scattering in Quantum Gravity
Banks, T; Banks, Tom; Fischler, Willy
1999-01-01
We present a model for high energy two body scattering in a quantum theory of gravity. The model is applicable for center of mass energies higher than the relevant Planck scale. At impact parameters smaller than the Schwarzchild radius appropriate to the center of mass energy and total charge of the initial state, the cross section is dominated by an inelastic process in which a single large black hole is formed. The black hole then decays by Hawking radiation. The elastic cross section is highly suppressed at these impact parameters because of the small phase space for thermal decay into a high energy two body state. For very large impact parameter the amplitude is dominated by eikonalized single graviton exchange. At intermediate impact parameters the scattering is more complicated, but since the Schwarzchild radius grows with energy, we speculate that a more sophisticated eikonal calculation which uses the nonlinear classical solutions of the field equations may provide a good approximation at all larger i...
Symmetry limit properties of decay amplitudes with mirror matter admixtures
Sánchez-Colón, G; Sanchez-Colon, Gabriel; Garcia, Augusto
2006-01-01
We extend our previous analysis on the symmetry limit properties of non-leptonic and weak radiative decay amplitudes of hyperons in a scheme of mirror matter admixtures in physical hadrons to include the two-body non-leptonic decays of $\\Omega^-$ and the two photon and two pion decays of kaons. We show that the so-called parity-conserving amplitudes predicted for all the decays vanish in the strong flavor SU(3) symmetry limit. We also establish the specific conditions under which the corresponding so-called parity-violating amplitudes vanish in the same limit.
Connecting physical resonant amplitudes and lattice QCD
Bolton, Daniel R; Wilson, David J
2015-01-01
We present a determination of the isovector, $P$-wave $\\pi\\pi$ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using $m_\\pi =236$ MeV. The finite volume spectra are described using extensions of L\\"uscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at $m_\\pi= 140$ MeV. The scattering phase shift is found to be in good agreement with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a $\\rho$-resonance pole at $E_\\rho= \\left[755(2)(1)(^{20}_{02})-\\frac{i}{2}\\,129(3)(1)(^{7}_{1})\\right]~{\\rm MeV}$. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.
A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
Ellis, Richard Keith; Kunszt, Z
2008-01-01
Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and implement the method in a numerical procedure. Our technique can be applied to any one-loop scattering amplitude and offers the possibility that one-loop calculations can be performed in an automatic fashion, as tree-level amplitudes are currently done. Instead of individual Feynman diagrams, the ingredients for our one-loop evaluation are tree-level amplitudes, which are often already known. To study the practicality of this method we evaluate the cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically, using the analytically known 4, 5 and 6 gluon tree-level amplitudes. Comparisons with analytic answers are performed to ascertain the numerical accuracy of the method.
Low energy + scattering on = nuclei
Indian Academy of Sciences (India)
Swapan Das; Arun K Jain
2003-11-01
The data for the total cross-section of + scattering on various nuclei have been analysed in the Glauber multiple scattering theory. Energy-dependent +-nucleus optical potential is generated using the forward +-nucleon scattering amplitude and the nuclear density distribution. Along with this, the calculated total +-nucleus cross-sections using the effective +-nucleon cross-section inside the nucleus are also presented.
Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (II) - Application
Institute of Scientific and Technical Information of China (English)
DAI Lian-Rong; PAN Feng
2001-01-01
Simple analytical expressions for one- and two-body matrix elements in the unitary group approach to the configuration interaction problems of many-electron systems are obtained based on the previous results for general Un irreps.
On The Dynamics and Design of a Two-body Wave Energy Converter
Liang, Changwei; Zuo, Lei
2016-09-01
A two-body wave energy converter oscillating in heave is studied in this paper. The energy is extracted through the relative motion between the floating and submerged bodies. A linearized model in the frequency domain is adopted to study the dynamics of such a two-body system with consideration of both the viscous damping and the hydrodynamic damping. The closed form solution of the maximum absorption power and corresponding power take-off parameters are obtained. The suboptimal and optimal designs for a two-body system are proposed based on the closed form solution. The physical insight of the optimal design is to have one of the damped natural frequencies of the two body system the same as, or as close as possible to, the excitation frequency. A case study is conducted to investigate the influence of the submerged body on the absorption power of a two-body system subjected to suboptimal and optimal design under regular and irregular wave excitations. It is found that the absorption power of the two-body system can be significantly higher than that of the single body system with the same floating buoy in both regular and irregular waves. In regular waves, it is found that the mass of the submerged body should be designed with an optimal value in order to achieve the maximum absorption power for the given floating buoy. The viscous damping on the submerged body should be as small as possible for a given mass in both regular and irregular waves.
Amplitudes, acquisition and imaging
Energy Technology Data Exchange (ETDEWEB)
Bloor, Robert
1998-12-31
Accurate seismic amplitude information is important for the successful evaluation of many prospects and the importance of such amplitude information is increasing with the advent of time lapse seismic techniques. It is now widely accepted that the proper treatment of amplitudes requires seismic imaging in the form of either time or depth migration. A key factor in seismic imaging is the spatial sampling of the data and its relationship to the imaging algorithms. This presentation demonstrates that acquisition caused spatial sampling irregularity can affect the seismic imaging and perturb amplitudes. Equalization helps to balance the amplitudes, and the dealing strategy improves the imaging further when there are azimuth variations. Equalization and dealiasing can also help with the acquisition irregularities caused by shot and receiver dislocation or missing traces. 2 refs., 2 figs.
Dremin, I. M.
2013-01-01
Colliding high-energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18-25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features can be seen that provide information on the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The steep Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoulders and dips, and then by a power-law decrease. Results from various theoretical approaches are compared with experimental data. Phenomenological models claiming to describe this process are reviewed. The unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power-law, hard parton scattering regime under high momentum transfer. Data on the interference of the Coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering amplitude. The real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude (the so-called overlap function) are also discussed. Problems related to the scaling behavior of the differential cross section are considered. The power-law regime at highest momentum transfer is briefly described.
Real topological string amplitudes
Narain, K. S.; Piazzalunga, N.; Tanzini, A.
2017-03-01
We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude G_{χ } , at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g' = -χ + 1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude F_g.
Amplitudes in N = 4 Super-Yang-Mills Theory
Spradlin, Marcus
These lecture notes provide a lightning introduction to some aspects of scattering amplitudes in maximally supersymmetric theory, aimed at the audience of students attending the 2014 TASI summer school "Journeys Through the Precision Frontier: Amplitudes for Colliders". Emphasis is placed on explaining modern terminology so that students needing to delve further may more easily access the available literature.
Amplitude Models for Discrimination and Yield Estimation
Energy Technology Data Exchange (ETDEWEB)
Phillips, William Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-09-01
This seminar presentation describes amplitude models and yield estimations that look at the data in order to inform legislation. The following points were brought forth in the summary: global models that will predict three-component amplitudes (R-T-Z) were produced; Q models match regional geology; corrected source spectra can be used for discrimination and yield estimation; three-component data increase coverage and reduce scatter in source spectral estimates; three-component efforts must include distance-dependent effects; a community effort on instrument calibration is needed.
Amplitudes and Ultraviolet Behavior of N = 8 Supergravity
Energy Technology Data Exchange (ETDEWEB)
Bern, Zvi; /UCLA; Carrasco, John Joseph; /Stanford U., Phys. Dept.; Dixon, Lance J.; /SLAC /CERN; Johansson, Henrik; /Saclay, SPhT; Roiban, Radu; /Penn State U.
2011-05-20
In this contribution we describe computational tools that permit the evaluation of multi-loop scattering amplitudes in N = 8 supergravity, in terms of amplitudes in N = 4 super-Yang-Mills theory. We also discuss the remarkable ultraviolet behavior of N = 8 supergravity, which follows from these amplitudes, and is as good as that of N = 4 super-Yang-Mills theory through at least four loops.
Relativistic two-body bound states in scalar QFT: variational basis-state approach
Energy Technology Data Exchange (ETDEWEB)
Emami-Razavi, Mohsen [Centre for Research in Earth and Space Science, York University, Toronto, Ontario, M3J 1P3 (Canada); Darewych, Jurij W [Department of Physics and Astronomy, York University, Toronto, Ontario, M3J 1P3 (Canada)
2006-08-15
We use the Hamiltonian formalism of quantum field theory and the variational basis-state method to derive relativistic coupled-state wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). A variational trial state comprised of two and four Fock-space states is used to derive coupled wave equations for a relativistic two (and four) body system. Approximate, variational two-body ground-state solutions of the relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields. The results show that the inclusion of virtual pairs has a large effect on the two-body binding energy at strong coupling. A comparison of the two-body binding energies with other calculations is presented.
Non-Perturbative Four-Point Scattering from First-Quantized Relativistic JWKB
Irizarry-Gelpí, M E
2016-01-01
We apply the quantum mechanical (first-quantized) JWKB approximation to a two-body path integral describing the near-forward scattering of two relativistic, heavy, non-identical, scalar particles in $D$ spacetime dimensions. In contrast to the loop expansion, in $D = 4$ this gives a strong-coupling expansion, and in $D = 3$ a non-perturbative weak-coupling expansion. When the interaction is mediated by massless quanta with spin $N$, we obtain explicit, relativistic results for the scattering amplitude when $N = 0$, $1$ and $2$. In $D = 4$ we find a Regge trajectory function that agrees with the usual quantum mechanical spectrum. We also find an exponentiated infrared divergence that becomes a pure phase factor when the Mandelstam invariants $s$ and $t$ are inside of the physical scattering region. In $D = 3$ we find a singularity whose position along the $s$ axis is dependent on $t$. When the interaction is mediated by a heavy scalar with mass $M$, in $D = 3$ we find an all-order scattering amplitude where th...
Analytical treatment of the two-body problem with slowly varying mass
Rahoma, W. A.; Abd El-Salam, F. A.; Ahmed, M. K.
2009-12-01
The present work is concerned with the two-body problem with varying mass in case of isotropic mass loss from both components of the binary systems. The law of mass variation used gives rise to a perturbed Keplerian problem depending on two small parameters. The problem is treated analytically in the Hamiltonian frame-work and the equations of motion are integrated using the Lie series developed and applied, separately by Delva (1984) and Hanslmeier (1984). A second order theory of the two bodies eject mass is constructed, returning the terms of the rate of change of mass up to second order in the small parameters of the problem.
Spin Structure of Many-Body Systems with Two-Body Random Interactions
Kaplan, L; Johnson, C W; Kaplan, Lev; Papenbrock, Thomas; Johnson, Calvin W.
2001-01-01
We investigate the spin structure of many-fermion systems with a spin-conserving two-body random interaction. We find a strong dominance of spin-0 ground states and considerable correlations between energies and wave functions of low-lying states with different spin, but no indication of pairing. The spectral densities exhibit spin-dependent shapes and widths, and depend on the relative strengths of the spin-0 and spin-1 couplings in the two-body random matrix. The spin structure of low-lying states can largely be explained analytically.
Analytical expressions for partial wave two-body Coulomb transition matrices at ground-state energy
Kharchenko, V. F.
2016-11-01
Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p-, d- and f-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states.
Analytical Treatment of the Two-Body Problem with Slowly Varying Mass
Indian Academy of Sciences (India)
W. A. Rahoma; F. A. Abd El-Salam; M. K. Ahmed
2009-09-01
The present work is concerned with the two-body problem with varying mass in case of isotropic mass loss from both components of the binary systems. The law of mass variation used gives rise to a perturbed Keplerian problem depending on two small parameters. The problem is treated analytically in the Hamiltonian frame-work and the equations of motion are integrated using the Lie series developed and applied, separately by Delva (1984) and Hanslmeier (1984). A second order theory of the two bodies eject mass is constructed, returning the terms of the rate of change of mass up to second order in the small parameters of the problem.
RANS Simulation of the Heave Response of a Two-Body Floating Point Wave Absorber: Preprint
Energy Technology Data Exchange (ETDEWEB)
Yu, Y.; Li, Y.
2011-03-01
A preliminary study on a two-body floating wave absorbers is presented in this paper. A Reynolds-Averaged Navier-Stokes computational method is applied for analyzing the hydrodynamic heave response of the absorber in operational wave conditions. The two-body floating wave absorber contains a float section and a submerged reaction section. For validation purposes, our model is first assumed to be locked. The two sections are forced to move together with each other. The locked single body model is used in a heave decay test, where the RANS result is validated with the experimental measurement. For the two-body floating point absorber simulation, the two sections are connected through a mass-spring-damper system, which is applied to simulate the power take-off mechanism under design wave conditions. Overall, the details of the flow around the absorber and its nonlinear interaction with waves are investigated, and the power absorption efficiency of the two-body floating wave absorber in waves with a constant value spring-damper system is examined.
Realization of the Fredkin gate using a series of one- and two-body operators
Chau, H F; Chau, Hoi Fung; Wilczek, F
1995-01-01
The Fredkin 3-bit gate is universal for computational logic, and is reversible. Classically, it is impossible to do universal computation using reversible 2-bit gates only. Here we construct the Fredkin gate using a combination of two one-body and seven two-body reversible (quantum) operators.
Computation of Two-Body Matrix Elements From the Argonne $v_{18}$ Potential
Mihaila, B; Mihaila, Bogdan; Heisenberg, Jochen H.
1998-01-01
We discuss the computation of two-body matrix elements from the Argonne $v_{18}$ interaction. The matrix elements calculation is presented both in particle-particle and in particle-hole angular momentum coupling. The procedures developed here can be applied to the case of other NN potentials, provided that they have a similar operator format.
Two-body depolarized cils spectra of krypton and xenon at 295 K
Zoppi, M.; Moraldi, M.; Barocchi, F.; Magli, R.; Bafile, U.
1981-10-01
We have experimentally determined the two-body depolarized CILS spectra of krypton and xenon at room temperature between 2 and 120 cm-1. Comparison of the first three even experimental moments of the spectra with theoretical calculations shows, as in argon, the necessity of introducing a short-range negative contribution to the induced pair polarizability.
78 FR 54756 - Extension of Expiration Dates for Two Body System Listings
2013-09-06
... ADMINISTRATION 20 CFR Part 404 RIN 0960-AH60 Extension of Expiration Dates for Two Body System Listings AGENCY: Social Security Administration. ACTION: Final rule. SUMMARY: We are extending the expiration dates of the... claims and continuing disability reviews. DATES: This final rule is effective on September 6, 2013....
Searching for new physics in two-body decays: Ideas and pitfalls
Arrieta Diaz, E; Büchler, A; Cieri, L J; Florez, A; Garces-Garcia, E; Gonçalves, B; Koetsveld, F; Leney, K J C; Marquez Falcon, H; Moncada, M; Quintero, P; Romero, D; Shaw, K; Swain, J; Zurita, M P
2010-01-01
Many new physics processes, and indeed many Standard Model interactions involve two-body decays. Although the kinematics are relatively simple, mistakes can easily be made when applying cuts to data in order to separate the signal from backgrounds. We present a short, but relevant list of possible sources of errors, and discuss the consequences of these.
Subleading Soft Factor for String Disk Amplitudes
Schwab, Burkhard U W
2014-01-01
We investigate the behavior of superstring disk scattering amplitudes in the presence of a soft external momentum at finite string tension. We prove that there are no $\\alpha'$-corrections to the field theory form of the subleading soft factor $S^{(1)}$. At the end of this work, we also comment on the possibility to find the corresponding subleading soft factors in closed string theory using our result and the KLT relations.
ABJM amplitudes and the positive orthogonal Grassmannian
Energy Technology Data Exchange (ETDEWEB)
Huang, Yu-tin [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Wen, CongKao [Centre for Research in String Theory, Department of Physics,Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)
2014-02-25
A remarkable connection between perturbative scattering amplitudes of four dimensional planar SYM, and the stratification of the positive Grassmannian, was revealed in the seminal work of Arkani-Hamed et al. Similar extension for three-dimensional ABJM theory was proposed. Here we establish a direct connection between planar scattering amplitudes of ABJM theory, and singularities thereof, to the stratification of the positive orthogonal Grassmannian. In particular, scattering processes are constructed through on-shell diagrams, which are simply iterative gluing of the fundamental four-point amplitude. Each diagram is then equivalent to the merging of fundamental OG{sub 2} orthogonal Grassmannian to form a larger OG{sub k}, where 2k is the number of external particles. The invariant information that is encoded in each diagram is precisely this stratification. This information can be easily read off via permutation paths of the on-shell diagram, which also can be used to derive a canonical representation of OG{sub k} that manifests the vanishing of consecutive minors as the singularity of all on-shell diagrams. Quite remarkably, for the BCFW recursion representation of the tree-level amplitudes, the on-shell diagram manifests the presence of all physical factorization poles, as well as the cancellation of the spurious poles. After analytically continuing the orthogonal Grassmannian to split signature, we reveal that each on-shell diagram in fact resides in the positive cell of the orthogonal Grassmannian, where all minors are positive. In this language, the amplitudes of ABJM theory is simply an integral of a product of dlog forms, over the positive orthogonal Grassmannian.
Euclidean formulation of diffractive scattering
Meggiolaro, E
2005-01-01
After a brief review (in the first part) of some relevant properties of the high-energy parton-parton scattering amplitudes, in the second part we shall discuss the infrared finiteness and some analyticity properties of the loop-loop scattering amplitudes in gauge theories, when going from Minkowskian to Euclidean theory, and we shall see how they can be related to the still unsolved problem of the s-dependence of the hadron-hadron total cross-sections.
Yan, Yangqian; Blume, D.
2015-09-01
The low-energy spectrum of N -boson clusters with pairwise zero-range interactions is believed to be governed by a three-body parameter. We study the ground state of N -boson clusters with infinite two-body s -wave scattering length by performing ab initio Monte Carlo simulations. To prevent Thomas collapse, different finite-range three-body regulators are used. The energy and structural properties for the three-body Hamiltonian with two-body zero-range interactions and three-body regulator are in much better agreement with the "ideal zero-range Efimov theory" results than those for Hamiltonian with two-body finite-range interactions. For larger clusters we find that the ground-state energy and structural properties of the Hamiltonian with two-body zero-range interactions and finite-range three-body regulators are not universally determined by the three-body parameter, i.e., dependencies on the specific form of the three-body regulator are observed. For comparison, we consider Hamiltonian with two-body van der Waals interactions and no three-body regulator. For the interactions considered, the ground-state energy of the N -body clusters is—if scaled by the three-body ground-state energy—fairly universal, i.e., the dependence on the short-range details of the two-body van der Waals potentials is small. Our results are compared with those in the literature.
Li, Chenyang
2016-01-01
The first nonperturbative version of the multireference driven similarity renormalization group (MR-DSRG) theory [C. Li and F. A. Evangelista, J. Chem. Theory Comput. $\\mathbf{11}$, 2097 (2015)] is introduced. The renormalization group structure of the MR-DSRG equations ensures numerical robustness and avoidance of the intruder state problem, while the connected nature of the amplitude and energy equations guarantees size consistency and extensivity. We approximate the MR-DSRG equations by keeping only one- and two-body operators and using a linearized recursive commutator approximation of the Baker--Campbell--Hausdorff expansion [T. Yanai and G. K.-L. Chan, J. Chem. Phys. $\\mathbf{124}$, 194106 (2006)]. The resulting MR-LDSRG(2) equations contain only 39 terms and scales as ${\\cal O}(N^2 N_{\\rm P}^2 N_{\\rm H}^2)$ where $N_{\\rm H}$, $N_{\\rm P}$, and $N$ correspond to the number of hole, particle, and total orbitals, respectively. Benchmark MR-LDSRG(2) computations on the hydrogen fluoride and molecular nitrog...
New Formulas for Amplitudes from Higher-Dimensional Operators
He, Song
2016-01-01
In this paper we study tree-level amplitudes from higher-dimensional operators, including $F^3$ operator of gauge theory, and $R^2$, $R^3$ operators of gravity, in the Cachazo-He-Yuan formulation. As a generalization of the reduced Pfaffian in Yang-Mills theory, we find a new, gauge-invariant object that leads to gluon amplitudes with a single insertion of $F^3$, and gravity amplitudes by Kawai-Lewellen-Tye relations. When reduced to four dimensions for given helicities, the new object vanishes for any solution of scattering equations on which the reduced Pfaffian is non-vanishing. This intriguing behavior in four dimensions explains the vanishing of graviton helicity amplitudes produced by the Gauss-Bonnet $R^2$ term, and provides a scattering-equation origin of the decomposition into self-dual and anti-self-dual parts for $F^3$ and $R^3$ amplitudes.
Antiproton-nucleus inelastic scattering and the spin-isospin dependence of the N anti N interaction
Energy Technology Data Exchange (ETDEWEB)
Dover, C.B.
1985-01-01
A general overview of the utility of antinucleon (anti N)-nucleus inelastic scattering studies is presented, emphasizing both the sensitivity of the cross sections to various components of the N anti N transition amplitudes and the prospects for the exploration of some novel aspects of nuclear structure. We start with an examination of the relation between NN and N anti N potentials, focusing on the coherences predicted for the central, spin-orbit and tensor components, and how these may be revealed by measurements of two-body spin observables. We next discuss the role of the nucleus as a spin and isospin filter, and show how, by a judicious choice of final state quantum numbers (natural or unnatural parity states, isospin transfer ..delta..T=0 or 1) and momentum transfer q, one can isolate different components of the N anti N transition amplitude. Various models for the N anti N interaction which give reasonable fits to the available two-body data are shown to lead to strikingly different predictions for certain spin-flip nuclear transitions. We suggest several possible directions for future anti N-nucleus inelastic scattering experiments at LEAR, for instance the study of spin observables which would be accessible with polarized anti N beams, charge exchange reactions, and higher resolution studies of the (anti p, anti p') reaction. We compare the antinucleon and the nucleon as a probe of nuclear modes of excitation. 34 refs.
An Algebraic Approach to the Scattering Equations
Huang, Rijun; Feng, Bo; He, Yang-Hui
2015-01-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
Twist decomposition of proton structure from BFKL and BK amplitudes
Motyka, Leszek
2014-01-01
An analysis of twist composition of Balitsky-Kovchegov (BK) amplitude is performed in the double logarithmic limit. In this limit the BK evolution of color dipole -- proton scattering is equivalent to BFKL evolution which follows from vanishing of the Bartels vertex in the collinear limit. We perform twist decomposition of the BFKL/BK amplitude for proton structure functions and find compact analytic expressions that provide accurate approximations for higher twist amplitudes. The BFKL/BK higher twist amplitudes are much smaller than those following from eikonal saturation models.
