N ≥ 4 Supergravity Amplitudes from Gauge Theory at Two Loops

International Nuclear Information System (INIS)

Boucher-Veronneau, Camille

2012-01-01

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.

Loop-quantum-gravity vertex amplitude.

Science.gov (United States)

Engle, Jonathan; Pereira, Roberto; Rovelli, Carlo

2007-10-19

Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one and it yields an SO(4)-covariant vertex amplitude for Euclidean loop gravity.

Loop amplitudes in an extended gravity theory

Science.gov (United States)

Dunbar, David C.; Godwin, John H.; Jehu, Guy R.; Perkins, Warren B.

2018-05-01

We extend the S-matrix of gravity by the addition of the minimal three-point amplitude or equivalently adding R3 terms to the Lagrangian. We demonstrate how Unitarity can be used to simply examine the renormalisability of this theory and determine the R4 counter-terms that arise at one-loop. We find that the combination of R4 terms that arise in the extended theory is complementary to the R4 counter-term associated with supersymmetric Lagrangians.

All three-loop four-point correlators of half-BPS operators in planar $ \\mathcal{N} $ = 4 SYM

CERN Document Server

Chicherin, Dmitry; Heslop, Paul; Sokatchev, Emery

2016-01-01

We obtain the planar correlation function of four half-BPS operators of arbitrary weights, up to three loops. Our method exploits only elementary properties of the integrand of the planar correlator, such as its symmetries and singularity structure. This allows us to write down a general ansatz for the integrand. The coefficients in the ansatz are fixed by means of a powerful light-cone OPE relation between correlators with different weights. Our result is formulated in terms of a limited number of functions built from known one-, two- and three-loop conformal integrals. These results are useful for checking recent integrability predictions for the OPE structure constants.

Two-Loop Splitting Amplitudes

International Nuclear Information System (INIS)

Bern, Z.

2004-01-01

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes

Two-loop splitting amplitudes

International Nuclear Information System (INIS)

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

2004-01-01

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes

One-loop triple collinear splitting amplitudes in QCD

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon; Buciuni, Francesco; Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)

2015-09-28

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.

Algebraic evaluation of rational polynomials in one-loop amplitudes

International Nuclear Information System (INIS)

Binoth, Thomas; Guillet, Jean-Philippe; Heinrich, Gudrun

2007-01-01

One-loop amplitudes are to a large extent determined by their unitarity cuts in four dimensions. We show that the remaining rational terms can be obtained from the ultraviolet behaviour of the amplitude, and determine universal form factors for these rational parts by applying reduction techniques to the Feynman diagrammatic representation of the amplitude. The method is valid for massless and massive internal particles. We illustrate this method by evaluating the rational terms of the one-loop amplitudes for gg→H, γγ→γγ, gg→gg,γγ→ggg and γγ→γγγγ

Conformal Behavior at Four Loops and Scheme (In)Dependence

DEFF Research Database (Denmark)

Ryttov, Thomas

2014-01-01

We search for infrared zeros of the beta function and evaluate the anomalous dimension of the mass at the associated fixed point for asymptotically free vector-like fermionic gauge theories with gauge group SU(N). The fixed points of the beta function are studied at the two, three and four loop l...... by the minimum and maximum value respectively over all three schemes and at three and four loops. Our analysis suggests that the former two theories lie in the conformal window while the latter belongs to the chirally broken phase....

Monodromy relations in higher-loop string amplitudes

Directory of Open Access Journals (Sweden)

S. Hohenegger

2017-12-01

Full Text Available New monodromy relations of loop amplitudes are derived in open string theory. We particularly study N-point (planar and non-planar one-loop amplitudes described by a world-sheet cylinder and derive a set of relations between subamplitudes of different color orderings. Various consistency checks are performed by matching α′-expansions of planar and non-planar amplitudes involving elliptic iterated integrals with the resulting periods giving rise to two sets of multiple elliptic zeta values. The latter refer to the two homology cycles on the once-punctured complex elliptic curve and the monodromy equations provide relations between these two sets of multiple elliptic zeta values. Furthermore, our monodromy relations involve new objects for which we present a tentative interpretation in terms of open string scattering amplitudes in the presence of a non-trivial gauge field flux. Finally, we provide an outlook on how to generalize the new monodromy relations to the non-oriented case and beyond the one-loop level. Comparing a subset of our results with recent findings in the literature we find therein several serious issues related to the structure and significance of monodromy phases and the relevance of missed contributions from contour integrations.

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

International Nuclear Information System (INIS)

Brandt, F.T.C.

1986-01-01

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

New BCJ representations for one-loop amplitudes in gauge theories and gravity

Science.gov (United States)

He, Song; Schlotterer, Oliver; Zhang, Yong

2018-05-01

We explain a procedure to manifest the Bern-Carrasco-Johansson duality between color and kinematics in n-point one-loop amplitudes of a variety of supersymmetric gauge theories. Explicit amplitude representations are constructed through a systematic reorganization of the integrands in the Cachazo-He-Yuan formalism. Our construction holds for any nonzero number of supersymmetries and does not depend on the number of spacetime dimensions. The cancellations from supersymmetry multiplets in the loop as well as the resulting power counting of loop momenta is manifested along the lines of the corresponding superstring computations. The setup is used to derive the one-loop version of the Kawai-Lewellen-Tye formula for the loop integrands of gravitational amplitudes.

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory

Energy Technology Data Exchange (ETDEWEB)

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence RI 02912 (United States)

2016-03-14

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory

International Nuclear Information System (INIS)

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia

2016-01-01

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

Two-Loop Gluon to Gluon-Gluon Splitting Amplitudes in QCD

International Nuclear Information System (INIS)

Bern, Z.

2004-01-01

Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g → 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 ε-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/ε pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula

Constructing QCD one-loop amplitudes

International Nuclear Information System (INIS)

Forde, D

2008-01-01

In the context of constructing one-loop amplitudes using a unitarity bootstrap approach we discuss a general systematic procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted after examining the behavior of the cut integrand as the unconstrained parameters of a specifically chosen parameterization of the cut loop momentum approach infinity. Measurements of new physics at the forthcoming experimental program at CERN's Large Hadron Collider (LHC) will require a precise understanding of processes at next-to-leading order (NLO). This places increased demands for the computation of new one-loop amplitudes. This in turn has spurred recent developments towards improved calculational techniques. Direct calculations using Feynman diagrams are in general inefficient. Developments of more efficient techniques have usually centered around unitarity techniques [1], where tree amplitudes are effectively 'glued' together to form loops. The most straightforward application of this method, in which the cut loop momentum is in D = 4, allows for the computation of 'cut-constructible' terms only, i.e. (poly)logarithmic containing terms and any related constants. QCD amplitudes contain, in addition to such terms, rational pieces which cannot be derived using such cuts. These 'missing' rational parts can be extracted using cut loop momenta in D = 4-2 (var e psilon). The greater difficulty of such calculations has restricted the application of this approach, although recent developments [3, 4] have provided new promise for this technique. Recently the application of on-shell recursion relations [5] to obtaining the 'missing' rational parts of one-loop processes [6] has provided an alternative very promising solution to this problem. In combination with unitarity methods an 'on-shell bootstrap' approach provides an efficient technique for computing complete one-loop QCD amplitudes [7]. Additionally

One-Loop BPS amplitudes as BPS-state sums

CERN Document Server

Angelantonj, Carlo; Pioline, Boris

2012-01-01

Recently, we introduced a new procedure for computing a class of one-loop BPS-saturated amplitudes in String Theory, which expresses them as a sum of one-loop contributions of all perturbative BPS states in a manifestly T-duality invariant fashion. In this paper, we extend this procedure to all BPS-saturated amplitudes of the form \\int_F \\Gamma_{d+k,d} {\\Phi}, with {\\Phi} being a weak (almost) holomorphic modular form of weight -k/2. We use the fact that any such {\\Phi} can be expressed as a linear combination of certain absolutely convergent Poincar\\'e series, against which the fundamental domain F can be unfolded. The resulting BPS-state sum neatly exhibits the singularities of the amplitude at points of gauge symmetry enhancement, in a chamber-independent fashion. We illustrate our method with concrete examples of interest in heterotic string compactifications.

Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts

Energy Technology Data Exchange (ETDEWEB)

Dixon, Lance

2002-03-08

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for ''observed'' particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg {yields} gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard {bar M}{bar S} coupling, {alpha}{sub s}. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD {beta} function in the FDH and dimensional reduction schemes.

Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts

International Nuclear Information System (INIS)

Dixon, Lance

2002-01-01

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for ''observed'' particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg → gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard MS coupling, α s . The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD β function in the FDH and dimensional reduction schemes

Reducing full one-loop amplitudes to scalar integrals at the integrand level

Science.gov (United States)

Ossola, Giovanni; Papadopoulos, Costas G.; Pittau, Roberto

2007-02-01

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation.

Reducing full one-loop amplitudes to scalar integrals at the integrand level

International Nuclear Information System (INIS)

Ossola, Giovanni; Papadopoulos, Costas G.; Pittau, Roberto

2007-01-01

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation

From maximal to minimal supersymmetry in string loop amplitudes

Energy Technology Data Exchange (ETDEWEB)

Berg, Marcus; Buchberger, Igor [Department of Physics, Karlstad University,651 88 Karlstad (Sweden); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,14476 Potsdam (Germany)

2017-04-28

We calculate one-loop string amplitudes of open and closed strings with N=1,2,4 supersymmetry in four and six dimensions, by compactification on Calabi-Yau and K3 orbifolds. In particular, we develop a method to combine contributions from all spin structures for arbitrary number of legs at minimal supersymmetry. Each amplitude is cast into a compact form by reorganizing the kinematic building blocks and casting the worldsheet integrals in a basis. Infrared regularization plays an important role to exhibit the expected factorization limits. We comment on implications for the one-loop string effective action.

Full colour for loop amplitudes in Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Ochirov, Alexander [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Page, Ben [Albert-Ludwigs-Universität Freiburg, Physikalisches Institut,D-79104 Freiburg (Germany)

2017-02-20

We present a general method to account for full colour dependence Yang-Mills amplitudes at loop level. The method fits most naturally into the framework of multi-loop integrand reduction and in a nutshell amounts to consistently retaining the colour structures of the unitarity cuts from which the integrand is gradually constructed. This technique has already been used in the recent calculation of the two-loop five-gluon amplitude in pure Yang-Mills theory with all positive helicities, (DOI: 10.1007/JHEP10(2015)064). In this note, we give a careful exposition of the method and discuss its connection to loop-level Kleiss-Kuijf relations. We also explore its implications for cancellation of nontrivial symmetry factors at two loops. As an example of its generality, we show how it applies to the three-loop case in supersymmetric Yang-Mills case.

Automation of loop amplitudes in numerical approach

International Nuclear Information System (INIS)

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

1997-01-01

An automatic calculating system GRACE-L1 of one-loop Feynman amplitude is reviewed. This system can be applied to 2 to 2-body one-loop processes. A sample calculation of 2 to 3-body one-loop amplitudes is also presented. (orig.)

Three-loop corrections to the soft anomalous dimension in multileg scattering

CERN Document Server

Almelid, Øyvind; Gardi, Einan

2016-01-01

We present the three-loop result for the soft anomalous dimension governing long-distance singularities of multi-leg gauge-theory scattering amplitudes of massless partons. We compute all contributing webs involving semi-infinite Wilson lines at three loops and obtain the complete three-loop correction to the dipole formula. We find that non-dipole corrections appear already for three coloured partons, where the correction is a constant without kinematic dependence. Kinematic dependence appears only through conformally-invariant cross ratios for four coloured partons or more, and the result can be expressed in terms of single-valued harmonic polylogarithms of weight five. While the non-dipole three-loop term does not vanish in two-particle collinear limits, its contribution to the splitting amplitude anomalous dimension reduces to a constant, and it only depends on the colour charges of the collinear pair, thereby preserving strict collinear factorization properties. Finally we verify that our result is consi...

Numerical evaluation of one-loop QCD amplitudes

DEFF Research Database (Denmark)

Badger, Simon David; Biedermann, Benedikt; Uwer, Peter

2012-01-01

We present the publicly available program NGluon allowing the numerical evaluation of primitive amplitudes at one-loop order in massless QCD. The program allows the computation of one-loop amplitudes for an arbitrary number of gluons. The focus of the present article is the extension to one-loop ...

The four-loop six-gluon NMHV ratio function

Energy Technology Data Exchange (ETDEWEB)

Dixon, Lance J. [SLAC National Accelerator Lab., Stanford, CA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States); von Hippel, Matt [Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); McLeod, Andrew J. [SLAC National Accelerator Lab., Stanford, CA (United States)

2016-01-11

We use the hexagon function bootstrap to compute the ratio function which characterizes the next-to-maximally-helicity-violating (NMHV) six-point amplitude in planar N = 4 super-Yang-Mills theory at four loops. A powerful constraint comes from dual superconformal invariance, in the form of a Q^- differential equation, which heavily constrains the first derivatives of the transcendental functions entering the ratio function. At four loops, it leaves only a 34-parameter space of functions. Constraints from the collinear limits, and from the multi-Regge limit at the leading-logarithmic (LL) and next-to-leading-logarithmic (NLL) order, suffice to fix these parameters and obtain a unique result. We test the result against multi- Regge predictions at NNLL and N³LL, and against predictions from the operator product expansion involving one and two flux-tube excitations; all cross-checks are satisfied. We also study the analytical and numerical behavior of the parity-even and parity-odd parts on various lines and surfaces traversing the three-dimensional space of cross ratios. As part of this program, we characterize all irreducible hexagon functions through weight eight in terms of their coproduct. Furthermore, we provide representations of the ratio function in particular kinematic regions in terms of multiple polylogarithms.

The four-loop six-gluon NMHV ratio function

Energy Technology Data Exchange (ETDEWEB)

Dixon, Lance J. [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Hippel, Matt von [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada); McLeod, Andrew J. [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States)

2016-01-11

We use the hexagon function bootstrap to compute the ratio function which characterizes the next-to-maximally-helicity-violating (NMHV) six-point amplitude in planar N=4 super-Yang-Mills theory at four loops. A powerful constraint comes from dual superconformal invariance, in the form of a Q̄ differential equation, which heavily constrains the first derivatives of the transcendental functions entering the ratio function. At four loops, it leaves only a 34-parameter space of functions. Constraints from the collinear limits, and from the multi-Regge limit at the leading-logarithmic (LL) and next-to-leading-logarithmic (NLL) order, suffice to fix these parameters and obtain a unique result. We test the result against multi-Regge predictions at NNLL and N{sup 3}LL, and against predictions from the operator product expansion involving one and two flux-tube excitations; all cross-checks are satisfied. We study the analytical and numerical behavior of the parity-even and parity-odd parts on various lines and surfaces traversing the three-dimensional space of cross ratios. As part of this program, we characterize all irreducible hexagon functions through weight eight in terms of their coproduct. We also provide representations of the ratio function in particular kinematic regions in terms of multiple polylogarithms.

String-inspired BCJ numerators for one-loop MHV amplitudes

International Nuclear Information System (INIS)

He, Song; Monteiro, Ricardo; Schlotterer, Oliver

2016-01-01

We find simple expressions for the kinematic numerators of one-loop MHV amplitudes in maximally supersymmetric Yang-Mills theory and supergravity, at any multiplicity. The gauge-theory numerators satisfy the Bern-Carrasco-Johansson (BCJ) duality between color and kinematics, so that the gravity numerators are simply the square of the gauge-theory ones. The duality holds because the numerators can be written in terms of structure constants of a kinematic algebra, which is familiar from the BCJ organization of self-dual gauge theory and gravity. The close connection that we find between one-loop amplitudes in the self-dual case and in the maximally supersymmetric case is reminiscent of the dimension-shifting formula. The starting point for arriving at our expressions is the dimensional reduction of ten-dimensional amplitudes obtained in the field-theory limit of open superstrings.

Multi-parton loop amplitudes and next-to-leading order jet cross-sections

International Nuclear Information System (INIS)

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

1998-02-01

The authors review recent developments in the calculation of QCD loop amplitudes with several external legs, and their application to next-to-leading order jet production cross-sections. When a number of calculational tools are combined together--helicity, color and supersymmetry decompositions, plus unitarity and factorization properties--it becomes possible to compute multi-parton one-loop QCD amplitudes without ever evaluating analytically standard one-loop Feynman diagrams. One-loop helicity amplitudes are now available for processes with five external partons (ggggg, q anti qggg and q anti qq anti q' g), and for an intermediate vector boson V ≡ γ * , Z, W plus four external partons (V q anti q and V q anti qq'anti q'). Using these amplitudes, numerical programs have been constructed for the next-to-leading order corrections to the processes p anti p → 3 jets (ignoring quark contributions so far) and e + e - → 4 jets

The five-gluon amplitude and one-loop integrals

International Nuclear Information System (INIS)

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

1992-12-01

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

Non-supersymmetric loop amplitudes and MHV vertices

International Nuclear Information System (INIS)

Bedford, James; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele

2005-01-01

We show how the MHV diagram description of Yang-Mills theories can be used to study non-supersymmetric loop amplitudes. In particular, we derive a compact expression for the cut-constructible part of the general one-loop MHV multi-gluon scattering amplitude in pure Yang-Mills theory. We show that in special cases this expression reduces to known amplitudes-the amplitude with adjacent negative-helicity gluons, and the five gluon non-adjacent amplitude. Finally, we briefly discuss the twistor space interpretation of our result

Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki; Ito, Katsushi; Satoh, Yuji; Suzuki, Junji

2014-06-01

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.

The Euclidean three-point function in loop and perturbative gravity

International Nuclear Information System (INIS)

Rovelli, Carlo; Zhang Mingyi

2011-01-01

We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of γ < 1. We find results consistent with Regge calculus in the limit γ → 0, j → ∞. We also compute the tree-level three-point function of perturbative quantum general relativity in position space and discuss the possibility of directly comparing the two results.

On soft singularities at three loops and beyond

CERN Document Server

Dixon, Lance J; Magnea, Lorenzo

2010-01-01

We report on further progress in understanding soft singularities of massless gauge theory scattering amplitudes. Recently, a set of equations was derived based on Sudakov factorization, constraining the soft anomalous dimension matrix of multi-leg scattering amplitudes to any loop order, and relating it to the cusp anomalous dimension. The minimal solution to these equations was shown to be a sum over color dipoles. Here we explore potential contributions to the soft anomalous dimension that go beyond the sum-over-dipoles formula. Such contributions are constrained by factorization and invariance under rescaling of parton momenta to be functions of conformally invariant cross ratios. Therefore, they must correlate the color and kinematic degrees of freedom of at least four hard partons, corresponding to gluon webs that connect four eikonal lines, which first appear at three loops. We analyze potential contributions, combining all available constraints, including Bose symmetry, the expected degree of transcen...

Iterative structure within the five-particle two-loop amplitude

International Nuclear Information System (INIS)

Cachazo, Freddy; Spradlin, Marcus; Volovich, Anastasia

2006-01-01

We find an unexpected iterative structure within the two-loop five-gluon amplitude in N=4 supersymmetric Yang-Mills theory. Specifically, we show that a subset of diagrams contributing to the full amplitude, including a two-loop pentagon-box integral with nontrivial dependence on five kinematical variables, satisfies an iterative relation in terms of one-loop scalar box diagrams. The implications of this result for the possible iterative structure of the full two-loop amplitude are discussed

Singularities in four-body final-state amplitudes

International Nuclear Information System (INIS)

Adhikari, S.K.

1978-01-01

Like three-body amplitudes, four-body amplitudes have subenergy threshold singularities over and above total-energy singularities. In the four-body problem we encounter a new type of subenergy singularity besides the usual two- and three-body subenergy threshold singularities. This singularity will be referred to as ''independent-pair threshold singularity'' and involves pair-subenergy threshold singularities in each of the two independent pair subenergies in four-body final states. We also study the particularly interesting case of resonant two- and three-body interactions in the four-body isobar model and the rapid (singular) dependence of the isobar amplitudes they generate in the four-body phase space. All these singularities are analyzed in the multiple-scattering formalism and it is shown that they arise from the ''next-to-last'' rescattering and hence may be represented correctly by an approximate amplitude which has that rescattering

Global structure of curves from generalized unitarity cut of three-loop diagrams

International Nuclear Information System (INIS)

Hauenstein, Jonathan D.; Huang, Rijun; Mehta, Dhagash; Zhang, Yang

2015-01-01

This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus of the algebraic curve. We use the Riemann-Hurwitz formula to compute the geometric genus of algebraic curves with the help of techniques involving convex hull polytopes and numerical algebraic geometry. Some interesting properties of genus for arbitrary loop orders are also explored where computing the genus serves as an initial step for integral or integrand reduction of three-loop amplitudes via an algebraic geometric approach.

On the loop-loop scattering amplitudes in Abelian and non-Abelian gauge theories

International Nuclear Information System (INIS)

Meggiolaro, Enrico

2005-01-01

The high-energy elastic scattering amplitude of two colour-singlet qq-bar pairs is governed by the correlation function of two Wilson loops, which follow the classical straight lines for quark (antiquark) trajectories. This quantity is expected to be free of IR divergences, differently from what happens for the parton-parton elastic scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR finiteness by a direct non-perturbative computation of the loop-loop scattering amplitudes in the (pedagogic, but surely physically interesting) case of quenched QED. The results obtained for the Abelian case will be generalized to the case of a non-Abelian gauge theory with Nc colours, but stopping to the order O(g4) in perturbation theory. In connection with the above-mentioned IR finiteness, we shall also discuss some analytic properties of the loop-loop scattering amplitudes in both Abelian and non-Abelian gauge theories, when going from Minkowskian to Euclidean theory, which can be relevant to the still unsolved problem of the s-dependence of hadron-hadron total cross-sections

Three- and two-point one-loop integrals in heavy particle effective theories

International Nuclear Information System (INIS)

Bouzas, A.O.

2000-01-01

We give a complete analytical computation of three- and two-point loop integrals occurring in heavy particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta. (orig.)

On-shell recurrence relations for one-loop QCD amplitudes

International Nuclear Information System (INIS)

Bern, Zvi; Dixon, Lance J.; Kosower, David A.

2005-01-01

We present examples of on-shell recurrence relations for determining rational functions appearing in one-loop QCD amplitudes. In particular, we give relations for one-loop QCD amplitudes with all legs of positive helicity, or with one leg of negative helicity and the rest of positive helicity. Our recurrence relations are similar to the tree-level ones described by Britto, Cachazo, Feng, and Witten. A number of new features arise for loop amplitudes in nonsupersymmetric theories like QCD, including boundary terms and double poles. We show how to eliminate the boundary terms, which would interfere with obtaining useful relations. Using the relations we give compact explicit expressions for the n-gluon amplitudes with one negative-helicity gluon, up through n=7

Topics in Nonsupersymmetric Scattering Amplitudes in Gauge and Gravity Theories

Science.gov (United States)

Nohle, Joshua David

In Chapters 1 and 2, we introduce and review the duality between color and kinematics in Yang-Mills theory uncovered by Bern, Carrasco and Johansson (BCJ). In Chapter 3, we provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions. In Chapter 4, we extend the four-point one-loop nonsupersymmetric pure Yang-Mills discussion of Chapter 3 to include fermions and scalars circulating in the loop with all external gluons. This gives another nontrivial loop-level example showing that the duality between color and kinematics holds in nonsupersymmetric gauge theory. The construction is valid in any spacetime dimension and written in terms of formal polarization vectors. We also convert these expressions into a four-dimensional form with explicit external helicity states. Using this, we compare our results to one-loop duality-satisfying amplitudes that are already present in literature. In Chapter 5, we switch from the topic of color-kinematics duality to discuss the recently renewed interest in the soft behavior of gravitons and gluons. Specifically, we discuss the subleading low-energy behavior. Cachazo and Strominger recently proposed an extension of the soft-graviton theorem found by Weinberg. In addition, they proved the validity of their extension at

Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity

OpenAIRE

Brandhuber, Andreas; McNamara, Simon; Spence, Bill; Travaglini, Gabriele

2005-01-01

We show how generalised unitarity cuts in D = 4 - 2 epsilon dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.

Loop amplitudes in pure Yang-Mills from generalised unitarity

International Nuclear Information System (INIS)

Brandhuber, Andreas; McNamara, Simon; Spence, Bill; Travaglini, Gabriele

2005-01-01

We show how generalised unitarity cuts in D = 4-2ε dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions

Loop amplitudes in pure Yang-Mills from generalised unitarity

Energy Technology Data Exchange (ETDEWEB)

Brandhuber, Andreas [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); McNamara, Simon [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); Spence, Bill [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); Travaglini, Gabriele [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom)

2005-10-15

We show how generalised unitarity cuts in D = 4-2{epsilon} dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.