Distribution of level spacing ratios using one- plus two-body random matrix ensembles
Indian Academy of Sciences (India)
N D Chavda
2015-02-01
Probability distribution (()) of the level spacing ratios has been introduced recently and is used to investigate many-body localization as well as to quantify the distance from integrability on finite size lattices. In this paper, we study the distribution of the ratio of consecutive level spacings using one-body plus two-body random matrix ensembles for finite interacting many-fermion and many-boson systems. () for these ensembles move steadily from the Poisson to the Gaussian orthogonal ensemble (GOE) form as the two-body interaction strength is varied. Other related quantities are also used in the analysis to obtain critical strength c for the transition. The c values deduced using the () analysis are in good agreement with the results obtained using the nearest neighbour spacing distribution (NNSD) analysis.
The two-body problem of a pseudo-rigid body and a rigid sphere
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Vereshchagin, M.; Gózdziewski, K.;
2012-01-01
n this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational and "re-labelling" symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken...... in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann's theorem on pseudo......-rigid bodies has an extension to this system for planar relative equilibria....
Energy Centroids of Spin $I$ States by Random Two-body Interactions
Zhao, Y M; Ogawa, K
2005-01-01
In this paper we study the behavior of energy centroids (denoted as $\\bar{E_I}$) of spin $I$ states in the presence of random two-body interactions, for systems ranging from very simple systems (e.g. single-$j$ shell for very small $j$) to very complicated systems (e.g., many-$j$ shells with different parities and with isospin degree of freedom). Regularities of $\\bar{E_I}$'s discussed in terms of the so-called geometric chaoticity (or quasi-randomness of two-body coefficients of fractional parentage) in earlier works are found to hold even for very simple systems in which one cannot assume the geometric chaoticity. It is shown that the inclusion of isospin and parity does not "break" the regularities of $\\bar{E_I}$'s.
A Tale of Three Equations Breit, Eddington-Guant, and Two-Body Dirac
Van Alstine, P; Alstine, Peter Van; Crater, Horace W.
1997-01-01
G.Breit's original paper of 1929 postulates the Breit equation as a correction to an earlier defective equation due to Eddington and Gaunt, containing a form of interaction suggested by Heisenberg and Pauli. We observe that manifestly covariant electromagnetic Two-Body Dirac equations previously obtained by us in the framework of Relativistic Constraint Mechanics reproduce the spectral results of the Breit equation but through an interaction structure that contains that of Eddington and Gaunt. By repeating for our equation the analysis that Breit used to demonstrate the superiority of his equation to that of Eddington and Gaunt, we show that the historically unfamiliar interaction structures of Two-Body Dirac equations (in Breit-like form) are just what is needed to correct the covariant Eddington Gaunt equation without resorting to Breit's version of retardation.
Weak Boson Production Amplitude Zeros; Equalities of the Helicity Amplitudes
Mamedov, F
2002-01-01
We investigate the radiation amplitude zeros exhibited by many Standard Model amplitudes for triple weak gauge boson production processes. We show that $WZ\\gamma$ production amplitudes have especially rich structure in terms of zeros, these amplitudes have zeros originating from several different sources. It is also shown that TYPE I current null zone is the special case of the equality of the specific helicity amplitudes.
Light Meson Distribution Amplitudes
Arthur, R.; Brommel, D.; Donnellan, M.A.; Flynn, J.M.; Juttner, A.; de Lima, H.Pedroso; Rae, T.D.; Sachrajda, C.T.; Samways, B.
2010-01-01
We calculated the first two moments of the light-cone distribution amplitudes for the pseudoscalar mesons ($\\pi$ and $K$) and the longitudinally polarised vector mesons ($\\rho$, $K^*$ and $\\phi$) as part of the UKQCD and RBC collaborations' $N_f=2+1$ domain-wall fermion phenomenology programme. These quantities were obtained with a good precision and, in particular, the expected effects of $SU(3)$-flavour symmetry breaking were observed. Operators were renormalised non-perturbatively and extrapolations to the physical point were made, guided by leading order chiral perturbation theory. The main results presented are for two volumes, $16^3\\times 32$ and $24^3\\times 64$, with a common lattice spacing. Preliminary results for a lattice with a finer lattice spacing, $32^3\\times64$, are discussed and a first look is taken at the use of twisted boundary conditions to extract distribution amplitudes.
Large-j Expansion Method for Two-Body Dirac Equation
Directory of Open Access Journals (Sweden)
Askold Duviryak
2006-02-01
Full Text Available By using symmetry properties, the two-body Dirac equation in coordinate representation is reduced to the coupled pair of radial second-order differential equations. Then the large-j expansion technique is used to solve a bound state problem. Linear-plus-Coulomb potentials of different spin structure are examined in order to describe the asymptotic degeneracy and fine splitting of light meson spectra.
Two bodies gravitational system with variable mass and damping-antidamping effect due to star wind
López, G V
2009-01-01
We study two-bodies gravitational problem where the mass of one of the bodies varies and suffers a damping-antidamping effect due to star wind during its motion. A constant of motion, a Lagrangian and a Hamiltonian are given for the radial motion of the system, and the period of the body is studied using the constant of motion of the system. An application to the comet motion is given, using the comet Halley as an example.
Kinematics of τ two-body decay near τ threshold at BESⅢ
Institute of Scientific and Technical Information of China (English)
莫晓虎
2010-01-01
The kinematic properties of two-body decay near τ threshold are studied according to the special capacity of the BEPC accelerator and the BESⅢ detector.Explicitly presented are the transformations of energy and momentum of hadronic particles between different reference frames,and the corresponding distributions.A brand new method is proposed to obtain the energy spread of the accelerator by fitting the energy distribution of hadron from τ semi-leptonic decays.
Quantitative Seismic Amplitude Analysis
Dey, A. K.
2011-01-01
The Seismic Value Chain quantifies the cyclic interaction between seismic acquisition, imaging and reservoir characterization. Modern seismic innovation to address the global imbalance in hydrocarbon supply and demand requires such cyclic interaction of both feed-forward and feed-back processes. Currently, the seismic value chain paradigm is in a feed-forward mode. Modern seismic data now have the potential to yield the best images in terms of spatial resolution, amplitude accuracy, and incre...
Regularities of many-body systems interacting by a two-body random ensemble
Energy Technology Data Exchange (ETDEWEB)
Zhao, Y.M. [Department of Physics, Shanghai Jiao-Tong University, Shanghai 200030 (China) and Cyclotron Center, Institute of Physical and Chemical Research - RIKEN, Hirosawa 2-1, Wako-shi, Saitama 351-0198 (Japan) and Department of Physics, Southeast University, Nanjing 210018 (China)]. E-mail: ymzhao@riken.jp; Arima, A. [Science Museum, Japan Science Foundation, 2-1 Kitanomaru-Koen, Chiyodaku, Tokyo 102-0091 (Japan); Yoshinaga, N. [Department of Physics, Saitama University, Saitama 338-0625 (Japan)
2004-10-01
The ground states of all even-even nuclei have angular momentum, I, equal to zero, I=0, and positive parity, {pi}=+. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, in the presence of two-body random interactions, the predominance of I{pi}=0+ ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as d bosons, sp bosons, sd bosons, and a few fermions in single-j shells for small j, there are a few approaches to predict and/or explain spin I ground state (I g.s.) probabilities. An empirical approach to predict I g.s. probabilities is available for general cases, such as fermions in a single-j (j>72) or many-j shells and various boson systems, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Further interesting results are also reviewed concerning other robust phenomena of many-body systems in the presence of random two-body interactions, such as the odd-even staggering of binding energies, generic collectivity, the behavior of average energies, correlations, and regularities of many-body systems interacting by a displaced two-body random ensemble.
Scattering and coherence in EUVL
Milster, Tomas D.; Beaudry, Neil A.
1998-06-01
We illustrate the importance of considering scattering from the illuminator in extreme UV lithography systems. Our results indicate that a significant amount of amplitude modulation noise is present in the aerial image if scatter is present in a Koehler illuminator. The effect depends on the spatial frequency of the pattern on the mask, the numerical aperture of the projection camera, the coherence factor, and placement of the plane in the illuminator where the scattering occurs.
$\\Lambda$ Scattering Equations
Gomez, Humberto
2016-01-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter $\\Lambda$ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting $\\Lambda$ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the $\\Lambda$ algorithm.
Relativistic Coulomb scattering of spinless bosons
Garcia, M G
2015-01-01
The relativistic scattering of spin-0 bosons by spherically symmetric Coulomb fields is analyzed in detail with an arbitrary mixing of vector and scalar couplings. It is shown that the partial wave series reduces the scattering amplitude to the closed Rutherford formula exactly when the vector and scalar potentials have the same magnitude, and as an approximation for weak fields. The behavior of the scattering amplitude near the conditions that furnish its closed form is also discussed. Strong suppressions of the scattering amplitude when the vector and scalar potentials have the same magnitude are observed either for particles or antiparticles with low incident momentum. We point out that such strong suppressions might be relevant in the analysis of the scattering of fermions near the conditions for the spin and pseudospin symmetries. From the complex poles of the partial scattering amplitude the exact closed form of bound-state solutions for both particles and antiparticles with different scenarios for the ...
The post-Keplerian orbital representations of the relativistic two-body problem
Klioner, S. A.; Kopeikin, S. M.
1994-06-01
Orbital parameterizations of the relativstic two-body problem due to Brumberg, Damour-Deruelle, Epstein-Haugan, and Blandford-Teukolsky as well as osculating elements are compared. Exact relations between constants describing the orbit in the parameterizations are derived. It is shown that all the parameterizations in question are valid not only in general relativity, but in a generic class of relatvistic theories of gravity. The obtained results provide us with an additional check of consistency of different models used in timing of binary pulsars.
Probing SUSY CP Violation in Two-Body Stop Decays at the LHC
Deppisch, Frank
2009-01-01
We study CP asymmetries in two-body decays of top squarks into neutralinos and sleptons at the LHC. These asymmetries are used to probe the CP phases possibly present in the stop and neutralino sector of the Minimal Supersymmetric Standard Model. Taking into account bounds from experimental electric dipole moment searches, we identify areas in the mSUGRA parameter space where CP asymmetries can be sizeable and discuss the feasibility of their observation at the LHC. As a result, potentially detectable CP asymmetries in stop decays at the LHC are found, motivating further detailed experimental studies for probing SUSY CP phases.
The two-body random spin ensemble and a new type of quantum phase transition
Energy Technology Data Exchange (ETDEWEB)
Pizorn, Iztok; Prosen, Tomaz [Department of Physics, FMF, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana (Slovenia); Mossmann, Stefan; Seligman, Thomas H [Instituto de Ciencias FIsicas, Universidad Nacional Autonoma de Mexico, CP 62132 Cuernavaca, Morelos (Mexico)], E-mail: tomaz.prosen@fmf.uni-lj.si
2008-02-15
We study in this paper the properties of a two-body random matrix ensemble for distinguishable spins. We require the ensemble to be invariant under the group of local transformations and analyze a parametrization in terms of the group parameters and the remaining parameters associated with the 'entangling' part of the interaction. We then specialize to a spin chain with nearest-neighbour interactions and numerically find a new type of quantum-phase transition related to the strength of a random external field, i.e. the time-reversal-breaking one-body interaction term.
The two-body random spin ensemble and a new type of quantum phase transition
Pižorn, Iztok; Prosen, Tomaž; Mossmann, Stefan; Seligman, Thomas H.
2008-02-01
We study in this paper the properties of a two-body random matrix ensemble for distinguishable spins. We require the ensemble to be invariant under the group of local transformations and analyze a parametrization in terms of the group parameters and the remaining parameters associated with the 'entangling' part of the interaction. We then specialize to a spin chain with nearest-neighbour interactions and numerically find a new type of quantum-phase transition related to the strength of a random external field, i.e. the time-reversal-breaking one-body interaction term.
Probing SUSY CP violation in two-body stop decays at the LHC
Deppisch, Frank F.; Kittel, Olaf
2009-09-01
We study CP asymmetries in two-body decays of top squarks into neutralinos and sleptons at the LHC. These asymmetries are used to probe the CP phases possibly present in the stop and neutralino sector of the Minimal Supersymmetric Standard Model. Taking into account bounds from experimental electric dipole moment searches, we identify areas in the mSUGRA parameter space where CP asymmetries can be sizeable and discuss the feasibility of their observation at the LHC. As a result, potentially detectable CP asymmetries in stop decays at the LHC are found, motivating further detailed experimental studies for probing SUSY CP phases.
Bianchi, Marco S; Mauri, Andrea; Penati, Silvia; Santambrogio, Alberto
2011-01-01
We study the correspondence between scattering amplitudes and Wilson loops in three-dimensional Chern-Simons matter theories. In particular, using N=2 superspace formalism, we compute at one loop the whole spectrum of four-point superamplitudes for generic N>=2 supersymmetric theories and find a vanishing result for N=6 ABJ(M) and N=8 BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known result for the ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the dual conformal invariance of our results and the relationship between the Feynman diagram computation and unitarity methods. While for the ABJM theory dual conformally invariant integrals exactly reproduce the amplitude, for the ABJ case this happens only up to a residual constant depending on the parity-violating parameter. Final...
Bootstrapping a Five-Loop Amplitude from Steinmann Relations
Caron-Huot, Simon; McLeod, Andrew; von Hippel, Matt
2016-01-01
The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.
A class of amplitude modulating and invisible inhomogeneous media
Vial, Benjamin; Horsley, Simon A R; Philbin, Thomas G; Hao, Yang
2016-01-01
We propose a general method to arbitrarily manipulate the amplitude of an electromagnetic wave propagating in a two-dimensional medium, without introducing any scattering. This leads to a whole class of isotropic spatially varying permittivity and permeability profiles that are invisible while shaping the field magnitude. In addition, we propose a metamaterial structure working in the infrared that demonstrates deep sub-wavelength control of the electric field amplitude and strong reduction of the scattering. This work offers an alternative strategy to achieve invisibility with isotropic materials and paves the way for tailoring the propagation of light at the nanoscale.
Vector-pseudoscalar two-meson distribution amplitudes in three-body $B$ meson decays
Chen Chuan Hung; Chen, Chuan-Hung; Li, Hsiang-nan
2004-01-01
We study three-body nonleptonic decays $B\\to VVP$ by introducing two-meson distribution amplitudes for the vector-pseudoscalar pair, such that the analysis is simplified into the one for two-body decays. The twist-2 and twist-3 $\\phi K$ two-meson distribution amplitudes, associated with longitudinally and transversally polarized $\\phi$ mesons, are constrained by the experimental data of the $\\tau\\to\\phi K\
Covariant Helicity Amplitude Analysis for J/ψ→γPP
Institute of Scientific and Technical Information of China (English)
WU Ning; RUAN Tu-Nan
2001-01-01
Covariant helicity amplitude analysis for the process of J/ψ →γPP is discussed.Starting from the S- matrix elements of decay process,we deduce the formulae of helicity coupling amplitudes for two-body decay process. These formulae are used to analyze intermediate resonance states in the process of J/ψ decay to γππ,γKK,γηη＇ etc.
Particle Distribution Modification by Low Amplitude Modes
Energy Technology Data Exchange (ETDEWEB)
White, R. B.; Gorelenkov, N.; Heidbrink, W. W.; Van Zeeland, M. A.
2009-08-28
Modification of a high energy particle distribution by a spectrum of low amplitude modes is investigated using a guiding center code. Only through resonance are modes effective in modifying the distribution. Diagnostics are used to illustrate the mode-particle interaction and to find which effects are relevant in producing significant resonance, including kinetic Poincare plots and plots showing those orbits with time averaged mode-particle energy transfer. Effects of pitch angle scattering and drag are studied, as well as plasma rotation and time dependence of the equilibrium and mode frequencies. A specific example of changes observed in a DIII-D deuterium beam distribution in the presence of low amplitude experimentally validated Toroidal Alfven (TAE) eigenmodes and Reversed Shear Alfven (RSAE) eigenmodes is examined in detail. Comparison with experimental data shows that multiple low amplitude modes can account for significant modification of high energy beam particle distributions. It is found that there is a stochastic threshold for beam profile modification, and that the experimental amplitudes are only slightly above this threshold.
Energy Technology Data Exchange (ETDEWEB)
Aguilar Benitez de Lugo, M.
1979-07-01
In this work we present several techniques developed for the extraction of the. Transversity amplitudes governing quasi two-body meson baryon reactions with hypercharge exchange. We review the methods used In processes having a pure spin configuration, as well as the more relevant results obtained with data from K{sup p} and Tp interactions at intermediate energies. The predictions of the additive quark model and the ones following from exchange degeneracy and etoxicity are discussed. We present a formalism for amplitude analysis developed for reactions with mixed spin configurations and discuss the methods of parametric estimation of the moduli and phases of.the amplitudes, as well as the various tests employed to check the goodness of the fits. The calculation of the generalized joint density matrices is given and we propose a method based on the generalization of the idea of multipole moments, which allows to investigate the structure of the decay angular correlations and establishes the quality of the fits and the validity of the simplifying assumptions currently used in this type of studies. (Author) 43 refs.
A detailed study of nonperturbative solutions of two-body Dirac equations
Energy Technology Data Exchange (ETDEWEB)
Crater, H.W.; Becker, R.L.; Wong, C.Y.; Van Alstine, P.
1992-12-01
In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions.
One plus two-body random matrix ensembles with parity: Density of states and parity ratios
Vyas, Manan; Srivastava, P C
2011-01-01
One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [EGOE(1+2)-$\\pi$] generated by a chaos producing two-body interaction in the presence of a mean-field, for spinless identical fermion systems, is defined in terms of two mixing parameters and a gap between the positive $(\\pi=+)$ and negative $(\\pi=-)$ parity single particle (sp) states. Numerical calculations are used to demonstrate, using realistic values of the mixing parameters appropriate for some nuclei, that this ensemble generates Gaussian form (with corrections) for fixed parity eigenvalue densities (i.e. state densities). The random matrix model also generates many features in parity ratios of state densities that are similar to those predicted by a method based on the Fermi-gas model for nuclei. We have also obtained a simple formula for the spectral variances defined over fixed-$(m_1,m_2)$ spaces, where $m_1$ is the number of fermions in the $+$ve parity sp states and $m_2$ is the number of fermions in the $-$ve ...
Global solutions to the electrodynamic two-body problem on a straight line
Bauer, G.; Deckert, D.-A.; Dürr, D.; Hinrichs, G.
2017-06-01
The classical electrodynamic two-body problem has been a long standing open problem in mathematics. For motion constrained to the straight line, the interaction is similar to that of the two-body problem of classical gravitation. The additional complication is the presence of unbounded state-dependent delays in the Coulomb forces due to the finiteness of the speed of light. This circumstance renders the notion of local solutions meaningless, and therefore, straightforward ODE techniques cannot be applied. Here, we study the time-symmetric case, i.e., the Fokker-Schwarzschild-Tetrode (FST) equations, comprising both advanced and retarded delays. We extend the technique developed in Deckert and Hinrichs (J Differ Equ 260:6900-6929, 2016), where existence of FST solutions was proven on the half line, to ensure global existence—a result that had been obtained by Bauer (Ein Existenzsatz für die Wheeler-Feynman-Elektrodynamik, Herbert Utz Verlag, München, 1997). Due to the novel technique, the presented proof is shorter and more transparent but also relies on the idea to employ asymptotic data to characterize solutions.
Energy spectra of massive two-body decay products and mass measurement
Agashe, Kaustubh; Hong, Sungwoo; Kim, Doojin
2016-01-01
We have recently established a new method for measuring the mass of unstable particles produced at hadron colliders based on the analysis of the energy distribution of a massless product from their two-body decays. The central ingredient of our proposal is the remarkable result that, for an unpolarized decaying particle, the location of the peak in the energy distribution of the observed decay product is identical to the (fixed) value of the energy that this particle would have in the rest-frame of the decaying particle, which, in turn, is a simple function of the involved masses. In addition, we utilized the property that this energy distribution is symmetric around the location of peak when energy is plotted on a logarithmic scale. The general strategy was demonstrated in several specific cases, including both beyond the SM particles, as well as for the top quark. In the present work, we generalize this method to the case of a massive decay product from a two-body decay; this procedure is far from trivial b...
Transition Distribution Amplitudes for gamma* gamma collisions
Lansberg, J P; Szymanowski, L
2008-01-01
We study the exclusive production of pi-pi and rho-pi in hard gamma* gamma scattering in the forward kinematical region where the virtuality of one photon provides us with a hard scale in the process. The newly introduced concept of Transition Distribution Amplitudes (TDA) is used to perform a QCD calculation of these reactions thanks to two simple models for TDAs. The sizable cross sections for rho-pi and pi-pi production may be tested at intense electron-positron colliders such as CLEO and B factories (Belle and BaBar).
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A V
2015-01-01
The eikonal approximation for moderately small scattering amplitudes is considered. With the purpose of using for their numerical estimations, the formulas are derived which contain no Bessel functions, and, hence, no rapidly oscillating integrands. To obtain these formulas, the improper integrals of the first kind which contain products of the Bessel functions J_0(z) are studied. The expression with four functions J_0(z) is generalized. The expressions for the integrals with the product of five and six Bessel functions J_0(z) are also found. The known formula for the improper integral with two functions J_nu(z) is generalized for non-integer nu.
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A. V.
2016-08-01
We consider the eikonal approximation for moderately small scattering amplitudes. To find numerical estimates of these approximations, we derive formulas that contain no Bessel functions and consequently no rapidly oscillating integrands. To obtain these formulas, we study improper integrals of the first kind containing products of the Bessel functions J0(z). We generalize the expression with four functions J0(z) and also find expressions for the integrals with the product of five and six Bessel functions. We generalize a known formula for the improper integral with two functions Jυ (az) to the case with noninteger υ and complex a.
A Note on Soft Factors for Closed String Scattering
Schwab, Burkhard U W
2014-01-01
In this note, it is shown that closed string graviton scattering amplitudes obey the same subleading soft limit as field theory graviton scattering amplitudes. The result is derived using a combination of recent results and methods including the subleading soft expansion for type I open string gluon disk scattering amplitudes, the single value projection for multiple $\\zeta$ values, and the KLT relations in field and string theory.
Bursting behaviours in cascaded stimulated Brillouin scattering
Institute of Scientific and Technical Information of China (English)
Liu Zhan-Jun; He Xian-Tu; Zheng Chun-Yang; Wang Yu-Gang
2012-01-01
Stimulated Brillouin scattering is studied by numerically solving the Vlasov-Maxwell system.A cascade of stimulated Brillouin scattering can occur when a linearly polarized laser pulse propagates in a plasma.It is found that a stimulated Brillouin scattering cascade can reduce the scattering and increase the transmission of light,as well as introduce a bursting behaviour in the evolution of the laser-plasma interaction.The bursting time in the reflectivity is found to be less than half the ion acoustic period.The ion temperature can affect the stimulated Brillouin scattering cascade,which can repeat several times at low ion temperatures and can be completely eliminated at high ion temperatures.For stimulated Brillouin scattering saturation,higher-harmonic generation and wave-wave interaction of the excited ion acoustic waves can restrict the amplitude of the latter.In addition,stimulated Brillouin scattering cascade can restrict the amplitude of the scattered light.