The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory

Science.gov (United States)

Litsey, Sean Christopher

form, and can. be decomposed into a pure integrand basis, with each basis element having unit leading. singularity. Through explicit calculation, we show that this is true for the two-loop fourpoint, three-loop four-point, and two-loop five-point amplitudes, and discuss the features of. each case. We then discuss the zero condition hypothesis, showing explicitly that it holds for the two-loop four-particle amplitude, and showing the set of conditions that fix the amplitude in the three-loop four-particle and two-loop five-particle cases without explicitly performing the fixing. This concludes the body of the dissertation. Two appendices complete the dissertation. Appendix B includes an in-depth discussion of. dlog forms, including purely mathematical examples and a discussion of their appearance in one-loop amplitudes. Finally, Appendix C redoes portions of the analysis of Chapter 3 for the two- and three-loop four-particle amplitudes, but gives representations that are not in a pure integrand basis. Instead diagram symmetry is imposed on the basis elements, and diagrams that lack maximal cuts are pushed into maximal-cut diagrams. This gives representations closer in spirit to the previously-constructed representations of these amplitudes, such as the BCJ representations. It also highlights the role of color Jacobi identities and the freedom in the amplitude representation they can generate, and contains an explicit discussion of these features that is unpublished elsewhere.

Universal dual amplitudes and asymptotic expansions for gg→ H and H→ γ γ in four dimensions

Science.gov (United States)

Driencourt-Mangin, Félix; Rodrigo, Germán; Sborlini, Germán F. R.

2018-03-01

Though the one-loop amplitudes of the Higgs boson to massless gauge bosons are finite because there is no direct interaction at tree level in the Standard Model, a well-defined regularization scheme is still required for their correct evaluation. We reanalyze these amplitudes in the framework of the four-dimensional unsubtraction and the loop-tree duality (FDU/LTD), and show how a local renormalization solves potential regularization ambiguities. The Higgs boson interactions are also used to illustrate new additional advantages of this formalism. We show that LTD naturally leads to very compact integrand expressions in four space-time dimensions of the one-loop amplitude with virtual electroweak gauge bosons. They exhibit the same functional form as the amplitudes with top quarks and charged scalars, thus opening further possibilities for simplifications in higher-order computations. Another outstanding application is the straightforward implementation of asymptotic expansions by using dual amplitudes. One of the main benefits of the LTD representation is that it is supported in a Euclidean space. This characteristic feature naturally leads to simpler asymptotic expansions.

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.

Calculation and modular properties of multi-loop superstring amplitudes

International Nuclear Information System (INIS)

Danilov, G S

2012-01-01

Multi-loop superstring amplitude is calculated in the conventional gauge where Grassmann moduli are carried by the 2D gravitino field. Generally, instead of the modular symmetry, the amplitudes hold the symmetry under modular transformations added by relevant transformations of the 2D local supersymmetry. If a number of loops are larger than 3, the integration measures are not modular forms. In this case the expression for the amplitude contains an integral over the bound of the fundamental region of the modular group. (paper)

New relations for gauge-theory amplitudes

International Nuclear Information System (INIS)

Bern, Z.; Carrasco, J. J. M.; Johansson, H.

2008-01-01

We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.

New relations for graviton-matter amplitudes

CERN Multimedia

CERN. Geneva

2018-01-01

I report on recent progress in finding compact expressions for scattering amplitudes involving gravitons and gluons as well as massive scalar and fermionic matter particles. At tree level the single graviton emission amplitudes may be expressed as linear combination of purely non-gravitational ones. At the one-loop level recent results on all four point Einstein-Yang-Mills amplitudes with at most one opposite helicity state using unitarity methods are reported. 

Unitarity cuts and Reduction to master integrals in d dimensions for one-loop amplitudes

CERN Document Server

Anastasiou, C; Feng, B; Kunszt, Z; Mastrolia, Pierpaolo; Anastasiou, Charalampos; Britto, Ruth; Feng, Bo; Kunszt, Zoltan; Mastrolia, Pierpaolo

2007-01-01

We present an alternative reduction to master integrals for one-loop amplitudes using a unitarity cut method in arbitrary dimensions. We carry out the reduction in two steps. The first step is a pure four-dimensional cut-integration of tree amplitudes with a mass parameter, and the second step is applying dimensional shift identities to master integrals. This reduction is performed at the integrand level, so that coefficients can be read out algebraically.

Four point functions in the SL(2,R) WZW model

Energy Technology Data Exchange (ETDEWEB)

Minces, Pablo [Instituto de Astronomia y Fisica del Espacio (IAFE), C.C. 67 Suc. 28, 1428 Buenos Aires (Argentina)]. E-mail: minces@iafe.uba.ar; Nunez, Carmen [Instituto de Astronomia y Fisica del Espacio (IAFE), C.C. 67 Suc. 28, 1428 Buenos Aires (Argentina) and Physics Department, University of Buenos Aires, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)]. E-mail: carmen@iafe.uba.ar

2007-04-19

We consider winding conserving four point functions in the SL(2,R) WZW model for states in arbitrary spectral flow sectors. We compute the leading order contribution to the expansion of the amplitudes in powers of the cross ratio of the four points on the worldsheet, both in the m- and x-basis, with at least one state in the spectral flow image of the highest weight discrete representation. We also perform certain consistency check on the winding conserving three point functions.

Four point functions in the SL(2,R) WZW model

International Nuclear Information System (INIS)

Minces, Pablo; Nunez, Carmen

2007-01-01

We consider winding conserving four point functions in the SL(2,R) WZW model for states in arbitrary spectral flow sectors. We compute the leading order contribution to the expansion of the amplitudes in powers of the cross ratio of the four points on the worldsheet, both in the m- and x-basis, with at least one state in the spectral flow image of the highest weight discrete representation. We also perform certain consistency check on the winding conserving three point functions

Four-loop collinear anomalous dimension in N=4 Yang-Mills theory

International Nuclear Information System (INIS)

Cachazo, Freddy; Spradlin, Marcus; Volovich, Anastasia

2007-01-01

We report a calculation in N=4 Yang-Mills of the four-loop term g (4) in the collinear anomalous dimension g(λ) which governs the universal subleading infrared structure of gluon scattering amplitudes. Using the method of obstructions to extract this quantity from the 1/ε singularity in the four-gluon iterative relation at four loops, we find g (4) =-1240.9 with an estimated numerical uncertainty of 0.02%. We also analyze the implication of our result for the strong coupling behavior of g(λ), finding support for the string theory prediction computed recently by Alday and Maldacena using AdS/CFT

Two-loop polygon Wilson loops in N = 4 SYM

International Nuclear Information System (INIS)

Anastasiou, C.; Brandhuber, A.; Heslop, P.; Spence, B.; Travaglini, G.; Khoze, V.V.

2009-01-01

We compute for the first time the two-loop corrections to arbitrary n-gon lightlike Wilson loops in N = 4 supersymmetric Yang-Mills theory, using efficient numerical methods. The calculation is motivated by the remarkable agreement between the finite part of planar six-point MHV amplitudes and hexagon Wilson loops which has been observed at two loops. At n = 6 we confirm that the ABDK/BDS ansatz must be corrected by adding a remainder function, which depends only on conformally invariant ratios of kinematic variables. We numerically compute remainder functions for n = 7,8 and verify dual conformal invariance. Furthermore, we study simple and multiple collinear limits of the Wilson loop remainder functions and demonstrate that they have precisely the form required by the collinear factorisation of the corresponding two-loop n-point amplitudes. The number of distinct diagram topologies contributing to the n-gon Wilson loops does not increase with n, and there is a fixed number of 'master integrals', which we have computed. Thus we have essentially computed general polygon Wilson loops, and if the correspondence with amplitudes continues to hold, all planar n-point two-loop MHV amplitudes in the N = 4 theory.

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

Energy Technology Data Exchange (ETDEWEB)

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

2006-05-15

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

NGluon. A package to calculate one-loop multi-gluon amplitudes

Energy Technology Data Exchange (ETDEWEB)

Badger, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Niels Bohr Institute, Copenhagen (Denmark). Niels Bohr International Academy and Discovery Center; Biedermann, B.; Uwer, P. [Humboldt Univ., Berlin (Germany). Inst. fuer Physik

2010-11-15

We present a computer library for the numerical evaluation of colour-ordered n-gluon amplitudes at one-loop order in pure Yang-Mills theory. The library uses the recently developed technique of generalised unitarity. Running in double precision the library yields reliable results for up to 14 gluons with only a small fraction of events requiring a re-evaluation using extended floating point arithmetic. We believe that the library presented here provides an important contribution to future LHC phenomenology. The program may also prove useful in cross checking results obtained by other methods. In addition, the code provides a sample implementation which may serve as a starting point for further developments. (orig.)

NGluon. A package to calculate one-loop multi-gluon amplitudes

International Nuclear Information System (INIS)

Badger, S.; Niels Bohr Institute, Copenhagen; Biedermann, B.; Uwer, P.

2010-11-01

We present a computer library for the numerical evaluation of colour-ordered n-gluon amplitudes at one-loop order in pure Yang-Mills theory. The library uses the recently developed technique of generalised unitarity. Running in double precision the library yields reliable results for up to 14 gluons with only a small fraction of events requiring a re-evaluation using extended floating point arithmetic. We believe that the library presented here provides an important contribution to future LHC phenomenology. The program may also prove useful in cross checking results obtained by other methods. In addition, the code provides a sample implementation which may serve as a starting point for further developments. (orig.)

One-loop QCD and Higgs bosons to partons processes using six-dimensional helicity and generalized unitarity

International Nuclear Information System (INIS)

Davies, Scott

2011-01-01

We combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a new formalism for computing one-loop amplitudes in dimensionally regularized QCD. With this procedure, we simultaneously obtain the pieces that are constructible from four-dimensional unitarity cuts and the rational pieces that are missed by them, while retaining a helicity formalism. We illustrate the procedure using four- and five-point one-loop amplitudes in QCD, including examples with external fermions. We also demonstrate the technique's effectiveness in next-to-leading order QCD corrections to Higgs processes by computing the next-to-leading order correction to the Higgs plus three positive-helicity gluons amplitude in the large top-quark mass limit.

FMFT. Fully massive four-loop tadpoles

Energy Technology Data Exchange (ETDEWEB)

Pikelner, Andrey [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2017-07-15

We present FMFT - a package written in FORM that evaluates four-loop fully massive tadpole Feynman diagrams. It is a successor of the MATAD package that has been successfully used to calculate many renormalization group functions at three-loop order in a wide range of quantum field theories especially in the Standard Model. We describe an internal structure of the package and provide some examples of its usage.

FMFT: fully massive four-loop tadpoles

Science.gov (United States)

Pikelner, Andrey

2018-03-01

We present FMFT - a package written in FORM that evaluates four-loop fully massive tadpole Feynman diagrams. It is a successor of the MATAD package that has been successfully used to calculate many renormalization group functions at three-loop order in a wide range of quantum field theories especially in the Standard Model. We describe an internal structure of the package and provide some examples of its usage.

Loop expansion in massless three-dimensional QED

International Nuclear Information System (INIS)

Guendelman, E.I.; Radulovic, Z.M.

1983-01-01

It is shown how the loop expansion in massless three-dimensional QED can be made finite, up to three loops, by absorbing the infrared divergences in a gauge-fixing term. The same method removes leading and first subleading singularities to all orders of perturbation theory, and all singularities of the fermion self-energy to four loops

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

International Nuclear Information System (INIS)

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

2004-01-01

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

The rational parts of one-loop QCD amplitudes I: The general formalism

International Nuclear Information System (INIS)

Xiao Zhiguang; Yang Gang; Zhu Chuanjie

2006-01-01

A general formalism for computing only the rational parts of one-loop QCD amplitudes is developed. Starting from the Feynman integral representation of the one-loop amplitude, we use tensor reduction and recursive relations to compute the rational parts directly. Explicit formulas for the rational parts are given for all bubble and triangle integrals. Formulas are also given for box integrals up to two-mass-hard boxes which are the needed ingredients to compute up to 6-gluon QCD amplitudes. We use this method to compute explicitly the rational parts of the 5- and 6-gluon QCD amplitudes in two accompanying papers

The low energy expansion of the one-loop type II superstring amplitude

CERN Document Server

Green, Michael B.; Green, Michael B.; Vanhove, Pierre

2000-01-01

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.

Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

CERN Document Server

Anastasiou, C; Bucherer, S; Daleo, A; Kunszt, Zoltán; Anastasiou, Charalampos; Beerli, Stefan; Bucherer, Stefan; Daleo, Alejandro; Kunszt, Zoltan

2007-01-01

We compute all two-loop master integrals which are required for the evaluation of next-to-leading order QCD corrections in Higgs boson production via gluon fusion. Many two-loop amplitudes for 2 -> 1 processes in the Standard Model and beyond can be expressed in terms of these integrals using automated reduction techniques. These integrals also form a subset of the master integrals for more complicated 2 -> 2 amplitudes with massive propagators in the loops. As a first application, we evaluate the two-loop amplitude for Higgs boson production in gluon fusion via a massive quark. Our result is the first independent check of the calculation of Spira, Djouadi, Graudenz and Zerwas. We also present for the first time the two-loop amplitude for gg -> h via a massive squark.

Equivalent D = 3 supergravity amplitudes from double copies of three-algebra and two-algebra gauge theories.

Science.gov (United States)

Huang, Yu-tin; Johansson, Henrik

2013-04-26

We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.

Explicit formulas for the one-, two-, three-, and four-loop string amplitudes in the critical dimension

International Nuclear Information System (INIS)

Morozov, A.Y.

1987-01-01

The explicit formulas of Belavin et al. [JETP Lett. 43, 411 (1986); Phys. Lett. 168B, 201 (1986); Sov. Phys. JETP 64, 214 (1986)] for the string loop diagrams in the first-quantized string theory are compiled

Scattering amplitudes in four- and six-dimensional gauge theories

International Nuclear Information System (INIS)

Schuster, Theodor

2014-01-01

We study scattering amplitudes in quantum chromodynamics (QCD), N=4 super Yang-Mills (SYM) theory and the six-dimensional N=(1,1) SYM theory, focusing on the symmetries of and relations between the tree-level scattering amplitudes in these three gauge theories. We derive the tree level and one-loop color decomposition of an arbitrary QCD amplitude into primitive amplitudes. Furthermore, we derive identities spanning the null space among the primitive amplitudes. We prove that every color ordered tree amplitude of massless QCD can be obtained from gluon-gluino amplitudes of N=4 SYM theory. Furthermore, we derive analytical formulae for all gluon-gluino amplitudes relevant for QCD. We compare the numerical efficiency and accuracy of evaluating these closed analytic formulae for color ordered QCD tree amplitudes to a numerically efficient implementation of the Berends-Giele recursion. We derive the symmetries of massive tree amplitudes on the coulomb branch of N=4 SYM theory, which in turn can be obtained from N=(1,1) SYM theory by dimensional reduction. Furthermore, we investigate the tree amplitudes of N=(1, 1) SYM theory and explain how analytical formulae can be obtained from a numerical implementation of the supersymmetric BCFW recursion relation and investigate a potential uplift of the massless tree amplitudes of N=4 SYM theory. Finally we study an alternative to dimensional regularization of N=4 SYM theory. The infrared divergences are regulated by masses obtained from a Higgs mechanism. The corresponding string theory set-up suggests that the amplitudes have an exact dual conformal symmetry. We confirm this expectation and illustrate the calculational advantages of the massive regulator by explicit calculations.

Long-distance singularities in multi-leg scattering amplitudes

CERN Document Server

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.

Unitarity relations for the four-body scattering amplitude

International Nuclear Information System (INIS)

Matsui, Y.

1988-01-01

A formal derivation of the general unitarity relation for the four-particle transition operator is given by generalizing the three-body formalism of Karlson and Zeiger to the four-body case. From this operator relation the on-shell unitarity relations for the amplitudes that describe elastic/rearrangement, partial breakup, and full breakup scattering processes are obtained

Analytic results for the one loop NMHV H anti qqgg amplitude

International Nuclear Information System (INIS)

Badger, Simon; Campbell, John M.; Williams, Ciaran

2009-01-01

We compute the one-loop amplitude for a Higgs boson, a quark-antiquark pair and a pair of gluons of negative helicity, i.e. for the next-to-maximally helicity violating (NMHV) case, A(H, 1 - anti q , 2 + q , 3 - g , 4 - g ). The calculation is performed using an effective Lagrangian which is valid in the limit of very large top quark mass. As a result of this paper all amplitudes for the transition of a Higgs boson into 4 partons are now known analytically at one-loop order. (orig.)

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...

Hidden beauty in multiloop amplitudes

International Nuclear Information System (INIS)

Cachazo, Freddy; Spradlin, Marcus; Volovich, Anastasia

2006-01-01

Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric Yang-Mills theory are believed to possess the remarkable property of satisfying iteration relations in L. We propose a simple new method for studying iteration relations for four-particle amplitudes which involves the use of certain linear differential operators and eliminates the need to fully evaluate any loop integrals. We carry out this procedure in explicit detail for the two-loop amplitude and prove that this method can be applied to any multiloop integral, allowing a conjectured iteration relation for any given amplitude to be tested up to polynomials in logarithms

Analytic results for the one loop NMHV H anti qqgg amplitude

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Campbell, John M. [Glasgow Univ. (United Kingdom). Dept. of Physics and Astronomy; Ellis, R. Keith [Fermilab, Batavia, IL (United States); Williams, Ciaran [Durham Univ. (United Kingdom). Dept. of Physics

2009-10-23

We compute the one-loop amplitude for a Higgs boson, a quark-antiquark pair and a pair of gluons of negative helicity, i.e. for the next-to-maximally helicity violating (NMHV) case, A(H, 1{sup -} {sub anti} {sub q}, 2{sup +}{sub q}, 3{sup -}{sub g}, 4{sup -}{sub g}). The calculation is performed using an effective Lagrangian which is valid in the limit of very large top quark mass. As a result of this paper all amplitudes for the transition of a Higgs boson into 4 partons are now known analytically at one-loop order. (orig.)

Characterization of double-loop four-Josephson-junction flux qubit

International Nuclear Information System (INIS)

Shimazu, Y.; Saito, Y.; Wada, Z.

2009-01-01

An advantage of a double-loop four-Josephson-junction (4-JJ) flux qubit is the tunability of the energy gap at a symmetry point, i.e., the point at which the double-well potential of the qubit is symmetric. The energy gap is controlled via the magnetic flux in a DC superconducting quantum interference device (DC-SQUID) loop incorporated in a 4-JJ qubit. We investigate the locus of the symmetry point in the plane of two control fluxes of the qubit, taking into account the asymmetry in the DC-SQUID, which is inevitable in practical cases. The observed positions of the qubit steps are in reasonable agreement with the calculated locus of the symmetry point. We estimate the asymmetry parameter of the DC-SQUID from this analysis.

Multi-leg one-loop gravity amplitudes from gauge theory

International Nuclear Information System (INIS)

Bern, Z.; Dixon, L.; Perelstein, M.; Rozowsky, J.S.

1999-01-01

By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the 'maximally helicity-violating' amplitudes in N = 8 supergravity, and the 'all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n ≤ 6, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found 'dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N = 4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n ≤ 6N = 8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations

The threshold expansion of the 2-loop sunrise self-mass master amplitudes

International Nuclear Information System (INIS)

Caffo, M.; Czyz, H.; Remiddi, E.

2001-01-01

The threshold behavior of the master amplitudes for two loop sunrise self-mass graph is studied by solving the system of differential equations, which they satisfy. The expansion at the threshold of the master amplitudes is obtained analytically for arbitrary masses

Colour decompositions of multi-quark one-loop QCD amplitudes

DEFF Research Database (Denmark)

Ita, Harald; Ozeren, Kemal

2012-01-01

We describe the decomposition of one-loop QCD amplitudes in terms of colour-ordered building blocks. We give new expressions for the coefficients of QCD colour structures in terms of ordered objects called primitive amplitudes, for processes with up to seven partons. These results are needed in c...... to the cross section for W+4-jet production at the Large Hadron Collider, and verify that it is very well approximated by keeping only the leading terms in an expansion around the formal limit of a large number of colours....

Loops in AdS from conformal field theory

Science.gov (United States)

Aharony, Ofer; Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric

2017-07-01

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1 /N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1 /N 2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of ϕ 4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the N = 4 super-Yang-Mills theory.

Electron contribution to the muon anomalous magnetic moment at four loops

International Nuclear Information System (INIS)

Kurz, Alexander; Liu, Tao; Smirnov, Alexander V.; Smirnov, Vladimir A.; Humboldt-Universitaet, Berlin; Humboldt-Universitaet, Berlin; Steinhauser, Matthias

2016-02-01

We present results for the QED contributions to the anomalous magnetic moment of the muon containing closed electron loops. The main focus is on perturbative corrections at four-loop order where the external photon couples to the external muon. Furthermore, all four-loop contributions involving simultaneously a closed electron and tau loop are computed. In combination with our recent results on the light-by-light-type corrections the complete four-loop electron-loop contribution to the anomalous magnetic moment of the muon has been obtained with an independent calculation. Our calculation is based on an asymptotic expansion in the ratio of the electron and the muon mass and shows the importance of higher order terms in this ratio. We perform a detailed comparison with results available in the literature and find good numerical agreement. As a by-product we present analytic results for the on-shell muon mass and wave function renormalization constants at three-loop order including massive closed electron and tau loops, which we also calculated using the method of asymptotic expansion.

Master integrals for the four-loop Sudakov form factor

International Nuclear Information System (INIS)

Boels, Rutger; Kniehl, Bernd A.; Yang, Gang; Chinese Academy of Sciences, Beijing

2015-08-01

The light-like cusp anomalous dimension is a universal function in the analysis of infrared divergences. In maximally (N=4) supersymmetric Yang-Mills theory (SYM) in the planar limit, it is known, in principle, to all loop orders. The non-planar corrections are not known in any theory, with the first appearing at the four-loop order. Probably the simplest quantity which contains this correction is the four-loop two-point form factor of the stress tensor multiplet. This form factor was obtained in integrand form in a previous work for N=4 SYM, up to a single parameter. In this work, a reduction of the appearing integrals obtained by solving integration-by-parts (IBP) identities using (a tweaked version of) Reduze is reported. The form factor is shown to be independent of the remaining parameter at integrand level due to an intricate pattern of cancellations after IBP reduction. The appearing master integrals are cross-checked using algebraic techniques explored in the Mint package. The latter results provide the basis of master integrals applicable to generic form factors, including those in Quantum Chromodynamics. Remaining bottlenecks to completing the computation of the four-loop non-planar cusp anomalous dimension in N=4 SYM and beyond are identified.

Automated evaluation of one-loop scattering amplitudes

International Nuclear Information System (INIS)

Deurzen, Hans van

2015-01-01

In this dissertation the developments toward fully automated evaluation of one-loop scattering amplitudes will be presented, as implemented in the GoSam framework. The code Xsamurai, part of GoSam, is described, which implements the integrand reduction algorithm including an extension to higher-rank capability. GoSam was used to compute several Higgs boson production channels at NLO QCD. An interface between GoSam and a Monte Carlo program was constructed, which enables computing any process at NLO precision needed in the LHC era.

Three-level grid-connected photovoltaic inverter with maximum power point tracking

International Nuclear Information System (INIS)

Tsang, K.M.; Chan, W.L.

2013-01-01

Highlight: ► This paper reports a novel 3-level grid connected photovoltaic inverter. ► The inverter features maximum power point tracking and grid current shaping. ► The inverter can be acted as an active filter and a renewable power source. - Abstract: This paper presents a systematic way of designing control scheme for a grid-connected photovoltaic (PV) inverter featuring maximum power point tracking (MPPT) and grid current shaping. Unlike conventional design, only four power switches are required to achieve three output levels and it is not necessary to use any phase-locked-loop circuitry. For the proposed scheme, a simple integral controller has been designed for the tracking of the maximum power point of a PV array based on an improved extremum seeking control method. For the grid-connected inverter, a current loop controller and a voltage loop controller have been designed. The current loop controller is designed to shape the inverter output current while the voltage loop controller can maintain the capacitor voltage at a certain level and provide a reference inverter output current for the PV inverter without affecting the maximum power point of the PV array. Experimental results are included to demonstrate the effectiveness of the tracking and control scheme.

The perturbative Regge-calculus regime of loop quantum gravity

International Nuclear Information System (INIS)

Bianchi, Eugenio; Modesto, Leonardo

2008-01-01

The relation between loop quantum gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of loop quantum gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two- and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed

Local integrands for two-loop all-plus Yang-Mills amplitudes

International Nuclear Information System (INIS)

Badger, Simon; Mogull, Gustav; Peraro, Tiziano

2016-01-01

We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4−2ϵ dimensions.

Local integrands for two-loop all-plus Yang-Mills amplitudes

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon; Mogull, Gustav; 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)

2016-08-09

We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4−2ϵ dimensions.

Involution-dependent constants and the cancellation of divergences in the 1-loop open string amplitude

International Nuclear Information System (INIS)

Nagao, G.

1987-12-01

We recalculate the bosonic 1-loop open string scattering amplitude using the results of the bosonic 1-loop closed string amplitude. The results show explicitly how the cancellation of divergences depends upon of a set of involution-dependent constants which relate the torus to the cylinder and Moebius strip. Such a set of involution-dependent constants exists at each loop level and thus provides a means with which to study the cancellation of divergences and the connection between the world-sheet and internal symmetries. 14 refs., 3 figs

The two loop superstring vacuum amplitude and canonical divisors

International Nuclear Information System (INIS)

Parkes, A.

1989-01-01

I use the prescription of placing the picture changing operators at the zeroes of some holomorphic one-form and calculate the two loop superstring vacuum amplitude in the language of theta functions. It vanishes pointwise on moduli space after the use of Fay's trisecant identity and generalised Riemann identities. I briefly discuss the higher genus case. (orig.)

Two-loop off-shell QCD amplitudes in FDR

CERN Document Server

Page, Ben

2015-01-01

We link the FDR treatment of ultraviolet (UV) divergences to dimensional regularization up to two loops in QCD. This allows us to derive the one-loop and two-loop coupling constant and quark mass shifts necessary to translate infrared finite quantities computed in FDR to the MSbar renormalization scheme. As a by-product of our analysis, we solve a problem analogous to the breakdown of unitarity in the Four Dimensional Helicity (FDH) method beyond one loop. A fix to FDH is then presented that preserves the renormalizability properties of QCD without introducing evanescent quantities.

Four-loop beta function in the Wess-Zumino model

International Nuclear Information System (INIS)

Avdeev, L.V.; Gorishny, S.G.

1982-01-01

A method for calculating momentum integrals, proposed by Chetyrkin and Tkachov, is applied to the foUr-loop calculations of the ν-function in the Wess-Zumino model. The main advantage of the used method is the existence of a relatively simple calculational algorithm that allows one to write an effective computer program on the system of analytical evaluations SCHOONSCHIP. Any three-loop integral with one external momentum can be computed by this program. The four-loop calculation in the WZ model is one of the first and simplest applications of the program

Three-loop mixed QCD-electroweak corrections to Higgs boson gluon fusion

Science.gov (United States)

Bonetti, Marco; Melnikov, Kirill; Tancredi, Lorenzo

2018-02-01

We compute the contribution of three-loop mixed QCD-electroweak corrections (αS2α2) to the g g →H scattering amplitude. We employ the method of differential equations to compute the relevant integrals and express them in terms of Goncharov polylogarithms.

On the low-energy limit of one-loop photon-graviton amplitudes

International Nuclear Information System (INIS)

Bastianelli, F.; Corradini, O.; Dávila, J.M.; Schubert, C.

2012-01-01

We present first results of a systematic study of the structure of the low-energy limit of the one-loop photon-graviton amplitudes induced by massive scalars and spinors. Our main objective is the search of KLT-type relations where effectively two photons merge into a graviton. We find such a relation at the graviton-photon-photon level. We also derive the diffeomorphism Ward identity for the 1PI one-graviton-N-photon amplitudes.

Control-structure interaction in precision pointing servo loops

Science.gov (United States)

Spanos, John T.

1989-01-01

The control-structure interaction problem is addressed via stability analysis of a generic linear servo loop model. With the plant described by the rigid body mode and a single elastic mode, structural flexibility is categorized into one of three types: (1) appendage, (2) in-the-loop minimum phase, and (3) in-the-loop nonminimum phase. Closing the loop with proportional-derivative (PD) control action and introducing sensor roll-off dynamics in the feedback path, stability conditions are obtained. Trade studies are conducted with modal frequency, modal participation, modal damping, loop bandwidth, and sensor bandwidth treated as free parameters. Results indicate that appendage modes are most likely to produce instability if they are near the sensor rolloff, whereas in-the-loop modes are most dangerous near the loop bandwidth. The main goal of this paper is to provide a fundamental understanding of the control-structure interaction problem so that it may benefit the design of complex spacecraft and pointing system servo loops. In this framework, the JPL Pathfinder gimbal pointer is considered as an example.

Zero point energy of renormalized Wilson loops

International Nuclear Information System (INIS)

Hidaka, Yoshimasa; Pisarski, Robert D.

2009-01-01

The quark-antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero when terms for extrinsic curvature are included. At one loop order, the nonperturbative contribution to the zero point energy is negative, regardless of the sign of the extrinsic curvature term.

Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics

Energy Technology Data Exchange (ETDEWEB)

Braun, V.M.; Strohmaier, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Manashov, A.N. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik; Moch, S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik

2017-03-15

Using the approach based on conformal symmetry we calculate the three-loop (NNLO) contribution to the evolution equation for flavor-nonsinglet leading twist operators in the MS scheme. The explicit expression for the three-loop kernel is derived for the corresponding light-ray operator in coordinate space. The expansion in local operators is performed and explicit results are given for the matrix of the anomalous dimensions for the operators up to seven covariant derivatives. The results are directly applicable to the renormalization of the pion light-cone distribution amplitude and flavor-nonsinglet generalized parton distributions.

Generalized unitarity for N=4 super-amplitudes

Energy Technology Data Exchange (ETDEWEB)

Drummond, J.M.; Henn, J. [LAPTH, Université de Savoie, CNRS B.P. 110, F-74941 Annecy-le-Vieux Cedex (France); Korchemsky, G.P., E-mail: Gregory.Korchemsky@cea.fr [Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex (France); Sokatchev, E. [LAPTH, Université de Savoie, CNRS B.P. 110, F-74941 Annecy-le-Vieux Cedex (France)

2013-04-21

We develop a manifestly supersymmetric version of the generalized unitarity cut method for calculating scattering amplitudes in N=4 SYM theory. We illustrate the power of this method by computing the one-loop n-point NMHV super-amplitudes. The result confirms two conjectures which we made in Drummond, et al., [1]. Firstly, we derive the compact, manifestly dual superconformally covariant form of the NMHV tree amplitudes for arbitrary number and types of external particles. Secondly, we show that the ratio of the one-loop NMHV to the MHV amplitude is dual conformal invariant.

A comprehensive coordinate space renormalization of quantum electrodynamics to two-loop order

International Nuclear Information System (INIS)

Haagensen, P.E.; Latorre, J.I.

1993-01-01

We develop a coordinate space renormalization of massless quantum electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all one- and two-loop 1PI diagrams, run renormalization group equations on them. and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle γ 5 problems

Local integrand representations of all two-loop amplitudes in planar SYM

International Nuclear Information System (INIS)

Bourjaily, Jacob L.; Trnka, Jaroslav

2015-01-01

We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and manifestly divergent terms — in a way that renders all infrared-safe observables (including ratio functions) calculable without any need for regulation. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a MATHEMATICA package which implements these results, available as part of this work’s source files on the arXiv.

Supersymmetric Yang-Mills and supergravity amplitudes at one loop

International Nuclear Information System (INIS)

Hall, Anthony

2009-01-01

By applying the known expressions for super Yang-Mills (SYM) and supergravity (SUGRA) tree amplitudes, we write generating functions for the next-to-next-to-maximally helicity violating (NNMHV) box coefficients of SYM as well as the maximally helicity violating, next-to-maximally helicity violating, and NNMHV box coefficients for SUGRA. The all-multiplicity generating functions utilize covariant, on-shell superspace whereby the contribution from arbitrary external states in the supermultiplet can be extracted by Grassmann operators. In support of the relation between dual-Wilson loops and SYM scattering amplitudes at weak coupling, the SYM amplitudes are presented in a manifestly dual superconformal form. We introduce ordered box coefficients for calculating SUGRA quadruple cuts and prove that ordered coefficients generate physical cut amplitudes after summing over permutations of the external legs. The ordered box coefficients are produced by sewing ordered subamplitudes, previously used in applying on-shell recursion relations at tree level. We describe our verification of the results against the literature, and a formula for extracting the contributions from external gluons or gravitons to NNMHV superamplitudes is presented.

Comment on non-renormalization theorem in the four dimensional superstrings

International Nuclear Information System (INIS)

Soda, Jiro; Nakazawa, Naohito; Sakai, Kenji; Ojima, Shuichi.

1987-10-01

We discuss non-renormalization theorem in the context of the four dimensional superstrings. We explicitly demonstrate that the graviton 3-point one-loop amplitude does not vanish in contrast to the ten dimensional superstring theories. (author)

Maximal Abelian and Curci-Ferrari gauges in momentum subtraction at three loops

Science.gov (United States)

Bell, J. M.; Gracey, J. A.

2015-12-01

The vertex structure of QCD fixed in the maximal Abelian gauge (MAG) and Curci-Ferrari gauge is analyzed at two loops at the fully symmetric point for the 3-point functions corresponding to the three momentum subtraction (MOM) renormalization schemes. Consequently, the three-loop renormalization group functions are determined for each of these three schemes in each gauge using properties of the renormalization group equation.

Gluon amplitudes as 2 d conformal correlators

Science.gov (United States)

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

2017-10-01

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

Master integrals for the four-loop Sudakov form factor

Directory of Open Access Journals (Sweden)

Rutger H. Boels

2016-01-01

Full Text Available The light-like cusp anomalous dimension is a universal function in the analysis of infrared divergences. In maximally (N=4 supersymmetric Yang–Mills theory (SYM in the planar limit, it is known, in principle, to all loop orders. The non-planar corrections are not known in any theory, with the first appearing at the four-loop order. The simplest quantity which contains this correction is the four-loop two-point form factor of the stress tensor multiplet. This form factor was largely obtained in integrand form in a previous work for N=4 SYM, up to a free parameter. In this work, a reduction of the appearing integrals obtained by solving integration-by-parts (IBP identities using a modified version of Reduze is reported. The form factor is shown to be independent of the remaining parameter at integrand level due to an intricate pattern of cancellations after IBP reduction. Moreover, two of the integral topologies vanish after reduction. The appearing master integrals are cross-checked using independent algebraic-geometry techniques explored in the Mint package. The latter results provide the basis of master integrals applicable to generic form factors, including those in Quantum Chromodynamics. Discrepancies between explicitly solving the IBP relations and the MINT approach are highlighted. Remaining bottlenecks to completing the computation of the four-loop non-planar cusp anomalous dimension in N=4 SYM and beyond are identified.

A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

International Nuclear Information System (INIS)

Badger, Simon; Mogull, Gustav; Ochirov, Alexander; O’Connell, Donal

2015-01-01

We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon; Mogull, Gustav; Ochirov, Alexander [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); O’Connell, Donal [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 (United States)

2015-10-09

We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

CFD simulation of a four-loop PWR at asymmetric operation conditions

Energy Technology Data Exchange (ETDEWEB)

Cheng, Jian-Ping; Yan, Li-Ming; Li, Feng-Chen, E-mail: lifch@hit.edu.cn

2016-04-15

Highlights: • A CFD numerical simulation procedure was established for simulating RPV of VVER-1000. • The established CFD approach was validated by comparing with available data. • Thermal hydraulic characteristics under asymmetric operation condition were investigated. • Apparent influences of the shutdown loop on its neighboring loops were obtained. - Abstract: The pressurized water reactor (PWR) with multiple loops may have abnormal working conditions with coolant pumps out of running in some loops. In this paper, a computational fluid dynamics (CFD) numerical study of the four-loop VVER-1000 PWR pressure vessel model was presented. Numerical simulations of the thermohydrodynamic characteristics in the pressure vessel were carried out at different inlet conditions with four and three loops running, respectively. At normal stead-state condition (four-loop running), different parameters were obtained for the full fluid domain, including pressure losses across different parts, pressure, velocity and temperature distributions in the reactor pressure vessel (RPV) and mass flow distribution of the coolant at the inlet of reactor core. The obtained results for pressure losses matched with the experimental reference values of the VVER-1000 PWR at Tianwan nuclear power plant (NPP). For most fuel assemblies (FAs), the inlet flow rates presented a symmetrical distribution about the center under full-loop operation conditions, which accorded with the practical distribution. These results indicate that it is now possible to study the dynamic transition process between different asymmetric operation conditions in a multi-loop PWR using the established CFD method.

The open superstring 6-point amplitude with manifest symmetries

International Nuclear Information System (INIS)

Barreiro, Luiz Antonio; Medina, Ricardo; Stieberger, Stephan

2011-01-01

Full text: The general tree level amplitude for massless bosons states of open superstrings has been known for a long time ago. It is clear how to obtain this general formula using vertex operators in the Ramond-Neveu-Schwarz formalism. From the beginning of the eighties the explicit expression for this formula has been known in the case of 3 and 4-point amplitudes. In that decade an attempt (with partial success) was done, by Kitazawa, to obtain the corresponding 5-point amplitude. Only in 2002 a complete and correct expression for this amplitude was obtained. Its low energy expansion was compared to the corresponding one from the low energy effective Lagrangian of the open superstring, finding a perfect match. A few years later, in 2005, it was realized that the 5-point formula could be written in a very much compact form, as a sum of two terms: each of them consisting of a momentum factor and a kinematic expression. This constituted a generalization of the 4-point amplitude case, which had been known to be cast in only one momentum factor multiplied by one kinematic expression. For this simplification to happen, known symmetries of the (tree level) scattering amplitudes were implemented in a manifest form. These symmetries are (on-shell) gauge symmetry, cyclic symmetry and twisting symmetry (or world sheet parity). In the recent years it has been realized that the N-point amplitude can be written as a sum of (N - 3)! terms (where N > 3). This result not only agrees with the 3, 4 and 5-point results, but also with the 6-point result which had been obtained by 2005, written as a sum of six terms. The expression that up to now has been obtained for the 6-point amplitude is quite complicated and, besides knowing that it consists of six terms, is not very illuminating. In this work we report on the recent result of writing the 6-point amplitude with gauge, cyclic and twisting symmetries manifest. Not only because of the manifest symmetries this result is important

Four loop wave function renormalization in the non-abelian Thirring model

International Nuclear Information System (INIS)

Ali, D.B.; Gracey, J.A.

2001-01-01

We compute the anomalous dimension of the fermion field with N f flavours in the fundamental representation of a general Lie colour group in the non-abelian Thirring model at four loops. The implications on the renormalization of the two point Green's function through the loss of multiplicative renormalizability of the model in dimensional regularization due to the appearance of evanescent four fermi operators are considered at length. We observe the appearance of one new colour group Casimir, d F abcd d F abcd , in the final four loop result and discuss its consequences for the relation of the Knizhnik-Zamolodchikov critical exponents in the Wess-Zumino-Witten-Novikov model to the non-abelian Thirring model. Renormalization scheme changes are also considered to ensure that the underlying Fierz symmetry broken by dimensional regularization is restored

Four-loop critical exponents for the Gross-Neveu-Yukawa models

International Nuclear Information System (INIS)

Zerf, Nikolai; Mihaila, Luminita N.; Herbut, Igor F.; Scherer, Michael M.

2017-09-01

We study the chiral Ising, the chiral XY and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4-ε dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order O(ε 4 ). Further, we provide Pade estimates for the correlation length exponent, the boson and fermion anomalous dimension as well as the leading correction to scaling exponent in 2+1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N=1/4 and N=1/2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

Four-loop critical exponents for the Gross-Neveu-Yukawa models

Energy Technology Data Exchange (ETDEWEB)

Zerf, Nikolai; Mihaila, Luminita N. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Marquard, Peter [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Herbut, Igor F. [Simon Fraser Univ., Burnaby, BC (Canada). Dept. of Physics; Scherer, Michael M. [Koeln Univ. (Germany). Inst. for Theoretical Physics

2017-09-15

We study the chiral Ising, the chiral XY and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4-ε dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order O(ε{sup 4}). Further, we provide Pade estimates for the correlation length exponent, the boson and fermion anomalous dimension as well as the leading correction to scaling exponent in 2+1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N=1/4 and N=1/2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

Numerical analysis on a four-stage looped thermoacoustic Stirling power generator for low temperature waste heat

International Nuclear Information System (INIS)

Wang, Kai; Qiu, Limin

2017-01-01

Highlights: • Four-stage looped thermoacoustic power generator for waste heat is studied. • Coupling position is found to have remarkable effects on performance. • Better efficiency is available when coupled near the cold ends of the cores. • The influence of the regenerator position on the efficiency is weak. • Matching between the acoustic impedances of engine and alternator is important. - Abstract: Recent developments in thermoacoustic technologies have demonstrated that multi-stage looped thermoacoustic Stirling engine would be a promising option for harvesting waste heat. Previous studies on multi-stage looped thermoacoustic systems were mainly focused on heat-driven refrigeration or heat pumping, while much fewer work were done on power generations, especially those for recovering low temperature heat. In this work, a four-stage looped thermoacoustic Stirling power generator for generating electricity from low temperature waste heat at 300 °C is systematically studied. A numerical model is built and then validated on an experimental four-stage looped thermoacoustic Stirling engine. On the basis of the validated model, the effects of the coupling position for the linear alternators and the regenerator position on the acoustic characteristics and performances of the power generation system are numerically investigated. The distributions of the acoustic fields along the loop, including the pressure amplitude, volume flow rate, phase angle, specific acoustic impedance and acoustic power, are presented and analysed for three representative coupling modes. Superior efficiency is achieved when the linear alternators are coupled near the cold ends of the thermoacoustic cores on the resonators, while more electric power is generated at the hot ends. The worst performance is expected when the linear alternators are connected at the middle of the resonators. The underling mechanisms are further explained detailedly by analysing the characteristics of the

Zero Point Energy of Renormalized Wilson Loops

OpenAIRE

Hidaka, Yoshimasa; Pisarski, Robert D.

2009-01-01

The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero wh...

Getting superstring amplitudes by degenerating Riemann surfaces

International Nuclear Information System (INIS)

Matone, Marco; Volpato, Roberto

2010-01-01

We explicitly show how the chiral superstring amplitudes can be obtained through factorisation of the higher genus chiral measure induced by suitable degenerations of Riemann surfaces. This powerful tool also allows to derive, at any genera, consistency relations involving the amplitudes and the measure. A key point concerns the choice of the local coordinate at the node on degenerate Riemann surfaces that greatly simplifies the computations. As a first application, starting from recent ansaetze for the chiral measure up to genus five, we compute the chiral two-point function for massless Neveu-Schwarz states at genus two, three and four. For genus higher than three, these computations include some new corrections to the conjectural formulae appeared so far in the literature. After GSO projection, the two-point function vanishes at genus two and three, as expected from space-time supersymmetry arguments, but not at genus four. This suggests that the ansatz for the superstring measure should be corrected for genus higher than four.

Four-loop non-singlet splitting functions in the planar limit and beyond

Energy Technology Data Exchange (ETDEWEB)

Moch, S. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Ruijl, B. [Nikhef, Amsterdam (Netherlands). Theory Group; Leiden Univ. (Netherlands). Leiden Centre of Data Science; Ueda, T.; Vermaseren, J.A.M. [Nikhef, Amsterdam (Netherlands). Theory Group; Vogt, A. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences

2017-08-15

We present the next-to-next-to-next-to-leading order (N{sup 3}LO) contributions to the non-singlet splitting functions for both parton distribution and fragmentation functions in perturbative QCD. The exact expressions are derived for the terms contributing in the limit of a large number of colours. For the remaining contributions, approximations are provided that are sufficient for all collider-physics applications. From their threshold limits we derive analytical and high-accuracy numerical results, respectively, for all contributions to the four-loop cusp anomalous dimension for quarks, including the terms proportional to quartic Casimir operators. We briefly illustrate the numerical size of the four-loop corrections, and the remarkable renormalization-scale stability of the N{sup 3}LO results, for the evolution of the non-singlet parton distribution and the fragmentation functions. Our results appear to provide a first point of contact of four-loop QCD calculations and the so-called wrapping corrections to anomalous dimensions in N=4 super Yang-Mills theory.

One-loop helicity amplitudes for t anti t production at hadron colliders

International Nuclear Information System (INIS)

Badger, Simon; Yundin, Valery

2011-01-01

We present compact analytic expressions for all one-loop helicity amplitudes contributing to t anti t production at hadron colliders. Using recently developed generalised unitarity methods and a traditional Feynman based approach we produce a fast and flexible implementation. (ORIG.)

One-loop helicity amplitudes for t anti t production at hadron colliders

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon [The Niels Bohr International Academy and Discovery Center, Copenhagen (Denmark). Niels Bohr Inst.; Sattler, Ralf [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Silesia Univ., Katowice (Poland). Inst. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2011-01-15

We present compact analytic expressions for all one-loop helicity amplitudes contributing to t anti t production at hadron colliders. Using recently developed generalised unitarity methods and a traditional Feynman based approach we produce a fast and flexible implementation. (ORIG.)

Perturbative Quantum Gravity from Gauge Theory

Science.gov (United States)

Carrasco, John Joseph

In this dissertation we present the graphical techniques recently developed in the construction of multi-loop scattering amplitudes using the method of generalized unitarity. We construct the three-loop and four-loop four-point amplitudes of N = 8 supergravity using these methods and the Kawaii, Lewellen and Tye tree-level relations which map tree-level gauge theory amplitudes to tree-level gravity theory amplitudes. We conclude by extending a tree-level duality between color and kinematics, generic to gauge theories, to a loop level conjecture, allowing the easy relation between loop-level gauge and gravity kinematics. We provide non-trivial evidence for this conjecture at three-loops in the particular case of maximal supersymmetry.

Some tree-level string amplitudes in the NSR formalism

International Nuclear Information System (INIS)

Becker, Katrin; Becker, Melanie; 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.

One loop beta functions and fixed points in higher derivative sigma models

International Nuclear Information System (INIS)

Percacci, Roberto; Zanusso, Omar

2010-01-01

We calculate the one loop beta functions of nonlinear sigma models in four dimensions containing general two- and four-derivative terms. In the O(N) model there are four such terms and nontrivial fixed points exist for all N≥4. In the chiral SU(N) models there are in general six couplings, but only five for N=3 and four for N=2; we find fixed points only for N=2, 3. In the approximation considered, the four-derivative couplings are asymptotically free but the coupling in the two-derivative term has a nonzero limit. These results support the hypothesis that certain sigma models may be asymptotically safe.

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

International Nuclear Information System (INIS)

Brandt, F.T.; Frenkel, J.

1985-01-01

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

Heptagons from the Steinmann cluster bootstrap

International Nuclear Information System (INIS)

Dixon, Lance J.; Drummond, James; Papathanasiou, Georgios

2017-01-01

We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planar N = 4 supersymmetric Yang-Mills theory, making higher-loop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and well-defined collinear limits suffice to determine uniquely the symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We also show that at three loops, relaxing the dual superconformal Q̄ relations and imposing dihedral symmetry (and for NMHV the absence of spurious poles) leaves only a single ambiguity in the heptagon amplitudes. These results point to a strong tension between the collinear properties of the amplitudes and the Steinmann relations.

Polynomial structures in one-loop amplitudes

International Nuclear Information System (INIS)

Britto, Ruth; Feng Bo; Yang Gang

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 (4-2ε)-dimensional master integrals; these formulas depend on an additional variable, u, which encodes the dimensional shift. Second, convert the u-dependent coefficients of (4-2ε)-dimensional master integrals to explicit coefficients of dimensionally shifted master integrals. This procedure requires the initial formulas for coefficients to have polynomial dependence on u. Here, we give a proof of this property in the case of massless propagators. The proof is constructive. Thus, as a byproduct, we produce different algebraic expressions for the scalar integral coefficients, in which the polynomial property is apparent. In these formulas, the box and pentagon contributions are separated explicitly.

Simplicity in the structure of QED and gravity amplitudes

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bjerrum-Bohr, N.E.J. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Vanhove, Pierre [Institut des Hautes Etudes Scientifiques IHES, Bures sur Yvette (France); CEA, IPhT, CNRS, URA, Gif-sur-Yvette, (France). Inst. de Physique Theorique

2008-11-15

We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and results in remarkable cancellations. We show that one-loop multi-photon amplitudes in QED with at least eight external photons are given only by scalar box integral functions. This QED 'no-triangle' property is true for all helicity configurations and has similarities to the 'notriangle' property found in the case of maximal N=8 supergravity. Results are derived both via a world-line formalism as well as using on-shell unitarity methods. We show that the simple structure of the loop amplitude originates from the extremely good BCFW scaling behaviour of the QED tree-amplitude. (orig.)

Simplicity in the structure of QED and gravity amplitudes

International Nuclear Information System (INIS)

Badger, Simon; Bjerrum-Bohr, N.E.J.; Vanhove, Pierre; CEA, IPhT, CNRS, URA, Gif-sur-Yvette,

2008-11-01

We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and results in remarkable cancellations. We show that one-loop multi-photon amplitudes in QED with at least eight external photons are given only by scalar box integral functions. This QED 'no-triangle' property is true for all helicity configurations and has similarities to the 'notriangle' property found in the case of maximal N=8 supergravity. Results are derived both via a world-line formalism as well as using on-shell unitarity methods. We show that the simple structure of the loop amplitude originates from the extremely good BCFW scaling behaviour of the QED tree-amplitude. (orig.)

Point-defect migration into an infinitesimal dislocation loop

International Nuclear Information System (INIS)

Woo, C.H.