Scattering in Relativistic Particle Mechanics.
de Bievre, Stephan
The problem of direct interaction in relativistic particle mechanics has been extensively studied and a variety of models has been proposed avoiding the conclusions of the so-called no-interaction theorems. In this thesis we study scattering in the relativistic two-body problem. We use our results to analyse gauge invariance in Hamiltonian constraint models and the uniqueness of the symplectic structure in manifestly covariant relativistic particle mechanics. We first present a general geometric framework that underlies approaches to relativistic particle mechanics. This permits a model-independent and geometric definition of the notions of asymptotic completeness and of Moller and scattering operators. Subsequent analysis of these concepts divides into two parts. First, we study the kinematic properties of the scattering transformation, i.e. those properties that arise solely from the invariance of the theory under the Poincare group. We classify all canonical (symplectic) scattering transformations on the relativistic phase space for two free particles in terms of a single function of the two invariants of the theory. We show how this function is determined by the center of mass time delay and scattering angle and vice versa. The second part of our analysis of the relativistic two-body scattering problem is devoted to the dynamical properties of the scattering process. Hence, we turn to two approaches to relativistic particle mechanics: the Hamiltonian constraint models and the manifestly covariant formalism. Using general geometric arguments, we prove "gauge invariance" of the scattering transformation in the Todorov -Komar Hamiltonian constraint model. We conclude that the scattering cross sections of the Todorov-Komar models have the same angular dependence as their non-relativistic counterpart, irrespective of a choice of gauge. This limits the physical relevance of those models. We present a physically non -trivial Hamiltonian constraint model, starting from
Crossing symmetric potential model of pion-nucleon scattering
Blankleider, B; Skawronski, T
2010-01-01
A crossing symmetric $\\pi N$ scattering amplitude is constructed through a complete attachment of two external pions to the dressed nucleon propagator of an underlying $\\pi N$ potential model. Our formulation automatically provides expressions also for the crossing symmetric and gauge invariant pion photoproduction and Compton scattering amplitudes. We show that our amplitudes are unitary if they coincide on-shell with the amplitudes obtained by attaching one pion to the dressed $\\pi NN$ vertex of the same potential model.
Theory overview on amplitude analyses with charm decays
Loiseau, B
2016-01-01
This contribution about amplitude analyses in multibody hadronic charm decays deals with some attempts to introduce theoretical constraints. Different effective hadronic formalism approaches are mentioned. A recent work, based on a basic weak interaction process and a Chiral unitary model to account for the final state interaction, is described in details for the $f_0(980)$ production in $D_s^+ \\to \\pi^+ \\pi^+ \\pi^-$ and $D_s^+ \\to \\pi^+ K^+ K^- $ decays. Within the framework of the diagrammatic approach and flavor symmetry, a global analysis of two-body $D$ decays into a vector meson and a pseudoscalar meson is presented. A quasi-two-body QCD factorization model for $D$ decays into three mesons and its recent application to $D^0 \\to K_S^0 \\pi^+ \\pi^-$ is outlined. For processes with final-state pions and kaons and as an alternative to the sum of Breit-Wigner amplitudes, often used in experimental Dalitz-plot analyses, amplitude parametrizations, in term of unitary $\\pi \\pi$, $\\pi K$ and $K \\bar K$ form facto...
Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
Anastasiou, C; Dixon, L; Kosower, D A
2003-01-01
The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N_c L-loop amplitudes should be simple enough to allow a resummation to all orders.
Inelastic Light Scattering Processes
Fouche, Daniel G.; Chang, Richard K.
1973-01-01
Five different inelastic light scattering processes will be denoted by, ordinary Raman scattering (ORS), resonance Raman scattering (RRS), off-resonance fluorescence (ORF), resonance fluorescence (RF), and broad fluorescence (BF). A distinction between fluorescence (including ORF and RF) and Raman scattering (including ORS and RRS) will be made in terms of the number of intermediate molecular states which contribute significantly to the scattered amplitude, and not in terms of excited state lifetimes or virtual versus real processes. The theory of these processes will be reviewed, including the effects of pressure, laser wavelength, and laser spectral distribution on the scattered intensity. The application of these processes to the remote sensing of atmospheric pollutants will be discussed briefly. It will be pointed out that the poor sensitivity of the ORS technique cannot be increased by going toward resonance without also compromising the advantages it has over the RF technique. Experimental results on inelastic light scattering from I(sub 2) vapor will be presented. As a single longitudinal mode 5145 A argon-ion laser line was tuned away from an I(sub 2) absorption line, the scattering was observed to change from RF to ORF. The basis, of the distinction is the different pressure dependence of the scattered intensity. Nearly three orders of magnitude enhancement of the scattered intensity was measured in going from ORF to RF. Forty-seven overtones were observed and their relative intensities measured. The ORF cross section of I(sub 2) compared to the ORS cross section of N2 was found to be 3 x 10(exp 6), with I(sub 2) at its room temperature vapor pressure.
PULSE AMPLITUDE DISTRIBUTION RECORDER
Cowper, G.
1958-08-12
A device is described for automatica1ly recording pulse annplitude distribution received from a counter. The novelty of the device consists of the over-all arrangement of conventional circuit elements to provide an easy to read permanent record of the pulse amplitude distribution during a certain time period. In the device a pulse analyzer separates the pulses according to annplitude into several channels. A scaler in each channel counts the pulses and operates a pen marker positioned over a drivable recorder sheet. Since the scalers in each channel have the sanne capacity, the control circuitry permits counting of the incoming pulses until one scaler reaches capacity, whereupon the input is removed and an internal oscillator supplies the necessary pulses to fill up the other scalers. Movement of the chart sheet is initiated wben the first scaler reaches capacity to thereby give a series of marks at spacings proportional to the time required to fill the remaining scalers, and accessory equipment marks calibration points on the recorder sheet to facilitate direct reading of the number of external pulses supplied to each scaler.
Hydrodynamic interactions between two bodies in waves in 3D time domain
Institute of Scientific and Technical Information of China (English)
WANG Jian-fang; LI Ji-de; CAI Xin-gong; TIAN Ming-qi; Hao Jin-feng
2005-01-01
In this paper, a 3D time domain technique is adopted to calculate the coupled hydrodynamic interaction between two bodies without flare in waves. For verifying the code, two same cylinders are selected to calculate coupled hydrodynamic effects by comparison with the results obtained by 3D frequency method which has been proved to be efficient for solving such problems. In order to improve efficiency of calculation, the effect of history time has been discussed, and an improved method is presented. Moreover, the effect of lateral separation distance is also discussed in detail. The technique developed here may serve as a more rigorous tool to analyze the related transient problems of two ships doing underway replenishment in waves.
One-body and Two-body Fractional Parentage Coefficients for Spinor Bose-Einstein Condensation
Institute of Scientific and Technical Information of China (English)
BAO Cheng-guang
2006-01-01
A very effective tool,namely,the analytical expression of the fractional parentage coefficients (FPC),is introduced in this paper to deal with the total spin states of N-body spinor bosonic systems,where N is supposed to be large and the spin of each boson is one.In particular,the analytical forms of the one-body and two-body FPC for the total spin states with {N} and {N-1,1} permutation symmetries have been derived.These coefficients facilitate greatly the calculation of related matrix elements,and they can be used even in the case of N →∞.Theyappear as a powerful tool for the establishment of an improved theory of spinor Bose-Einstein condensation,where the eigenstates have the total spin S and its Z-component being both conserved.
Charmless Hadronic Two-body Decays of $B_{u}$ and $B_{d}$ Mesons
Chen, Y H; Tseng, B; Yang, K C; Chen, Yaw-Hwang; Cheng, Hai-Yang; Yang, Kwei-Chou
1999-01-01
Two-body charmless nonleptonic decays of B_u and B_d mesons are studied within the framework of generalized factorization in which the effective Wilson coefficients $c^{eff}_i$ are renormalization-scale and -scheme independent while factorization is applied to the tree-level hadronic matrix elements. Contrary to previous studies, our $c_i^{eff}$ do not suffer from gauge and infrared problems. Nonfactorizable effects are parametrized in terms of N_c(LL) and N_c(LR), the effective numbers of colors arising from (V-A)(V-A) and (V-A)(V+A) four-quark operators, respectively. Tree and penguin transitions are classified into six different classes. The data of $B^-\\to\\rho^0\\pi^-$ and $B^-\\to\\phi K^-$ clearly indicate that $N_c(LR)\
Rivera, R.; Villarroel, D.
1997-11-01
An exactly solvable two-body problem dealing with the Lorentz-Dirac equation is constructed in this paper. It corresponds to the motion of two identical charges rotating at opposite ends of a diameter, in a fixed circle, at constant angular velocity. The external electromagnetic field that allows this motion consists of a tangential time-independent electric field with a fixed value over the orbit circle, and a homogeneous time-independent magnetic field that points orthogonally to the orbit plane. Because of the geometrical symmetries of the charges' motion, in this case it is possible to obtain the rate of radiation emitted by the charges directly from the equation of motion. The rate of radiation is also calculated by studying the energy flux across a sphere of a very large radius, using the far retarded fields of the charges. Both calculations lead to the same result, in agreement with energy conservation.
Parametric Study of Two-Body Floating-Point Wave Absorber
Institute of Scientific and Technical Information of China (English)
Atena Amiri; Roozbeh Panahi; Soheil Radfar
2016-01-01
In this paper, we present a comprehensive numerical simulation of a point wave absorber in deep water. Analyses are performed in both the frequency and time domains. The converter is a two-body floating-point absorber (FPA) with one degree of freedom in the heave direction. Its two parts are connected by a linear mass-spring-damper system. The commercial ANSYS-AQWA software used in this study performs well in considering validations. The velocity potential is obtained by assuming incompressible and irrotational flow. As such, we investigated the effects of wave characteristics on energy conversion and device efficiency, including wave height and wave period, as well as the device diameter, draft, geometry, and damping coefficient. To validate the model, we compared our numerical results with those from similar experiments. Our study results can clearly help to maximize the converter’s efficiency when considering specific conditions.
Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem
Oltean, Marius; Bonetti, Luca; Spallicci, Alessandro D. A. M.; Sopuerta, Carlos F.
2016-09-01
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are theorems which have been proposed for proving the nonexistence of entropy in the latter sense. We explicate, clarify, and extend the proofs of these theorems to some standard matter (scalar and electromagnetic) field theories in curved spacetime, and then we show why these proofs fail in general relativity; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the noncompactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and hence entropy production.
Non-Collision Singularities in the Planar Two-Center-Two-Body Problem
Xue, Jinxin; Dolgopyat, Dmitry
2016-08-01
In this paper, we study a restricted four-body problem called the planar two-center-two-body problem. In the plane, we have two fixed centers Q 1 and Q 2 of masses 1, and two moving bodies Q 3 and Q 4 of masses {μ≪ 1}. They interact via Newtonian potential. Q 3 is captured by Q 2, and Q 4 travels back and forth between two centers. Based on a model of Gerver, we prove that there is a Cantor set of initial conditions that lead to solutions of the Hamiltonian system whose velocities are accelerated to infinity within finite time avoiding all earlier collisions. This problem is a simplified model for the planar four-body problem case of the Painlevé conjecture.
Low-Thrust Orbital Transfers in the Two-Body Problem
Directory of Open Access Journals (Sweden)
A. A. Sukhanov
2012-01-01
Full Text Available Low-thrust transfers between given orbits within the two-body problem are considered; the thrust is assumed power limited. A simple method for obtaining the transfer trajectories based on the linearization of the motion near reference orbits is suggested. Required calculation accuracy can be reached by means of use of a proper number of the reference orbits. The method may be used in the case of a large number of the orbits around the attracting center; no averaging is necessary in this case. The suggested method also is applicable to the cases of partly given final orbit and if there are constraints on the thrust direction. The method gives an optimal solution to the linearized problem which is not optimal for the original nonlinear problem; the difference between the optimal solutions to the original and linearized problems is estimated using a numerical example. Also examples illustrating the method capacities are given.
Calculation of the Two-body T-matrix in Configuration Space
Rawitscher, George
2007-01-01
A spectral integral method (IEM) for solving the two-body Schroedinger equation in configuration space is generalized to the calculation of the corresponding T-matrix. It is found that the desirable features of the IEM, such as the economy of mesh-points for a given required accuracy, are carried over also to the solution of the T-matrix. However the algorithm is considerably more complex, because the T-matrix is a function of two variables r and r', rather than only one variable r, and has a slope discontinuity at r=r'. For a simple exponential potential an accuracy of 7 significant figures is achieved, with the number N of Chebyshev support points in each partition equal to 17. For a potential with a large repulsive core, such as the potential between two He atoms, the accuracy decreases to 4 significant figures, but is restored to 7 if N is increased to 65.
Regularization of the collision in the electromagnetic two-body problem
Hollander, Efrain Buksman; De Luca, Jayme
2004-12-01
We derive a differential equation that is regular at the collision of two equal-mass bodies with attractive interaction in the relativistic action-at-a-distance electrodynamics. We use the energy constant related to the Poincaré invariance of the theory to define finite variables with finite derivatives at the collision. The collision orbits are calculated numerically using the regular equation adapted in a self-consistent minimization method (a stable numerical method that chooses only nonrunaway solutions). This dynamical system appeared 100 years ago as an example of covariant time-symmetric two-body dynamics and acquired the status of electrodynamics in the 1940s by the works of Dirac, Wheeler, and Feynman. We outline the method with an emphasis on the physics of this complex conservative dynamical system.
Branching ratios for pbarp annihilation at rest into two-body final states
Abele, A; Amsler, Claude; Baker, C A; Barnett, B M; Batty, C J; Benayoun, M; Bischoff, S; Blüm, P; Braune, K; Bugg, D V; Case, T; Crowe, K M; Degener, T; Doser, Michael; Dünnweber, W; Engelhardt, D; Faessler, M A; Giarritta, P; Haddock, R P; Heinsius, F H; Heinzelmann, M; Herbstrith, A; Herz, M; Hessey, N P; Hidas, P; Hodd, C; Holtzhaussen, C; Jamnik, D; Kalinowsky, H; Kammel, P; Kisiel, J; Klempt, E; Koch, H; Kunze, M; Kurilla, U; Lakata, M; Landua, Rolf; Matthäy, H; McCrady, R; Meier, J; Meyer, C A; Montanet, Lucien; Ouared, R; Peters, K; Pick, B; Ratajczak, M; Regenfus, C; Röthel, W; Spanier, S; Stöck, H; Strassburger, C; Strohbusch, U; Suffert, Martin; Suh, J S; Thoma, U; Tischhäuser, M; Uman, I; Völcker, C; Wallis-Plachner, S; Walther, D; Wiedner, U; Wittmack, K; Zou, B S
2001-01-01
Measurements of two-body branching ratios for pbarp annihilations at rest in liquid and gaseous (12 rho sub S sub T sub P) hydrogen are reported. Channels studied are pbarp-> pi sup 0 pi sup 0 ,pi sup 0 eta, K sup 0 sub S K sup 0 sub L , K sup + K sup -. The branching ratio for the pi sup 0 pi sup 0 channel in liquid H sub 2 is measured to be (6.14+-0.40)x10 sup - sup 4. The results are compared with those from other experiments. The fraction of P-state annihilation for a range of target densities from 0.002 rho sub S sub T sub P to liquid H sub 2 is determined. Values obtained include 0.11+-0.02 in liquid H sub 2 and 0.48+-0.04 in 12 rho sub S sub T sub P H sub 2 gas.
a Study of the Charged Two-Body Decays of the Neutral D Mesons
Peng, Kuang-Chung (K. C.).
1995-01-01
The charged two-body decays of D^0 mesons produced by 500 GeV/c pi -incident on platium and carbon foil targets at the Fermilab Tagged Particle Laboratory have been analyzed. Three measurements are presented in this thesis: (1) Branching Ratios of Charged Two-body Decays: {Gamma(D^0to K^+K^-)overGamma(D^0to K^-pi^+)}= 0.107+/-0.003 +/-0.003, {Gamma(D^0to pi^+pi^-)over Gamma(D ^0to K^-pi^+)} =0.040 +/-0.002+/-0.002, {Gamma(D^0 to K^+K^-)overGamma(D^0 topi^+pi^-)}=2.65+/-0.14 +/-0.13, and {Gamma(D^0 to K^-pi^-pi^+pi ^+)overGamma(D^0to K^ -pi^+)} =2.19+/-.0.3+/-.0.08; (2) Lifetime Difference: tau_ {KK}=0.414+/-0.012+/-0.014, tau _{Kpi}=0.409+/-0.003+/-0.004, with Deltagamma= {-}0.06 +/-0.15+/-0.15, or the upper limit of Mixing rate as {cal R}_sp {rm mix}{it y}<0.00079 (due to lifetime difference only) at mix 90% confidence level; and (3) CP Asymmetry Parameters: A_sp{CP}{BR}(K^+/- K^mp) = {-}0.018+/-0.054+/-0.012, A_sp{CP}{BR}( pi^+/-pi^mp) = { -}0.053+/-0.093+/-0.029, and A _sp{CP}{BR}(K3pi) - {-}0.018+/-0.023+/-0.002.. All measurements are consistent with most theoretical predictions and world average experimental values.
Two-body wear of dental porcelain and substructure oxide ceramics.
Rosentritt, Martin; Preis, Verena; Behr, Michael; Hahnel, Sebastian; Handel, Gerhard; Kolbeck, Carola
2012-06-01
The aim of this in vitro study was to investigate the two-body wear of different ceramics. Two-body wear tests were performed in a chewing simulator with steatite and enamel antagonists, respectively. Specimens were loaded in a pin-on-block design with a vertical load of 50 N for 1.2 × 10(5) cycles; (f = 1.6 Hz; lateral movement, 1 mm; mouth opening: 2 mm). Human enamel was used as a reference. Three zirconia ceramics, three veneering porcelains, two glass-infiltrated and one lithium disilicate ceramic were investigated. Veneering and lithium disilicate ceramics were glazed before testing. Surface roughness Ra (SP6, Perthen-Feinprüf, G) and wear depth were determined using a 3D scanner (Laserscan 3D, Willytec, G). SEM (Quanta FEG 400, FEI, USA) pictures of the worn specimens and antagonists were made for evaluating wear performance. Veneering porcelain provided wear traces between 71.2 and 124.1 μm (enamel antagonist) and 117.4 and 274.1 μm (steatite). Wear of the steatite antagonists varied between 0.618 and 2.85 mm². No wear was found for zirconia and glass-infiltrated substructure ceramics. Also, no wear was found for the corresponding antagonists. Wear of specimens and antagonists was strongly material dependent. No visible wear was found on zirconia and glass-infiltrated ceramics. Porcelain and lithium disilicate ceramic showed a comparable or lower wear than the enamel reference. Antagonist wear was found to be lower when specimens were made of substructure oxide ceramics instead of veneering porcelain. From the point of wear testing, zirconia may be used for the fabrication of fixed dental prosthesis without veneering.
Street, K. W. Jr.; Kobrick, R. L.; Klaus, D. M.
2011-01-01
A limitation has been identified in the existing test standards used for making controlled, two-body abrasion scratch measurements based solely on the width of the resultant score on the surface of the material. A new, more robust method is proposed for analyzing a surface scratch that takes into account the full three-dimensional profile of the displaced material. To accomplish this, a set of four volume- displacement metrics was systematically defined by normalizing the overall surface profile to denote statistically the area of relevance, termed the Zone of Interaction. From this baseline, depth of the trough and height of the plowed material are factored into the overall deformation assessment. Proof-of-concept data were collected and analyzed to demonstrate the performance of this proposed methodology. This technique takes advantage of advanced imaging capabilities that allow resolution of the scratched surface to be quantified in greater detail than was previously achievable. When reviewing existing data analysis techniques for conducting two-body abrasive scratch tests, it was found that the ASTM International Standard G 171 specified a generic metric based only on visually determined scratch width as a way to compare abraded materials. A limitation to this method was identified in that the scratch width is based on optical surface measurements, manually defined by approximating the boundaries, but does not consider the three-dimensional volume of material that was displaced. With large, potentially irregular deformations occurring on softer materials, it becomes unclear where to systematically determine the scratch width. Specifically, surface scratches on different samples may look the same from a top view, resulting in an identical scratch width measurement, but may vary in actual penetration depth and/or plowing deformation. Therefore, two different scratch profiles would be measured as having identical abrasion properties, although they differ
Multiple scattering expansion with distortion
Tandy, P. C.; Thaler, R. M.
1980-12-01
A multiple scattering description of elastic scattering is formulated in terms of impulsive scatterings from single target nucleons and pairs of target nucleons. In this description, distortion effects on the projectile from the residual medium are also described by multiple scattering in terms of the same single and pair amplitudes. At the level of single scattering, this procedure yields the first order optical potential result of Kerman, McManus, and Thaler. When scattering from both single nucleons and pairs of nucleons is included, the method leads to a one-body integral equation which requires the physical projectile-nucleon and projectile-pair transition amplitudes as input. This input is similar, but not exactly equivalent to that required by the spectator expansion for the optical potential truncated at second order. A principal advantage of the present formulation is that there need be no explicit dependence upon the projection operator Q which projects off the target ground state. This feature introduces a scaling which appears to be a direct extension of the first order Kerman, McManus, and Thaler type of scaling. We follow up suggestions arising in the foregoing to show that the exact optical potential to second order in the spectator expansion can also be cast into a form having no explicit dependence upon Q, and requiring physical projectile-nucleon and projectile-pair transition amplitudes as input. NUCLEAR REACTIONS Multiple scattering from single nucleons, pairs of nucleons in nucleus. Distortion from residual medium. Optical potential. spectator expansion.
Method of complex scattering amplitude in quantum mechanics
Sedrakian, D M
2002-01-01
The problem of description of the electron motion in the field of an arbitrary central-symmetric potential is considered. It is shown that the problem of finding the partial waves of the wave function can be reduced to the Cauchy problem for the radial Schroedinger wave equation. The equation determining the energy spectrum for bound electron states is found. It is also shown that, if the spectrum of the bound states is known, the problem of determination of bound states is also reduced to the problem of solution of the Schroedinger equation with given initial conditions. Generalization of the approach for the electron motion in an arbitrary cylindrical-symmetric potential field is also performed
Helgesson, J; Ekman, J; Helgesson, Johan; Ghetti, Roberta; Jorgen Ekman
2006-01-01
From velocity-gated small-angle correlation functions the emission chronology can be deduced for non-identical particles, if the emission is independent. This is not the case for non-identical particles that originate from two-body decay of fragments. Experimental results may contain contributions from both independent emission and two-body decay, so care is needed in interpreting the velocity-gated correlation functions. It is shown that in some special cases, it is still possible to deduce the emission chronology, even if there is a contribution from two-body decay.