1981-11-01

Point-defect migration into an infinitesimal dislocation loop in an isotropic linear elastic medium is described. Particular care has been taken to include the effects of the saddle-point shape anisotropy of the point defect. Expressions for the reaction radii and the bias are derived, both in the presence and absence of an external applied stress. These are found to depend on intrinsic parameters, such as the loop strength, the loop nature (vacancy or interstitial), the relaxation volume, the saddle-point shape, and extrinsic parameters, such as the magnitude and direction of the external stress, and the temperature. The implications of the results are discussed

An automated four-point scale scoring of segmental wall motion in echocardiography using quantified parametric images

International Nuclear Information System (INIS)

Kachenoura, N; Delouche, A; Ruiz Dominguez, C; Frouin, F; Diebold, B; Nardi, O

2010-01-01

The aim of this paper is to develop an automated method which operates on echocardiographic dynamic loops for classifying the left ventricular regional wall motion (RWM) in a four-point scale. A non-selected group of 37 patients (2 and 4 chamber views) was studied. Each view was segmented according to the standardized segmentation using three manually positioned anatomical landmarks (the apex and the angles of the mitral annulus). The segmented data were analyzed by two independent experienced echocardiographists and the consensual RWM scores were used as a reference for comparisons. A fast and automatic parametric imaging method was used to compute and display as static color-coded parametric images both temporal and motion information contained in left ventricular dynamic echocardiograms. The amplitude and time parametric images were provided to a cardiologist for visual analysis of RWM and used for RWM quantification. A cross-validation method was applied to the segmental quantitative indices for classifying RWM in a four-point scale. A total of 518 segments were analyzed. Comparison between visual interpretation of parametric images and the reference reading resulted in an absolute agreement (Aa) of 66% and a relative agreement (Ra) of 96% and kappa (κ) coefficient of 0.61. Comparison of the automated RWM scoring against the same reference provided Aa = 64%, Ra = 96% and κ = 0.64 on the validation subset. Finally, linear regression analysis between the global quantitative index and global reference scores as well as ejection fraction resulted in correlations of 0.85 and 0.79. A new automated four-point scale scoring of RWM was developed and tested in a non-selected database. Its comparison against a consensual visual reading of dynamic echocardiograms showed its ability to classify RWM abnormalities.

Heptagons from the Steinmann cluster bootstrap

International Nuclear Information System (INIS)

Dixon, Lance J.; McLeod, Andrew J.; Drummond, James; Harrington, Thomas; Spradlin, Marcus; Papathanasiou, Georgios; Stanford Univ., CA

2016-12-01

We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planar N=4 supersymmetric Yang-Mills theory, making higher-loop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and well-defined collinear limits suffice to determine uniquely the symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We also show that at three loops, relaxing the dual superconformal (anti Q) relations and imposing dihedral symmetry (and for NMHV the absence of spurious poles) leaves only a single ambiguity in the heptagon amplitudes. These results point to a strong tension between the collinear properties of the amplitudes and the Steinmann relations.

Heptagons from the Steinmann cluster bootstrap

Energy Technology Data Exchange (ETDEWEB)

Dixon, Lance J.; McLeod, Andrew J. [Stanford Univ., CA (United States). SLAC National Accelerator Lab.; Drummond, James [Southampton Univ. (United Kingdom). School of Physics and Astronomy; Harrington, Thomas; Spradlin, Marcus [Brown Univ., Providence, RI (United States). Dept. of Physics; Papathanasiou, Georgios [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Stanford Univ., CA (United States). SLAC National Accelerator Lab.

2016-12-15

We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planar N=4 supersymmetric Yang-Mills theory, making higher-loop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and well-defined collinear limits suffice to determine uniquely the symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We also show that at three loops, relaxing the dual superconformal (anti Q) relations and imposing dihedral symmetry (and for NMHV the absence of spurious poles) leaves only a single ambiguity in the heptagon amplitudes. These results point to a strong tension between the collinear properties of the amplitudes and the Steinmann relations.

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.

The massless two-loop two-point function

International Nuclear Information System (INIS)

Bierenbaum, I.; Weinzierl, S.

2003-01-01

We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter ε. As a side product, we show that in the Laurent expansion of the two-loop integral only rational numbers and multiple zeta values occur. Our method of calculation obtains the two-loop integral as a convolution product of two primitive one-loop integrals. We comment on the generalization of this product structure to higher loop integrals. (orig.)

Hedgehog bases for A{sub n} cluster polylogarithms and an application to six-point amplitudes

Energy Technology Data Exchange (ETDEWEB)

Parker, Daniel E.; Scherlis, Adam; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University, Providence RI 02912 (United States)

2015-11-20

Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the A{sub n} cluster algebra. Using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

Energy Technology Data Exchange (ETDEWEB)

Duca, Vittorio Del [Institute for Theoretical Physics, ETH Zürich,Hönggerberg, 8093 Zürich (Switzerland); Druc, Stefan; Drummond, James [School of Physics & Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); Duhr, Claude [Theoretical Physics Department, CERN,Route de Meyrin, CH-1211 Geneva 23 (Switzerland); Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Dulat, Falko [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Marzucca, Robin [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Papathanasiou, Georgios [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Verbeek, Bram [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium)

2016-08-25

We show that scattering amplitudes in planar N=4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L+4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

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)....

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.

Nonsinglet pentagons and NMHV amplitudes

Energy Technology Data Exchange (ETDEWEB)

Belitsky, A.V., E-mail: andrei.belitsky@asu.edu

2015-07-15

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.

Anomalies in Ward identities revisited. Explicit calculation of the three point functions

International Nuclear Information System (INIS)

Dalmolin, Fabricio Tronco

2007-01-01

others already performed within the same issue. In particular, in one of such investigation a pioneer and traditional reference has been revisited by using the alternative strategy mentioned above. In such study, a systematic treatment of purely fermionic one, two and three point functions, associated to scalar, pseudo-scalar, vector and axial-vector densities, has done. There, however, only the explicit expressions for one and two point functions were developed. The conclusions pointed out, in a very clear way, that the association between intrinsic ambiguities of the perturbative calculation and violations in symmetry properties is not consistent. At the same time, it was concluded that only in an investigation where the explicit forms for the three point functions involved are considered clean and sound conclusions can be extracted. This is due to the fact that, in the relevant symmetry properties, it is involved three ward identities and a low energy limit. This is precisely the main purpose of the present work: to promote a detailed investigation of the relations among green functions and ward identities, within the context of a model having only one specie of 1/2 spin fermionic field, that consider all the amplitudes having superficial degree of divergence higher than the logarithmic one, in a similar way as that made in the work of Gerstein and Jackiw, taking however the explicit form for the three point functions. This is one to get in the analysis, simultaneously, the ward identities and the low energy limits involved in the anomalous amplitudes as required by the Sutherland-Veltman theorem, in order to get an adequate understanding of the anomaly phenomena. We will show that our final results can be mapped in those found with the use of the Dimensional Regularization, in situation where this technique can be applied, or in those of Gerstein and Jackiw, however with conflicting interpretations. Finally, we will show that in the context of the adopted technique

Top-forms of leading singularities in nonplanar multi-loop amplitudes

Energy Technology Data Exchange (ETDEWEB)

Chen, Baoyi; Cheung, Yeuk-Kwan E.; Xie, Ruofei; Xin, Yuan [Nanjing University, Department of Physics, Nanjing (China); Chen, Gang [Zhejiang Normal University, Department of Physics, Jinhua (China); Nanjing University, Department of Physics, Nanjing (China)

2018-02-15

The on-shell diagram is a very important tool in studying scattering amplitudes. In this paper we discuss the on-shell diagrams without external BCFW bridges. We introduce an extra step of adding an auxiliary external momentum line. Then we can decompose the on-shell diagrams by removing external BCFW bridges to a planar diagram whose top-form is well known now. The top-form of the on-shell diagram with the auxiliary line can be obtained by adding the BCFW bridges in an inverse order as discussed in our former paper (Chen et al. in Eur Phys J C 77(2):80 2017). To get the top-form of the original diagram, the soft limit of the auxiliary line is needed. We obtain the evolution rule for the Grassmannian integral and the geometry constraint in the soft limit. This completes the top-form description of leading singularities in nonplanar scattering amplitudes of N = 4 Super Yang-Mills (SYM), which is valid for arbitrary higher-loops and beyond the Maximally-Helicity-Violation (MHV) amplitudes. (orig.)

High-energy evolution to three loops

Science.gov (United States)

Caron-Huot, Simon; Herranen, Matti

2018-02-01

The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to the equation in planar N = 4 super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the threeloop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in crosssection calculations in the planar limit. We compare our result in the linear regime with a recent prediction for the so-called Pomeron trajectory, and compare its collinear limit with predictions from the spectrum of twist-two operators.

Mechanical failure of anodized aluminum under three and four-point bending tests

International Nuclear Information System (INIS)

Bargui, M.; Bensalah, W.; Elleuch, K.; Ayedi, H.F.

2013-01-01

Highlights: • We study the flexural behavior of anodic oxide layers formed on aluminum. • Three and four-point bending tests were used as techniques. • Changing the beam configuration will change the flexural response. - Abstract: In this work, three and four-point bending tests were adopted as methods for characterizing anodized aluminum beams in a sulfuric acid bath. The failure behavior of sandwich beams having aluminum oxide face sheets and aluminum core were tested. In so doing, many configurations were adopted by anodizing aluminum beams on one and both sides to investigate faces in place of tension and compression. Bending tests showed different behaviors. When the oxide was only on the top side of the beam (working in compression) a slight sudden decrease of the load was observed. This fact was absent on beams with oxide layers working in tensile. The bending behavior of sandwich beams was similar to those with oxide on top sides but with much higher loads. The mechanical failure of the oxide was mainly caused by its failure when it is placed in compression beneath the loading rollers. Finally, a morphological study of the aluminum oxide layers after bending tests was conducted by optical microscopy

Quark mass relations to four-loop order

International Nuclear Information System (INIS)

Marquard, Peter; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias

2015-02-01

We present results for the relation between a heavy quark mass defined in the on-shell and MS scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS heavy quark masses.

(g-2){sub μ} at four loops in QED

Energy Technology Data Exchange (ETDEWEB)

Marquard, Peter [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Smirnov, Alexander V. [Moscow State Univ. (Russian Federation). Research Computing Center; Smirnov, Vladimir A. [Moscow State Univ. (Russian Federation). Skobeltsyn Inst. of Nuclear Physics; Steinhauser, Matthias; Wellmann, David [Karlsruher Institut fuer Technologie (KIT), Karlsruhe (Germany). Inst. fuer Theoretische Teilchenphysik

2017-08-15

We review the four-loop QED corrections to the anomalous magnetic moment of the muon. The fermionic contributions with closed electron and tau contributions are discussed. Furthermore, we report on a new independent calculation of the universal four-loop contribution and compare with existing results.

One loop integration with hypergeometric series by using recursion relations

International Nuclear Information System (INIS)

Watanabe, Norihisa; Kaneko, Toshiaki

2014-01-01

General one-loop integrals with arbitrary mass and kinematical parameters in d-dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects (n + 1)-point to n-point functions. In solving this recursion relation, we have shown that one-loop integrals are expressed by a newly defined hypergeometric function, which is a special case of Aomoto-Gelfand hypergeometric functions. We have also obtained coefficients of power series expansion around 4-dimensional space-time for two-, three- and four-point functions. The numerical results are compared with ''LoopTools'' for the case of two- and three-point functions as examples

Two-loop renormalization of quantum gravity simplified

Science.gov (United States)

Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex

2017-02-01

The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

The amplitude and phase control of the ALS Storage Ring RF System

International Nuclear Information System (INIS)

Lo, C.C.; Taylor, B.; Baptiste, K.

1995-03-01

A 500MHz, 300KW Klystron power amplifier provides RF power to the ALS Storage Ring. In order to accommodate the amplitude and phase changes during beam stacking and decay, which demand continuously varying power levels from the Klystron, four loops are used to keep the system operating properly, with two of those loops dedicated to keeping the two cavity tuners on tune. Description of the control loops and their performance data will be given. Using the modulation anode of the Klystron in the amplitude loop will be discussed

The two-loop master integrals for qq-bar→VV

International Nuclear Information System (INIS)

Gehrmann, Thomas; Manteuffel, Andreas von; Tancredi, Lorenzo; Weihs, Erich

2014-01-01

We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes for vector boson pair production at hadron colliders, qq-bar→VV, and thus to compute this process to next-to-next-to-leading order accuracy in QCD. The master integrals are derived using the method of differential equations, employing a canonical basis for the integrals. We obtain analytical results for all integrals, expressed in terms of multiple polylogarithms. We optimize our results for numerical evaluation by employing functions which are real valued for physical scattering kinematics and allow for an immediate power series expansion

Cluster polylogarithms for scattering amplitudes

International Nuclear Information System (INIS)

Golden, John; Paulos, Miguel F; Spradlin, Marcus; Volovich, Anastasia

2014-01-01

Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define cluster polylogarithm functions. We find that all such functions of weight four are made up of a single simple building block associated with the A 2 cluster algebra. Adding the requirement of locality on generalized Stasheff polytopes, we find that these A 2 building blocks arrange themselves to form a unique function associated with the A 3 cluster algebra. This A 3 function manifests all of the cluster algebraic structure of the two-loop n-particle MHV amplitudes for all n, and we use it to provide an explicit representation for the most complicated part of the n = 7 amplitude as an example. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)

A differential operator for integrating one-loop scattering equations

Energy Technology Data Exchange (ETDEWEB)

Wang, Tianheng [Department of Physics, Nanjing University,Nanjing, Jiangsu Province (China); Chen, Gang [Department of Physics, Zhejiang Normal University,Jinhua, Zhejiang Province (China); Department of Physics and Astronomy, Uppsala University,Uppsala (Sweden); Department of Physics, Nanjing University,Nanjing, Jiangsu Province (China); Cheung, Yeuk-Kwan E. [Department of Physics, Nanjing University,Nanjing, Jiangsu Province (China); Xu, Feng [Weavi Corporation Limited, Nanjing,Jiangsu Province (China)

2017-01-09

We propose a differential operator for computing the residues associated with a class of meromorphic n-forms that frequently appear in the Cachazo-He-Yuan form of the scattering amplitudes. This differential operator is conjectured to be uniquely determined by the local duality theorem and the intersection number of the divisors in the n-form. We use the operator to evaluate the one-loop integrand of Yang-Mills theory from their generalized CHY formulae. The method can reduce the complexity of the calculation. In addition, the expression for the 1-loop four-point Yang-Mills integrand obtained in our approach has a clear correspondence with the Q-cut results.

F4 symmetric ϕ3 theory at four loops

Science.gov (United States)

Gracey, J. A.

2017-03-01

The renormalization group functions for six dimensional scalar ϕ3 theory with an F4 symmetry are provided at four loops in the modified minimal subtraction (MS ¯ ) scheme. Aside from the anomalous dimension of ϕ and the β -function this includes the mass operator and a ϕ2-type operator. The anomalous dimension of the latter is computed explicitly at four loops for the 26 and 324 representations of F4. The ɛ expansion of all the related critical exponents are determined to O (ɛ4). For instance the value for Δϕ agrees with recent conformal bootstrap estimates in 5 and 5.95 dimensions. The renormalization group functions are also provided at four loops for the group E6.

Rectangular amplitudes, conformal blocks, and applications to loop models

Energy Technology Data Exchange (ETDEWEB)

Bondesan, Roberto, E-mail: roberto.bondesan@cea.fr [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Jacobsen, Jesper L. [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Universite Pierre et Marie Curie, 4 place Jussieu, 75252 Paris (France); Saleur, Hubert [Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Physics Department, USC, Los Angeles, CA 90089-0484 (United States)

2013-02-21

In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan, et al., Nucl. Phys. B 862 (2012) 553-575]. Here we develop a general formalism of rectangle boundary states using conformal field theory, adapted to describe geometries supporting different boundary conditions. We discuss the computation of rectangular amplitudes and their modular properties, presenting explicit results for the case of free theories. In a second part of the paper we focus on applications to loop models, discussing in details lattice discretizations using both numerical and analytical calculations. These results allow to interpret geometrically conformal blocks, and as an application we derive new probability formulas for self-avoiding walks.

Four-point functions in N=4 SYM

International Nuclear Information System (INIS)

Heslop, Paul J.; Howe, Paul S.

2003-01-01

A new derivation is given of four-point functions of charge Q chiral primary multiplets in N=4 supersymmetric Yang-Mills theory. A compact formula, valid for arbitrary Q, is given which is manifestly superconformal and analytic in the internal bosonic coordinates of analytic superspace. This formula allows one to determine the spacetime four-point function of any four component fields in the multiplets in terms of the four-point function of the leading chiral primary fields. The leading term is expressed in terms of 1/2Q(Q-1) functions of two conformal invariants and a number of single variable functions. Crossing symmetry reduces the number of independent functions, while the OPE implies that the single-variable functions arise from protected operators and should therefore take their free form. This is the partial non-renormalisation property of such four-point functions which can be viewed as a consequence of the OPE and the non-renormalisation of three-point functions of protected operators. (author)

Heavy-quark QCD vacuum polarisation function. Analytical results at four loops

International Nuclear Information System (INIS)

Kniehl, B.A.; Kotikov, A.V.

2006-07-01

The first two moments of the heavy-quark vacuum polarisation function at four loops in quantum chromo-dynamics are found in fully analytical form by evaluating the missing massive four-loop tadpole master integrals. (orig.)

Conformal anomaly of generalized form factors and finite loop integrals

Science.gov (United States)

Chicherin, Dmitry; Sokatchev, Emery

2018-04-01

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an ℓ-loop integral is a 2nd-order differential equation whose right-hand side is an (ℓ - 1)-loop integral. It could serve as a new useful tool to find/test analytic expressions for conformal integrals. We illustrate this point with several examples of known integrals. We propose a new differential equation for the four-dimensional scalar double box.

MHV, CSW and BCFW: field theory structures in string theory amplitudes

International Nuclear Information System (INIS)

Boels, Rutger; Larsen, Kasper Jens; Obers, Niels A.; Vonk, Marcel

2008-01-01

Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of α'-corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the α' 3 -correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.

High performance control strategy for single-phase three-level neutral-point-clamped traction four-quadrant converters

DEFF Research Database (Denmark)

Kejian, Song; Konstantinou, Georgios; Jing, Li

2017-01-01

Operational data from Chinese railways indicate a number of challenges for traction four-quadrant converter (4QC) control including low-order voltage and current harmonics and reference tracking. A control strategy for a single-phase three-level neutral-point-clamped 4QC employed in the electric...

Four loop massless propagators: An algebraic evaluation of all master integrals

International Nuclear Information System (INIS)

Baikov, P.A.; Chetyrkin, K.G.

2010-01-01

The old 'glue-and-cut' symmetry of massless propagators, first established in Ref. (Chetyrkin and Tkachov, 1981), leads -after reduction to master integrals is performed - to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas (ζ 2n ) in the Adler function and other similar functions essentially reducible to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

CERN Document Server

Dixon, Lance J.; Henn, Johannes M.

2011-01-01

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\\tilde\\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\\\mathcal{N}=4$ super-Yang-Mills theory, $\\Omega^{(1)}$ and $\\Omega^{(2)}$. The derivative of $\\Omega^{(2)}$ with respect to one of the conformal invariants yields $\\tilde\\Phi_6$, while another first-order differential operator applied to $\\tilde\\Phi_6$ yields $\\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\\\\mathcal{N}=4$ super-Yang-Mills.

Gluons and gravitons at one loop from ambitwistor strings

Science.gov (United States)

Geyer, Yvonne; Monteiro, Ricardo

2018-03-01

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

Scattering Amplitudes via Algebraic Geometry Methods

CERN Document Server

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 ...

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

International Nuclear Information System (INIS)

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

2007-01-01

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

A Fast-Processing Modulation Strategy for Three-Phase Four-Leg Neutral-Point-Clamped Inverter Based on the Circuit-Level Decoupling Concept

DEFF Research Database (Denmark)

Ghoreishy, Hoda; Zhang, Zhe; Thomsen, Ole Cornelius

2012-01-01

In this paper, a modulation strategy based on the circuit-level decoupling concept is proposed and investigated for the three-level four-leg neutral-point-clamped (NPC) inverter,with the aim of delivering power to all sorts of loads, linear/nonlinear and balanced/unbalanced. By applying the propo......In this paper, a modulation strategy based on the circuit-level decoupling concept is proposed and investigated for the three-level four-leg neutral-point-clamped (NPC) inverter,with the aim of delivering power to all sorts of loads, linear/nonlinear and balanced/unbalanced. By applying...... the proposed modulation strategy, the four-leg NPC inverter can be decoupled into three three-level Buck converters in each defined operating section. This makes the controller design much simpler compared to the conventional four-leg NPC inverter controllers. Also, this technique can be implemented...

Four loop massless propagators: An algebraic evaluation of all master integrals

Energy Technology Data Exchange (ETDEWEB)

Baikov, P.A., E-mail: baikov@theory.sinp.msu.r [Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119991 (Russian Federation); Chetyrkin, K.G., E-mail: konstantin.chetyrkin@kit.ed [Institut fuer Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe (Germany)] [Institute for Nuclear Research, Russian Academy of Sciences, Moscow 117312 (Russian Federation)

2010-10-01

The old 'glue-and-cut' symmetry of massless propagators, first established in Ref. (Chetyrkin and Tkachov, 1981), leads -after reduction to master integrals is performed - to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas ({zeta}{sub 2n}) in the Adler function and other similar functions essentially reducible to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.

Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph

International Nuclear Information System (INIS)

Remiddi, Ettore; Tancredi, Lorenzo

2014-01-01

A new class of identities for Feynman graph amplitudes, dubbed Schouten identities, valid at fixed integer value of the dimension d is proposed. The identities are then used in the case of the two-loop sunrise graph with arbitrary masses for recovering the second-order differential equation for the scalar amplitude in d=2 dimensions, as well as a chained set of equations for all the coefficients of the expansions in (d−2). The shift from d≈2 to d≈4 dimensions is then discussed

arXiv Conformal anomaly of generalized form factors and finite loop integrals

CERN Document Server

Chicherin, Dmitry

2018-04-16

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an ℓ−loop integral is a 2nd-order differential equation whose right-hand side is an (ℓ − 1)−loop integral. It could serve as a new useful tool to find/test analytic expressions for conformal integrals. We illustrate this point with several examples of known integrals. We propose a new differential equation for the four-dimensional sca...

Onset of Spin Polarization in Four-Gate Quantum Point Contacts

Science.gov (United States)

Jones, Alex

A series of simulations which utilize a Non-equilibrium Green's function (NEGF) formalism is suggested which can provide indirect evidence of the fine and non-local electrostatic tuning of the onset of spin polarization in two closely spaced quantum point contacts (QPCs) that experience a phenomenon known as lateral spin-orbit coupling (LSOC). Each of the QPCs that create the device also has its own pair of side gates (SGs) which are in-plane with the device channel. Numerical simulations of the conductance of the two closely spaced QPCs or four-gate QPC are carried out for different biasing conditions applied to two leftmost and rightmost SGs. Conductance plots are then calculated as a function of the variable, Vsweep, which is the common sweep voltage applied to the QPC. When Vsweep is only applied to two of the four side gates, the plots show several conductance anomalies, i.e., below G0 = 2e2/h, characterized by intrinsic bistability, i.e., hysteresis loops due to a difference in the conductance curves for forward and reverse common voltage sweep simulations. The appearance of hysteresis loops is attributed to the co-existence of multistable spin textures in the narrow channel of the four-gate QPC. The shape, location, and number of hysteresis loops are very sensitive to the biasing conditions on the four SGs. The shape and size of the conductance anomalies and hysteresis loops are shown to change when the biasing conditions on the leftmost and rightmost SGs are swapped, a rectifying behavior providing an additional indirect evidence for the onset of spontaneous spin polarization in nanoscale devices made of QPCs. The results of the simulations reveal that the occurrence and fine tuning of conductance anomalies in QPC structures are highly sensitive to the non-local action of closely spaced SGs. It is therefore imperative to take into account this proximity effect in the design of all electrical spin valves making use of middle gates to fine tune the spin

Green-Schwarz action and loop calculations for superstring

International Nuclear Information System (INIS)

Kallosh, R.; Morozov, A.

1988-01-01

The authors that Green-Schwartz explicitly 10d supersymmetric and 2d covariant approach without spin 1/2 and 3/2 fields on world sheet may appear suitable for calculations of loops in superstring theory. The way the cancellation of Polyakov anomaly is realized and the answer for 1-loop 4-point amplitudes are reproduced

Flat Knitting Loop Deformation Simulation Based on Interlacing Point Model

Directory of Open Access Journals (Sweden)

Jiang Gaoming

2017-12-01

Full Text Available In order to create realistic loop primitives suitable for the faster CAD of the flat-knitted fabric, we have performed research on the model of the loop as well as the variation of the loop surface. This paper proposes an interlacing point-based model for the loop center curve, and uses the cubic Bezier curve to fit the central curve of the regular loop, elongated loop, transfer loop, and irregular deformed loop. In this way, a general model for the central curve of the deformed loop is obtained. The obtained model is then utilized to perform texture mapping, texture interpolation, and brightness processing, simulating a clearly structured and lifelike deformed loop. The computer program LOOP is developed by using the algorithm. The deformed loop is simulated with different yarns, and the deformed loop is applied to design of a cable stitch, demonstrating feasibility of the proposed algorithm. This paper provides a loop primitive simulation method characterized by lifelikeness, yarn material variability, and deformation flexibility, and facilitates the loop-based fast computer-aided design (CAD of the knitted fabric.

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.

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.

Scattering amplitudes over finite fields and multivariate functional reconstruction

International Nuclear Information System (INIS)

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 topologies in Yang-Mills theory, for a complete set of independent helicity configurations.