Helicity Selection Rules and Non-Interference for BSM Amplitudes
Azatov, Aleksandr; Machado, Camila S.; Riva, Francesco
2016-01-01
Precision studies of scattering processes at colliders provide powerful indirect constraints on new physics. We study the helicity structure of scattering amplitudes in the SM and in the context of an effective Lagrangian description of BSM dynamics. Our analysis reveals a novel set of helicity selection rules according to which, in the majority of 2 to 2 scattering processes at high energy, the SM and the leading BSM effects do not interfere. In such situations, the naive expectation that dimension-6 operators represent the leading BSM contribution is compromised, as corrections from dimension-8 operators can become equally (if not more) important well within the validity of the effective field theory approach.
Journeys through the Precision Frontier: Amplitudes for Colliders
Petriello, Frank; TASI 2014; TASI2014; 2014 Theoretical Advanced Study Institute in Elementary Particle Physics
2014-01-01
This volume is a compilation of the lectures at TASI 2014. The coverage focuses on modern calculational techniques for scattering amplitudes, and on the phenomenology of QCD in hadronic collisions. Introductions to flavor physics, dark matter, and physics beyond the Standard Model are also provided. The lectures are accessible to graduate students at the initial stages of their research careers.
Gauge and Gravity Amplitudes from Trees to Loops
DEFF Research Database (Denmark)
Huang, Rijun
This thesis describes two subjects that I mainly work on during my PhD study. They are both about scattering amplitudes, covering gravity and gauge theories, tree and loop level, with or without supersymmetry. The rst subject is Kawai-Lewellen-Tye(KLT) relation in field theory, which mysteriously...
Hadron scattering and resonances in QCD
Energy Technology Data Exchange (ETDEWEB)
Dudek, Jozef J. [Old Dominion Univ., Norfolk, VA (United States)
2016-05-01
I describe how hadron-hadron scattering amplitudes are related to the eigenstates of QCD in a finite cubic volume. The discrete spectrum of such eigenstates can be determined from correlation functions computed using lattice QCD, and the corresponding scattering amplitudes extracted. I review results from the Hadron Spectrum Collaboration who have used these finite volume methods to study pi pi elastic scattering, including the rho resonance, as well as coupled-channel pi K, eta K scattering. Ongoing calculations are advertised and the outlook for finite volume approaches is presented.
Integration Rules for Scattering Equations
Baadsgaard, Christian; Bourjaily, Jacob L; Damgaard, Poul H
2015-01-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any M\\"obius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Integration rules for scattering equations
Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-09-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints fo any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Amplitude dependent closest tune approach
Tomas Garcia, Rogelio; Franchi, Andrea; Maclean, Ewen Hamish; CERN. Geneva. ATS Department
2016-01-01
Recent observations in the LHC point to the existence of an amplitude dependent closest tune approach. However this dynamical behavior and its underlying mechanism remain unknown. This effect is highly relevant for the LHC as an unexpectedly closest tune approach varying with amplitude modifies the frequency content of the beam and, hence, the Landau damping. Furthermore the single particle stability would also be affected by this effect as it would modify how particles with varying amplitudes approach and cross resonances. We present analytic derivations that lead to a mechanism generating an amplitude dependent closest tune approach.
Graviton amplitudes from collinear limits of gauge amplitudes
Energy Technology Data Exchange (ETDEWEB)
Stieberger, Stephan, E-mail: stephan.stieberger@mpp.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Taylor, Tomasz R. [Department of Physics, Northeastern University, Boston, MA 02115 (United States)
2015-05-11
We express all tree-level graviton amplitudes in Einstein's gravity as the collinear limits of a linear combination of pure Yang–Mills amplitudes in which each graviton is represented by two gauge bosons, each of them carrying exactly one half of graviton's momentum and helicity.
On the Period-Amplitude and Amplitude-Period Relationships
Wilson, Robert M.; Hathaway, David H.
2008-01-01
Examined are Period-Amplitude and Amplitude-Period relationships based on the cyclic behavior of the 12-month moving averages of monthly mean sunspot numbers for cycles 0.23, both in terms of Fisher's exact tests for 2x2 contingency tables and linear regression analyses. Concerning the Period-Amplitude relationship (same cycle), because cycle 23's maximum amplitude is known to be 120.8, the inferred regressions (90-percent prediction intervals) suggest that its period will be 131 +/- 24 months (using all cycles) or 131 +/- 18 months (ignoring cycles 2 and 4, which have the extremes of period, 108 and 164 months, respectively). Because cycle 23 has already persisted for 142 months (May 1996 through February 2008), based on the latter prediction, it should end before September 2008. Concerning the Amplitude-Period relationship (following cycle maximum amplitude versus preceding cycle period), because cycle 23's period is known to be at least 142 months, the inferred regressions (90-percent prediction intervals) suggest that cycle 24's maximum amplitude will be about less than or equal to 96.1 +/- 55.0 (using all cycle pairs) or less than or equal to 91.0 +/- 36.7 (ignoring statistical outlier cycle pairs). Hence, cycle 24's maximum amplitude is expected to be less than 151, perhaps even less than 128, unless cycle pair 23/24 proves to be a statistical outlier.
Nuclear structure with unitarily transformed two-body plus phenomenological three-body interactions
Energy Technology Data Exchange (ETDEWEB)
Guenther, Anneke
2011-02-02
calculate the {sup 4}He ground-state energy. As they are of direct interest for nuclear astrophysics collective excitation modes, namely giant resonances, are investigated in the framework of the Random Phase Approximation. Including the full three-body interaction would be very time-demanding. Therefore, a density-dependent two-body interaction is used instead. This simple interaction leads to a significant improvement in the description of the isovector dipole and isoscalar quadrupole resonances while the isoscalar monopole resonances remain in good agreement with experimental data compared to the results obtained with pure unitarily transformed two-body interactions. (orig.)
Regularities in Many-body Systems Interacting by a Two-body Random Ensemble
Zhao, Y M; Yoshinaga, N
2003-01-01
The even-even nuclei always have zero ground state angular momenta $I$ and positive parities $\\pi$. This feature was believed to be just a consequence of the attractive short-range interactions between nucleons. However, in the presence of two-body random interactions, the predominance of $I^{\\pi}=0^+$ ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as $d$ bosons, $sp$ bosons, $sd$ bosons, and a few fermions in single-$j$ shells for small $j$, there are a few approaches to predict and/or explain the distribution of angular momentum $I$ ground state probabilities. An empirical recipe to predict the $I$ g.s. probabilities is available for general cases, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Other interesting results are also reviewed concerning other robust phenomena of many-body systems in the presence of random interactions, such as odd-even staggering of binding energies, gen...
Charmless Hadronic Two-body Decays of the $B_s$ Mesons
Chen, Y H; Tseng, B; Chen, Yaw-Hwang; Cheng, Hai-Yang
1999-01-01
Two-body charmless nonleptonic decays of the B_s meson are studied within the framework of generalized factorization in which factorization is applied to the tree level matrix elements while the effective Wilson coefficients are $\\mu$ and renormalization scheme independent, and nonfactorizable effects are parametrized in terms of N_c(LL) and N_c(LR), the effective numbers of colors arising from (V-A)(V-A) and (V-A)(V+A) four-quark operators, respectively. Branching ratios of $B_s\\to PP,PV,VV$ decays are calculated as a function of N_c(LR) with two different considerations for N_c(LL). We find that (i) the electroweak penguin contributions account for about 85% (for N_c(LL)=2) of the decay rates of $B_s\\to \\eta\\pi,\\eta'\\pi,\\eta\\rho,\\eta'\\rho,\\phi\\pi,\\phi\\rho$, which receive contributions only from tree and electroweak penguin diagrams; a measurement of them will provide a clean determination of the electroweak penguin coefficient a_9, (ii) electroweak penguin corrections to $B_s\\to\\omega as QCD penguin effects...
Electromagnetic two-body problem: recurrent dynamics in the presence of state-dependent delay
Energy Technology Data Exchange (ETDEWEB)
De Luca, Jayme [Departamento de Fisica, Universidade Federal de Sao Carlos, Caixa Postal 676, Sao Carlos, Sao Paulo 13565-905 (Brazil); Guglielmi, Nicola [Dipartimento di Matematica Pura ed Applicata, Universita degli Studi di L' Aquila, I-67010, L' Aquila (Italy); Humphries, Tony [Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 2K6 (Canada); Politi, Antonio, E-mail: deluca@df.ufscar.b [Istituto dei Sistemi Complessi, CNR Via Madonna del Piano 10-Sesto, Fiorentino I-50019 (Italy)
2010-05-21
We study the electromagnetic two-body problem of classical electrodynamics as a prototype dynamical system with state-dependent delays. The equations of motion are analysed with reference to motion along a straight line in the presence of an electrostatic field. We consider the general electromagnetic equations of motion for point charges with advanced and retarded interactions and study two limits, (a) retarded-only interactions (Dirac electrodynamics) and (b) half-retarded plus half-advanced interactions (Wheeler-Feynman electrodynamics). A fixed point is created where the electrostatic field balances the Coulombian attraction, and we use local analysis near this fixed point to derive necessary conditions for a Hopf bifurcation. In case (a), we study a Hopf bifurcation about an unphysical fixed point and find that it is subcritical. In case (b), there is a Hopf bifurcation about a physical fixed point and we study several families of periodic orbits near this point. The bifurcating periodic orbits are illustrated and simulated numerically, by introducing a surrogate dynamical system into the numerical analysis which transforms future data into past data by exploiting the periodicity, thus obtaining systems with only delays.
Electromagnetic two-body problem: recurrent dynamics in the presence of state-dependent delay
De Luca, Jayme; Guglielmi, Nicola; Humphries, Tony; Politi, Antonio
2010-05-01
We study the electromagnetic two-body problem of classical electrodynamics as a prototype dynamical system with state-dependent delays. The equations of motion are analysed with reference to motion along a straight line in the presence of an electrostatic field. We consider the general electromagnetic equations of motion for point charges with advanced and retarded interactions and study two limits, (a) retarded-only interactions (Dirac electrodynamics) and (b) half-retarded plus half-advanced interactions (Wheeler-Feynman electrodynamics). A fixed point is created where the electrostatic field balances the Coulombian attraction, and we use local analysis near this fixed point to derive necessary conditions for a Hopf bifurcation. In case (a), we study a Hopf bifurcation about an unphysical fixed point and find that it is subcritical. In case (b), there is a Hopf bifurcation about a physical fixed point and we study several families of periodic orbits near this point. The bifurcating periodic orbits are illustrated and simulated numerically, by introducing a surrogate dynamical system into the numerical analysis which transforms future data into past data by exploiting the periodicity, thus obtaining systems with only delays.
Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem
Oltean, Marius; Spallicci, Alessandro D A M; Sopuerta, Carlos F
2016-01-01
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are theorems which have been proposed for proving the non-existence of entropy in the latter sense. We explicate, clarify and extend the proofs of these theorems to some standard matter (scalar and electromagnetic) field theories in curved spacetime, and then we show why these proofs fail in general relativity; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the non-compactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and hence entropy producti...
Quartet correlations in N = Z nuclei induced by realistic two-body interactions
Energy Technology Data Exchange (ETDEWEB)
Sambataro, M. [Istituto Nazionale di Fisica Nucleare - Sezione di Catania, Catania (Italy); Sandulescu, N. [National Institute of Physics and Nuclear Engineering, Bucharest-Magurele (Romania)
2017-03-15
Two variational quartet models previously employed in a treatment of pairing forces are extended to the case of a general two-body interaction. One model approximates the nuclear states as a condensate of identical quartets with angular momentum J = 0 and isospin T = 0 while the other let these quartets to be all different from each other. With these models we investigate the role of alpha-like quartet correlations both in the ground state and in the lowest J = 0, T = 0 excited states of even-even N = Z nuclei in the sd -shell. We show that the ground-state correlations of these nuclei can be described to a good extent in terms of a condensate of alpha-like quartets. This turns out to be especially the case for the nucleus {sup 32}S for which the overlap between this condensate and the shell model wave function is found close to one. In the same nucleus, a similar overlap is found also in the case of the first excited 0{sup +} state. No clear correspondence is observed instead between the second excited states of the quartet models and the shell model eigenstates in all the cases examined. (orig.)
Reactive two-body and three-body collisions of Ba$^+$ in an ultracold Rb gas
Krükow, Artjom; Härter, Arne; Denschlag, Johannes Hecker
2016-01-01
We analyze reactive collisions of a single Ba$^+$ ion in contact with an ultracold gas of Rb atoms at mK$\\times k_{\\mathrm{B}}$ collision energies. Mapping out the Ba$^+$ loss rate dependence on the Rb atom density we can discern two-body reactive collisions from three-body ones and for the first time determine both rate coefficients which are $k_2=3.1(6)(6)\\times 10^{-13}\\textrm{cm}^{3}\\textrm{s}^{-1}$ and $k_3=1.04(4)(45)\\times 10^{-24}\\textrm{cm}^{6}\\textrm{s}^{-1}$, respectively (statistical and systematic errors in parenthesis). Thus, the measured ternary recombination dominates over binary reactions even at moderate atom densities of $n\\approx 10^{12}\\: \\textrm{cm}^{-3}$. The results for Ba$^+$ and Rb are representative for a wide range of cold ion-atom systems and can serve as a guidance for the future development of the field of hybrid atom-ion research.
Large amplitude oscillatory elongation flow
DEFF Research Database (Denmark)
Rasmussen, Henrik K.; Laillé, Philippe; Yu, Kaijia
2008-01-01
A filament stretching rheometer (FSR) was used for measuring the elongation flow with a large amplitude oscillative elongation imposed upon the flow. The large amplitude oscillation imposed upon the elongational flow as a function of the time t was defined as epsilon(t) =(epsilon) over dot(0)t + ...
Closed string amplitudes as single-valued open string amplitudes
Energy Technology Data Exchange (ETDEWEB)
Stieberger, Stephan, E-mail: stephan.stieberger@mpp.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Taylor, Tomasz R. [Department of Physics, Northeastern University, Boston, MA 02115 (United States)
2014-04-15
We show that the single trace heterotic N-point tree-level gauge amplitude A{sub N}{sup HET} can be obtained from the corresponding type I amplitude A{sub N}{sup I} by the single-valued (sv) projection: A{sub N}{sup HET}=sv(A{sub N}{sup I}). This projection maps multiple zeta values to single-valued multiple zeta values. The latter represent a subclass of multiple zeta values originating from single-valued multiple polylogarithms at unity. Similar relations between open and closed string amplitudes or amplitudes of different string vacua can be established. As a consequence the α{sup ′}-expansion of a closed string amplitude is dictated by that of the corresponding open string amplitude. The combination of single-valued projections, Kawai–Lewellen–Tye relations and Mellin correspondence reveal a unity of all tree-level open and closed superstring amplitudes together with the maximally supersymmetric Yang–Mills and supergravity theories.
Some tree-level string amplitudes in the NSR formalism
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,4242 TAMU, College Station, TX 77843 (United States); Melnikov, Ilarion V. [Department of Mathematics, Harvard University,One Oxford Street, Cambridge, MA 02138 (United States); Robbins, Daniel; Royston, Andrew B. [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,4242 TAMU, College Station, TX 77843 (United States)
2015-12-02
We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point functions involving bosons and fermions. We calculate the five-point amplitude for massless gluons and find agreement with an earlier result by Brandt, Machado and Medina. We then compute the five-point amplitudes involving two and four fermions respectively, the general form of which has not been previously obtained in the NSR formalism. The results nicely confirm expectations from the supersymmetric F{sup 4} effective action. Finally we use the prescription of Kawai, Lewellen and Tye (KLT) to compute the amplitudes for the closed string sector.
BFKL approach and 2->5 MHV amplitude
Bartels, J; Lipatov, L N; Prygarin, A
2011-01-01
We study MHV amplitude for the 2 -> 5 scattering in the multi-Regge kinematics. The Mandelstam cut correction to the BDS amplitude is calculated in the leading logarithmic approximation (LLA) and the corresponding remainder function is given to any loop order in a closed integral form. We show that the LLA remainder function at two loops for 2 -> 5 amplitude can be written as a sum of two 2 -> 4 remainder functions due to recursive properties of the leading order impact factors. We also make some generalizations for the MHV amplitudes with more external particles. The results of the present study are in agreement with all leg two loop symbol derived by Caron-Huot as shown in a parallel paper of one of the authors with collaborators.
N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
Energy Technology Data Exchange (ETDEWEB)
Boucher-Veronneau, C.; Dixon, L.J.; /SLAC
2012-02-15
We present the full two-loop four-graviton amplitudes in N = 4, 5, 6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N = 0, 1, 2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N = 8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.
Some tree-level string amplitudes in the NSR formalism
Becker, Katrin; Melnikov, Ilarion V; Robbins, Daniel; Royston, Andrew B
2015-01-01
We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point functions involving bosons and fermions. We calculate the five-point amplitude for massless gluons and find agreement with an earlier result by Brandt, Machado and Medina. We then compute the five-point amplitudes involving two and four fermions respectively, the general form of which has not been previously obtained in the NSR formalism. The results nicely confirm expectations from the supersymmetric $F^4$ effective action. Finally we use the prescription of Kawai, Lewellen and Tye (KLT) to compute the amplitudes for the closed string sector.
Kristensen, Tom; Simoni, Andrea; Launay, Jean-Michel
2016-05-01
We compute scattering and bound state properties for two ultracold molecules in a pure 1D optical lattice. We introduce reference functions with complex quasi-momentum that naturally account for the effect of excited energy bands. Our exact results for a short-range interaction are first compared with the simplest version of the standard Bose-Hubbard (BH) model. Such comparison allows us to highlight the effect of the excited bands, of the non-on-site interaction and of tunneling with distant neighbor, that are not taken into account in the BH model. The effective interaction can depend strongly on the particle quasi-momenta and can present a resonant behavior even in a deep lattice. As a second step, we study scattering of two polar particles in the optical lattice. Peculiar Wigner threshold laws stem from the interplay of the long range dipolar interaction and the presence of the energy bands. We finally assess the validity of an extended Bose-Hubbard model for dipolar gases based on our exact two-body calculations. This work was supported by the Agence Nationale de la Recherche (Contract No. ANR-12-BS04-0020-01).
Analysis of two-body nonleptonic B decays involving light mesons in the standard model
Ali, A.; Greub, C.
1998-03-01
We report a theoretical analysis of the exclusive nonleptonic decays of the B+/- and B0 mesons into two light mesons, some of which have been measured recently by the CLEO Collaboration. Our analysis is carried out in the context of an effective Hamiltonian based on the standard model (SM), using next-to-leading order perturbative QCD calculations. We explicitly take into account the O(αs) penguin-loop diagrams of all four-Fermi operators and the O(αs) tree-level diagram of the chromomagnetic dipole operator, and give a prescription for including their effects in nonleptonic two-body decays. Using a factorization ansatz for the hadronic matrix elements, we show that existing data, in particular, the branching ratios B(B+/--->η'K+/-), B(B+/--->π+/-K0), B(B0(B0¯)-->π-/+K+/-), and B(B+/--->ωh+/-)(h+/-=π+/-,K+/-), can be accounted for in this approach. Thus, theoretical scenarios with a substantially enhanced Wilson coefficient of the chromomagnetic dipole operator (as compared to the SM) and/or those with a substantial color-singlet cc¯ component in the wave function of η' are not required by these data. We predict, among other decay rates, the branching ratios for the decays B0(B0¯)-->π+/-π-/+ and B+/--->π0π+/-, which are close to the present experimental limits. Implications of some of these measurements for the parameters of the CKM matrix are presented.
Nonlocality in many-body quantum systems detected with two-body correlators
Energy Technology Data Exchange (ETDEWEB)
Tura, J., E-mail: jordi.tura@icfo.es [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Augusiak, R.; Sainz, A.B. [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Lücke, B.; Klempt, C. [Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover (Germany); Lewenstein, M.; Acín, A. [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); ICREA—Institució Catalana de Recerca i Estudis Avançats, Lluis Campanys 3, 08010 Barcelona (Spain)
2015-11-15
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, “theorist- and experimentalist-friendly” many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states—ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.
Energy Technology Data Exchange (ETDEWEB)
Kostorz, G. [Eidgenoessische Technische Hochschule, Angewandte Physik, Zurich (Switzerland)
1996-12-31
While Bragg scattering is characteristic for the average structure of crystals, static local deviations from the average lattice lead to diffuse elastic scattering around and between Bragg peaks. This scattering thus contains information on the occupation of lattice sites by different atomic species and on static local displacements, even in a macroscopically homogeneous crystalline sample. The various diffuse scattering effects, including those around the incident beam (small-angle scattering), are introduced and illustrated by typical results obtained for some Ni alloys. (author) 7 figs., 41 refs.
One-loop corrections from higher dimensional tree amplitudes
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2016-08-01
We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n + 2 particles in five dimensions, one assumes that two of them cannot be "detected" and therefore an integration over their LIPS is carried out. The resulting object, function of the remaining n particles, is taken to be four-dimensional by restricting the corresponding momenta. We perform this procedure in the context of the tree-level CHY formulation of amplitudes. The scattering equations obtained in the procedure coincide with those derived by Geyer et al. from ambitwistor constructions and recently studied by two of the authors for bi-adjoint scalars. They have two sectors of solutions: regular and singular. We prove that the contribution from regular solutions generically gives rise to unphysical poles. However, using a BCFW argument we prove that the unphysical contributions are always homogeneous functions of the loop momentum and can be discarded. We also show that the contribution from singular solutions turns out to be homogeneous as well.
One-Loop Corrections from Higher Dimensional Tree Amplitudes
Cachazo, Freddy; Yuan, Ellis Ye
2015-01-01
We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n+2 particles in five dimensions, one assumes that two of them cannot be "detected" and therefore an integration over their LIPS is carried out. The resulting object, function of the remaining n particles, is taken to be four-dimensional by restricting the corresponding momenta. We perform this procedure in the context of the tree-level CHY formulation of amplitudes. The scattering equations obtained in the procedure coincide with those derived by Geyer et al from ambitwistor constructions and recently studied by two of the authors for bi-adjoint scalars. They have two sectors of solutions: regular and singular. We prove that the contribution from regular solutions generically gives rise to unphysical poles. However, using a BCFW argument we prove that the unphysical contributions are always homogeneous f...
K to \\pi\\pi decays and the K to \\sigma weak amplitude
Trofimenkoff, N N
2012-01-01
We use a twice-subtracted partial-wave dispersion relation in the elastic unitarity approximation for final-state interactions to study the amplitude for the delta I = 1/2 CP-conserving weak process K+spurion->pi+pi. We use a simple parameterization to approximate the low energy I = 0 S-wave pipi->pipi scattering phase shift and extract the residue of the sigma pole in the weak amplitude obtained from the dispersion relation. Using this residue, we relate the K->pipi decay amplitude, the weak amplitude at the soft pion point and the K->sigma weak amplitude.
Amplitude path corrections for regional phases in China
Energy Technology Data Exchange (ETDEWEB)
Phillips, W.S.; Velasco, A.A.; Taylor, S.R.; Randall, G.E.
1998-12-31
The authors investigate the effectiveness of amplitude path corrections for regional phases on seismic event discrimination and magnitude estimation. Waveform data from digital stations in China for regional, shallow (< 50 km) events were obtained from the IRIS Data Management Center (DMC) for years 1986 to 1996 using the USGS Preliminary Determination of Epicenters (PDE) and the Chinese State Seismological Bureau (SSB) catalogs. For each event, the amplitudes for each regional phase (P{sub n}, P{sub g}, S{sub n}, L{sub g}) were measured, as well as the P{sub g} and L{sub g} coda. Measured amplitudes were corrected for source scaling using estimates of m{sub b} and for distance using a power law that accounts for attenuation and spreading. The amplitude residuals were interpolated and mapped as 2-D amplitude correction surfaces. The authors employ several methods to create the amplitude correction surfaces: a waveguide method, and two interpolation methods (Baysian kriging and a circular moving window mean smoother). They explore the sensitivities of the surfaces to the method and to regional propagation, and apply these surfaces to correct amplitude data to reduce scatter in discrimination ratios and magnitude estimates.
PKP precursors : Implications for global scatterers
Waszek, Lauren; Thomas, Christine; Deuss, Arwen
2015-01-01
Precursors to the core phase PKP are generated by scattering of seismic energy from heterogeneities in the mantle. Here we examine a large global data set of PKP precursors in individual seismograms and array data, to better understand scattering locations. The precursor amplitudes from individual s
Energy Technology Data Exchange (ETDEWEB)
Igamov, S.B. [Institute of Nuclear Physics, Uzbekistan Academy of Sciences, 702132 Tashkent (Uzbekistan); Yarmukhamedov, R. [Institute of Nuclear Physics, Uzbekistan Academy of Sciences, 702132 Tashkent (Uzbekistan)]. E-mail: rakhim@inp.uz
2007-01-01
A modified two-body potential approach is proposed for determination of both the asymptotic normalization coefficient (ANC) (or the respective nuclear vertex constant (NVC)) for the A+a->B (for the virtual decay B->A+a) from an analysis of the experimental S-factor for the peripheral direct capture a+A->B+{gamma} reaction and the astrophysical S-factor, S(E), at low experimentally inaccessible energy regions. The approach proposed involves two additional conditions which verify the peripheral character of the considered reaction and expresses S(E) in terms of the ANC. The connection between NVC (ANC) and the effective range parameters for Aa-scattering is derived. To test this approach we reanalyse the precise experimental astrophysical S-factors for t+{alpha}->Li7+{gamma} reaction at energies E=<1200 keV [C.R. Brune et al., Phys. Rev. C 50 (1994) 2205]. The same Wood-Saxon potential form both for the bound (t+{alpha})-state wave function and for the {alpha}t-scattering wave function is used to guarantee selfconsistency. New estimates have been obtained for the values of the ANC's (the NVC's) for the {alpha}+t->Li7(g.s.), {alpha}+t->Li7(0.478 MeV) and of S(E) at E=<50 keV. These ANC values have been used for getting information about the ''indirect'' measured values of the effective range parameters and the p-wave phase shift for {alpha}t-scattering in the energy range of 100-bar E-bar 180 keV.
Polarization phenomena in hyperon-nucleon scattering
Ishikawa, S; Iseri, Y; Yamamoto, Y
2004-01-01
We investigate polarization observables in hyperon-nucleon scattering by decomposing scattering amplitudes into spin-space tensors, where each component describes scattering by corresponding spin-dependent interactions, so that contributions of the interactions in the observables are individually identified. In this way, for elastic scattering we find some linear combinations of the observables sensitive to particular spin-dependent interactions such as symmetric spin-orbit (LS) interactions and antisymmetric LS ones. These will be useful to criticize theoretical predictions of the interactions when the relevant observables are measured. We treat vector analyzing powers, depolarizations, and coefficients of polarization transfers and spin correlations, a part of which is numerically examined in $\\Sigma^{+} p$ scattering as an example. Total cross sections are studied for polarized beams and targets as well as for unpolarized ones to investigate spin dependence of imaginary parts of forward scattering amplitud...
Model selection for amplitude analysis
Guegan, Baptiste; Stevens, Justin; Williams, Mike
2015-01-01
Model complexity in amplitude analyses is often a priori under-constrained since the underlying theory permits a large number of amplitudes to contribute to most physical processes. The use of an overly complex model results in reduced predictive power and worse resolution on unknown parameters of interest. Therefore, it is common to reduce the complexity by removing from consideration some subset of the allowed amplitudes. This paper studies a data-driven method for limiting model complexity through regularization during regression in the context of a multivariate (Dalitz-plot) analysis. The regularization technique applied greatly improves the performance. A method is also proposed for obtaining the significance of a resonance in a multivariate amplitude analysis.
Wave-scattering from a gently curved surface
Bimonte, Giuseppe
2016-01-01
We study wave scattering from a gently curved surface. We show that the recursive relations, implied by shift invariance, among the coefficients of the perturbative series for the scattering amplitude allow to perform an infinite resummation of the perturbative series to all orders in the amplitude of the corrugation. The resummed series provides a derivative expansion of the scattering amplitude in powers of derivatives of the height profile, which is expected to become exact in the limit of quasi-specular scattering. We discuss the relation of our results with the so-called small-slope approximation introduced some time ago by Voronovich.
Baryon-to-meson transition distribution amplitudes: formalism and models
Pire, B; Szymanowski, L
2016-01-01
In specific kinematics, hard exclusive amplitudes may be factorized into a short distance dominated part computable in a perturbative way on the one hand, and universal, confinement related hadronic matrix elements on the other hand. The extension of this description to processes such as backward meson electroproduction and forward meson production in antiproton-nucleon scattering leads to define new hadronic matrix elements of three quark operators on the light cone, the nucleon-to-meson transition distribution amplitudes, which shed a new light on the nucleon structure.
All tree amplitudes of supersymmetric Einstein-Yang-Mills theory
Adamo, Tim; Roehrig, Kai A; Skinner, David
2015-01-01
We present a new formula for all tree amplitudes in four dimensional supergravity coupled to super Yang-Mills. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but with momenta written in terms of spinor helicity variables. Supersymmetry and parity are both manifest. In the pure gravity and pure Yang-Mills sectors, it reduces to the known twistor-string formulae. We show that the formula behaves correctly under factorization. We sketch how these amplitudes may be obtained from a four-dimensional (ambi)twistor string.
Baryon-to-Meson Transition Distribution Amplitudes: Formalism and Models
Pire, B.; Semenov-Tian-Shansky, K.; Szymanowski, L.
2017-03-01
In specific kinematics, hard exclusive amplitudes may be factorized into a short distance dominated part computable in a perturbative way on the one hand, and universal, confinement related hadronic matrix elements on the other hand. The extension of this description to processes such as backward meson electroproduction and forward meson production in antiproton-nucleon scattering leads to define new hadronic matrix elements of three quark operators on the light cone, the nucleon-to-meson transition distribution amplitudes, which shed a new light on the nucleon structure.
The Structure of the Bern-Kosower Integrand for the N-Gluon Amplitude
Schubert, C
1998-01-01
An ambiguity inherent in the partial integration procedure leading to the Bern-Kosower rules is fixed in a way which preserves the complete permutation symmetry in the scattering states. This leads to a canonical version of the Bern-Kosower representation for the one-loop N - photon/gluon amplitudes, and to a natural decomposition of those amplitudes into permutation symmetric gauge invariant partial amplitudes. This decomposition exhibits a simple recursive structure.
Quantum scattering on a cone revisited
Barroso, V. S.; Pitelli, J. P. M.
2017-07-01
We revisit the scattering of quantum test particles on the conical (2 +1 )-dimensional spacetime and find the scattering amplitude as a function of the boundary conditions imposed at the apex of the cone. We show that the boundary condition is responsible for a purely analytical term in the scattering amplitude, in addition to those coming from purely topological effects. Since it is possible to have nonequivalent physical evolutions for the wave packet (each one corresponding to a different boundary condition), it seems crucial to have an observable quantity specifying which evolution has been prescribed.
Graviton and gluon scattering from first principles
Boels, Rutger H
2016-01-01
Graviton and gluon scattering are studied from minimal physical assumptions such as Poincare and gauge symmetry as well as unitarity. The assumptions lead to an interesting and surprisingly restrictive set of linear equations. This shows gluon and graviton scattering to be related in many field and string theories, explaining and extending several known results. By systematic analysis exceptional graviton scattering amplitudes are derived which in general dimensions can not be related to gluon amplitudes. The simplicity of the formalism guarantees wide further applicability to gauge and gravity theories.
Experimental study of the two-body spin-orbit force
Burgunder, G; Nowacki, F; Giron, S; Hammache, F; Moukaddam, M; eville, N De S er; Beaumel, D; aceres, L C; ément, E Cl; Duchêne, G; Ebran, J P; Fernandez-Dominguez, B; Flavigny, F; Franchoo, S; Gibelin, J; Gillibert, A; évy, S Gr; Guillot, J; Lapoux, V; Lepailleur, A; Matea, I; Matta, A; Nalpas, L; Obertelli, A; Otsuka, T; Pancin, J; Poves, A; Raabe, R; Scarpaci, J A; Stefan, I; Stodel, C; Suzuki, T; Thomas, J C
2014-01-01
Energies and spectroscopic factors of the first $7/2^-$, $3/2^-$, $1/2^-$ and $5/2^-$ states in the $^{35}$Si$_{21}$ nucleus were determined by means of the (d,p) transfer reaction in inverse kinematics at GANIL using the MUST2 and EXOGAM detectors. By comparing the spectroscopic information on the $^{35}$Si and $^{37}$S isotones, a reduction of the $p_{3/2} - p_{1/2}$ spin-orbit splitting by about 25% is proposed, while the $f_{7/2} -f_{5/2}$ spin-orbit splitting seems to remain constant. These features, derived after having unfolded nuclear correlations using shell model calculations, have been attributed to the properties of the 2-body spin-orbit interaction, the amplitude of which is derived for the first time in an atomic nucleus. The present results, remarkably well reproduced by using several realistic nucleon-nucleon forces, provide a unique touchstone for the modeling of the spin-orbit interaction in atomic nuclei.
Two-body charmed B(Bs) decays involving a light scalar meson
Zou, Zhi-Tian; liu, Xin
2016-01-01
Based on the assumption of two-quark structure for the light scalar mesons, within the framework of perturbative QCD approach, we investigate the $B_{q}\\to D_{(s)}^{(*)} S(q=u,d,s)$ decays induced by $b\\to u $ transition, where $S$ denotes a light scalar meson. Under two different scenarios, we calculate the branching ratios of 96 decay modes totally, which are in the range of $10^{-5}$ to $10^{-8}$. The comparison between our predictions and the experimental data will allow us to probe the inner structure of the scalar mesons. In the standard model, since all decays can only occur through tree operators, there are no $CP$ asymmetries. From our calculations, it has been shown that the annihilation type diagrams, especially the nonfactorizable annihilation diagrams, play important roles in the decay amplitudes, especially for these color-suppressed and pure annihilation type decay modes. We also find that the branching ratios of color-allowed type decays are sensitive to the different scenarios, so the measure...
Validation of Proposed Metrics for Two-Body Abrasion Scratch Test Analysis Standards
Street, Kenneth W., Jr.; Kobrick, Ryan L.; Klaus, David M.
2013-01-01
Abrasion of mechanical components and fabrics by soil on Earth is typically minimized by the effects of atmosphere and water. Potentially abrasive particles lose sharp and pointed geometrical features through erosion. In environments where such erosion does not exist, such as the vacuum of the Moon, particles retain sharp geometries associated with fracturing of their parent particles by micrometeorite impacts. The relationship between hardness of the abrasive and that of the material being abraded is well understood, such that the abrasive ability of a material can be estimated as a function of the ratio of the hardness of the two interacting materials. Knowing the abrasive nature of an environment (abrasive)/construction material is crucial to designing durable equipment for use in such surroundings. The objective of this work was to evaluate a set of standardized metrics proposed for characterizing a surface that has been scratched from a two-body abrasion test. This is achieved by defining a new abrasion region termed Zone of Interaction (ZOI). The ZOI describes the full surface profile of all peaks and valleys, rather than just measuring a scratch width. The ZOI has been found to be at least twice the size of a standard width measurement; in some cases, considerably greater, indicating that at least half of the disturbed surface area would be neglected without this insight. The ZOI is used to calculate a more robust data set of volume measurements that can be used to computationally reconstruct a resultant profile for de tailed analysis. Documenting additional changes to various surface roughness par ameters also allows key material attributes of importance to ultimate design applications to be quantified, such as depth of penetration and final abraded surface roughness. Further - more, by investigating the use of custom scratch tips for specific needs, the usefulness of having an abrasion metric that can measure the displaced volume in this standardized
Robinson, S J Q; Robinson, Shadow J.Q.; Zamick, Larry
2002-01-01
Calculations of the spectra of various even-even nuclei in the fp shell ($^{44}$Ti, $^{46}$Ti, $^{48}$Cr, and $^{50}$Cr) are performed with two sets of two-body interaction matrix elements. The first set consists of the matrix elements of the FPD6 interaction. The second set have the same T=1 two-body matrix elements as the FPD6 interaction, but all the T=0 two-body matrix elements are set equal to zero. Despite the drastic differences between the two interactions, the spectra they yield are very similar and indeed it is difficult to say which set gives a better fit to experiment. That the results for the yrast spectra are insensitive to the presence or absence of T=0 two-body matrix elements is surprising because the only bound two nucleon system has T=0, namely the deuteron. Also there is the general folklore that T=0 matrix elements are responsible for nuclear collectivity. Electric quadrupole transition rates are also examined. It is found that the reintroduction of T=0 matrix elements leads to an enhance...
Resonances in Coupled-Channel Scattering
Wilson, David J
2016-01-01
Excited hadrons are seen as resonances in the scattering of lighter stable hadrons like $\\pi$, $K$ and $\\eta$. Many decay into multiple final states necessitating coupled-channel analyses. Recently it has become possible to obtain coupled-channel scattering amplitudes from lattice QCD. Using large diverse bases of operators it is possible to obtain reliable finite volume spectra at energies where multiple channels are open. Utilising the finite volume formalism proposed by L\\"uscher and extended by several others, scattering amplitudes can be extracted from the finite volume spectra. Recent applications will be discussed where the energy dependence of scattering amplitudes is mapped out in several quantum numbers. These are then continued to complex energies to extract resonance poles and couplings.
Topographical scattering of waves: a spectral approach
Magne, R; Rey, V; Herbers, T H C; Magne, Rudy; Ardhuin, Fabrice; Rey, Vincent; Herbers, Thomas H. C.
2005-01-01
The topographical scattering of gravity waves is investigated using a spectral energy balance equation that accounts for first order wave-bottom Bragg scattering. This model represents the bottom topography and surface waves with spectra, and evaluates a Bragg scattering source term that is theoretically valid for small bottom and surface slopes and slowly varying spectral properties. The robustness of the model is tested for a variety of topographies uniform along one horizontal dimension including nearly sinusoidal, linear ramp and step profiles. Results are compared with reflections computed using an accurate method that applies integral matching along vertical boundaries of a series of steps. For small bottom amplitudes, the source term representation yields accurate reflection estimates even for a localized scatterer. This result is proved for small bottom amplitudes $h$ relative to the mean water depth $H$. Wave reflection by small amplitude bottom topography thus depends primarily on the bottom elevati...
Zero energy scattering calculation in Euclidean space
Carbonell, J
2016-01-01
We show that the Bethe-Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and Minkowski amplitudes is only possible for zero energy scattering observables and allows determining the scattering length from the Euclidean Bethe-Salpeter amplitude. Such a possibility strongly simplifies the numerical solution of the Bethe-Salpeter equation and suggests an alternative way to compute the scattering length in Lattice Euclidean calculations without using the Luscher formalism. The derivations contained in this work were performed for scalar particles and one-boson exchange kernel. They can be generalized to the fermion case and more involved interactions.
Zero energy scattering calculation in Euclidean space
Directory of Open Access Journals (Sweden)
J. Carbonell
2016-03-01
Full Text Available We show that the Bethe–Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and Minkowski amplitudes is only possible for zero energy scattering observables and allows determining the scattering length from the Euclidean Bethe–Salpeter amplitude. Such a possibility strongly simplifies the numerical solution of the Bethe–Salpeter equation and suggests an alternative way to compute the scattering length in Lattice Euclidean calculations without using the Luscher formalism. The derivations contained in this work were performed for scalar particles and one-boson exchange kernel. They can be generalized to the fermion case and more involved interactions.
Zero energy scattering calculation in Euclidean space
Energy Technology Data Exchange (ETDEWEB)
Carbonell, J. [Institut de Physique Nucléaire, Université Paris-Sud, IN2P3-CNRS, 91406 Orsay Cedex (France); Karmanov, V.A., E-mail: karmanov@sci.lebedev.ru [Lebedev Physical Institute, Leninsky Prospekt 53, 119991 Moscow (Russian Federation)
2016-03-10
We show that the Bethe–Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and Minkowski amplitudes is only possible for zero energy scattering observables and allows determining the scattering length from the Euclidean Bethe–Salpeter amplitude. Such a possibility strongly simplifies the numerical solution of the Bethe–Salpeter equation and suggests an alternative way to compute the scattering length in Lattice Euclidean calculations without using the Luscher formalism. The derivations contained in this work were performed for scalar particles and one-boson exchange kernel. They can be generalized to the fermion case and more involved interactions.
Zero energy scattering calculation in Euclidean space
Carbonell, J.; Karmanov, V. A.
2016-03-01
We show that the Bethe-Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and Minkowski amplitudes is only possible for zero energy scattering observables and allows determining the scattering length from the Euclidean Bethe-Salpeter amplitude. Such a possibility strongly simplifies the numerical solution of the Bethe-Salpeter equation and suggests an alternative way to compute the scattering length in Lattice Euclidean calculations without using the Luscher formalism. The derivations contained in this work were performed for scalar particles and one-boson exchange kernel. They can be generalized to the fermion case and more involved interactions.
Ma, Ai-Jun; Wang, Wen-Fei; Xiao, Zhen-Jun
2016-01-01
In this paper, we study the $B_{(s)} \\to (D_{(s)},\\bar{D}_{(s)}) \\rho \\to (D_{(s)}, \\bar{D}_{(s)})\\pi \\pi$ decays by employing a framework for the quasi-two-body decays in the perturbative QCD(PQCD) factorization approach. We use the two-pion distribution amplitudes $\\Phi_{\\pi\\pi}$, which contains both resonant and nonresonant contributions from the pion pair to explain the final-state interactions between the pions in the resonant regions. We found that (a) for the four $B\\to (\\bar{D}^0,D^-) \\rho \\to (\\bar{D}^0,D^-) \\pi\\pi$ and $B_s \\to D_s^- \\rho^+ \\to D_s^- \\pi^+\\pi^0$ decays, the PQCD predictions for their branching ratios can be as large as $10^{-4}-10^{-2}$; (b) for other ten considered decays, the PQCD predictions for their decay rates are around $10^{-8}$ to $10^{-5}$ mainly due to strong CKM suppressions; and (c) the PQCD predictions based on the quasi-two-body and the two-body framework agree well with each other, and also be consistent with currently available experimental measurements.
On Fine Structure of Strings: The Universal Correction to the Veneziano Amplitude
CERN. Geneva
2017-01-01
We consider theories of weakly interacting higher spin particles in flat spacetime. We focus on the four-point scattering amplitude at high energies and imaginary scattering angles. The leading asymptotic of the amplitude in this regime is universal and equal to the corresponding limit of the Veneziano amplitude. In this paper, we find that the first sub-leading correction to this asymptotic is universal as well. We compute the correction using a model of relativistic strings with massive endpoints. We argue that it is unique using holography, effective theory of long strings and bootstrap techniques.
TASI 2014: Lectures on Gauge and Gravity Amplitude Relations
Carrasco, John Joseph M.
In these lectures I talk about simplifications and universalities found in scattering amplitudes for gauge and gravity theories. In contrast to Ward identities, which are understood to arise from familiar symmetries of the classical action, these structures are currently only understood in terms of graphical organizational principles, such as the gauge-theoretic color-kinematics duality and the gravitational double-copy structure, for local representations of multi-loop S-matrix elements. These graphical principles make manifest new relationships in and between gauge and gravity scattering amplitudes. My lectures will focus on arriving at such graphical organizations for generic theories with examples presented from maximal supersymmetry, and their use in unitarity-based multiloop integrand construction.
The CHY representation of tree-level primitive QCD amplitudes
de la Cruz, Leonardo; Weinzierl, Stefan
2015-01-01
In this paper we construct a CHY representation for all tree-level primitive QCD amplitudes. The quarks may be massless or massive. We define a generalised cyclic factor $\\hat{C}(w,z)$ and a generalised permutation invariant function $\\hat{E}(z,p,\\varepsilon)$. The amplitude is then given as a contour integral encircling the solutions of the scattering equations with the product $\\hat{C} \\hat{E}$ as integrand. Equivalently, it is given as a sum over the inequivalent solutions of the scattering equations, where the summand consists of a Jacobian times the product $\\hat{C} \\hat{E}$. This representation separates information: The generalised cyclic factor does not depend on the helicities of the external particles, the generalised permutation invariant function does not depend on the ordering of the external particles.
K- nuclear potentials based on chiral meson-baryon amplitudes
Mareš, J.; Cieplý, A.; Gazda, D.; Friedman, E.; Gal, A.