The correlation function for density perturbations in an expanding universe. III The three-point and predictions of the four-point and higher order correlation functions

Science.gov (United States)

Mcclelland, J.; Silk, J.

1978-01-01

Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.

Eikonal Approximation in AdS/CFT From Shock Waves to Four-Point Functions

CERN Document Server

Cornalba, L; Costa, Miguel S; Penedones, Joao; Cornalba, Lorenzo; Costa, M S; Penedones, J; Schiappa, Ricardo

2007-01-01

We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ _{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ , where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.

Topological amplitudes in string theory

International Nuclear Information System (INIS)

Antoniadis, I.; Taylor, T.R.

1993-07-01

We show that certain type II string amplitudes at genus g are given by the topological partition F g discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional effective action of the form Σ g F g W 2g , where W is the chiral superfield of N = 2 supergravitational multiplet. The holomorphic anomaly of F g is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings. (author). 22 refs, 2 figs

Four-loop on-shell integrals. MS-on-shell relation and g-2

Energy Technology Data Exchange (ETDEWEB)

Marquard, P.

2013-12-15

We present first results towards a full four-loop calculation for both the anomalous magnetic moment of the muon and the MS-on-shell relation. The calculation requires the detailed study of an up to now not considered class of diagrams, so-called on-shell diagrams, at four-loop order.

Calculation and modular properties of multiloop superstring amplitudes

International Nuclear Information System (INIS)

Danilov, G. S.

2013-01-01

Multiloop superstring amplitudes are calculated within an extensively used gauge where the two-dimensional gravitino field carries Grassmann moduli. In general, the amplitudes possess, instead of modular symmetry, symmetry with respect to modular transformation supplemented with appropriate transformations of two-dimensional local supersymmetry. If the number of loops is larger than three, the integrationmeasures are notmodular forms, while the expression for the amplitude contains integrals along the boundary of the fundamental region of the modular group.

Quark mass relations to four-loop order in perturbative QCD.

Science.gov (United States)

Marquard, Peter; Smirnov, Alexander V; Smirnov, Vladimir A; Steinhauser, Matthias

2015-04-10

We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS[over ¯]) scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS[over ¯] quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS[over ¯] heavy quark masses.

The effect of drive frequency and set point amplitude on tapping forces in atomic force microscopy: simulation and experiment

International Nuclear Information System (INIS)

Legleiter, Justin

2009-01-01

In tapping mode atomic force microscopy (AFM), a sharp probe tip attached to an oscillating cantilever is allowed to intermittently strike a surface. By raster scanning the probe while monitoring the oscillation amplitude of the cantilever via a feedback loop, topographical maps of surfaces with nanoscale resolution can be acquired. While numerous studies have employed numerical simulations to elucidate the time-resolved tapping force between the probe tip and surface, until recent technique developments, specific read-outs from such models could not be experimentally verified. In this study, we explore, via numerical simulation, the impact of imaging parameters, i.e. set point ratio and drive frequency as a function of resonance, on time-varying tip-sample force interactions, which are directly compared to reconstructed tapping forces from real AFM experiments. As the AFM model contains a feedback loop allowing for the simulation of the entire scanning process, we further explore the impact that various tip-sample force have on the entire imaging process.

Large-nf contributions to the four-loop splitting functions in QCD

Directory of Open Access Journals (Sweden)

J. Davies

2017-02-01

Full Text Available We have computed the fourth-order nf2 contributions to all three non-singlet quark–quark splitting functions and their four nf3 flavour-singlet counterparts for the evolution of the parton distributions of hadrons in perturbative QCD with nf effectively massless quark flavours. The analytic form of these functions is presented in both Mellin N-space and momentum-fraction x-space; the large-x and small-x limits are discussed. Our results agree with all available predictions derived from lower-order information. The large-x limit of the quark–quark cases provides the complete nf2 part of the four-loop cusp anomalous dimension which agrees with two recent partial computations.

N-loop string amplitude

International Nuclear Information System (INIS)

Mandelstam, S.

1986-06-01

Work on the derivation of an explicit perturbation series for string and superstring amplitudes is reviewed. The light-cone approach is emphasized, but some work on the Polyakov approach is also mentioned, and the two methods are compared. The calculation of the measure factor is outlined in the interacting-string picture

New expressions for string loop amplitudes leading to an ultra-simple conception of string dynamics

International Nuclear Information System (INIS)

Chan Hongmo; Tsou Sheungtsun; Bordes, J.; Nellen, L.

1990-11-01

New expressions are derived for string loop amplitudes as overlap integrals of string wave functionals. They are shown to take the form of exchange terms coming from the Bose-Einstein symmetrisation between string segments. One is thus led to the ultra-simple conception that string theory is basically free, and that 'string interactions' are due merely to the fact that strings are composite objects with Bose-Einstein segments as constituents. (author)

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

Science.gov (United States)

Eden, Burkhard; Smirnov, Vladimir A.

2016-10-01

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

Energy Technology Data Exchange (ETDEWEB)

Eden, Burkhard [Institut für Mathematik und Physik, Humboldt-Universität zu Berlin,Zum großen Windkanal 6, 12489 Berlin (Germany); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics, Moscow State University,119992 Moscow (Russian Federation)

2016-10-21

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

Generating Tree Amplitudes in $N$=4 SYM and $N$ = 8 SG

CERN Document Server

Bianchi, Massimo; Freedman, Daniel Z

2008-01-01

We study n-point tree amplitudes of N=4 super Yang-Mills theory and N=8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general external states. Amplitudes derived from them obey SUSY Ward identities, and the generating functions characterize and count amplitudes in the MHV and NMHV sectors. The MHV generating function provides an efficient way to perform the intermediate state helicity sums required to obtain loop amplitudes from trees. The NMHV generating functions rely on the MHV-vertex expansion obtained from recursion relations associated with a 3-line shift of external momenta involving a reference spinor |X]. The recursion relations remain valid for a subset of N=8 supergravity amplitudes although they do not vanish asymptotically for all |X]. The MHV-vertex expansion of the n-graviton NMHV amplitude for n=5,6,...,11 is independent of |X] and exhibits the asymptotic behavior z^{n-12}. This pres...

First order correction to quasiclassical scattering amplitude

International Nuclear Information System (INIS)

Kuz'menko, A.V.

1978-01-01

First order (with respect to h) correction to quasiclassical with the aid of scattering amplitude in nonrelativistic quantum mechanics is considered. This correction is represented by two-loop diagrams and includes the double integrals. With the aid of classical equations of motion, the sum of the contributions of the two-loop diagrams is transformed into the expression which includes one-dimensional integrals only. The specific property of the expression obtained is that the integrand does not possess any singularities in the focal points of the classical trajectory. The general formula takes much simpler form in the case of one-dimensional systems

Multiscalar production amplitudes beyond threshold

CERN Document Server

Argyres, E N; Kleiss, R H

1993-01-01

We present exact tree-order amplitudes for $H^* \\to n~H$, for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that satisfy unitarity, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculate $2\\to n$ tree amplitudes at threshold and show that for the unbroken $\\phi^4$ theory they vanish for $n>4~$, for the Standard Model Higgs they vanish for $n\\ge 3~$ and for a model potential, respecting tree-order unitarity, for $n$ even and $n>4~$. Finally, we calculate the imaginary part of the one-loop $1\\to n$ amplitude in both symmetric and spontaneously broken $\\phi^4$ theory.

A Contrast on Conductor Galloping Amplitude Calculated by Three Mathematical Models with Different DOFs

Directory of Open Access Journals (Sweden)

Bin Liu

2014-01-01

Full Text Available It is pivotal to find an effective mathematical model revealing the galloping mechanism. And it is important to compare the difference between the existing mathematical models on the conductor galloping. In this paper, the continuum cable model for transmission lines was proposed using the Hamilton principle. Discrete models of one DOF, two DOFs, and three DOFs were derived from the continuum model by using the Garlekin method. And the three models were compared by analyzing the galloping vertical amplitude and torsional angle with different influence factors. The influence factors include wind velocity, flow density, span length, damping ratio, and initial tension. The three-DOF model is more accurate at calculating the galloping characteristics than the other two models, but the one-DOF and two-DOF models can also present the trend of galloping amplitude change from the point view of qualitative analysis. And the change of the galloping amplitude relative to the main factors was also obtained, which is very essential to the antigalloping design applied in the actual engineering.

Use of helicity methods in evaluating loop integrals: a QCD example

International Nuclear Information System (INIS)

Koerner, J.G.; Sieben, P.

1991-01-01

We discuss the use of helicity methods in evaluating loop diagrams by analyzing a specific example: the one-loop concentration to e + e - → qanti qg in massless QCD. By using covariant helicity representations for the spinor and vector wave functins we obtain the helicity amplitudes directly from the Feynman loop diagrams by covariant contraction. The necessary loop integrations are considerably simplified since one encounters only scalar loop integrals after contraction. We discuss crossing relations that allow one to obtain the corresponding one-loop helicity amplitudes for the crossed processes as e.g. qanti q → (W, Z, γ * ) + g including the real photon cases. As we treat the spin degrees of freedom in four dimensions and only continue momenta to n dimensions (dimensional reduction scheme) we explicate how our results are related to the usual dimensional regularization results. (orig.)

Analytic properties of high energy production amplitudes in N=4 SUSY

International Nuclear Information System (INIS)

Lipatov, L.N.; Hamburg Univ.

2010-08-01

We investigate analytic properties of the six point planar amplitude in N=4 SUSY at the multi-Regge kinematics for final state particles. For inelastic processes the Steinmann relations play an important role because they give a possibility to fix the phase structure of the Regge pole and Mandelstam cut contributions. The analyticity and factorization constraints allow us to reproduce the two-loop correction to the 6- point BDS amplitude in N=4 SUSY obtained earlier in the leading logarithmic approximation with the use of the s-channel unitarity. The cut contribution has the Moebius invariant form in the transverse momentum subspace. The exponentiation hypothesis for the amplitude in the multi-Regge kinematics is also investigated in LLA. (orig.)

Analytic properties of high energy production amplitudes in N=4 SUSY

Energy Technology Data Exchange (ETDEWEB)

Lipatov, L.N. [St. Petersburg Inst. of Nuclear Physics, Gatchina (Russian Federation); Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik

2010-08-15

We investigate analytic properties of the six point planar amplitude in N=4 SUSY at the multi-Regge kinematics for final state particles. For inelastic processes the Steinmann relations play an important role because they give a possibility to fix the phase structure of the Regge pole and Mandelstam cut contributions. The analyticity and factorization constraints allow us to reproduce the two-loop correction to the 6- point BDS amplitude in N=4 SUSY obtained earlier in the leading logarithmic approximation with the use of the s-channel unitarity. The cut contribution has the Moebius invariant form in the transverse momentum subspace. The exponentiation hypothesis for the amplitude in the multi-Regge kinematics is also investigated in LLA. (orig.)

Three-point statistics of cosmological stochastic gravitational waves

International Nuclear Information System (INIS)

Adshead, Peter; Lim, Eugene A.

2010-01-01

We consider the three-point function (i.e. the bispectrum or non-Gaussianity) for stochastic backgrounds of gravitational waves. We estimate the amplitude of this signal for the primordial inflationary background, gravitational waves generated during preheating, and for gravitational waves produced by self-ordering scalar fields following a global phase transition. To assess detectability, we describe how to extract the three-point signal from an idealized interferometric experiment and compute the signal to noise ratio as a function of integration time. The three-point signal for the stochastic gravitational wave background generated by inflation is unsurprisingly tiny. For gravitational radiation generated by purely causal, classical mechanisms we find that, no matter how nonlinear the process is, the three-point correlations produced vanish in direct detection experiments. On the other hand, we show that in scenarios where the B-mode of the cosmic microwave background is sourced by gravitational waves generated by a global phase transition, a strong three-point signal among the polarization modes is also produced. This may provide another method of distinguishing inflationary B-modes. To carry out this computation, we have developed a diagrammatic approach to the calculation of stochastic gravitational waves sourced by scalar fluids, which has applications beyond the present scenario.

Fermionic contributions to the three-loop static potential

International Nuclear Information System (INIS)

Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias

2008-01-01

We consider the three-loop corrections to the static potential which are induced by a closed fermion loop. For the reduction of the occurring integrals a combination of the Groebner and Laporta algorithm has been used and the evaluation of the master integrals has been performed with the help of the Mellin-Barnes technique. The fermionic three-loop corrections amount to 2% of the tree-level result for top quarks, 8% for bottom quarks and 27% for the charm quark system

Fermionic contributions to the three-loop static potential

Energy Technology Data Exchange (ETDEWEB)

Smirnov, Alexander V. [Scientific Research Computing Center, Moscow State University, 119992 Moscow (Russian Federation); Institut fuer Theoretische Teilchenphysik, Universitaet Karlsruhe (Thailand), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Smirnov, Vladimir A. [Nuclear Physics Institute, Moscow State University, 119992 Moscow (Russian Federation); Institut fuer Theoretische Teilchenphysik, Universitaet Karlsruhe (Thailand), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Steinhauser, Matthias [Institut fuer Theoretische Teilchenphysik, Universitaet Karlsruhe (Thailand), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany)], E-mail: matthias.steinhauser@uka.de

2008-10-16

We consider the three-loop corrections to the static potential which are induced by a closed fermion loop. For the reduction of the occurring integrals a combination of the Groebner and Laporta algorithm has been used and the evaluation of the master integrals has been performed with the help of the Mellin-Barnes technique. The fermionic three-loop corrections amount to 2% of the tree-level result for top quarks, 8% for bottom quarks and 27% for the charm quark system.

Cluster algebras in scattering amplitudes with special 2D kinematics

Energy Technology Data Exchange (ETDEWEB)

Torres, Marcus A.C. [Institut de Physique Theorique, CEA-Saclay, Gif-sur-Yvette Cedex (France)

2014-02-15

We study the cluster algebra of the kinematic configuration space Conf{sub n}(P{sup 3}P3) of an n-particle scattering amplitude restricted to the special 2D kinematics. We found that the n-point two-loop MHVremainder function in special 2D kinematics depends on a selection of the X-coordinates that are part of a special structure of the cluster algebra related to snake triangulations of polygons. This structure forms a necklace of hypercube beads in the corresponding Stasheff polytope. Furthermore at n = 12, the cluster algebra and the selection of theX-coordinates in special2Dkinematics replicates the cluster algebra and the selection of X-coordinates of the n = 6 two-loop MHV amplitude in 4D kinematics. (orig.)

Conformal boundary loop models

International Nuclear Information System (INIS)

Jacobsen, Jesper Lykke; Saleur, Hubert

2008-01-01

We study a model of densely packed self-avoiding loops on the annulus, related to the Temperley-Lieb algebra with an extra idempotent boundary generator. Four different weights are given to the loops, depending on their homotopy class and whether they touch the outer rim of the annulus. When the weight of a contractible bulk loop x≡q+q -1 element of (-2,2], this model is conformally invariant for any real weight of the remaining three parameters. We classify the conformal boundary conditions and give exact expressions for the corresponding boundary scaling dimensions. The amplitudes with which the sectors with any prescribed number and types of non-contractible loops appear in the full partition function Z are computed rigorously. Based on this, we write a number of identities involving Z which hold true for any finite size. When the weight of a contractible boundary loop y takes certain discrete values, y r ≡([r+1] q )/([r] q ) with r integer, other identities involving the standard characters K r,s of the Virasoro algebra are established. The connection with Dirichlet and Neumann boundary conditions in the O(n) model is discussed in detail, and new scaling dimensions are derived. When q is a root of unity and y=y r , exact connections with the A m type RSOS model are made. These involve precise relations between the spectra of the loop and RSOS model transfer matrices, valid in finite size. Finally, the results where y=y r are related to the theory of Temperley-Lieb cabling

Hexagon functions and the three-loop remainder function

Energy Technology Data Exchange (ETDEWEB)

Dixon, Lance J.; Drummond, James M.; von Hippel, Matt; Pennington, Jeffrey

2013-12-01

We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar NN = 4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann ζ valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.

Scattering Amplitudes and Worldsheet Models of QFTs

CERN Multimedia

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.

One-loop soft theorems via dual superconformal symmetry

Energy Technology Data Exchange (ETDEWEB)

Brandhuber, Andreas; Hughes, Edward; Spence, Bill; Travaglini, Gabriele [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom)

2016-03-14

We study soft theorems at one loop in planar N = 4 super Yang-Mills theory through finite order in the infrared regulator and to subleading order in the soft parameter δ. In particular, we derive a universal constraint from dual superconformal symmetry, which we use to bootstrap subleading log δ behaviour. Moreover, we determine the complete infrared-finite subleading soft contribution of n-point MHV amplitudes using momentum twistors. Finally, we compute the subleading log δ behaviour of one-loop NMHV ratio functions at six and seven points, finding that universality holds within but not between helicity sectors.

Wilson loop OPE, analytic continuation and multi-Regge limit

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki

2014-05-01

We explore a direct connection between the collinear limit and the multi-Regge limit for scattering amplitudes in the N=4 super Yang-Mills theory. Starting with the collinear expansion for the six-gluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the so-called Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multi-Regge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the ''collinear-Regge'' limit up to five loops. Our results agree with all the known results up to four loops. At five-loop, our results up to the next-to-next-to-leading logarithmic approximation (NNLLA) also reproduce the known results, and for the N 3 LLA and the N 4 LLA give non-trivial predictions. We further present an all-loop prediction for the imaginary part of the next-to-double-leading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multi-Regge limit with the help of the OPE.

Four-point probe measurements using current probes with voltage feedback to measure electric potentials

Science.gov (United States)

Lüpke, Felix; Cuma, David; Korte, Stefan; Cherepanov, Vasily; Voigtländer, Bert

2018-02-01

We present a four-point probe resistance measurement technique which uses four equivalent current measuring units, resulting in minimal hardware requirements and corresponding sources of noise. Local sample potentials are measured by a software feedback loop which adjusts the corresponding tip voltage such that no current flows to the sample. The resulting tip voltage is then equivalent to the sample potential at the tip position. We implement this measurement method into a multi-tip scanning tunneling microscope setup such that potentials can also be measured in tunneling contact, allowing in principle truly non-invasive four-probe measurements. The resulting measurement capabilities are demonstrated for \

Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring

International Nuclear Information System (INIS)

Berkovits, Nathan

2004-01-01

A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and to construct a suitable b ghost. A super-Poincare covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N 4 terms in the effective action receive no perturbative contributions above one loop. (author)

The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Dixon, Lance J. [SLAC National Accelerator Laboratory,Stanford University, Stanford, CA 94309 (United States); Drummond, James M. [CERN,Geneva 23 (Switzerland); School of Physics and Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); LAPTH, CNRS et Université de Savoie,F-74941 Annecy-le-Vieux Cedex (France); Duhr, Claude [Institute for Particle Physics Phenomenology, University of Durham,Durham, DH1 3LE (United Kingdom); Pennington, Jeffrey [SLAC National Accelerator Laboratory,Stanford University, Stanford, CA 94309 (United States)

2014-06-19

We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar N=4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at N{sup 3}LLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large regions in the space of cross ratios, and they are not far from the value expected at asymptotically large orders of perturbation theory.

Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

International Nuclear Information System (INIS)

Bluemlein, Johannes; Phan, Khiem Hong; Vietnam National Univ., Ho Chi Minh City; Riemann, Tord; Silesia Univ., Chorzow

2017-11-01

Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension d in terms of (generalized) hypergeometric functions 2 F 1 and F 1 . Values at asymptotic or exceptional kinematic points as well as expansions around the singular points at d=4+2n, n non-negative integers, may be derived from the representations easily. The Feynman integrals studied here may be used as building blocks for the calculation of one-loop and higher-loop scalar and tensor amplitudes. From the recursion relation presented, higher n-point functions may be obtained in a straightforward manner.

Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

Energy Technology Data Exchange (ETDEWEB)

Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Phan, Khiem Hong [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Vietnam National Univ., Ho Chi Minh City (Viet Nam). Univ. of Science; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Silesia Univ., Chorzow (Poland). Inst. of Physics

2017-11-15

Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension d in terms of (generalized) hypergeometric functions {sub 2}F{sub 1} and F{sub 1}. Values at asymptotic or exceptional kinematic points as well as expansions around the singular points at d=4+2n, n non-negative integers, may be derived from the representations easily. The Feynman integrals studied here may be used as building blocks for the calculation of one-loop and higher-loop scalar and tensor amplitudes. From the recursion relation presented, higher n-point functions may be obtained in a straightforward manner.

Novel string field theory with also negative energy constituents/objects gives Veneziano amplitude

Science.gov (United States)

Nielsen, H. B.; Ninomiya, M.

2018-02-01

We have proposed a new type of string field theory. The main point of the present article is to cure some technical troubles: missing two out three terms in Veneziano amplitude. Our novel string field theory, describes a theory with many strings in terms of "objects", which are not exactly, but close to Charles Thorn's string bits. The new point is that the objects in terms of which the universe states are constructed, and which have an essentially 26-momentum variable called J μ , can have the energy J 0 be also negative as well as positive. We get a long way in deriving in this model the Veneziano model and obtain all the three terms needed for a four point amplitude. This result strongly indicates that our novel string field theory is indeed string theory.

Meson-baryon four-body reaction amplitudes in exact SU(4)

International Nuclear Information System (INIS)

Liede, I.; Maalampi, J.; Roos, M.

1976-01-01

Fully SU(4) symmetric meson-baryon four body reaction amplitudes are presented in terms of SU(4) eigenamplitudes. The mesons and baryons considered belong to the SU(4) representations 15 and 20, respectively. Using these reletions, the cross-sections for the production of charmed particles can be predicted from known uncharmed reactions. (author)

Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro

International Nuclear Information System (INIS)

Jing, Jin; Hai-Ting, Tian; Xiong, Pan; Ning-Fang, Song

2010-01-01

The phase modulation and the closed-loop controller can generate electrical crosstalk-coupling in digital closed-loop fibre optic gyro. Four electrical cross-coupling paths are verified by the open-loop testing approach. It is found the variation of ramp amplitude will lead to the alternation of gyro bias. The amplitude and the phase parameters of the electrical crosstalk signal are measured by lock-in amplifier, and the variation of gyro bias is confirmed to be caused by the alternation of phase according to the amplitude of the ramp. A digital closed-loop fibre optic gyro electrical crosstalk-coupling model is built by approximating the electrical cross-coupling paths as a proportion and integration segment. The results of simulation and experiment show that the modulation signal electrical crosstalk-coupling can cause the dead zone of the gyro when a small angular velocity is inputted, and it could also lead to a periodic vibration of the bias error of the gyro when a large angular velocity is inputted

Conformal anomaly of super Wilson loop

Energy Technology Data Exchange (ETDEWEB)

Belitsky, A.V., E-mail: andrei.belitsky@asu.edu [Department of Physics, Arizona State University, Tempe, AZ 85287-1504 (United States)

2012-09-11

Classically supersymmetric Wilson loop on a null polygonal contour possesses all symmetries required to match it onto non-MHV amplitudes in maximally supersymmetric Yang-Mills theory. However, to define it quantum mechanically, one is forced to regularize it since perturbative loop diagrams are not well defined due to presence of ultraviolet divergences stemming from integration in the vicinity of the cusps. A regularization that is adopted by practitioners by allowing one to use spinor helicity formalism, on the one hand, and systematically go to higher orders of perturbation theory is based on a version of dimensional regularization, known as Four-Dimensional Helicity scheme. Recently it was demonstrated that its use for the super Wilson loop at one loop breaks both conformal symmetry and Poincare supersymmetry. Presently, we exhibit the origin for these effects and demonstrate how one can undo this breaking. The phenomenon is alike the one emerging in renormalization group mixing of conformal operators in conformal theories when one uses dimensional regularization. The rotation matrix to the diagonal basis is found by means of computing the anomaly in the Ward identity for the conformal boost. Presently, we apply this ideology to the super Wilson loop. We compute the one-loop conformal anomaly for the super Wilson loop and find that the anomaly depends on its Grassmann coordinates. By subtracting this anomalous contribution from the super Wilson loop we restore its interpretation as a dual description for reduced non-MHV amplitudes which are expressed in terms of superconformal invariants.

On conformal-invariant behaviour of four-point theories in ultraviolet asymptotics

International Nuclear Information System (INIS)

Ushveridze, A.G.

1977-01-01

A method is presented to obtain scale- and conformal-invariant solutions of four-point field theories in the ultraviolet asymptotics by means of reduction to the three-point problem. To do this a supplementary sigma field without a kinetic term is introduced and the Lagrangian is modified correspondingly. For the three-point problems the equations in form of the generalized unitarity conditions are solved further

Extracting Loop Bounds for WCET Analysis Using the Instrumentation Point Graph

Science.gov (United States)

Betts, A.; Bernat, G.

2009-05-01

Every calculation engine proposed in the literature of Worst-Case Execution Time (WCET) analysis requires upper bounds on loop iterations. Existing mechanisms to procure this information are either error prone, because they are gathered from the end-user, or limited in scope, because automatic analyses target very specific loop structures. In this paper, we present a technique that obtains bounds completely automatically for arbitrary loop structures. In particular, we show how to employ the Instrumentation Point Graph (IPG) to parse traces of execution (generated by an instrumented program) in order to extract bounds relative to any loop-nesting level. With this technique, therefore, non-rectangular dependencies between loops can be captured, allowing more accurate WCET estimates to be calculated. We demonstrate the improvement in accuracy by comparing WCET estimates computed through our HMB framework against those computed with state-of-the-art techniques.

Multi-loop string amplitudes and Riemann surfaces

International Nuclear Information System (INIS)

Taylor, J.G.

1986-01-01

The paper was presented at the workshop on 'Supersymmetry and its applications', Cambridge, United Kingdom, 1985. Super-string theory is discussed under the following topic headings: the functional approach to the string amplitude, Rieman surfaces, the determinants Δsub(epsilon)(1) and Δsub(epsilon)(2), Green's functions, total amplitude, and divergence analysis. (U.K.)

Higgs Amplitudes from N=4 Supersymmetric Yang-Mills Theory.

Science.gov (United States)

Brandhuber, Andreas; Kostacińska, Martyna; Penante, Brenda; Travaglini, Gabriele

2017-10-20

Higgs plus multigluon amplitudes in QCD can be computed in an effective Lagrangian description. In the infinite top-mass limit, an amplitude with a Higgs boson and n gluons is computed by the form factor of the operator TrF^{2}. Up to two loops and for three gluons, its maximally transcendental part is captured entirely by the form factor of the protected stress tensor multiplet operator T_{2} in N=4 supersymmetric Yang-Mills theory. The next order correction involves the calculation of the form factor of the higher-dimensional, trilinear operator TrF^{3}. We present explicit results at two loops for three gluons, including the subleading transcendental terms derived from a particular descendant of the Konishi operator that contains TrF^{3}. These are expressed in terms of a few universal building blocks already identified in earlier calculations. We show that the maximally transcendental part of this quantity, computed in nonsupersymmetric Yang-Mills theory, is identical to the form factor of another protected operator, T_{3}, in the maximally supersymmetric theory. Our results suggest that the maximally transcendental part of Higgs amplitudes in QCD can be entirely computed through N=4 super Yang-Mills theory.

Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM

CERN Document Server

Eden, Burkhard; Korchemsky, Gregory P; Sokatchev, Emery

2012-01-01

We present a construction of the integrand of the correlation function of four stress-tensor multiplets in N=4 SYM at weak coupling. It does not rely on Feynman diagrams and makes use of the recently discovered symmetry of the integrand under permutations of external and integration points. This symmetry holds for any gauge group, so it can be used to predict the integrand both in the planar and non-planar sectors. We demonstrate the great efficiency of graph-theoretical tools in the systematic study of the possible permutation symmetric integrands. We formulate a general ansatz for the correlation function as a linear combination of all relevant graph topologies, with arbitrary coefficients. Powerful restrictions on the coefficients come from the analysis of the logarithmic divergences of the correlation function in two singular regimes: Euclidean short-distance and Minkowski light-cone limits. We demonstrate that the planar integrand is completely fixed by the procedure up to six loops and probably beyond. ...

Checking the transverse Ward-Takahashi relation at one-loop order in four dimensions

International Nuclear Information System (INIS)

Pennington, M R; Williams, R

2006-01-01

Some time ago Takahashi derived the so-called transverse relations relating Green's functions of different orders to complement the well-known Ward-Green-Takahashi identities of gauge theories by considering wedge rather than inner products. These transverse relations have the potential to determine the full fermion-boson vertex in terms of the renormalization functions of the fermion propagator. He and Yu have given an indicative proof at one-loop level in four dimensions. However, their construct involves the fourth-rank Levi-Civita tensor defined only unambiguously in four dimensions exactly where the loop integrals diverge. Consequently, here we explicitly check the proposed transverse Ward-Takahashi relation holds at one-loop order in d-dimensions, with d = 4 + ε

Prototype phase and amplitude feedback-control systems for the FMIT accelerator

International Nuclear Information System (INIS)

Fazio, M.V.; Patton, R.D.

1983-01-01

The phase and amplitude feedback-control systems for the Fusion Materials irradiation Test (FMIT) accelerator have been successfully prototyped and tested. The testing was performed at low power with two 100-W rf systems driving a high-Q resonant cavity at 80 MHz. The control systems can maintain the cavity field amplitude to within +-1% and the phase to within +-1 0 of the set-point values. When there are multiple rf systems independently driving a resonant cavity through individual drive loops, amplitude matching and proper phasing between the outputs of each rf system are essential for proper system operation. Experimental results are presented

Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations

Energy Technology Data Exchange (ETDEWEB)

Henn, Johannes M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Moch, Sven [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Naculich, Stephen G. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Bowdoin College, Brunswick, ME (United States). Dept. of Physics

2011-09-15

The IR-divergent scattering amplitudes of N=4 supersymmetric Yang-Mills theory can be regulated in a variety of ways, including dimensional regularization and massive (or Higgs) regularization. The IR-finite part of an amplitude in different regularizations generally differs by an additive constant at each loop order, due to the ambiguity in separating finite and divergent contributions. We give a prescription for defining an unambiguous, regulator-independent finite part of the amplitude by factoring off a product of IR-divergent ''wedge'' functions. For the cases of dimensional regularization and the common-mass Higgs regulator, we define the wedge function in terms of a form factor, and demonstrate the regularization independence of the n-point amplitude through two loops. We also deduce the form of the wedge function for the more general differential-mass Higgs regulator, although we lack an explicit operator definition in this case. Finally, using extended dual conformal symmetry, we demonstrate the link between the differential-mass wedge function and the anomalous dual conformal Ward identity for the finite part of the scattering amplitude. (orig.)

Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations

International Nuclear Information System (INIS)

Henn, Johannes M.; Naculich, Stephen G.; Bowdoin College, Brunswick, ME

2011-09-01

The IR-divergent scattering amplitudes of N=4 supersymmetric Yang-Mills theory can be regulated in a variety of ways, including dimensional regularization and massive (or Higgs) regularization. The IR-finite part of an amplitude in different regularizations generally differs by an additive constant at each loop order, due to the ambiguity in separating finite and divergent contributions. We give a prescription for defining an unambiguous, regulator-independent finite part of the amplitude by factoring off a product of IR-divergent ''wedge'' functions. For the cases of dimensional regularization and the common-mass Higgs regulator, we define the wedge function in terms of a form factor, and demonstrate the regularization independence of the n-point amplitude through two loops. We also deduce the form of the wedge function for the more general differential-mass Higgs regulator, although we lack an explicit operator definition in this case. Finally, using extended dual conformal symmetry, we demonstrate the link between the differential-mass wedge function and the anomalous dual conformal Ward identity for the finite part of the scattering amplitude. (orig.)

Efficient analytic computation of higher-order QCD amplitudes

International Nuclear Information System (INIS)

Bern, Z.; Chalmers, G.; Dunbar, D.C.; Kosower, D.A.

1995-01-01

The authors review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. Particularly useful are the constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes. Certain sequences of one-loop helicity amplitudes with an arbitrary number of external gluons have been obtained using these constraints

Control of one- and two-photon absorption in a four-level atomic system by changing the amplitude and phase of a driving microwave field

International Nuclear Information System (INIS)

Hou, B P; Wang, S J; Yu, W L; Sun, W L

2005-01-01

We consider the one- and two-photon absorption spectra of a four-level Y-type atom with the two highest lying levels driven by a microwave field. We found that in the one-photon absorption case, the microwave field can lead to the probe gain, and the absorption and gain spectral structures depend strongly on the microwave field amplitude. For the two-photon absorption case, the strong microwave field can enhance the absorption. When the microwave field amplitude is reduced to a certain value, the single absorption peak in the two-photon spectrum changes into a structure of two-peak structure with different magnitudes. Moreover, the one- and two-photon absorption spectra can be modulated by the phase of the microwave field which produces a closed-loop configuration. Finally, we use the analytic solutions in terms of dressed-state basis to explain the results from our numerical calculation

Scattering amplitudes in super-renormalizable gravity

International Nuclear Information System (INIS)

Donà, Pietro; Giaccari, Stefano; Modesto, Leonardo; Rachwał, Lesław; Zhu, Yiwei

2015-01-01

We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local and weakly nonlocal gravitational theories that are quadratic in both, the Ricci and scalar curvature with form factors of the d’Alembertian operator inserted between. More specifically we are interested in renormalizable, super-renormalizable or finite theories. The scattering amplitudes for these theories turn out to be the same as the ones of Einstein gravity regardless of the explicit form of the form factors. As a special case the four-graviton scattering amplitudes in Weyl conformal gravity are identically zero. Using a field redefinition, we prove that the outcome is correct for any number of external gravitons (on-shell n−point functions) and in any dimension for a large class of theories. However, when an operator quadratic in the Riemann tensor is added in any dimension (with the exception of the Gauss-Bonnet term in four dimensions) the result is completely altered, and the scattering amplitudes depend on all the form factors introduced in the action.

Loop Growth and Point-Defect Profiles during HVEM Irradiation

DEFF Research Database (Denmark)

Leffers, Torben; Singh, Bachu Narain

1979-01-01

The point-defect profile in a thin foil is included in the model for the growth of dislocation loops during HVEM irradiation suggested by Kiritani, Yoshida, Takata, and Maehara, and the possible effect of divacancies is discussed. It is found that there is a fairly wide transition range between...

Analytic properties of the partial amplitudes in the three-body problem

International Nuclear Information System (INIS)

Blokhintsev, L.D.; Simonov, Yu.A.

1978-01-01

The singularities of the partial waves for a multiple scattering series of a system of three nonrelativistic particles with arbitrary masses are studied. Both on-shell and off-shell diagrams are considered for binary processes (2→2), break-up processes (2→3) and also three-particle scattering (3→3). For any diagram there are obtained: 1) simple analytic expressions for the loci of the nonpotential singularities of the partial amplitudes, i.e. for the singularities independent of the form of interaction between particles; 2) necessary and sufficient conditions of an existence of these singularities on the physical sheet; 3) a character of the singularities. A criterium is found for the kinematic possibility of a process of N subsequent pair collisions in a classical system of three point like masses with the contact interaction the maximal number Nsub(max) of these collisions is deduced

Three-Dimensional Printing of Vitrification Loop Prototypes for Aquatic Species.

Science.gov (United States)

Tiersch, Nolan J; Childress, William M; Tiersch, Terrence R

2018-05-16

Vitrification is a method of cryopreservation that freezes samples rapidly, while forming an amorphous solid ("glass"), typically in small (μL) volumes. The goal of this project was to create, by three-dimensional (3D) printing, open vitrification devices based on an elliptical loop that could be efficiently used and stored. Vitrification efforts can benefit from the application of 3D printing, and to begin integration of this technology, we addressed four main variables: thermoplastic filament type, loop length, loop height, and method of loading. Our objectives were to: (1) design vitrification loops with varied dimensions; (2) print prototype loops for testing; (3) evaluate loading methods for the devices; and (4) classify vitrification responses to multiple device configurations. The various configurations were designed digitally using 3D CAD (Computer Aided Design) software, and prototype devices were produced with MakerBot ® 3D printers. The thermoplastic filaments used to produce devices were acrylonitrile butadiene styrene (ABS) and polylactic acid (PLA). Vitrification devices were characterized by the film volumes formed with different methods of loading (pipetting or submersion). Frozen films were classified to determine vitrification quality: zero (opaque, or abundant crystalline ice formation); one (translucent, or partial vitrification), or two (transparent, or substantial vitrification, glass). A published vitrification solution was used to conduct experiments. Loading by pipetting formed frozen films more reliably than by submersion, but submersion yielded fewer filling problems and was more rapid. The loop designs that yielded the highest levels of vitrification enabled rapid transfer of heat, and most often were characterized as being longer and consisting of fewer layers (height). 3D printing can assist standardization of vitrification methods and research, yet can also provide the ability to quickly design and fabricate custom devices when

A gauge/gravity relation in the one-loop effective action

International Nuclear Information System (INIS)

Basar, Goekce; Dunne, Gerald V

2010-01-01

We identify an unusual new gauge/gravity relation: the one-loop effective action for a massive spinor in 2n-dimensional AdS space is expressed in terms of precisely the same function (a certain multiple gamma function) as the one-loop effective action for a massive charged scalar in 4n dimensions in a maximally symmetric background electromagnetic field (one for which the eigenvalues of F μν are maximally degenerate, corresponding in four dimensions to a self-dual field, equivalently to a field of definite helicity), subject to the identification F 2 ↔Λ, where Λ is the gravitational curvature. Since these effective actions generate the low energy limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a nontrivial gauge/gravity relation at the non-perturbative level and at the amplitude level. (fast track communication)

Low-energy moments of non-diagonal quark current correlators at four loops

International Nuclear Information System (INIS)

Maier, A.

2015-06-01

We complete the leading four physical terms in the low-energy expansions of heavy-light quark current correlators at four-loop order. As a by-product we reproduce the corresponding top-induced non-singlet correction to the electroweak ρ parameter.

The SU(2|3) dynamic two-loop form factors

International Nuclear Information System (INIS)

Brandhuber, A.; Kostacińska, M.; Penante, B.; Travaglini, G.; Young, D.

2016-01-01

We compute two-loop form factors of operators in the SU(2|3) closed subsector of N = 4 supersymmetric Yang-Mills. In particular, we focus on the non-protected, dimension-three operators Tr(X[Y,Z]) and Tr(ψψ) for which we compute the four possible two-loop form factors, and corresponding remainder functions, with external states 〈X̄ȲZ̄| and 〈ψ̄ψ̄|. Interestingly, the maximally transcendental part of the two-loop remainder of 〈X̄ȲZ̄|Tr(X[Y,Z])|0〉 turns out to be identical to that of the corresponding known quantity for the half-BPS operator Tr(X"3). We also find a surprising connection between the terms subleading in transcendentality and certain a priori unrelated remainder densities introduced in the study of the spin chain Hamiltonian in the SU(2) sector. Next, we use our calculation to resolve the mixing, recovering anomalous dimensions and eigenstates of the dilatation operator in the SU(2|3) sector at two loops. We also speculate on potential connections between our calculations in N = 4 super Yang-Mills and Higgs + multi-gluon amplitudes in QCD in an effective Lagrangian approach.

The SU(2|3) dynamic two-loop form factors

Energy Technology Data Exchange (ETDEWEB)

Brandhuber, A.; Kostacińska, M. [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom); Penante, B. [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom); Institut für Physik und IRIS Adlershof, Humboldt Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); Travaglini, G.; Young, D. [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom)

2016-08-23

We compute two-loop form factors of operators in the SU(2|3) closed subsector of N = 4 supersymmetric Yang-Mills. In particular, we focus on the non-protected, dimension-three operators Tr(X[Y,Z]) and Tr(ψψ) for which we compute the four possible two-loop form factors, and corresponding remainder functions, with external states 〈X̄ȲZ̄| and 〈ψ̄ψ̄|. Interestingly, the maximally transcendental part of the two-loop remainder of 〈X̄ȲZ̄|Tr(X[Y,Z])|0〉 turns out to be identical to that of the corresponding known quantity for the half-BPS operator Tr(X{sup 3}). We also find a surprising connection between the terms subleading in transcendentality and certain a priori unrelated remainder densities introduced in the study of the spin chain Hamiltonian in the SU(2) sector. Next, we use our calculation to resolve the mixing, recovering anomalous dimensions and eigenstates of the dilatation operator in the SU(2|3) sector at two loops. We also speculate on potential connections between our calculations in N = 4 super Yang-Mills and Higgs + multi-gluon amplitudes in QCD in an effective Lagrangian approach.

Higgs bosons and QCD jets at two loops

International Nuclear Information System (INIS)

Koukoutsakis, Athanasios

2003-04-01

In this thesis we present techniques for the calculation of two-loop integrals contributing to the virtual corrections to physical processes with three on-shell and one off-shell external particles. First, we describe a set of basic tools that simplify the manipulation of complicated two-loop integrals. A technique for deriving helicity amplitudes with use of a set of projectors is demonstrated. Then we present an algorithm, introduced by Laporta, that helps reduce all possible two-loop integrals to a basic set of 'master integrals'. Subsequently, these master integrals are analytically evaluated by deriving and solving differential equations on the external scales of the process. Two-loop matrix elements and helicity amplitudes are calculated for the physical processes γ* → qq-barg and H → ggg respectively. Conventional Dimensional Regularization is used in the evaluation of Feynman diagrams. For both processes the infrared singular behavior is shown to agree with the one predicted by Catani. (author)

Four-loop divergences of the two-dimensional (1,1) supersymmetric non-linear sigma model with a Wess-Zumino-Witten term

International Nuclear Information System (INIS)

Deriglazov, A.A.; Ketov, S.V.

1991-01-01

The four-loop divergences of the (1,1) supersymmetric two-dimensional non-linear σ-model with a Wess-Zumino-Witten term are analyzed. All the four-loop 1/ε-divergences in the general case (and an overall coefficient at the total four-loop contribution to the β-function) are shown to be reducible to only structures proportional to ζ(3). We explicitly calculate non-derivative contributions to the four-loop β-function from logarithmically divergent graphs. As a by-product, we obtain the complete four-loop β-function for the supersymmetric Wess-Zumino-Witten model. We use the partial results for the general four-loop β-function to shed some light on the structure of the (α') 3 -corrections to the superstring effective-action with antisymmetric-tensor field coupling. An inconsistency of the supersymmetrical dimensional regularisation via dimensional reduction in the presence of torsion is discovered at four loops, unless the string interpretation for the σ-model is adopted. (orig.)

Towards next-to-leading order transport coefficients from the four-particle irreducible effective action

International Nuclear Information System (INIS)

Carrington, M. E.; Kovalchuk, E.

2010-01-01

Transport coefficients can be obtained from two-point correlators using the Kubo formulas. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the resummed two-point function that is obtained from the three-loop three-particle irreducible resummed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the four-loop four-particle irreducible effective action for a scalar theory with cubic and quartic interactions, with a nonvanishing field expectation value. We obtain a set of integral equations that determine the resummed two-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.

Extracting OPE coefficient of Konishi at four loops

Energy Technology Data Exchange (ETDEWEB)

Goncalves, Vasco [ICTP South American Institute for Fundamental Research Instituto de Fisica Teorica,UNESP, Universidad Estadual Paulista, Rua Dr. Bento T. Ferraz 271, 01140-070, Sao Paulo, SP (Brazil)

2017-03-15

In this short note we compute the OPE coefficient of two 20{sup ′} operators and the Konishi operator. To this end, we use the OPE decomposition of a four point function of four 20{sup ′} operators and the method of asymptotic expansions to compute the leading term, in the OPE limit, of all integrals contributing to the four point function.

A bag model calculation of the electroweak s → dγ loop

International Nuclear Information System (INIS)

Eeg, J.O.; Ruud, J.Aa.

1990-10-01

The CP-conservering electroweak transitions s → dγ have been considered. In order to include confinement effects below the charm scale, the loop calculations within the bag model were performed. According to the calculations, confinement effects are rather important and give amplitudes three orders of magnitude larger than those obtained from the free quark loop, which is ∼eG F m c 2 /M W 2 . Moreover, the amplitude is of the same order of magnitude as the perturbative two-loop amplitude ∼eG F α s ln(m c /μ). For the decay mode Ω - → γΞ - , a branching ratio 4.4 x 10 -5 was obtained. Other radiative decays of strange baryons are known to be dominated by pole diagrams. 14 refs., 1 fig

Tilting the balance between canonical and noncanonical conformations for the H1 hypervariable loop of a llama VHH through point mutations.

Science.gov (United States)

Mahajan, Sai Pooja; Velez-Vega, Camilo; Escobedo, Fernando A

2013-01-10

Nanobodies are single-domain antibodies found in camelids. These are the smallest naturally occurring binding domains and derive functionality via three hypervariable loops (H1-H3) that form the binding surface. They are excellent candidates for antibody engineering because of their favorable characteristics like small size, high solubility, and stability. To rationally engineer antibodies with affinity for a specific target, the hypervariable loops can be tailored to obtain the desired binding surface. As a first step toward such a goal, we consider the design of loops with a desired conformation. In this study, we focus on the H1 loop of the anti-hCG llama nanobody that exhibits a noncanonical conformation. We aim to "tilt" the stability of the H1 loop structure from a noncanonical conformation to a (humanized) type 1 canonical conformation by studying the effect of selected mutations to the amino acid sequence of the H1, H2, and proximal residues. We use all-atomistic, explicit-solvent, biased molecular dynamic simulations to simulate the wild-type and mutant loops in a prefolded framework. We thus find mutants with increasing propensity to form a stable type 1 canonical conformation of the H1 loop. Free energy landscapes reveal the existence of conformational isomers of the canonical conformation that may play a role in binding different antigenic surfaces. We also elucidate the approximate mechanism and kinetics of transitions between such conformational isomers by using a Markovian model. We find that a particular three-point mutant has the strongest thermodynamic propensity to form the H1 type 1 canonical structure but also to exhibit transitions between conformational isomers, while a different, more rigid three-point mutant has the strongest propensity to be kinetically trapped in such a canonical structure.

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

Scattering amplitudes in open superstring theory

International Nuclear Information System (INIS)

Schlotterer, Oliver

2011-01-01

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

Three-dimensional loop quantum gravity: towards a self-gravitating quantum field theory

International Nuclear Information System (INIS)

Noui, Karim

2007-01-01

In a companion paper, we have emphasized the role of the Drinfeld double DSU(2) in the context of three-dimensional Riemannian loop quantum gravity coupled to massive spinless point particles. We make use of this result to propose a model for a self-gravitating quantum field theory (massive spinless non-causal scalar field) in three-dimensional Riemannian space. We start by constructing the Fock space of the free self-gravitating field: the vacuum is the unique DSU(2) invariant state, one-particle states correspond to DSU(2) unitary irreducible simple representations and any multi-particles states are obtained as the symmetrized tensor product between simple representations. The associated quantum field is defined by the usual requirement of covariance under DSU(2). Then, we introduce a DSU(2)-invariant self-interacting potential (the obtained model is a group field theory) and explicitly compute the lowest order terms (in the self-interaction coupling constant λ) of the propagator and of the three-point function. Finally, we compute the lowest order quantum gravity corrections (in the Newton constant G) to the propagator and to the three-point function

Perturbative quantum gravity as a double copy of gauge theory.

Science.gov (United States)

Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

2010-08-06

In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

Boson-fermion mass splittings in four-dimensional heterotic string models with anomalous U(1) gauge groups

International Nuclear Information System (INIS)

Yamaguchi, Masahiro; Yamamoto, Hisashi; Onogi, Tetsuya

1989-01-01

In four-dimensional heterotic string models with anomalous U(1) gauge groups, space-time supersymmetry (SUSY) breaks down spontaneously at one loop. In this paper, the Ward-Takahashi identity of broken SUSY in one-loop two-point amplitudes is investigated in all generalities. The boson-fermion mass splitting of any supersymmetric pair in an arbitrary model is proportional to the product of the D-term expectation value (the sum of (chirality)x(U(1) charge) of massless fermions in the model) and the U(1) charge of the external particle. In order to give a better understanding of the results, we present some examples of the mass splittings in a simple Z 3 orbifold model. (orig.)

Conformal anomaly of generalized form factors and finite loop integrals

CERN Document Server

Chicherin, Dmitry

2017-01-01

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an $\\ell-$loop integral is a 2nd-order differential equation whose right-hand side is an $(\\ell-1)-$loop integral. We show several examples, in particular the four-dimensional scalar double box.

Mandelstam cuts and light-like Wilson loops in N=4 SUSY

Energy Technology Data Exchange (ETDEWEB)

Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; St. Petersburg Inst. of Nuclear Physics, Gatchina (Russian Federation); Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2010-08-15

We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY. (orig.)

Mandelstam cuts and light-like Wilson loops in N=4 SUSY

International Nuclear Information System (INIS)

Lipatov, L.N.; Prygarin, A.

2010-08-01

We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY. (orig.)

Five-loop Konishi in N=4 SYM

International Nuclear Information System (INIS)

Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P.; Smirnov, Vladimir A.; Sokatchev, Emery

2012-01-01

We present a new method for computing the Konishi anomalous dimension in N=4 SYM at weak coupling. It does not rely on the conventional Feynman diagram technique and is not restricted to the planar limit. It is based on the OPE analysis of the four-point correlation function of stress-tensor multiplets, which has been recently constructed up to six loops. The Konishi operator gives the leading contribution to the singlet SU(4) channel of this OPE. Its anomalous dimension is the coefficient of the leading single logarithmic singularity of the logarithm of the correlation function in the double short-distance limit, in which the operator positions coincide pairwise. We regularize the logarithm of the correlation function in this singular limit by a version of dimensional regularization. At any loop level, the resulting singularity is a simple pole whose residue is determined by a finite two-point integral with one loop less. This drastically simplifies the five-loop calculation of the Konishi anomalous dimension by reducing it to a set of known four-loop two-point integrals and two unknown integrals which we evaluate analytically. We obtain an analytic result at five loops in the planar limit and observe perfect agreement with the prediction based on integrability in AdS/CFT.