2012-09-01
K- nuclear optical potentials are constructed from in-medium subthreshold K¯N scattering amplitudes within a chirally motivated coupled-channel model. We demonstrate how the strong energy and density dependence of the scattering amplitudes at and below threshold leads to a deep K- nuclear potential VK- for kaonic atoms and K- nuclear quasibound states. Selfconsistent evaluations yield K- potential depths -ReVK- (ρ0) of order 100 MeV. Allowing for K- NN absorption, better agreement with K- atoms data is achieved, leading to increased potential depths, -ReVK- (ρ0) ˜ 175 MeV, in accord with density dependent potentials obtained in purely phenomenological fits. Self consistent dynamical calculations of K- nuclear quasibound states are reported and discussed, as well.
Factorization of Chiral String Amplitudes
Huang, Yu-tin; Yuan, Ellis Ye
2016-01-01
We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: As found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.
Factorization of chiral string amplitudes
Huang, Yu-tin; Siegel, Warren; Yuan, Ellis Ye
2016-09-01
We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: as found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.
Shape of Pion Distribution Amplitude
Energy Technology Data Exchange (ETDEWEB)
Radyushkin, Anatoly
2009-11-01
A scenario is investigated in which the leading-twist pion distribution amplitude $\\varphi_\\pi (x)$ is approximated by the pion decay constant $f_\\pi$ for all essential values of the light-cone fraction $x$. A model for the light-front wave function $\\Psi (x, k_\\perp)$ is proposed that produces such a distribution amplitude and has a rapidly decreasing (exponential for definiteness) dependence on the light-front energy combination $ k_\\perp^2/x(1-x)$. It is shown that this model easily reproduces the fit of recent large-$Q^2$ BaBar data on the photon-pion transition form factor. Some aspects of scenario with flat pion distribution amplitude are discussed.
Multiple exchange and high-energy fixed-angle scattering
Halliday, I G; Orzalesi, C A; Tau, M
1975-01-01
The application of the eikonal ansatz to fermion fermion elastic scattering with Abelian vector gluon exchanges is discussed. The behaviours of the elastic scattering amplitude and the elastic form factor are considered and an important mechanism for fixed angle high energy elastic scattering is identified. (6 refs).
Closed String Amplitudes from Gauge Fixed String Field Theory
Drukker, Nadav
2002-01-01
Closed string diagrams are derived from cubic open string field theory using a gauge fixed kinetic operator. The basic idea is to use a string propagator that does not generate a boundary to the world sheet. Using this propagator and the closed string vertex, the moduli space of closed string surfaces is covered, so closed string scattering amplitudes should be reproduced. This kinetic operator could be a gauge fixed form of the string field theory action around the closed string vacuum.
Classical gluon production amplitude in heavy-ion collisions
Directory of Open Access Journals (Sweden)
Chirilli Giovanni Antonio
2016-01-01
Full Text Available The distribution of quarks and gluons produced in the initial stages of nuclear collisions, known as the initial condition of the Quark-Gluon Plasma formation, is the fundamental building block of heavy-ion theory. I will present the scattering amplitude, beyond the leading order, of the classical gluon produced in heavy-ion collisions. The result is obtained in the framework of saturation physics and Wilson lines formalism.
Closed String Amplitudes from Gauge Fixed String Field Theory
Drukker, Nadav
2002-01-01
Closed string diagrams are derived from cubic open string field theory using a gauge fixed kinetic operator. The basic idea is to use a string propagator that does not generate a boundary to the world sheet. Using this propagator and the closed string vertex, the moduli space of closed string surfaces is covered, so closed string scattering amplitudes should be reproduced. This kinetic operator could be a gauge fixed form of the string field theory action around the closed string vacuum.
Quasi-two-body decays B(s )→P ρ →P π π in the perturbative QCD approach
Li, Ya; Ma, Ai-Jun; Wang, Wen-Fei; Xiao, Zhen-Jun
2017-03-01
In this work, we calculate the C P -averaged branching ratios and the direct C P -violating asymmetries of the quasi-two-body decays B(s )→P (ρ →)π π by employing the perturbative QCD (PQCD) approach (here P stands for a light pseudoscalar meson π , K , η or η'). The vector current timelike form factor Fπ, which contains the final-state interactions between the pion pair in the resonant region associated with the P -wave states ρ (770 ) along with the two-pion distribution amplitudes, is employed to describe the interactions between the ρ and the pion pair under the hypothesis of the conserved vector current. We found that (a) the PQCD predictions for the branching ratios and the direct C P -violating asymmetries for most considered B(s )→P (ρ →)π π decays agree with currently available data within errors, (b) for B (B →π0ρ0→π0(π+π-) , the PQCD prediction is much smaller than the measured one, and (c) for the B+→π+(ρ0→)π+π- decay mode, there is a negative C P asymmetry (-27.5-3.7+3.0)% , which agrees with other theoretical predictions but is different in sign from those reported by the BABAR and LHCb Collaborations.
String amplitudes: from field theories to number theory
CERN. Geneva
2017-01-01
In a variety of recent developments, scattering amplitudes hint at new symmetries of and unexpected connections between physical theories which are otherwise invisible in their conventional description via Feynman diagrams or Lagrangians. Yet, many of these hidden structures are conveniently accessible to string theory where gauge interactions and gravity arise as the low-energy excitations of open and closed strings. In this talk, I will give an intuitive picture of gravity as a double copy of gauge interactions and extend the web of relations to scalar field theories including chiral Lagrangians for Goldstone bosons. The string corrections to gauge and gravity amplitudes beyond their point-particle limit exhibit elegant mathematical structures and offer a convenient laboratory to explore modern number-theoretic concepts in a simple context. As a common theme with Feynman integrals, string amplitudes introduce a variety of periods and special functions including multiple zeta values and polylogarithms, orga...
On the four-dimensional formulation of dimensionally regulated amplitudes
Energy Technology Data Exchange (ETDEWEB)
Fazio, A.R. [Universidad Nacional de Colombia, Departamento de Fisica, Bogota (Colombia); Mastrolia, P. [Universita di Padova, Dipartimento di Fisica e Astronomia, Padua (Italy); Max-Planck-Institut fuer Physik, Munich (Germany); INFN, Padova (Italy); Mirabella, E. [Max-Planck-Institut fuer Physik, Munich (Germany); Torres Bobadilla, W.J. [Universidad Nacional de Colombia, Departamento de Fisica, Bogota (Colombia); Universita di Padova, Dipartimento di Fisica e Astronomia, Padua (Italy); INFN, Padova (Italy)
2014-12-01
Elaborating on the four-dimensional helicity scheme, we propose a pure four-dimensional formulation (FDF) of the d-dimensional regularization of one-loop scattering amplitudes. In our formulation particles propagating inside the loop are represented by massive internal states regulating the divergences. The latter obey Feynman rules containing multiplicative selection rules which automatically account for the effects of the extra-dimensional regulating terms of the amplitude. We present explicit representations of the polarization and helicity states of the four-dimensional particles propagating in the loop. They allow for a complete, four-dimensional, unitarity-based construction of d-dimensional amplitudes. Generalized unitarity within the FDF does not require any higher-dimensional extension of the Clifford and the spinor algebra. Finally we show how the FDF allows for the recursive construction of d-dimensional one-loop integrands, generalizing the four-dimensional open-loop approach. (orig.)
Thermodynamic constraints on the amplitude of quantum oscillations
Shekhter, Arkady; Modic, K. A.; McDonald, R. D.; Ramshaw, B. J.
2017-03-01
Magneto-quantum oscillation experiments in high-temperature superconductors show a strong thermally induced suppression of the oscillation amplitude approaching the critical dopings [B. J. Ramshaw et al., Science 348, 317 (2014), 10.1126/science.aaa4990; H. Shishido et al., Phys. Rev. Lett. 104, 057008 (2010), 10.1103/PhysRevLett.104.057008; P. Walmsley et al., Phys. Rev. Lett. 110, 257002 (2013), 10.1103/PhysRevLett.110.257002]—in support of a quantum-critical origin of their phase diagrams. We suggest that, in addition to a thermodynamic mass enhancement, these experiments may directly indicate the increasing role of quantum fluctuations that suppress the quantum oscillation amplitude through inelastic scattering. We show that the traditional theoretical approaches beyond Lifshitz-Kosevich to calculate the oscillation amplitude in correlated metals result in a contradiction with the third law of thermodynamics and suggest a way to rectify this problem.
Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
Bourjaily, Jacob L; Tran, Vuong-Viet
2016-01-01
We introduce two new graphical-level relations among possible contributions to the four-point correlation function and scattering amplitude in planar, maximally supersymmetric Yang-Mills theory. When combined with the rung rule, these prove powerful enough to fully determine both functions through ten loops. This then also yields the full five-point amplitude to eight loops and the parity-even part to nine loops. We derive these rules, illustrate their applications, compare their relative strengths for fixing coefficients, and survey some of the features of the previously unknown nine and ten loop expressions. Explicit formulae for amplitudes and correlators through ten loops are available at: http://goo.gl/JH0yEc.
Amplitudes and correlators to ten loops using simple, graphical bootstraps
Bourjaily, Jacob L.; Heslop, Paul; Tran, Vuong-Viet
2016-11-01
We introduce two new graphical-level relations among possible contributions to the four-point correlation function and scattering amplitude in planar, maximally supersymmetric Yang-Mills theory. When combined with the rung rule, these prove powerful enough to fully determine both functions through ten loops. This then also yields the full five-point amplitude to eight loops and the parity-even part to nine loops. We derive these rules, illustrate their applications, compare their relative strengths for fixing coefficients, and survey some of the features of the previously unknown nine and ten loop expressions. Explicit formulae for amplitudes and correlators through ten loops are available at: http://goo.gl/JH0yEc.
Employing Helicity Amplitudes for Resummation
Moult, Ian; Tackmann, Frank J; Waalewijn, Wouter J
2015-01-01
Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in $4$- and $d$-dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard m...
Employing Helicity Amplitudes for Resummation
Moult, I.; Stewart, I.W.; Tackmann, F.J.; Waalewijn, W.J.
2015-01-01
Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are dire
Extracting amplitudes from photoproduction data
Workman, R. L.
2011-09-01
We consider the problems associated with amplitude extraction, from meson photoproduction data, over the first resonance regions. The notion of a complete experiment has motivated the FROST program at Jefferson Lab. Exercises applied to pion photoproduction data illustrate the problems to be confronted in any attempt to extract underlying resonance signals from these data (without introducing a model for the resonant process).
Dunn, M.; Watson, D. K.; Loeser, J. G.
2006-08-01
In this paper, we develop an analytic N-body wave function for identical particles under quantum confinement with a general two-body interaction. A systematic approach to correlation is developed by combining three theoretical methods: dimensional perturbation theory, the FG method of Wilson et. al., and the group theory of the symmetric group. Analytic results are achieved for a completely general interaction potential. Unlike conventional perturbation methods which are applicable only for weakly interacting systems, this analytic approach is applicable to both weakly and strongly interacting systems. This method directly accounts for each two-body interaction, rather than an average interaction so even lowest-order results include beyond-mean-field effects. One major advantage is that N appears as a parameter in the analytical expressions for the energy so results for different N are easy to obtain.
Evidence for the two-body nature of the E1 transition operator in the sdf-interacting boson model
Energy Technology Data Exchange (ETDEWEB)
Barfield, A.F.; Brentano, P. von; Dewald, A.; Zell, K.O.; Zamfir, N.V.; Bucurescu, D.; Ivascu, M.; Scholten, O.
1989-01-01
Two new a absolute transition rates are reported for the nucleus /sup 144/Sm following an (..cap alpha.., ..cap alpha..') Coulomb excitation study. They are B(E3;3/sup -/ -> 0/sup +/)=(38+-3)W.u. and B(E1;3/sup -/ -> 2/sup +/)=2.8+-0.4)x10/sup -3/W.u. This large E1 matrix element, along with the previously known B(E1;1/sup -/ -> 0/sup +/) value support the interpretation of the 1/sup -/ state in this nucleus as 2-phonon 2/sup +/x3/sup -/ excitation. In the frame of the IBM-1+f-boson model we show the need for a two-body term in the E1 transition operator. Estimates for the strenghts of the one and two-body parts of the E1 transition operator are obtained from these experimental data.
Helicity selection rules and noninterference for BSM amplitudes
Azatov, Aleksandr; Contino, Roberto; Machado, Camila S.; Riva, Francesco
2017-03-01
Precision studies of scattering processes at colliders provide powerful indirect constraints on new physics. We study the helicity structure of scattering amplitudes in the standard model (SM) and in the context of an effective Lagrangian description of beyond-the-SM (BSM) dynamics. Our analysis reveals a novel set of helicity selection rules according to which, in the majority of 2 →2 scattering processes at high energy, the SM and the leading BSM effects do not interfere. In such situations, the naive expectation that dimension-6 operators represent the leading BSM contribution is compromised, as corrections from dimension-8 operators can become equally (if not more) important well within the validity of the effective field theory approach.
A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
Bedford, J; Spence, B; Travaglini, G; Bedford, James; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
Long, W. S.
1977-01-01
Attempts are made to generate acceptable coordinate systems for two-body configurations. The first method to be tried was to use the body-fitted coordinate system technique to obtain the best system. This technique alone did not produce very good results, so another approach was investigated. This new approach involved using a combination of the body fitted coordinate system procedure and a complex variable transformation method that was used successfully in conformal mapping.
Weinstein, Galina
2015-01-01
Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution and the singularity within it while working in Princeton on the unified field theory and with his assistant Nathan Rosen, on the theory of the Einstein-Rosen bridges. He was also occupied with quantum theory. He believed that quantum theory was an incomplete representation of real things. Together with Rosen and Boris Podolsky he invented the EPR paradox. I demonstrate that the two-body problem in general relativity ...
Measurement of branching fractions and CP violation for charmless charged two-body B decays at LHCb
Perazzini, Stefano
Charmless charged two-body B decays are sensitive probes of the CKM matrix, that parameterize CP violation in the Standard Model (SM), and have the potential to reveal the presence of New Physics. The framework of CP violation within the SM, the role of the CKM matrix, with its basic formalism, and the current experimental status are presented. The theoretical tools commonly used to deal with hadronic B decays and an overview of the phenomenology of charmless two-body B decays are outlined. LHCb is one of the four main experiments operating at the Large Hadron Collider (LHC), devoted to the measurement of CP violation and rare decays of charm and beauty hadrons. The LHCb detector is described, focusing on the technologies adopted for each sub-detector and summarizing their performances. The status-of-the-art of the LHCb measurements with charmless two-body B decays is then presented. Using the 37/pb of integrated luminosity collected at sqrt(s) = 7 TeV by LHCb during 2010, the direct CP asymmetries ACP(B0 -> ...
Charmed Meson Scattering from Lattice QCD
Moir, Graham
2016-01-01
State-of-the-art lattice QCD calculations of scattering amplitudes in coupled-channel $D\\pi$, $D\\eta$ and $D_{s}\\bar{K}$ scattering, as well elastic $DK$ scattering are discussed. The methodology employed allows a determination of the relevant poles in the scattering matrix, while also providing a measure of the coupling of each channel to a given pole. By investigating $S$, $P$ and $D$ wave interactions, the nature of states with $J^{P} = 0^{+}$, relevant for the $D^{*}_{0}(2400)$ and $D^{*}_{s0}(2317)$, as well as states with $J^{P} = 1^{-}, 2^{+}$ are discussed.
Energy Technology Data Exchange (ETDEWEB)
Stirling, W.G. [Liverpool Univ., Dep. of Physics, Liverpool (United Kingdom); Perry, S.C. [Keele Univ. (United Kingdom). Dept. of Physics
1996-12-31
We outline the theoretical and experimental background to neutron scattering studies of critical phenomena at magnetic and structural phase transitions. The displacive phase transition of SrTiO{sub 3} is discussed, along with examples from recent work on magnetic materials from the rare-earth (Ho, Dy) and actinide (NpAs, NpSb, USb) classes. The impact of synchrotron X-ray scattering is discussed in conclusion. (author) 13 figs., 18 refs.
Scattering of sound waves by a compressible vortex
Colonius, Tim; Lele, Sanjiva K.; Moin, Parviz
1991-01-01
Scattering of plane sound waves by a compressible vortex is investigated by direct computation of the two-dimensional Navier-Stokes equations. Nonreflecting boundary conditions are utilized, and their accuracy is established by comparing results on different sized domains. Scattered waves are directly measured from the computations. The resulting amplitude and directivity pattern of the scattered waves is discussed, and compared to various theoretical predictions. For compact vortices (zero circulation), the scattered waves directly computed are in good agreement with predictions based on an acoustic analogy. Strong scattering at about + or - 30 degrees from the direction of incident wave propagation is observed. Back scattering is an order of magnitude smaller than forward scattering. For vortices with finite circulation refraction of the sound by the mean flow field outside the vortex core is found to be important in determining the amplitude and directivity of the scattered wave field.
High Amplitude Secondary Mass Drive
Energy Technology Data Exchange (ETDEWEB)
DYCK,CHRISTOPHER WILLIAM; ALLEN,JAMES J.; HUBER,ROBERT JOHN; SNIEGOWSKI,JEFFRY J.
2000-07-06
In this paper we describe a high amplitude electrostatic drive for surface micromachined mechanical oscillators that may be suitable for vibratory gyroscopes. It is an advanced design of a previously reported dual mass oscillator (Dyck, et. al., 1999). The structure is a 2 degree-of-freedom, parallel-plate driven motion amplifier, termed the secondary mass drive oscillator (SMD oscillator). During each cycle the device contacts the drive plates, generating large electrostatic forces. Peak-to-peak amplitudes of 54 {micro}m have been obtained by operating the structure in air with an applied voltage of 11 V. We describe the structure, present the analysis and design equations, and show recent results that have been obtained, including frequency response data, power dissipation, and out-of- plane motion.
Pulse amplitude modulated chlorophyll fluorometer
Energy Technology Data Exchange (ETDEWEB)
Greenbaum, Elias; Wu, Jie
2015-12-29
Chlorophyll fluorometry may be used for detecting toxins in a sample because of changes in micro algae. A portable lab on a chip ("LOAC") based chlorophyll fluorometer may be used for toxin detection and environmental monitoring. In particular, the system may include a microfluidic pulse amplitude modulated ("PAM") chlorophyll fluorometer. The LOAC PAM chlorophyll fluorometer may analyze microalgae and cyanobacteria that grow naturally in source drinking water.
Decay of boson systems with large scattering length
Energy Technology Data Exchange (ETDEWEB)
Sorensen, O; Fedorov, D V; Jensen, A S [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)
2003-06-01
We investigate systems of identical bosons with the focus on two-body correlations. We apply a Faddeev type of decomposition of the wavefunction. At large scattering length a series of spatially extended many-body bound states appears, analogously to the three-body Efimov states. We discuss a recombination process with these many-body Efimov states as intermediate states.
Scattering solutions of Bethe-Salpeter equation in Minkowski and Euclidean spaces
Carbonell, J
2016-01-01
We shortly review different methods to obtain the scattering solutions of the Bethe-Salpeter equation in Minkowski space. We emphasize the possibility to obtain the zero energy observables in terms of the Euclidean scattering amplitude.
Optical scattering methods applicable to drops and bubbles
Marston, Philip L.
1990-01-01
An overview of optical scattering properties of drops and bubbles is presented. The properties lead to unconventional methods for optically monitoring the size or shape of a scatterer and are applicable to acoustically levitated objects. Several of the methods are applicable to the detection and measurement of small amplitude oscillations. Relevant optical phenomena include: (1) rainbows; (2) diffraction catastrophes from spheroids; (3) critical angle scattering; (4) effects of coatings; (5) glory scattering; and (6) optical levitation.
All-Multiplicity Amplitudes with Massive Scalars
Forde, D; Forde, Darren; Kosower, David A.
2005-01-01
We compute two infinite series of tree-level amplitudes with a massive scalar pair and an arbitrary number of gluons. We provide results for amplitudes where all gluons have identical helicity, and amplitudes with one gluon of opposite helicity. These amplitudes are useful for unitarity-based one-loop calculations in nonsupersymmetric gauge theories generally, and QCD in particular.
Crisis in Amplitude Control Hides in Multistability
Li, Chunbiao; Sprott, Julien Clinton; Xing, Hongyan
2016-12-01
A crisis of amplitude control can occur when a system is multistable. This paper proposes a new chaotic system with a line of equilibria to demonstrate the threat to amplitude control from multistability. The new symmetric system has two coefficients for amplitude control, one of which is a partial amplitude controller, while the other is a total amplitude controller that simultaneously controls the frequency. The amplitude parameter rescales the basins of attraction and triggers a state switch among different states resulting in a failure of amplitude control to the desired state.
Calculation of multi-loop superstring amplitudes
Danilov, G. S.
2016-12-01
The multi-loop interaction amplitudes in the closed, oriented superstring theory are obtained by the integration of local amplitudes. The local amplitude is represented by a sum over the spinning string local amplitudes. The spinning string local amplitudes are given explicitly through super-Schottky group parameters and through interaction vertex coordinates on the (1| 1) complex, non-split supermanifold. The obtained amplitudes are free from divergences. They are consistent with the world-sheet spinning string symmetries. The vacuum amplitude vanishes along with 1-, 2- and 3-point amplitudes of massless states. The vanishing of the above-mentioned amplitude occurs after the integration of the corresponding local amplitude has been performed over the super-Schottky group limiting points and over interaction vertex coordinate, except for those (3| 2) variables which are fixed due to SL(2)-symmetry.
One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
Brandhuber, A; Travaglini, G; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of MHV one-loop scattering amplitudes with an arbitrary number of external legs in N=4 super Yang-Mills. Remarkably, our approach naturally leads to a representation of the amplitudes as dispersion integrals, which we evaluate exactly. Our results for the MHV amplitudes are in precise agreement with the expressions for this class of amplitudes obtained previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
Weinstein, Galina
2015-01-01
Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution and the singularity within it while working in Princeton on the unified field theory and with his assistant Nathan Rosen, on the theory of the Einstein-Rosen bridges. He was also occupied with quantum theory. He believed that quantum theory was an incomplete representation of real things. Together with Rosen and Boris Podolsky he invented the EPR paradox. I demonstrate that the two-body problem in general relativity was a heuristic guide in Einstein's and collaborators' 1935 work on the Einstein-Rosen bridge and EPR paradox.
Santos, L F; Jacquod, P; Kusnezov, Dimitri; Jacquod, Ph.
2002-01-01
We explore generic ground-state and low-energy statistical properties of many-body bosonic and fermionic one- and two-body random ensembles (TBRE) in the dense limit, and contrast them with Random Matrix Theory (RMT). Weak differences in distribution tails can be attributed to the regularity or chaoticity of the corresponding Hamiltonians rather than the particle statistics. We finally show the universality of the distribution of the angular momentum gap between the lowest energy levels in consecutive J-sectors for the four models considered.