The Higgs boson inclusive decay channels $H \\to b\\bar{b}$ and $H \\to gg$ up to four-loop level

OpenAIRE

Wang, Sheng-Quan; Wu, Xing-Gang; Zheng, Xu-Chang; Shen, Jian-Ming; Zhang, Qiong-Lian

2013-01-01

The principle of maximum conformality (PMC) has been suggested to eliminate the renormalization scheme and renormalization scale uncertainties, which are unavoidable for the conventional scale setting and are usually important errors for theoretical estimations. In this paper, by applying PMC scale setting, we analyze two important inclusive Standard Model Higgs decay channels, H→bb¯ and H→gg , up to four-loop and three-loop levels, respectively. After PMC scale setting, it is found that the ...

Three loop HTL perturbation theory at finite temperature and chemical potential

Energy Technology Data Exchange (ETDEWEB)

Strickland, Michael [Department of Physics, Kent State University, Kent, OH 44242 (United States); Andersen, Jens O. [Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim (Norway); Bandyopadhyay, Aritra; Haque, Najmul; Mustafa, Munshi G. [Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India); Su, Nan [Faculty of Physics, University of Bielefeld, D-33615 Bielefeld (Germany)

2014-11-15

In this proceedings contribution we present a recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculation of the thermodynamic potential for a finite temperature and chemical potential system of quarks and gluons. We compare the resulting pressure, trace anomaly, and diagonal/off-diagonal quark susceptibilities with lattice data. We show that there is good agreement between the three-loop HTLpt analytic result and available lattice data.

Results of safety analysis on PWR type nuclear power plants with two and three loops

International Nuclear Information System (INIS)

1979-01-01

The results of safety analysis on PWR type nuclear power plants with two and three loops are presented, which was conducted by the Resource and Energy Agency, in June, 1979. This analysis was made simulating the phenomenon relating to the pressurizer level gauge at the time of the TMI accident. The model plants were the Ikata nuclear power plant with two loops and the Takahama No. 1 nuclear power plant with three loops. The premise conditions for this safety analysis were as follows: 1) the main feed water flow is totally lost suddenly at the full power operation of the plants, and the feed water pump is started manually 15 minutes after the accident initiation, 2) the relief valve on the pressurizer is kept open even after the pressure drop in the primary cooling system, and the primary cooling water flows out into the containment vessel through the rupture disc of the pressurizer relief tank, and 3) the electric circuit, which sends out the signal of safety injection at the abnormal low pressure in the reactor vessel, is added from the view-point of starting the operation of the emergency core cooling system as early as possible. Relating to the analytical results, the pressure in the reactor vessels changes less, the water level in the pressurizers can be regulated, and the water level in the steam generators is recovered safely in both two and three-loop plants. It is recognized that the plants with both two- and three loops show the safe transient phenomena, and the integrity of the cores is kept under the premise conditions. The evaluation for each analyzed result was conducted in detail. (Nakai, Y.)

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.)

Dynamic scaling near the lambda point of liquid helium and at bicritical points

International Nuclear Information System (INIS)

Dohm, V.

1979-02-01

The critical dynamics of liquid helium and of uniaxial antiferromagnets at bicritical points are studied by means of renormalized field theory. The problem of dynamic scaling is analyzed in detail. Explicit calculations are performed using the epsilon-expansion in d = 4 - epsilon dimensions. Results in one- and two-loop order, i.e. first and second order in epsilon, are obtained for dynamic critical exponents, dynamic transient exponents, amplitude ratios and scaling functions at and above the critical points. (orig.)

Multichannel 1 → 2 transition amplitudes in a finite volume

Energy Technology Data Exchange (ETDEWEB)

Briceno, Raul A. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Hansen, Maxwell T. [Univ. of Washington, Seattle, WA (United States); Walker-Loud, Andre [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)

2015-02-03

We perform a model-independent, non-perturbative investigation of two-point and three-point finite-volume correlation functions in the energy regime where two-particle states can go on-shell. We study three-point functions involving a single incoming particle and an outgoing two-particle state, relevant, for example, for studies of meson decays (e.g., B⁰ → K*l⁺l⁻) or meson photo production (e.g., πγ* → ππ). We observe that, while the spectrum solely depends upon the on-shell scattering amplitude, the correlation functions also depend upon off-shell amplitudes. The main result of this work is a non-perturbative generalization of the Lellouch-Luscher formula relating matrix elements of currents in finite and infinite spatial volumes. We extend that work by considering a theory with multiple, strongly-coupled channels and by accommodating external currents which inject arbitrary four-momentum as well as arbitrary angular-momentum. The result is exact up to exponentially suppressed corrections governed by the pion mass times the box size. We also apply our master equation to various examples, including two processes mentioned above as well as examples where the final state is an admixture of two open channels.

Three-loop corrections in a covariant effective field theory

International Nuclear Information System (INIS)

McIntire, Jeff

2008-01-01

Chiral effective field theories have been used with success in the study of nuclear structure. It is of interest to systematically improve these energy functionals (particularly that of quantum hadrodynamics) through the inclusion of many-body correlations. One possible source of improvement is the loop expansion. Using the techniques of Infrared Regularization, the short-range, local dynamics at each order in the loops is absorbed into the parameterization of the underlying effective Lagrangian. The remaining nonlocal, exchange correlations must be calculated explicitly. Given that the interactions of quantum hadrodynamics are relatively soft, the loop expansion may be manageable or even perturbative in nuclear matter. This work investigates the role played by the three-loop contributions to the loop expansion for quantum hadrodynamics

Generating tree amplitudes in N = 4 SYM and N = 8 SG

International Nuclear Information System (INIS)

Bianchi, Massimo; Elvang, Henriette; Freedman, Daniel Z.

2008-01-01

We study n-point tree amplitudes of N = 4 super Yang-Mills theory and N = 8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general external states. Amplitudes derived from them obey SUSY Ward identities, and the generating functions characterize and count amplitudes in the MHV and NMHV sectors. The MHV generating function provides an efficient way to perform the intermediate state helicity sums required to obtain loop amplitudes from trees. The NMHV generating functions rely on the MHV-vertex expansion obtained from recursion relations associated with a 3-line shift of external momenta involving a reference spinor |X]. When the shifted amplitude vanishes for large z for all |X], the sum of MHV-vertex diagrams is independent of |X] and gives the correct amplitude. If the shifted amplitude does not vanish for large z, Cauchy's theorem includes a term at infinity. Examples show that special choices of |X] eliminate this term and the MHV vertex expansion becomes valid at these values. We show that the MHV-vertex expansion of the n-graviton NMHV amplitude for n = 5,6,...,11 is independent of |X] and exhibits the asymptotic behavior z n-12 . Generating functions show how the symmetries of supergravity can be implemented in the quadratic map between supergravity and gauge theory embodied in the KLT and other similar relations between amplitudes in the two theories.

Anomalies in Ward identities revisited. Explicit calculation of the three point functions; Anomalias em identidades de Ward revisitadas. Calculo explicito das funcoes de tres pontos

Energy Technology Data Exchange (ETDEWEB)

Dalmolin, Fabricio Tronco

2007-07-01

others already performed within the same issue. In particular, in one of such investigation a pioneer and traditional reference has been revisited by using the alternative strategy mentioned above. In such study, a systematic treatment of purely fermionic one, two and three point functions, associated to scalar, pseudo-scalar, vector and axial-vector densities, has done. There, however, only the explicit expressions for one and two point functions were developed. The conclusions pointed out, in a very clear way, that the association between intrinsic ambiguities of the perturbative calculation and violations in symmetry properties is not consistent. At the same time, it was concluded that only in an investigation where the explicit forms for the three point functions involved are considered clean and sound conclusions can be extracted. This is due to the fact that, in the relevant symmetry properties, it is involved three ward identities and a low energy limit. This is precisely the main purpose of the present work: to promote a detailed investigation of the relations among green functions and ward identities, within the context of a model having only one specie of 1/2 spin fermionic field, that consider all the amplitudes having superficial degree of divergence higher than the logarithmic one, in a similar way as that made in the work of Gerstein and Jackiw, taking however the explicit form for the three point functions. This is one to get in the analysis, simultaneously, the ward identities and the low energy limits involved in the anomalous amplitudes as required by the Sutherland-Veltman theorem, in order to get an adequate understanding of the anomaly phenomena. We will show that our final results can be mapped in those found with the use of the Dimensional Regularization, in situation where this technique can be applied, or in those of Gerstein and Jackiw, however with conflicting interpretations. Finally, we will show that in the context of the adopted technique

Two-point boundary correlation functions of dense loop models

Directory of Open Access Journals (Sweden)

Alexi Morin-Duchesne, Jesper Lykke Jacobsen

2018-06-01

Full Text Available We investigate six types of two-point boundary correlation functions in the dense loop model. These are defined as ratios $Z/Z^0$ of partition functions on the $m\\times n$ square lattice, with the boundary condition for $Z$ depending on two points $x$ and $y$. We consider: the insertion of an isolated defect (a and a pair of defects (b in a Dirichlet boundary condition, the transition (c between Dirichlet and Neumann boundary conditions, and the connectivity of clusters (d, loops (e and boundary segments (f in a Neumann boundary condition. For the model of critical dense polymers, corresponding to a vanishing loop weight ($\\beta = 0$, we find determinant and pfaffian expressions for these correlators. We extract the conformal weights of the underlying conformal fields and find $\\Delta = -\\frac18$, $0$, $-\\frac3{32}$, $\\frac38$, $1$, $\\tfrac \\theta \\pi (1+\\tfrac{2\\theta}\\pi$, where $\\theta$ encodes the weight of one class of loops for the correlator of type f. These results are obtained by analysing the asymptotics of the exact expressions, and by using the Cardy-Peschel formula in the case where $x$ and $y$ are set to the corners. For type b, we find a $\\log|x-y|$ dependence from the asymptotics, and a $\\ln (\\ln n$ term in the corner free energy. This is consistent with the interpretation of the boundary condition of type b as the insertion of a logarithmic field belonging to a rank two Jordan cell. For the other values of $\\beta = 2 \\cos \\lambda$, we use the hypothesis of conformal invariance to predict the conformal weights and find $\\Delta = \\Delta_{1,2}$, $\\Delta_{1,3}$, $\\Delta_{0,\\frac12}$, $\\Delta_{1,0}$, $\\Delta_{1,-1}$ and $\\Delta_{\\frac{2\\theta}\\lambda+1,\\frac{2\\theta}\\lambda+1}$, extending the results of critical dense polymers. With the results for type f, we reproduce a Coulomb gas prediction for the valence bond entanglement entropy of Jacobsen and Saleur.

A minimal approach to the scattering of physical massless bosons

Science.gov (United States)

Boels, Rutger H.; Luo, Hui

2018-05-01

Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integration-by-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A number of proof-of-concept examples are presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. Dimensional regularisation is employed throughout; different regularisation schemes are worked out explicitly. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, in the introduced approach iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the so-called rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control colour

Two-point functions in (loop) quantum cosmology

Energy Technology Data Exchange (ETDEWEB)

Calcagni, Gianluca; Oriti, Daniele [Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); Gielen, Steffen [Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

2011-07-01

We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions, with particular but non-exclusive reference to loop quantum cosmology (LQC). Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

Two-point functions in (loop) quantum cosmology

Energy Technology Data Exchange (ETDEWEB)

Calcagni, Gianluca; Gielen, Steffen; Oriti, Daniele, E-mail: calcagni@aei.mpg.de, E-mail: gielen@aei.mpg.de, E-mail: doriti@aei.mpg.de [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany)

2011-06-21

The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

Two-point functions in (loop) quantum cosmology

International Nuclear Information System (INIS)

Calcagni, Gianluca; Gielen, Steffen; Oriti, Daniele

2011-01-01

The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

Planar plane-wave matrix theory at the four loop order: integrability without BMN scaling

International Nuclear Information System (INIS)

Fischbacher, Thomas; Klose, Thomas; Plefka, Jan

2005-01-01

We study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program to perform large scale distributed symbolic algebra and generation of planar graphs. The number of graphs here was in the deep billions. The outcome of our computation establishes the four-loop integrability of the planar plane-wave matrix model. To elucidate the integrable structure we apply the recent technology of the perturbative asymptotic Bethe ansatz to our model. The resulting S-matrix turns out to be structurally similar but nevertheless distinct to the so far considered long-range spin-chain S-matrices of Inozemtsev, Beisert-Dippel-Staudacher and Arutyunov-Frolov-Staudacher in the AdS/CFT context. In particular our result displays a breakdown of BMN scaling at the four-loop order. That is, while there exists an appropriate identification of the matrix theory mass parameter with the coupling constant of the N=4 superconformal Yang-Mills theory which yields an eighth order lattice derivative for well separated impurities (naively implying BMN scaling) the detailed impurity contact interactions ruin this scaling property at the four-loop order. Moreover we study the issue of 'wrapping' interactions, which show up for the first time at this loop-order through a Konishi descendant length four operator. (author)

M-strings, Elliptic Genera and N=4 String Amplitudes

CERN Document Server

Hohenegger, Stefan

2014-01-01

We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M-strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of R^4 through a (singular) theta-transform. This form appears naturally as a specific class of one-loop scattering amplitudes in type II string theory on T^2, which we calculate explicitly.

The method of contour rotations and the three particle amplitudes

International Nuclear Information System (INIS)

Brinati, J.R.

1980-01-01

The application of the method of contour rotations to the solution of the Faddeev-Lovelace equations and the calculation of the break-up and stripping amplitudes in a system of three distinct particles is reviewed. A relationship between the masses of the particles is obtained, which permits the break-up amplitude to be calculated from a single iteration of the final integral equation. (Author) [pt

Two-loop anomalous dimensions for four-Fermi operators in supersymmetric theories

Directory of Open Access Journals (Sweden)

Junji Hisano

2017-09-01

Full Text Available We derive two-loop anomalous dimensions for four-Fermi operators in supersymmetric theories using the effective Kähler potential. We introduce the general forms in generic gauge theories and apply our results to the flavor-changing operators in (minimal supersymmetric standard models.

Color guided amplitudes

Energy Technology Data Exchange (ETDEWEB)

Broedel, Johannes [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA (United States); Dixon, Lance J. [SLAC National Accelerator Laboratory, Stanford University, Stanford, CA (United States)

2012-07-01

Amplitudes in gauge thoeries obtain contributions from color and kinematics. While these two parts of the amplitude seem to exhibit different symmetry structures, it turns out that they can be reorganized in a way to behave equally, which leads to the so-called color-kinematic dual representations of amplitudes. Astonishingly, the existence of those representations allows squaring to related gravitational theories right away. Contrary to the Kawaii-Levellen-Tye relations, which have been used to relate gauge theories and gravity previously, this method is applicable not only to tree amplitudes but also at loop level. In this talk, the basic technique is introduced followed by a discussion of the existence of color-kinematic dual representations for amplitudes derived from gauge theory actions which are deformed by higher-operator insertions. In addition, it is commented on the implications for deformed gravitational theories.

Scattering Amplitudes via Algebraic Geometry Methods

DEFF Research Database (Denmark)

Søgaard, Mads

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...

Homological Order in Three and Four dimensions: Wilson Algebra, Entanglement Entropy and Twist Defects

Science.gov (United States)

Roy, Abhishek; Chen, Xiao; Teo, Jeffrey

2013-03-01

We investigate homological orders in two, three and four dimensions by studying Zk toric code models on simplicial, cellular or in general differential complexes. The ground state degeneracy is obtained from Wilson loop and surface operators, and the homological intersection form. We compute these for a series of closed 3 and 4 dimensional manifolds and study the projective representations of mapping class groups (modular transformations). Braiding statistics between point and string excitations in (3+1)-dimensions or between dual string excitations in (4+1)-dimensions are topologically determined by the higher dimensional linking number, and can be understood by an effective topological field theory. An algorithm for calculating entanglemnent entropy of any bipartition of closed manifolds is presented, and its topological signature is completely characterized homologically. Extrinsic twist defects (or disclinations) are studied in 2,3 and 4 dimensions and are shown to carry exotic fusion and braiding properties. Simons Fellowship

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

International Nuclear Information System (INIS)

Corbera, Montserrat; Llibre, Jaume; Perez-Chavela, Ernesto

2006-01-01

In this paper we consider vector fields in R 3 that are invariant under a suitable symmetry and that possess a 'generalized heteroclinic loop' L formed by two singular points (e + and e - ) and their invariant manifolds: one of dimension 2 (a sphere minus the points e + and e - ) and one of dimension 1 (the open diameter of the sphere having endpoints e + and e - ). In particular, we analyse the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar? map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R 3 , and the second one is the charged rhomboidal four-body problem

[Hypothesis on the equilibrium point and variability of amplitude, speed and time of single-joint movement].

Science.gov (United States)

Latash, M; Gottleib, G

1990-01-01

Problems of single-joint movement variability are analysed in the framework of the equilibrium-point hypothesis (the lambda-model). Control of the movements is described with three parameters related to movement amplitude speed, and time. Three strategies emerge from this description. Only one of them is likely to lead to a Fitts' type speed-accuracy trade-off. Experiments were performed to test one of the predictions of the model. Subjects performed identical sets of single-joint fast movements with open or closed eyes and some-what different instructions. Movements performed with closed eyes were characterized with higher peak speeds and unchanged variability in seeming violation of the Fitt's law and in a good correspondence to the model.

Motion systems providing three or four degrees of freedom

Science.gov (United States)

Chou, Richard C. (Inventor)

1982-01-01

A motion system is provided by a platform generally parallel to a base and connected thereto by a column and powered and controlled extensible members, at least three of which are connected between distributed points around the column. In a three degree of freedom device, the column is conical, rigidly supported at its base with a universal joint at its top. The points of attachment define triangles in the base and in the platform surrounding the column with one extensible member connected between each. In the four degree of freedom version, the column is modified by making it effectively a column which is pivoted or guided at the base or contains an extensible member, preferably retains its triangular shape and its universal joint connection to the platform at its apex. For stability four powered and controlled extensible members are provided between points in the base and platform distributed around the column, a preferred pattern of arrangement being a square with the column at the center.

Loop calculations in the three dimensional Gribov-Zwanziger Lagrangian

International Nuclear Information System (INIS)

Gracey, J.A.

2010-01-01

The three dimensional Gribov-Zwanziger Lagrangian is analysed at one and two loops. Specifically, the two loop gap equation is evaluated and the Gribov mass is expressed in terms of the coupling constant. The one loop corrections to the propagators of all the fields are determined. It is shown that when the gap equation is satisfied the Faddeev-Popov ghost and both Bose and Grassmann localizing ghosts all enhance in the infrared limit at one loop. This verifies that the Kugo-Ojima confinement criterion holds to this order and we also show that both Grassmann ghosts are enhanced at two loops. For the Bose ghost we determine the full form of the propagator in the zero momentum limit for both the transverse and longitudinal pieces and confirm Zwanziger's recent general analysis for the low energy behaviour. We provide an alternative but equivalent version of the horizon condition expressing it as the vacuum expectation value of an operator involving only the localizing Bose ghost field. The one loop static potential is also determined. (orig.)

One-loop mass shifts in O(32) open superstring theory

International Nuclear Information System (INIS)

Yamamoto, Hisashi.

1987-08-01

One-loop amplitudes of O(N) open superstring with emission of massive bosons are studied. Divergences appearing at λ = 0 (λ: the over-all Teichmueller parameter) are shown to be canceled if N = 32 just as in the massless case. We explicitly evaluate the two-point on-shell amplitudes for all the levels of bosons lying on the leading (m 2 = 2 l, J = l + 1, m:mass J:spin l:level number of an excited state) and the next-to-leading (m 2 = 2 l, J = l) Regge trajectories and observe that they are nonvanishing even at N = 32. This implies that O(32) open super-string one-loop amplitudes with massive bosons generally suffer from external-line divergences. Further the obtained expressions of on-shell self energies (mass shifts δm 2 (l)) seem to have nontrivial dependences on l (being not proportional to l), although mass degeneracies remain. This strongly suggests that the Regge trajectories form a set of parallel polygonal lines at one-loop level so that the mass shifts cannot be absorbed by the shift of the slope parameter. The divergences would have to be cured by the vertex operator renormalizations at every excited level. (author)

Cosmological perturbation theory at three-loop order

Energy Technology Data Exchange (ETDEWEB)

Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-09-15

We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

Cosmological perturbation theory at three-loop order

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas

2013-09-01

We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

Constraints from conformal symmetry on the three point scalar correlator in inflation

International Nuclear Information System (INIS)

Kundu, Nilay; Shukla, Ashish; Trivedi, Sandip P.

2015-01-01

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.

Amplitude and Ascoli analysis

International Nuclear Information System (INIS)

Hansen, J.D.

1976-01-01

This article discusses the partial wave analysis of two, three and four meson systems. The difference between the two approaches, referred to as amplitude and Ascoli analysis is discussed. Some of the results obtained with these methods are shown. (B.R.H.)

Summation of all-loop UV divergences in maximally supersymmetric gauge theories

International Nuclear Information System (INIS)

Borlakov, A.T.; Kazakov, D.I.; Tolkachev, D.M.; Vlasenko, D.E.

2016-01-01

We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results. The key issue is that the summation of infinite series for the leading and the subleading divergences does improve the situation and does not allow one to remove the regularization and obtain the finite answer. This means that despite numerous cancellations of divergent diagrams these theories remain non-renormalizable.

Summation of all-loop UV divergences in maximally supersymmetric gauge theories

Energy Technology Data Exchange (ETDEWEB)

Borlakov, A.T. [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,Dubna (Russian Federation); Moscow Institute of Physics and Technology,Dolgoprudny (Russian Federation); Kazakov, D.I. [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,Dubna (Russian Federation); Alikhanov Institute for Theoretical and Experimental Physics,Moscow (Russian Federation); Moscow Institute of Physics and Technology,Dolgoprudny (Russian Federation); Tolkachev, D.M. [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,Dubna (Russian Federation); Stepanov Institute of Physics,Minsk (Belarus); Vlasenko, D.E. [Department of Physics, South Federal State University,Rostov-Don (Russian Federation)

2016-12-29

We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results. The key issue is that the summation of infinite series for the leading and the subleading divergences does improve the situation and does not allow one to remove the regularization and obtain the finite answer. This means that despite numerous cancellations of divergent diagrams these theories remain non-renormalizable.

Mitochondrial variability in the D-loop of four equine breeds shown by PCR-SSCP analysis

Directory of Open Access Journals (Sweden)

Mirol Patricia M.

2002-01-01

Full Text Available A fragment of 466 base pairs from a highly variable peripheral region of the mitochondrial D-loop of horses was amplified and analyzed by single stranded conformational polymorphism (SSCP. Fourteen distinct SSCP variants were detected in 100 horses belonging to four breeds (Arabian, ARB; Thoroughbred, TB; Argentinian Creole, ARC; and Peruvian Paso from Argentina, PPA. Each breed showed four to eight SSCP variants, many of which were shared between two or three of the studied breeds. Arabian horses were the most variable (eigth variants, with three variants unique to the breed. PPA and ARC showed two and one characteristic SSCP variants, respectively, while TB shared all its variants with at least one of the other breeds. An analysis based on the presence/absence of the variants revealed a closer relationship between PPA and TB, which was not completely unexpected considering the mixed ancestry of the PPA mares. The results also confirm the efficiency of SSCP to detect variability in horse mitochondrial DNA.

Secondary Voltage Unbalance Compensation for Three-Phase Four-Wire Islanded Microgrids

DEFF Research Database (Denmark)

Tang, Fen; Zhou, Xiao; Meng, Lexuan

2014-01-01

This paper proposes a secondary voltage unbalance control approach that compensate voltage unbalances in three-phase four-wire islanded microgrid systems. It is implemented in the secondary control level of the microgrid hierarchical control structure. By sending information through low......-bandwidth communication links to the primary control level, the required unbalanced factors at sensitive buses are achieved. Also, negative and zero sequence equivalent circuits and unbalance compensation principle are derived. Finally, real-time hardware-in-the-loop results show the feasibility of the proposed approach...

BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills

International Nuclear Information System (INIS)

Lipatov, L.N.; Prygarin, A.

2010-12-01

We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2→4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops. (orig.)

BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills

Energy Technology Data Exchange (ETDEWEB)

Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; St. Petersburg Inst. of Nuclear Physics, Gatchina (Russian Federation); Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2010-12-15

We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2{yields}4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops. (orig.)

N=4 scattering amplitudes and the deformed Graßmannian

International Nuclear Information System (INIS)

Ferro, Livia; Łukowski, Tomasz; Staudacher, Matthias

2014-01-01

Some time ago the general tree-level scattering amplitudes of N=4 Super Yang–Mills theory were expressed as certain Graßmannian contour integrals. These remarkable formulas allow to clearly expose the super-conformal, dual super-conformal, and Yangian symmetries of the amplitudes. Using ideas from integrability it was recently shown that the building blocks of the amplitudes permit a natural multi-parameter deformation. However, this approach had been criticized by the observation that it seemed impossible to reassemble the building blocks into Yangian-invariant deformed non-MHV amplitudes. In this note we demonstrate that the deformations may be succinctly summarized by a simple modification of the measure of the Graßmannian integrals, leading to a Yangian-invariant deformation of the general tree-level amplitudes. Interestingly, the deformed building blocks appear as residues of poles in the spectral parameter planes. Given that the contour integrals also contain information on the amplitudes at loop-level, we expect the deformations to be useful there as well. In particular, applying meromorphicity arguments, they may be expected to regulate all notorious infrared divergences. We also point out relations to Gelfand hypergeometric functions and the quantum Knizhnik–Zamolodchikov equations

Low-amplitude instability as a premise for the spontaneous symmetry breaking in the new integrable semidiscrete nonlinear system

International Nuclear Information System (INIS)

Vakhnenko, Oleksiy O.; Vakhnenko, Vyacheslav O.