Eikonal quantum gravity and Planckian scattering
Kabat, D; Kabat, Dan; Ortiz, Miguel
1992-01-01
Various approaches to high energy forward scattering in quantum gravity are compared using the eikonal approximation. The massless limit of the eikonal is shown to be equivalent to other approximations for the same process, specifically the semiclassical calculation due to G. 't Hooft and the topological field theory due to H. and E. Verlinde. This comparison clarifies these previous results, as it is seen that the amplitude arises purely from a linearised gravitational interaction. The interpretation of poles in the scattering amplitude is also clarified.
On Born approximation in black hole scattering
Energy Technology Data Exchange (ETDEWEB)
Batic, D. [University of West Indies, Department of Mathematics, Kingston (Jamaica); Kelkar, N.G.; Nowakowski, M. [Universidad de los Andes, Departamento de Fisica, Bogota (Colombia)
2011-12-15
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstroem and Reissner-Nordstroem-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes. (orig.)
Müller, Christof
2000-01-01
The nature of seismic scattering was investigated by elastic scattering theory and numerical experiment. Seismic scattering situations can be classified by analyzing the amplitude versus scattering angle behavior of the scattered seismic wave field. The shape of large objects has significant impact on the dynamics of the scattered wave field. Gather oriented as well as prestack methods capable of enhancing the scattering response and assisting in classification were developed. A new 3D migrat...
Amplitude recruitment of cochlear potential
Institute of Scientific and Technical Information of China (English)
LI Xingqi; SUN Wei; SUN Jianhe; YU Ning; JIANG Sichang
2001-01-01
Intracellular recordings were made from outer hair cells (OHC) and the cochlear microphonics (CM) were recorded from scala media (SM) in three turn of guinea pig cochlea,the compound action potential (CAP) were recorded at the round window (RW) before and after the animal were exposed to white noise. The results suggest that the nonlinear properties with “saduration” of Input/output (I/O) function of OHC AC recepter potential and CM were founded; the nonlinear properties with “Low”, “Platean” and “high” of CAP also were investigated. After explosion, the threshold shift of CAP has about 10 dB. The I/O of OHC responses and CM were changed in a linearizing (i.e., nonlinearity loss), the “platean” of I/O CAP disappeared and the growth rate of CAP amplitude were larger than before explosion. The response amplitude recruitment of OHC appears to result from reduction in gain (i.e., hearing loss); It was due to the nonlinear growth function of OHC receptor potentials was changed in linearzing that the basilar membrance motion was changed in linearizing. Since intensity coding in the inner ear depends on an interactions of nonlinear basilar membrance and nerve fibers. So that it must lead to a linearizing of CAP as input responses.
Two-Loop Gluon to Gluon-Gluon Splitting Amplitudes in QCD
Energy Technology Data Exchange (ETDEWEB)
Bern, Z.
2004-04-30
Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g {yields} gg splitting amplitudes in QCD, N = 1, and N = 4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The {epsilon}-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/{epsilon} pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.
Energy Technology Data Exchange (ETDEWEB)
Wilson, David J. [Old Dominion University, Norfolk, VA
2014-06-23
We have obtained clear signals of resonances in coupled-channel pi K - eta K scattering. Using distillation and a large basis of operators we are able to extract a precise spectrum of energy levels using the variational method. These energies are analysed using inelastic extensions of the Luescher method to obtain scattering amplitudes that clearly describe S, P and D wave resonances, corresponding to the physical K_0^*(1430), the K^*(892) and the K_2^*(1430).
First evidence for the two-body charmless baryonic decay $B^0 \\to p \\bar{p}$
INSPIRE-00258707; Adeva, B; Adinolfi, M; Adrover, C; Affolder, A; Ajaltouni, Z; Albrecht, J; Alessio, F; Alexander, M; Ali, S; Alkhazov, G; Alvarez Cartelle, P; Alves Jr, A A; Amato, S; Amerio, S; Amhis, Y; Anderlini, L; Anderson, J; Andreassen, R; Andrews, J E; Appleby, R B; Aquines Gutierrez, O; Archilli, F; Artamonov, A; Artuso, M; Aslanides, E; Auriemma, G; Baalouch, M; Bachmann, S; Back, J J; Baesso, C; Balagura, V; Baldini, W; Barlow, R J; Barschel, C; Barsuk, S; Barter, W; Bauer, Th; Bay, A; Beddow, J; Bedeschi, F; Bediaga, I; Belogurov, S; Belous, K; Belyaev, I; Ben-Haim, E; Bencivenni, G; Benson, S; Benton, J; Berezhnoy, A; Bernet, R; Bettler, M -O; van Beuzekom, M; Bien, A; Bifani, S; Bird, T; Bizzeti, A; Bjørnstad, P M; Blake, T; Blanc, F; Blouw, J; Blusk, S; Bocci, V; Bondar, A; Bondar, N; Bonivento, W; Borghi, S; Borgia, A; Bowcock, T J V; Bowen, E; Bozzi, C; Brambach, T; van den Brand, J; Bressieux, J; Brett, D; Britsch, M; Britton, T; Brook, N H; Brown, H; Burducea, I; Bursche, A; Busetto, G; Buytaert, J; Cadeddu, S; Callot, O; Calvi, M; Calvo Gomez, M; Camboni, A; Campana, P; Campora Perez, D; Carbone, A; Carboni, G; Cardinale, R; Cardini, A; Carranza-Mejia, H; Carson, L; Carvalho Akiba, K; Casse, G; Castillo Garcia, L; Cattaneo, M; Cauet, Ch; Cenci, R; Charles, M; Charpentier, Ph; Chen, P; Chiapolini, N; Chrzaszcz, M; Ciba, K; Cid Vidal, X; Ciezarek, G; Clarke, P E L; Clemencic, M; Cliff, H V; Closier, J; Coca, C; Coco, V; Cogan, J; Cogneras, E; Collins, P; Comerma-Montells, A; Contu, A; Cook, A; Coombes, M; Coquereau, S; Corti, G; Couturier, B; Cowan, G A; Cowie, E; Craik, D C; Cunliffe, S; Currie, R; D'Ambrosio, C; David, P; David, P N Y; Davis, A; De Bonis, I; De Bruyn, K; De Capua, S; De Cian, M; De Miranda, J M; De Paula, L; De Silva, W; De Simone, P; Decamp, D; Deckenhoff, M; Del Buono, L; Déléage, N; Derkach, D; Deschamps, O; Dettori, F; Di Canto, A; Dijkstra, H; Dogaru, M; Donleavy, S; Dordei, F; Dosil Suárez, A; Dossett, D; Dovbnya, A; Dupertuis, F; Durante, P; Dzhelyadin, R; Dziurda, A; Dzyuba, A; Easo, S; Egede, U; Egorychev, V; Eidelman, S; van Eijk, D; Eisenhardt, S; Eitschberger, U; Ekelhof, R; Eklund, L; El Rifai, I; Elsasser, Ch; Falabella, A; Färber, C; Fardell, G; Farinelli, C; Farry, S; Ferguson, D; Fernandez Albor, V; Ferreira Rodrigues, F; Ferro-Luzzi, M; Filippov, S; Fiore, M; Fitzpatrick, C; Fontana, M; Fontanelli, F; Forty, R; Francisco, O; Frank, M; Frei, C; Frosini, M; Furcas, S; Furfaro, E; Gallas Torreira, A; Galli, D; Gandelman, M; Gandini, P; Gao, Y; Garofoli, J; Garosi, P; Garra Tico, J; Garrido, L; Gaspar, C; Gauld, R; Gersabeck, E; Gersabeck, M; Gershon, T; Ghez, Ph; Gibson, V; Giubega, L; Gligorov, V V; Göbel, C; Golubkov, D; Golutvin, A; Gomes, A; Gorbounov, P; Gordon, H; Gotti, C; Grabalosa Gándara, M; Graciani Diaz, R; Granado Cardoso, L A; Graugés, E; Graziani, G; Grecu, A; Greening, E; Gregson, S; Griffith, P; Grünberg, O; Gui, B; Gushchin, E; Guz, Yu; Gys, T; Hadjivasiliou, C; Haefeli, G; Haen, C; Haines, S C; Hall, S; Hamilton, B; Hampson, T; Hansmann-Menzemer, S; Harnew, N; Harnew, S T; Harrison, J; Hartmann, T; He, J; Head, T; Heijne, V; Hennessy, K; Henrard, P; Hernando Morata, J A; van Herwijnen, E; Hess, M; Hicheur, A; Hicks, E; Hill, D; Hoballah, M; Hombach, C; Hopchev, P; Hulsbergen, W; Hunt, P; Huse, T; Hussain, N; Hutchcroft, D; Hynds, D; Iakovenko, V; Idzik, M; Ilten, P; Jacobsson, R; Jaeger, A; Jans, E; Jaton, P; Jawahery, A; Jing, F; John, M; Johnson, D; Jones, C R; Joram, C; Jost, B; Kaballo, M; Kandybei, S; Kanso, W; Karacson, M; Karbach, T M; Kenyon, I R; Ketel, T; Keune, A; Khanji, B; Kochebina, O; Komarov, I; Koopman, R F; Koppenburg, P; Korolev, M; Kozlinskiy, A; Kravchuk, L; Kreplin, K; Kreps, M; Krocker, G; Krokovny, P; Kruse, F; Kucharczyk, M; Kudryavtsev, V; Kurek, K; Kvaratskheliya, T; La Thi, V N; Lacarrere, D; Lafferty, G; Lai, A; Lambert, D; Lambert, R W; Lanciotti, E; Lanfranchi, G; Langenbruch, C; Latham, T; Lazzeroni, C; Le Gac, R; van Leerdam, J; Lees, J -P; Lefèvre, R; Leflat, A; Lefrançois, J; Leo, S; Leroy, O; Lesiak, T; Leverington, B; Li, Y; Li Gioi, L; Liles, M; Lindner, R; Linn, C; Liu, B; Liu, G; Lohn, S; Longstaff, I; Lopes, J H; Lopez-March, N; Lu, H; Lucchesi, D; Luisier, J; Luo, H; Machefert, F; Machikhiliyan, I V; Maciuc, F; Maev, O; Malde, S; Manca, G; Mancinelli, G; Maratas, J; Marconi, U; Marino, P; Märki, R; Marks, J; Martellotti, G; Martens, A; Martín Sánchez, A; Martinelli, M; Martinez Santos, D; Martins Tostes, D; Martynov, A; Massafferri, A; Matev, R; Mathe, Z; Matteuzzi, C; Maurice, E; Mazurov, A; McCarthy, J; McNab, A; McNulty, R; McSkelly, B; Meadows, B; Meier, F; Meissner, M; Merk, M; Milanes, D A; Minard, M -N; Molina Rodriguez, J; Monteil, S; Moran, D; Morawski, P; Mordà, A; Morello, M J; Mountain, R; Mous, I; Muheim, F; Müller, K; Muresan, R; Muryn, B; Muster, B; Naik, P; Nakada, T; Nandakumar, R; Nasteva, I; Needham, M; Neubert, S; Neufeld, N; Nguyen, A D; Nguyen, T D; Nguyen-Mau, C; Nicol, M; Niess, V; Niet, R; Nikitin, N; Nikodem, T; Nomerotski, A; Novoselov, A; Oblakowska-Mucha, A; Obraztsov, V; Oggero, S; Ogilvy, S; Okhrimenko, O; Oldeman, R; Orlandea, M; Otalora Goicochea, J M; Owen, P; Oyanguren, A; Pal, B K; Palano, A; Palczewski, T; Palutan, M; Panman, J; Papanestis, A; Pappagallo, M; Parkes, C; Parkinson, C J; Passaleva, G; Patel, G D; Patel, M; Patrick, G N; Patrignani, C; Pavel-Nicorescu, C; Pazos Alvarez, A; Pellegrino, A; Penso, G; Pepe Altarelli, M; Perazzini, S; Perez Trigo, E; Pérez-Calero Yzquierdo, A; Perret, P; Perrin-Terrin, M; Pescatore, L; Pesen, E; Petridis, K; Petrolini, A; Phan, A; Picatoste Olloqui, E; Pietrzyk, B; Pilař, T; Pinci, D; Playfer, S; Plo Casasus, M; Polci, F; Polok, G; Poluektov, A; Polycarpo, E; Popov, A; Popov, D; Popovici, B; Potterat, C; Powell, A; Prisciandaro, J; Pritchard, A; Prouve, C; Pugatch, V; Puig Navarro, A; Punzi, G; Qian, W; Rademacker, J H; Rakotomiaramanana, B; Rangel, M S; Raniuk, I; Rauschmayr, N; Raven, G; Redford, S; Reid, M M; dos Reis, A C; Ricciardi, S; Richards, A; Rinnert, K; Rives Molina, V; Roa Romero, D A; Robbe, P; Roberts, D A; Rodrigues, E; Rodriguez Perez, P; Roiser, S; Romanovsky, V; Romero Vidal, A; Rouvinet, J; Ruf, T; Ruffini, F; Ruiz, H; Ruiz Valls, P; Sabatino, G; Saborido Silva, J J; Sagidova, N; Sail, P; Saitta, B; Salustino Guimaraes, V; Sanmartin Sedes, B; Sannino, M; Santacesaria, R; Santamarina Rios, C; Santovetti, E; Sapunov, M; Sarti, A; Satriano, C; Satta, A; Savrie, M; Savrina, D; Schaack, P; Schiller, M; Schindler, H; Schlupp, M; Schmelling, M; Schmidt, B; Schneider, O; Schopper, A; Schune, M -H; Schwemmer, R; Sciascia, B; Sciubba, A; Seco, M; Semennikov, A; Senderowska, K; Sepp, I; Serra, N; Serrano, J; Seyfert, P; Shapkin, M; Shapoval, I; Shatalov, P; Shcheglov, Y; Shears, T; Shekhtman, L; Shevchenko, O; Shevchenko, V; Shires, A; Silva Coutinho, R; Sirendi, M; Skidmore, N; Skwarnicki, T; Smith, N A; Smith, E; Smith, J; Smith, M; Sokoloff, M D; Soler, F J P; Soomro, F; Souza, D; Souza De Paula, B; Spaan, B; Sparkes, A; Spradlin, P; Stagni, F; Stahl, S; Steinkamp, O; Stevenson, S; Stoica, S; Stone, S; Storaci, B; Straticiuc, M; Straumann, U; Subbiah, V K; Sun, L; Swientek, S; Syropoulos, V; Szczekowski, M; Szczypka, P; Szumlak, T; T'Jampens, S; Teklishyn, M; Teodorescu, E; Teubert, F; Thomas, C; Thomas, E; van Tilburg, J; Tisserand, V; Tobin, M; Tolk, S; Tonelli, D; Topp-Joergensen, S; Torr, N; Tournefier, E; Tourneur, S; Tran, M T; Tresch, M; Tsaregorodtsev, A; Tsopelas, P; Tuning, N; Ubeda Garcia, M; Ukleja, A; Urner, D; Ustyuzhanin, A; Uwer, U; Vagnoni, V; Valenti, G; Vallier, A; Van Dijk, M; Vazquez Gomez, R; Vazquez Regueiro, P; Vázquez Sierra, C; Vecchi, S; Velthuis, J J; Veltri, M; Veneziano, G; Vesterinen, M; Viaud, B; Vieira, D; Vilasis-Cardona, X; Vollhardt, A; Volyanskyy, D; Voong, D; Vorobyev, A; Vorobyev, V; Voß, C; Voss, H; Waldi, R; Wallace, C; Wallace, R; Wandernoth, S; Wang, J; Ward, D R; Watson, N K; Webber, A D; Websdale, D; Whitehead, M; Wicht, J; Wiechczynski, J; Wiedner, D; Wiggers, L; Wilkinson, G; Williams, M P; Williams, M; Wilson, F F; Wimberley, J; Wishahi, J; Wislicki, W; Witek, M; Wotton, S A; Wright, S; Wu, S; Wyllie, K; Xie, Y; Xing, Z; Yang, Z; Young, R; Yuan, X; Yushchenko, O; Zangoli, M; Zavertyaev, M; Zhang, F; Zhang, L; Zhang, W C; Zhang, Y; Zhelezov, A; Zhokhov, A; Zhong, L; Zvyagin, A
2013-01-01
The results of a search for the rare two-body charmless baryonic decays $B^0 \\to p \\bar{p}$ and $B_s^0 \\to p \\bar{p}$ are reported. The analysis uses a data sample, corresponding to an integrated luminosity of 0.9 fb$^{-1}$, of $pp$ collision data collected by the LHCb experiment at a centre-of-mass energy of 7 TeV. An excess of $B^0 \\to p \\bar{p}$ candidates with respect to background expectations is seen with a statistical significance of 3.3 standard deviations. This is the first evidence for a two-body charmless baryonic $B^0$ decay. No significant $B_s^0 \\to p \\bar{p}$ signal is observed, leading to an improvement of three orders of magnitude over previous bounds. If the excess events are interpreted as signal, the 68.3\\% confidence level intervals on the branching fractions are \\begin{eqnarray} \\cal{B}(\\rm{B}^0 \\to p \\bar{p}) & = & ( 1.47 \\,^{+0.62}_{-0.51} \\,^{+0.35}_{-0.14} ) \\times 10^{-8} \\,, \
Launey, K D; Dytrych, T; Draayer, J P
2014-01-01
We present a program in C that employs spectral distribution theory for studies of characteristic properties of a many-particle quantum-mechanical system and the underlying few-body interaction. In particular, the program focuses on two-body nuclear interactions given in a JT-coupled harmonic oscillator basis and calculates correlation coefficients, a measure of similarity of any two interactions, as well as Hilbert-Schmidt norms specifying interaction strengths. An important feature of the program is its ability to identify the monopole part (centroid) of a 2-body interaction, as well as its 'density-dependent' one-body and two-body part, thereby providing key information on the evolution of shell gaps and binding energies for larger nuclear systems. As additional features, we provide statistical measures for 'density-dependent' interactions, as well as a mechanism to express an interaction in terms of two other interactions. This, in turn, allows one to identify, e.g., established features of the nuclear in...
Zhao, Y M; Yoshinaga, N
2002-01-01
In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interact...
Energy Technology Data Exchange (ETDEWEB)
Hanson, P.
1982-10-01
The two and quasi-two body final states ..sigma../sup +/K/sup +/, ..sigma../sup +/K* (892)/sup +/, ..sigma..*(1385)/sup +/K/sup +/, ..sigma..(1385)/sup +/K*(892)/sup +/ produced by neutral strangeness exchange in ..pi../sup +/p interactions are studied using our own 1-3 GeV/c data, comprising the 14 incident momenta of a two million picture bubble chamber experiment, in combination with the world data on the same and related channels. Because low energy resonance formation is not strongly coupled to the ..sigma..,..sigma..* production channels, at very modest incident momenta their dominant features are seen to be understandable in terms of high energy hypercharge exchange phenomenology. We find that Regge models fitted to data in the 10 to 20 GeV/c range adequately describe the ..sigma.. and ..sigma..* channels down to within a few hundred MeV/c of threshold and out to large center of mass scattering angles, and that over the range of the available world data weak exchange degeneracy expectations for these reactions are at least qualitatively successful. We observe that the SU(2), SU(3) flavor symmetries successfully describe these hypercharge exchange processes and relate them to charge exchange via sum rules and equalities expressing flavor independence of the strong interaction; in particular, we derive and test on the available world data a mass broken SU(3) sum rule for ..pi../sup +/p ..-->.. K/sup +/..sigma../sup +/, ..pi../sup -/p ..-->.. K/sup 0/..lambda.., K/sup -/p ..-->.. anti K/sup 0/n and test over a wider range of momenta than before an earlier expression relating ..sigma..* and ..delta.. production. We also find at least qualitative agreement between quark model predictions for forward hypercharge exchange and the data, and we find that 90/sup 0/ hypercharge exchange cross sections also conform to the expectations of the quark constituent picture for hadrons.
Electroweak 2 -> 2 amplitudes for electron-positron annihilation at TeV energies
Barroso, A; Greco, Mario; Oliveira, S M; Troyan, S I
2003-01-01
The non-radiative scattering amplitudes for electron-positron annihilation into quark and lepton pairs in the TeV energy range are calculated in the double-logarithmic approximation. The expressions for the amplitudes are obtained using infrared evolution equations with different cut-offs for virtual photons and for W and Z bosons, and compared with previous results obtained with an universal cut-off.
Calculations of bar K-nuclear quasi-bound states using chiral bar KN amplitudes
Mareš, J.; Barnea, N.; Cieplý, A.; Friedman, E.; Gal, A.; Gazda, D.
2014-03-01
We review our recent calculations of K- quasi-bound states in nuclear systems using subthreshold energy dependent chiral bar KN amplitudes. Strong energy dependence of the scattering amplitudes requires self-consistent evaluation of the involved bar KN interactions. In view of sizable widths predicted by our calculations, an unambiguous identification of K--nuclear quasi-bound states in ongoing experimental searches would be difficult.
Once and twice subtracted dispersion relations in the analysis of pi pi amplitudes
Kaminski, R; Peláez, J R; Ynduráin, F J
2009-01-01
Once and twice subtracted crossing symmetric dispersion relations applied to $\\pi\\pi \\to \\pi\\pi$ scattering data are analyzed and compared. Both sets of dispersion relations can be used to test the $\\pi\\pi$ amplitudes in low partial waves up to about 1 GeV. We show how once subtracted dispersion relations can provide stronger constraints for $\\pi\\pi$ amplitudes than twice subtracted ones in the 400 to 1100 MeV range, given the same experimental input.
Integrable amplitude deformations for N =4 super Yang-Mills and ABJM theory
Bargheer, Till; Huang, Yu-Tin; Loebbert, Florian; Yamazaki, Masahito
2015-01-01
We study Yangian-invariant deformations of scattering amplitudes in 4d N =4 super Yang-Mills theory and 3d N =6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Graßmannian integral for 4d N =4 supersymmetric Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Graßmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.
Electromagnetic Field Scattering on rf-SQUID Based Metasurfaces
Сaputo J.G; Gabitov I.R.; Kudyshev Zh.; Kupaev T.; Maimistov A.I.
2015-01-01
Electromagnetic field scattering on a 2D array of rf-SQUIDs is considered. We show that the scattering changes for large amplitudes of the incident electromagnetic wave; above a critical amplitude, two different refraction states occur (bistability). In particular, for these two states, the transmitted wave polarization and angle of refraction are different. One could then switch the direction of propagation of the electromagnetic wave and its polarization with a “thin film”, whose thickness ...
Electromagnetic Field Scattering on rf-SQUID Based Metasurfaces
Raputo, J. G.; Gabitov, I. R.; Kudyshev, Zh.; Kupaev, T.; Maimistov, A. I.
2015-09-01
Electromagnetic field scattering on a 2D array of rf-SQUIDs is considered. We show that the scattering changes for large amplitudes of the incident electromagnetic wave; above a critical amplitude, two different refraction states occur (bistability). In particular, for these two states, the transmitted wave polarization and angle of refraction are different. One could then switch the direction of propagation of the electromagnetic wave and its polarization with a "thin film", whose thickness is much smaller than the wavelength.
Solving Bethe-Salpeter scattering state equation in Minkowski space
Carbonell, J
2014-01-01
We present a method to directly solving the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the singularities which appear in the kernel, propagators and Bethe-Salpeter amplitude itself. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange is computed for the first time.
Remote identification of the vibration amplitude of ship hull
Directory of Open Access Journals (Sweden)
A. N. Pinchuk
2014-01-01
Full Text Available The aim is to develop the methodological support to determine vibration amplitude of the ship hull remotely using a coherent radar centimeter range based on the variation of the Doppler signal spectrum reflected from a vibrating surface.The paper presents a synthesized mathematical model of the radio signal reflected from the vibrating surface. It is the signal of coherent radar of continuous radiation with a known carrier frequency and the amplitude of the radiated signal. In the synthesis it was believed that the displacement in the radial direction with respect to the vibrating surface radar was sinusoidal.The dependences of the vibration amplitude on the value of the normalized Doppler radio signal spectrum at the second harmonic frequency are obtained. Cycle results of field experiments to study the variability of the sea surface, determining the level of its roughness, allows us to establish that the energy of surface waves of gravitational-capillary range has a high correlation with the wind speed. It is proved that the ratio of the spectral density levels at vibration frequency and its multiple frequencies is specified by the index of phase modulation linearly related to the amplitude of vibration of the ship hull.The results are significant for radar (radar detection of water targets using the coherent radar of centimeter range, ensuring the correct records of noise generated by the scattering of radio waves from the water surface.
Evaluation of the Cachazo-He-Yuan gauge amplitude
Lam, C. S.; Yao, York-Peng
2016-05-01
The Cachazo-He-Yuan (CHY) formula for n -gluon scattering is known to give the same amplitude as the one obtained from Feynman diagrams, though the former contains neither vertices nor propagators explicitly. The equivalence was shown by indirect means, not by a direct evaluation of the (n -3 )-dimensional integral in the CHY formula. The purpose of this paper is to discuss how such a direct evaluation can be carried out. There are two basic difficulties in the calculation: how to handle the large number of terms in the reduced Pfaffian, and how to carry out the integrations in the presence of a σ dependence much more complicated than the Parke-Taylor form found in a CHY double-color scalar amplitude. We have solved both of these problems, and have formulated a method that can be applied to any n . Many examples are provided to illustrate these calculations.
Hexagon Wilson loop = six-gluon MHV amplitude
Drummond, J M; Korchemsky, G P; Sokatchev, E
2008-01-01
We compare the two-loop corrections to the finite part of the light-like hexagon Wilson loop with the recent numerical results for the finite part of the MHV six-gluon amplitude in N=4 SYM theory by Bern, Dixon, Kosower, Roiban, Spradlin, Vergu and Volovich (arXiv:0803.1465 [hep-th]) and demonstrate that they coincide within the error bars and, at the same time, they differ from the BDS ansatz by a non-trivial function of (dual) conformal kinematical invariants. This provides strong evidence that the Wilson loop/scattering amplitude duality holds in planar N=4 SYM theory to all loops for an arbitrary number of external particles.
Gluon Wavefunctions and Amplitudes on the Light-Front
Cruz-Santiago, Christian A
2013-01-01
We investigate the tree level multi-gluon components of the gluon light cone wavefunctions in the light cone gauge keeping the exact kinematics of the gluon emissions. We focus on the components with all helicities identical to the helicity of the incoming gluon. The recurrence relations for the gluon wavefunctions are derived. In the case when the virtuality of the incoming gluon is neglected the exact form of the multi-gluon wavefunction as well as the fragmentation function is obtained. Furthermore we analyze the 2 to N tree-level gluon scattering in the framework of light-front perturbation theory and we demonstrate that the amplitude for this process can be obtained from the 1 to N+1 gluon wavefunction. Finally, we demonstrate that our results for selected helicity configurations are equivalent to the Parke-Taylor amplitudes.
Relations Between Helicity Coupling Amplitude and L-S Coupling Amplitude
Institute of Scientific and Technical Information of China (English)
WU Ning; RUAN Tu-Nan
2001-01-01
Relations between helicity coupling amplitude and L-S coupling amplitude are discussed. The equivalence condition for these two kinematic analysis methods and the limitations of the L-S coupling amplitude are also studied in this paper.``
Holonomy-flux spinfoam amplitude
Perini, Claudio
2012-01-01
We introduce a holomorphic representation for the Lorentzian EPRL spinfoam on arbitrary 2-complexes. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\\~ao-Thiemann heat kernel coherent state transform. The new variables are classical holonomy-flux phase space variables $(h,X)\\simeq \\mathcal T^*SU(2)$ of Hamiltonian loop quantum gravity prescribing the holonomies of the Ashtekar connection $A=\\Gamma + \\gamma K$, and their conjugate gravitational fluxes. For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter. We briefly comment on the possibility to use the alternative flipped classical limit.
Constructing Amplitudes from Their Soft Limits
Energy Technology Data Exchange (ETDEWEB)
Boucher-Veronneau, Camille; Larkoski, Andrew J.; /SLAC
2011-12-09
The existence of universal soft limits for gauge-theory and gravity amplitudes has been known for a long time. The properties of the soft limits have been exploited in numerous ways; in particular for relating an n-point amplitude to an (n-1)-point amplitude by removing a soft particle. Recently, a procedure called inverse soft was developed by which 'soft' particles can be systematically added to an amplitude to construct a higher-point amplitude for generic kinematics. We review this procedure and relate it to Britto-Cachazo-Feng-Witten recursion. We show that all tree-level amplitudes in gauge theory and gravity up through seven points can be constructed in this way, as well as certain classes of NMHV gauge-theory amplitudes with any number of external legs. This provides us with a systematic procedure for constructing amplitudes solely from their soft limits.
Constructing amplitudes from their soft limits
Boucher-Veronneau, Camille; Larkoski, Andrew J.
2011-09-01
The existence of universal soft limits for gauge-theory and gravity amplitudes has been known for a long time. The properties of the soft limits have been exploited in numerous ways; in particular for relating an n-point amplitude to an ( n - 1)-point amplitude by removing a soft particle. Recently, a procedure called inverse soft was developed by which "soft" particles can be systematically added to an amplitude to construct a higher-point amplitude for generic kinematics. We review this procedure and relate it to Britto-Cachazo-Feng-Witten recursion. We show that all tree-level amplitudes in gauge theory and gravity up through seven points can be constructed in this way, as well as certain classes of NMHV gauge-theory amplitudes with any number of external legs. This provides us with a systematic procedure for constructing amplitudes solely from their soft limits.
Energy Technology Data Exchange (ETDEWEB)
Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-16
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
A Note on Loop Amplitudes in QED
Brandhuber, Andreas; Vincon, Massimiliano
2009-01-01
We consider the two-loop four-point amplitude in N=2 super QED, and show that there exists an approximate recursive structure similar to that captured by the ABDK/BDS ansatz for MHV amplitudes in N=4 super Yang-Mills. Furthermore, we present a simple relation between the box coefficients of one-loop photon MHV amplitudes in (super) QED, and sums of box coefficients of one-loop MHV amplitudes in (super) Yang-Mills.
Energy Technology Data Exchange (ETDEWEB)
Friedrich, Harald [Technische Univ. Muenchen, Garching (Germany). Physik-Department
2013-08-01
Written by the author of the widely acclaimed textbook. Theoretical Atomic Physics Includes sections on quantum reflection, tunable Feshbach resonances and Efimov states. Useful for advanced students and researchers. This book presents a concise and modern coverage of scattering theory. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. The level of abstraction is kept as low as at all possible, and deeper questions related to mathematical foundations of scattering theory are passed by. The book should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. It is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Friedrich, Harald
2016-01-01
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is k...
Isospin odd pi K scattering length
Schweizer, J
2005-01-01
We make use of the chiral two-loop representation of the pi K scattering amplitude [J. Bijnens, P. Dhonte and P. Talavera, JHEP 0405 (2004) 036] to investigate the isospin odd scattering length at next-to-next-to-leading order in the SU(3) expansion. This scattering length is protected against contributions of m_s in the chiral expansion, in the sense that the corrections to the current algebra result are of order M_pi^2. In view of the planned lifetime measurement on pi K atoms at CERN it is important to understand the size of these corrections.
Isospin odd {pi}K scattering length
Energy Technology Data Exchange (ETDEWEB)
Schweizer, J. [Institut fuer Theoretische Physik, University of Vienna, A-1090 Vienna (Austria)]. E-mail: julia.schweizer@univie.ac.at
2005-10-13
We make use of the chiral two-loop representation of the {pi}K scattering amplitude [J. Bijnens, P. Dhonte, P. Talavera, JHEP 0405 (2004) 036] to investigate the isospin odd scattering length at next-to-next-to-leading order in the SU(3) expansion. This scattering length is protected against contributions of m{sub s} in the chiral expansion, in the sense that the corrections to the current algebra result are of order M{sub {pi}}{sup 2}. In view of the planned lifetime measurement on {pi}K atoms at CERN it is important to understand the size of these corrections.
Bini, Donato
2013-01-01
We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing the gravitational interaction of two bodies within the effective one-body formalism. The (non logarithmic) coefficient a_5 (nu) measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio nu. Its nu-independent part a_5 (0) is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation. Its nu-linear part a_5 (nu) - a_5 (0) is deduced from recent results of Jaranowski and Sch\\"afer, and is found to be significantly negative.
Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potential: 1D and 2D Case
Shapeev, Alexander V
2010-01-01
This paper concerns the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystalline materials. It has been widely recognized that the most practical coupled methods exhibit finite errors on the atomistic/continuum interface (which are often attributed to spurious forces called "ghost forces"). There are only few existing works that propose a coupling which is sufficiently accurate near the interface under certain limitations. In this paper a novel coupling that is free from "ghost forces" is proposed for a two-body interaction potential under the assumptions of either (i) one spatial dimension, or (ii) two spatial dimensions and piecewise affine finite elements for describing the continuum deformation. The computational efficiency of the proposed coupling is demonstrated with numerical experiments. The coupling strategy is based on judiciously defining the contributions of the atomistic bonds to the discrete and the cont...
Twist-4 photon helicity-flip amplitude in DVCS on a nucleon in the Wandzura-Wilczek approximation
Kivel, N A
2001-01-01
We computed twist-4 part of the photon spin-flip amplitude in deeply virtual Compton scattering on a nucleon in the Wandzura-Wilczek approximation. We found a factorizable contribution, which arises from photon scattering on quarks with non-zero angular momentum along the collision axis. As the genuine twist-2 amplitude arises at the NLO, for moderate virtualities of the hard photon, $Q^2 \\le 10$ GeV$^2$, kinematical twist-4 correction can give numerically important contribution to the photon helicity-flip amplitude.
Directory of Open Access Journals (Sweden)
Lukas eHeydrich
2013-12-01
Full Text Available In neurology and psychiatry the detailed study of illusory own body perceptions has suggested close links between bodily processing and self-consciousness. One such illusory own body perception is heautoscopy where patients have the sensation of being reduplicated and to exist at two or even more locations. In previous experiments, using a video head-mounted display, self-location and self-identification were manipulated by applying conflicting visuo-tactile information. Yet the experienced singularity of the self was not affected, i.e. participants did not experience having multiple bodies or selves. In two experiments presented in this paper, we investigated self-location and self-identification while participants saw two virtual bodies (video-generated in study 1 and 3D computer generated in study 2 that were stroked either synchronously or asynchronously with their own body. In both experiments, we report that self-identification with two virtual bodies was stronger during synchronous stroking. Furthermore, in the video generated setup with synchronous stroking participants reported a greater feeling of having multiple bodies than in the control conditions. In study 1, but not in study 2, we report that self-location – measured by anterior posterior drift – was significantly shifted towards the two bodies in the synchronous condition only. Self-identification with two bodies, the sensation of having multiple bodies, and the changes in self-location show that the experienced singularity of the self can be studied experimentally. We discuss our data with respect to ownership for supernumerary hands and heautoscopy. We finally compare the effects of the video and 3D computer generated head-mounted display technology and discuss the possible benefits of using either technology to induce changes in illusory self-identification with a virtual body.
Heydrich, Lukas; Dodds, Trevor J.; Aspell, Jane E.; Herbelin, Bruno; Bülthoff, Heinrich H.; Mohler, Betty J.; Blanke, Olaf
2013-01-01
In neurology and psychiatry the detailed study of illusory own body perceptions has suggested close links between bodily processing and self-consciousness. One such illusory own body perception is heautoscopy where patients have the sensation of being reduplicated and to exist at two or even more locations. In previous experiments, using a video head-mounted display, self-location and self-identification were manipulated by applying conflicting visuo-tactile information. Yet the experienced singularity of the self was not affected, i.e., participants did not experience having multiple bodies or selves. In two experiments presented in this paper, we investigated self-location and self-identification while participants saw two virtual bodies (video-generated in study 1 and 3D computer generated in study 2) that were stroked either synchronously or asynchronously with their own body. In both experiments, we report that self-identification with two virtual bodies was stronger during synchronous stroking. Furthermore, in the video generated setup with synchronous stroking participants reported a greater feeling of having multiple bodies than in the control conditions. In study 1, but not in study 2, we report that self-location – measured by anterior posterior drift – was significantly shifted towards the two bodies in the synchronous condition only. Self-identification with two bodies, the sensation of having multiple bodies, and the changes in self-location show that the experienced singularity of the self can be studied experimentally. We discuss our data with respect to ownership for supernumerary hands and heautoscopy. We finally compare the effects of the video and 3D computer generated head-mounted display technology and discuss the possible benefits of using either technology to induce changes in illusory self-identification with a virtual body. PMID:24385970
HFOLD - A program package for calculating two-body MSSM Higgs decays at full one-loop level.
Frisch, W; Eberl, H; Hluchá, H
2011-10-01
HFOLD (Higgs Full One Loop Decays) is a Fortran program package for calculating all MSSM Higgs two-body decay widths and the corresponding branching ratios at full one-loop level. The package is done in the SUSY Parameter Analysis convention and supports the SUSY Les Houches Accord input and output format. PROGRAM SUMMARY: Program title: HFOLD Catalogue identifier: AEJG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 340 621 No. of bytes in distributed program, including test data, etc.: 1 760 051 Distribution format: tar.gz Programming language: Fortran 77 Computer: Workstation, PC Operating system: Linux RAM: 524 288 000 Bytes Classification: 11.1 External routines: LoopTools 2.2 (http://www.feynarts.de/looptools/), SLHALib 2.2 (http://www.feynarts.de/slha/). The LoopTools code is included in the distribution package. Nature of problem: A future high-energy e+e- linear collider will be the best environment for the precise measurements of masses, cross sections, branching ratios, etc. Experimental accuracies are expected at the per-cent down to the per-mile level. These must be matched from the theoretical side. Therefore higher order calculations are mandatory. Solution method: This program package calculates all MSSM Higgs two-body decay widths and the corresponding branching ratios at full one-loop level. The renormalization is done in the DR scheme following the SUSY Parameter Analysis convention. The program supports the SUSY Les Houches Accord input and output format. Running time: The example provided takes only a few seconds to run.
Trapped particle bounds on stimulated scatter in the large k/kD regime
Rose, H A
2002-01-01
In the strongly damped regime, the convective gain rate for stimulated scatter varies inversely with the plasma wave damping rate. Electron trapping effects reduce the damping but also lead to loss of resonance for large enough amplitude waves. This leads to a gain rate bound and corresponding optimum scattered light frequency and plasma wave amplitude.
Tsunami Focusing and Leading Amplitude
Kanoglu, U.
2016-12-01
Tsunamis transform substantially through spatial and temporal spreading from their source region. This substantial spreading might result unique maximum tsunami wave heights which might be attributed to the source configuration, directivity, the waveguide structures of mid-ocean ridges and continental shelves, focusing and defocusing through submarine seamounts, random focusing due to small changes in bathymetry, dispersion, and, most likely, combination of some of these effects. In terms of the maximum tsunami wave height, after Okal and Synolakis (2016 Geophys. J. Int. 204, 719-735), it is clear that dispersion would be one of the reasons to drive the leading wave amplitude in a tsunami wave train. Okal and Synolakis (2016), referring to this phenomenon as sequencing -later waves in the train becoming higher than the leading one, considered Hammack's (1972, Ph.D. Dissertation, Calif. Inst. Tech., 261 pp) formalism, in addition to LeMéhauté and Wang's (1995 Water waves generated by underwater explosion, World Scientific, 367 pp), to evaluate linear dispersive tsunami propagation from a circular plug uplifted on an ocean of constant depth. They identified transition distance, as the second wave being larger, performing parametric study for the radius of the plug and the depth of the ocean. Here, we extend Okal and Synolakis' (2016) analysis to an initial wave field with a finite crest length and, in addition, to a most common tsunami initial wave form of N-wave (Tadepalli and Synolakis, 1994 Proc. R. Soc. A: Math. Phys. Eng. Sci. 445, 99-112). First, we investigate the focusing feature in the leading-depression side, which enhance tsunami wave height as presented by Kanoglu et al. (2013 Proc. R. Soc. A: Math. Phys. Eng. Sci. 469, 20130015). We then discuss the results in terms of leading wave amplitude presenting a parametric study and identify a simple relation for the transition distance. The solution presented here could be used to better analyze dispersive
Generating all tree amplitudes in {N} = 4{{SYM}} by Inverse Soft Limit
Nandan, Dhritiman; Wen, Congkao
2012-08-01
The idea of adding particles to construct amplitudes has been utilized in various ways in exploring the structure of scattering amplitudes. This idea is often called Inverse Soft Limit, namely it is the reverse mechanism of taking particles to be soft. We apply the Inverse Soft Limit to the tree-level amplitudes in {N} = 4 super Yang-Mills theory, which allows us to generate full tree-level superamplitudes by adding "soft" particles in a certain way. With the help from Britto-Cachazo-Feng-Witten recursion relations, a systematic and concrete way of adding particles is determined recursively. The amplitudes constructed solely by adding particles not only have manifest Yangian symmetry, but also make the soft limit transparent. The method of generating amplitudes by Inverse Soft Limit can also be generalized for constructing form factors.
Quantum Amplitude Amplification and Estimation
Brassard, G; Mosca, M; Tapp, A; Brassard, Gilles; Hoyer, Peter; Mosca, Michele; Tapp, Alain
2000-01-01
Consider a Boolean function $\\chi: X \\to \\{0,1\\}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $\\chi(x)=1$ and bad otherwise. Consider also a quantum algorithm $\\mathcal A$ such that $A \\ket{0} = \\sum_{x\\in X} \\alpha_x \\ket{x}$ is a quantum superposition of the elements of $X$, and let $a$ denote the probability that a good element is produced if $A \\ket{0}$ is measured. If we repeat the process of running $A$, measuring the output, and using $\\chi$ to check the validity of the result, we shall expect to repeat $1/a$ times on the average before a solution is found. *Amplitude amplification* is a process that allows to find a good $x$ after an expected number of applications of $A$ and its inverse which is proportional to $1/\\sqrt{a}$, assuming algorithm $A$ makes no measurements. This is a generalization of Grover's searching algorithm in which $A$ was restricted to producing an equal superposition of all members of $X$ and we had a promise that a single $x$ existed such tha...
The azimuthal decorrelation of forward jets in deep inelastic scattering
Energy Technology Data Exchange (ETDEWEB)
Sabio Vera, A. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Schwennsen, F. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2007-08-15
We study the azimuthal angle decorrelation of forward jets in Deep Inelastic Scattering. We make predictions for this observable at HERA describing the high energy limit of the relevant scattering amplitudes with quasi-multi-Regge kinematics together with a collinearly improved evolution kernel for multiparton emissions. (orig.)
The Scattering of Fast Nucleons from Nuclei
Kerman, A. K.; McManus, H.; Thaler, R. M.
2000-04-01
The formal theory of the scattering of high-energy nucleons by nuclei is developed in terms of the nucleon-nucleon scattering amplitude. The most important approximations necessary to make numerical calculation feasible are then examined. The optical model potential is derived on this basis and compared with the optical model parameters found from experiment. The elastic scattering and polarization of nucleons from light nuclei is predicted and compared with experiment. The effect of nuclear correlations is discussed. The polarization of inelastically scattered nucleons is discussed and predictions compared with experiments. To within the validity of the approximations the experimental data on the scattering of nucleons from nuclei at energies above ˜100 Mev appears to be consistent with the theory.
The scattering of fast nucleons from nuclei
Energy Technology Data Exchange (ETDEWEB)
Kerman, A. K. [Massachusetts Institute of Technology, Cambridge, Massachusetts (United States); McManus, H. [Chalk River Laboratory, Chalk River, Ontario, (Canada); Thaler, R. M. [Los Alamos Scientific Laboratory, Los Alamos, New Mexico (United States)
2000-04-10
The formal theory of the scattering of high-energy nucleons by nuclei is developed in terms of the nucleon nucleon scattering amplitude. The most important approximations necessary to make numerical calculation feasible are then examined. The optical model potential is derived on this basis and compared with the optical model parameters found from experiment. The elastic scattering and polarization of nucleons from light nuclei is predicted and compared with experiment. The effect of nuclear correlations is discussed. The polarization of inelastically scattered nucleons is discussed and predictions compared with experiments. To within the validity of the approximations the experimental data on the scattering of nucleons from nuclei at energies above {approx}100 Mev appears to be consistent with the theory. (c) 2000 Academic Press, Inc.
Klenk, K F
1973-01-01
The changing slope of d sigma /dt at small mod t mod observed in the CERN-ISR p-p scattering data can be reproduced in the Glauber multiple quark scattering model by a quark-quark scattering amplitude that is an undamped rapidly oscillating function of momentum transferred to the quark. (9 refs).
Superradiant Forward Scattering in Multiple Scattering
Chabe, Julien; Bienaime, Tom; Bachelard, Romain; Piovella, Nicola; Kaiser, Robin
2012-01-01
We report on an interference effect in multiple scattering by resonant scatterers resulting in enhanced forward scattering, violating Ohm's law for photons. The underlying mechanism of this wave effect is superradiance, which we have investigated using cold atoms as a toy model. We present numerical and experimental evidences for this superradiant forward scattering, which is robust against disorder and configuration averaging.