2014-01-01

The new integrable semidiscrete multicomponent nonlinear system characterized by two coupling parameters is presented. Relying upon the lowest local conservation laws the concise form of the system is given and its selfconsistent symmetric parametrization in terms of four independent field variables is found. The comprehensive analysis of quartic dispersion equation for the system low-amplitude excitations is made. The criteria distinguishing the domains of stability and instability of low-amplitude excitations are formulated and a collection of qualitatively distinct realizations of a dispersion law are graphically presented. The loop-like structure of a low-amplitude dispersion law of reduced system emerging within certain windows of adjustable coupling parameter turns out to resemble the loop-like structure of a dispersion law typical of beam-plasma oscillations. Basing on the peculiarities of low-amplitude dispersion law as the function of adjustable coupling parameter it is possible to predict the windows of spontaneous symmetry breaking even without an explicit knowledge of the system Lagrangian function. Having been rewritten in terms of properly chosen modified field variables the reduced four wave integrable system can be qualified as consisting of two coupled nonlinear lattice subsystems, namely the self-dual ladder network and the vibrational ones

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon

Energy Technology Data Exchange (ETDEWEB)

Drummond, J.M. [School of Physics & Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ (United Kingdom); Theory Division, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); LAPTh, CNRS, Université de Savoie, F-74941 Annecy-le-Vieux Cedex (France); Papathanasiou, G. [LAPTh, CNRS, Université de Savoie, F-74941 Annecy-le-Vieux Cedex (France); Spradlin, M. [Department of Physics, Brown University, Providence, RI 02912 (United States)

2015-03-16

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr (4,7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the 7∥6 collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the three-loop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n>6.

RECOLA2: REcursive Computation of One-Loop Amplitudes 2

Science.gov (United States)

Denner, Ansgar; Lang, Jean-Nicolas; Uccirati, Sandro

2018-03-01

We present the Fortran95 program RECOLA2 for the perturbative computation of next-to-leading-order transition amplitudes in the Standard Model of particle physics and extended Higgs sectors. New theories are implemented via model files in the 't Hooft-Feynman gauge in the conventional formulation of quantum field theory and in the Background-Field method. The present version includes model files for Two-Higgs-Doublet Model and the Higgs-Singlet Extension of the Standard Model. We support standard renormalization schemes for the Standard Model as well as many commonly used renormalization schemes in extended Higgs sectors. Within these models the computation of next-to-leading-order polarized amplitudes and squared amplitudes, optionally summed over spin and colour, is fully automated for any process. RECOLA2 allows the computation of colour- and spin-correlated leading-order squared amplitudes that are needed in the dipole subtraction formalism. RECOLA2 is publicly available for download at http://recola.hepforge.org.

One-loop correlation functions in the model of noncritical fermionic strings

International Nuclear Information System (INIS)

Belokurov, V.V.; Iofa, M.Z.

1996-01-01

In the model of noncritical fermionic strings, the David-Distler-Kawai ansatz is used to study one-loop n-point (n≤4) correlation functions for the vertex operators of massless bosonic states. The action functional of the model is the sum of super-Liouville action functional for the conformal mode and the action functional of d scalar supermultiplets. It is assumed that the total cosmological term is equal to zero. The amplitudes are calculated as the residues at the pole of the correlation function that corresponds to the conservation of Liouville momentum in the form Σβi=Q(1-h), where Q=√(9-d)/2 and h is the genus of the work sheet. In the one-loop approximation, the amplitudes can be obtained in the modular-invariant form, provided that the coefficients appearing in the sum over spin structures depend on moduli. In this case, the modular measure is defined up to a modular-invariant factor. This arbitrariness can be used to represent one-point correlation functions in the same functional form as for strings of critical dimension

Analytic computations of massive one-loop amplitudes

International Nuclear Information System (INIS)

Badger, Simon; Yundin, Valery; Sattler, Ralf

2010-06-01

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

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.

Leakage Current Elimination of Four-Leg Inverter for Transformerless Three-Phase PV Systems

DEFF Research Database (Denmark)

Guo, Xiaoqiang; He, Ran; Jian, Jiamin

2016-01-01

Eliminating the leakage current is one of the most important issues for transformerless three phase photovoltaic (PV) systems. In this paper, the leakage current elimination of a three-phase four-leg PV inverter is investigated. With the common mode loop model established, the generation mechanism...... of the leakage current is clearly identified. Different typical carrier-based modulation methods and their corresponding common mode voltages are discussed. A new modulation strategy with Boolean logic function is proposed to achieve the constant common mode voltage for the leakage current reduction. Finally...

Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

International Nuclear Information System (INIS)

Baikov, P.A.; Chetyrkin, K.G.; Kühn, J.H.

2017-01-01

We extend the O(α s 5 ) result of the analytic calculation of the quark mass anomalous dimension in pQCD https://www.doi.org/10.1007/JHEP10(2014)076 to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.

Single-Axis Three-Beam Amplitude Monopulse Antenna-Signal Processing Issues

Energy Technology Data Exchange (ETDEWEB)

Doerry, Armin W. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bickel, Douglas L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-05-01

Typically, when three or more antenna beams along a single axis are required, the answer has been multiple antenna phase-centers, essentially a phase-monopulse system. Such systems and their design parameters are well-reported in the literature. Less appreciated is that three or more antenna beams can also be generated in an amplitude-monopulse fashion. Consequently, design guidelines and performance analysis of such antennas is somewhat under-reported in the literature. We provide discussion herein of three beams arrayed in a single axis with an amplitude-monopulse configuration. Acknowledgements The preparation of this report is the result of an unfunded research and development activity. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administ ration under contract DE-AC04-94AL85000.

Four-loop relation between the MS and on-shell quark mass

International Nuclear Information System (INIS)

Marquard, Peter; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias

2016-01-01

In this contribution we discuss the four-loop relation between the on-shell and MS definition of heavy quark masses which is applied to the top, bottom and charm case. We also present relations between the MS quark mass and various threshold mass definitions and discuss the uncertainty at next-to-next-to-next-to-leading order.

On the singularities of massive superstring amplitudes

NARCIS (Netherlands)

Foda, O.

1987-01-01

Superstring one-loop amplitudes with massive external states are shown to be in general ill-defined due to internal on-shell propagators. However, we argue that since any massive string state (in the uncompactified theory) has a finite lifetime to decay into massless particles, such amplitudes are

Digital limiter for a self-excited loop

International Nuclear Information System (INIS)

Joshi, G.; Singh, P.; Agarwal, V.; Kumar, G.

2015-01-01

Limiter is one of the main signal processing modules of a self-excited loop (SEL). It plays a crucial role in initiating and stabilizing the amplitude of the RF field in a free running SEL. In a recently reported implementation of a self excited loop in digital domain, the limiter has been realized at based band in the form of a feedback loop. This feedback loop stabilizes the amplitude of the RF phasor present at its input without affecting its phase. In the present work we study the suitability of this implementation of limiter through analysis and simulations. An approximate equivalent model of an SEL, incorporating the digital limiter, is created in analog domain. It is demonstrated that even in the presence for large transients, such as, at the start up of oscillations, SEL continues to exhibit smooth and predictable response. In free running mode of operation the coupling from loop oscillation frequency change to resonator field amplitude change is absent, thus avoiding instability due to electro-mechanical coupling. In the locked mode, the transmission of amplitude jitter through the limiter is far exceeded by that through the controller gain thereby keeping the behavior of the digital SEL close to its analog counterpart. (author)

Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

Energy Technology Data Exchange (ETDEWEB)

Baikov, P.A. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,1(2), Leninskie gory, Moscow 119991 (Russian Federation); Chetyrkin, K.G.; Kühn, J.H. [Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT),Wolfgang-Gaede-Straße 1, 726128 Karlsruhe (Germany)

2017-04-20

We extend the O(α{sub s}{sup 5}) result of the analytic calculation of the quark mass anomalous dimension in pQCD https://www.doi.org/10.1007/JHEP10(2014)076 to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.

A naturally large four-point function in single field inflation

International Nuclear Information System (INIS)

Senatore, Leonardo; Zaldarriaga, Matias

2011-01-01

Non-Gaussianities of the primordial density perturbations have emerged as a very powerful possible signal to test the dynamics that drove the period of inflation. While in general the most sensitive observable is the three-point function in this paper we show that there are technically natural inflationary models where the leading source of non-Gaussianity is the four-point function. Using the recently developed Effective Field Theory of Inflation, we are able to show that it is possible to impose an approximate parity symmetry and an approximate continuos shift symmetry on the inflaton fluctuations that allow, when the dispersion relation if of the form ω ∼ c s k, for a unique quartic operator, while approximately forbidding all the cubic ones. The resulting shape for the four-point function is unique. In the models where the dispersion relation is of the form ω ∼ k 2 /M a similar construction can be carried out and additional shapes are possible

Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order

International Nuclear Information System (INIS)

Kurz, Alexander; Smirnov, Alexander V.; Smirnov, Vladimir A.

2015-08-01

The numerically dominant QED contributions to the anomalous magnetic moment of the muon stem from Feynman diagrams with internal electron loops. We consider such corrections and present a calculation of the four-loop light-by-light-type corrections where the external photon couples to a closed electron or muon loop. We perform an asymptotic expansion in the ratio of electron and muon mass and reduce the resulting integrals to master integrals which we evaluate using analytical and numerical methods. We confirm the results present in the literature which are based on different computational methods.

The three-loop form factor in N=4 super Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Gehrmann, Thomas [Universitaet Zuerich (Switzerland); Henn, Johannes [IAS Princeton (United States); Huber, Tobias [Universitaet Siegen (Germany)

2012-07-01

We present the calculation of the Sudakov form factor in N=4 super Yang-Mills theory to the three-loop order. At leading colour, the latter is expressed in terms of planar and non-planar loop integrals. We show that it is possible to choose a representation in which each loop integral has uniform transcendentality in the Riemann {zeta}-function. We comment on the expected exponentiation of the infrared divergences and the values of the three-loop cusp and collinear anomalous dimensions in dimensional regularisation. We also compare the form factor in N=4 super Yang-Mills to the leading transcendentality pieces of the quark and gluon form factor in QCD. Finally, we investigate the ultraviolet properties of the form factor in D>4 dimensions.

Best-estimate analysis of a loss-of-coolant accident in a four-loop US PWR using TRAC-PD2

International Nuclear Information System (INIS)

Ireland, J.R.

1982-01-01

A 200-percent double-ended cold-leg break loss-of-coolant accident (LOCA) in a typical US pressurized water reactor (PWR) was simulated using the Transient Reactor Analysis Code (TRAC-PD2). The reactor system modeled represented a typical US PWR with four loops (three intact, one broken) and cold-leg emergency-core-cooling systems (ECCS). The finely noded TRAC model employed 440 three dimensional (r, THETA, z) vessel cells along with approximately 300 one-dimensional cells that modeled the primary system loops. The calculated peak-clad temperature of 950 0 K occurred during blowdown and the clad temperature excursion was terminated at 175 s, when complete core quenching occurred. Accumulator flows were initiated at 10 s, when the system pressure reached 4.08 MPa, and the refill phase ended at 36 s when the lower plenum refilled. During reflood, both bottom and falling film quench fronts were calculated

Scattering amplitudes in gauge theories with and without supersymmetry

International Nuclear Information System (INIS)

Ochirov, Alexander

2014-01-01

This thesis aims at providing better understanding of the perturbative expansion of gauge theories with and without supersymmetry. At tree level, the BCFW recursion relations are analyzed with respect to their validity for general off-shell objects in Yang-Mills theory, which is a significant step away from their established zone of applicability. Unphysical poles constitute a new potential problem in addition to the boundary behavior issue, common to the on-shell case as well. For an infinite family of massive fermion currents, both obstacles are shown to be avoided under the certain conditions, which provides a natural recursion relation. At one loop, scattering amplitudes can be calculated from unitarity cuts through their expansion into known scalar integrals with free coefficients. A powerful method to obtain these coefficients, namely spinor integration, is discussed and rederived in a somewhat novel form. It is then used to compute analytically the infinite series of one-loop gluon amplitudes in N = 1 super-Yang-Mills theory with exactly three negative helicities. The final part of this thesis concerns the intriguing relationship between gluon and graviton scattering amplitudes, which involves a beautiful duality between the color and kinematic content of gauge theories. This BCJ duality is extended to include particles in the fundamental representation of the gauge group, which is shown to relieve the restriction of the BCJ construction to factorizable gravities and thus give access to amplitudes in generic (super-)gravity theories. (author) [fr

Fundamental size limitations of micro four-point probes

DEFF Research Database (Denmark)

Ansbæk, Thor; Petersen, Dirch Hjorth; Hansen, Ole

2009-01-01

The continued down-scaling of integrated circuits and magnetic tunnel junctions (MTJ) for hard disc read heads presents a challenge to current metrology technology. The four-point probes (4PP), currently used for sheet resistance characterization in these applications, therefore must be down......-scaled as well in order to correctly characterize the extremely thin films used. This presents a four-point probe design and fabrication challenge. We analyze the fundamental limitation on down-scaling of a generic micro four-point probe (M4PP) in a comprehensive study, where mechanical, thermal, and electrical...

Enforced neutrality and color-flavor unlocking in the three-flavor Polyakov-loop Nambu-Jona-Lasinio model

International Nuclear Information System (INIS)

Abuki, H.; Ciminale, M.; Nardulli, G.; Ruggieri, M.; Gatto, R.

2008-01-01

We study how the charge neutrality affects the phase structure of the three-flavor Polyakov-loop Nambu-Jona-Lasinio (PNJL) model. We point out that, within the conventional PNJL model at finite density, the color neutrality is missing because the Wilson line serves as an external colored field coupled to dynamical quarks. In this paper we heuristically assume that the model may still be applicable. To get color neutrality, one has then to allow nonvanishing color chemical potentials. We study how the quark matter phase diagram in (T,m s 2 /μ)-plane is affected by imposing neutrality and by including the Polyakov-loop dynamics. Although these two effects are correlated in a nonlinear way, the impact of the Polyakov loop turns out to be significant in the T direction, while imposing neutrality brings a remarkable effect in the m s 2 /μ direction. In particular, we find a novel unlocking transition, when the temperature is increased, even in the chiral SU(3) limit. We clarify how and why this is possible once the dynamics of the colored Polyakov loop is taken into account. Also we succeed in giving an analytic expression for T c for the transition from two-flavor pairing (2SC) to unpaired quark matter in the presence of the Polyakov loop.

Superconformal quantum field theories in string. Gauge theory dualities

Energy Technology Data Exchange (ETDEWEB)

Wiegandt, Konstantin

2012-08-14

In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

Superconformal quantum field theories in string. Gauge theory dualities

International Nuclear Information System (INIS)

Wiegandt, Konstantin

2012-01-01

In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

Higgs amplitudes from supersymmetric form factors Part I: $\\mathcal{N}=4$ super Yang-Mills arXiv

CERN Document Server

Brandhuber, Andreas; Penante, Brenda; Travaglini, Gabriele

In the large top-mass limit, Higgs plus multi-gluon amplitudes in QCD can be computed using an effective field theory. This approach turns the computation of such amplitudes into that of form factors of operators of increasing classical dimension. In this paper we focus on the first finite top-mass correction, arising from the operator ${\\rm Tr}(F^3)$, up to two loops and three gluons. Setting up the calculation in the maximally supersymmetric theory requires identification of an appropriate supersymmetric completion of ${\\rm Tr}(F^3)$, which we recognise as a descendant of the Konishi operator. We provide detailed computations for both this operator and the component operator ${\\rm Tr}(F^3)$, preparing the ground for the calculation in $\\mathcal{N}<4$, to be detailed in a companion paper. Our results for both operators are expressed in terms of a few universal functions of transcendental degree four and below, some of which have appeared in other contexts, hinting at universality of such quantities. An im...

On-shell diagrams for N=8 supergravity amplitudes

Energy Technology Data Exchange (ETDEWEB)

Heslop, Paul; Lipstein, Arthur E. [Department of Mathematical Sciences, Durham University,Lower Mountjoy, Stockton Road, Durham, DH1 3LE (United Kingdom)

2016-06-10

We define recursion relations for N=8 supergravity amplitudes using a generalization of the on-shell diagrams developed for planar N=4 super-Yang-Mills. Although the recursion relations generically give rise to non-planar on-shell diagrams, we show that at tree-level the recursion can be chosen to yield only planar diagrams, the same diagrams occurring in the planar N=4 theory. This implies non-trivial identities for non-planar diagrams as well as interesting relations between the N=4 and N=8 theories. We show that the on-shell diagrams of N=8 supergravity obey equivalence relations analogous to those of N=4 super-Yang-Mills, and we develop a systematic algorithm for reading off Grassmannian integral formulae directly from the on-shell diagrams. We also show that the 1-loop 4-point amplitude of N=8 supergravity can be obtained from on-shell diagrams.

Scattering amplitudes from multivariate polynomial division

Energy Technology Data Exchange (ETDEWEB)

Mastrolia, Pierpaolo, E-mail: pierpaolo.mastrolia@cern.ch [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Dipartimento di Fisica e Astronomia, Universita di Padova, Padova (Italy); INFN Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Mirabella, Edoardo, E-mail: mirabell@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Ossola, Giovanni, E-mail: GOssola@citytech.cuny.edu [New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States); Peraro, Tiziano, E-mail: peraro@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)

2012-11-15

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Groebner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.

Conformal four point functions and the operator product expansion

International Nuclear Information System (INIS)

Dolan, F.A.; Osborn, H.

2001-01-01

Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u,v. A recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function is derived. This is solved explicitly in two and four dimensions in terms of ordinary hypergeometric functions of variables z,x which are simply related to u,v. The operator product expansion analysis is applied to the explicit expressions for the four point function found for free scalar, fermion and vector field theories in four dimensions. The results for four point functions obtained by using the AdS/CFT correspondence are also analysed in terms of functions related to those appearing in the operator product discussion

Current singularities at finitely compressible three-dimensional magnetic null points

International Nuclear Information System (INIS)

Pontin, D.I.; Craig, I.J.D.

2005-01-01

The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed

The three-loop splitting functions Pqg(2) and Pgg(2 ,NF)

Science.gov (United States)

Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

2017-09-01

We calculate the unpolarized twist-2 three-loop splitting functions Pqg(2) (x) and Pgg(2 ,NF) (x) and the associated anomalous dimensions using massive three-loop operator matrix elements. While we calculate Pgg(2 ,NF) (x) directly, Pqg(2) (x) is computed from 1200 even moments, without any structural prejudice, using a hierarchy of recurrences obtained for the corresponding operator matrix element. The largest recurrence to be solved is of order 12 and degree 191. We confirm results in the foregoing literature.

Systematic approximation of multi-scale Feynman integrals arXiv

CERN Document Server

Borowka, Sophia; Hulme, Daniel

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

A three-point Taylor algorithm for three-point boundary value problems

NARCIS (Netherlands)

J.L. López; E. Pérez Sinusía; N.M. Temme (Nico)

2011-01-01

textabstractWe consider second-order linear differential equations $\\varphi(x)y''+f(x)y'+g(x)y=h(x)$ in the interval $(-1,1)$ with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions given at three points of the interval: the two extreme points $x=\\pm 1$ and an interior point

On the singularities of massive superstring amplitudes

Energy Technology Data Exchange (ETDEWEB)

Foda, O.

1987-06-04

Superstring one-loop amplitudes with massive external states are shown to be in general ill-defined due to internal on-shell propagators. However, we argue that since any massive string state (in the uncompactified theory) has a finite lifetime to decay into massless particles, such amplitudes are not terms in the perturbative expansion of physical S-matrix elements: These can be defined only with massless external states. Consistent massive amplitudes repuire an off-shell formalism.

Three key points along an intrinsic reaction coordinate

Indian Academy of Sciences (India)

Unknown

Abstract. The concept of the reaction force is presented and discussed in detail. For typical processes with energy barriers, it has a universal form which defines three key points along an intrinsic reaction co- ordinate: the force minimum, zero and maximum. We suggest that the resulting four zones be interpreted as involving ...

Reduction formalism for dimensionally regulated one-loop N-point integrals

International Nuclear Information System (INIS)

Binoth, T.; Guillet, J.Ph.; Heinrich, G.

2000-01-01

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional external momenta to box integrals in (4-2ε) dimensions. We derive a formula valid for arbitrary N and give an explicit expression for N=6. Further a tensor reduction method for N-point tensor integrals is presented. We prove that generically higher dimensional integrals contribute only to order ε for N≥5. The tensor reduction can be solved iteratively such that any tensor integral is expressible in terms of scalar integrals. Explicit formulas are given up to N=6

N=4 SUSY Yang-Mills: Three loops made simple(r)

Energy Technology Data Exchange (ETDEWEB)

Dokshitzer, Yu.L. [LPTHE, Universities of Paris-VI and VII and CNRS, Paris (France); Marchesini, G. [University of Milano-Bicocca and INFN Sezione di Milano-Bicocca, Milan (Italy)]. E-mail: marchesini@mib.infn.it

2007-03-15

We construct universal parton evolution equation that produces space- and time-like anomalous dimensions for the maximally super-symmetric N=4 Yang-Mills field theory model, and find that its kernel satisfies the Gribov-Lipatov reciprocity relation in three loops. Given a simple structure of the evolution kernel, this should help to generate the major part of multi-loop contributions to QCD anomalous dimensions, due to classical soft gluon radiation effects.

Two-loop conformal generators for leading-twist operators in QCD

International Nuclear Information System (INIS)

Braun, V.M.; Strohmaier, M.; Manashov, A.N.; Hamburg Univ.; Moch, S.

2016-01-01

QCD evolution equations in minimal subtraction schemes have a hidden symmetry: One can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer d=4-2ε space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in d=4-2ε effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD β-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.

Two-Loop Master Integrals for $\\gamma^{*} \\to 3$ Jets the Non-Planar Topologies

CERN Document Server

Gehrmann, T

2001-01-01

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper, we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in $\\e=(4-d)/2$, where $d$ is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies.

The three-loop splitting functions Pqg(2 and Pgg(2,NF

Directory of Open Access Journals (Sweden)

J. Ablinger

2017-09-01

Full Text Available We calculate the unpolarized twist-2 three-loop splitting functions Pqg(2(x and Pgg(2,NF(x and the associated anomalous dimensions using massive three-loop operator matrix elements. While we calculate Pgg(2,NF(x directly, Pqg(2(x is computed from 1200 even moments, without any structural prejudice, using a hierarchy of recurrences obtained for the corresponding operator matrix element. The largest recurrence to be solved is of order 12 and degree 191. We confirm results in the foregoing literature.

Xenon oscillation tests in four-loop PWR cores

International Nuclear Information System (INIS)

Aoki, Norihiko; Osaka, Kenichi; Shimada, Shoichiro; Tochihara, Hiroshi; Machii, Seigo

1980-01-01

The Kansai Electric Power Co.'s OHI Unit 1 and 2 are the first 4-loop PWRs in Japan which use 17 x 17 fuel assemblies and have essentially the same plant parameters. A 4-loop core has larger core radius and higher power density than those of 2- or 3-loop cores, and is less stable for Xe oscillation. It is therefore important to confirm that Xe oscillations in radial direction are sufficiently stable in a 4-loop core. Radial and axial Xe oscillation tests were performed during the startup physics tests of OHI Unit 1 and 2; Xe oscillation was induced by perturbation of control rods and the Xe effect on power distribution observed periodically. The test results show that the transverse Xe oscillation in the 4-loop core is sufficiently stable and that the agreement between the measurement and the calculated prediction is good. (author)

Three-loop massive tadpoles and polylogarithms through weight six

Energy Technology Data Exchange (ETDEWEB)

Kniehl, B.A.; Pikelner, Andrey F.; Veretin, Oleg L. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2017-05-15

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylogarithms of arguments e{sup kiπ/3}.

On the singularities of massive superstring amplitudes

International Nuclear Information System (INIS)

Foda, O.

1987-01-01

Superstring one-loop amplitudes with massive external states are shown to be in general ill-defined due to internal on-shell propagators. However, we argue that since any massive string state (in the uncompactified theory) has a finite lifetime to decay into massless particles, such amplitudes are not terms in the perturbative expansion of physical S-matrix elements: These can be defined only with massless external states. Consistent massive amplitudes repuire an off-shell formalism. (orig.)

Worldsheet four-point functions in AdS{sub 3}/CFT{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Cardona, Carlos A. [Instituto de Astronomia y Fisica del Espacio (CONICET-UBA), Buenos Aires (Argentina); Kirsch, Ingo [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2010-07-15

We calculate some extremal and non-extremal four-point functions on the sphere of certain chiral primary operators for strings on AdS{sub 3} x S{sup 3} x T{sup 4}. The computation is done for small values of the spacetime cross-ratio where global SL(2) and SU(2) descendants may be neglected in the intermediate channel. Ignoring also current algebra descendants, we find that in the non-extremal case the integrated worldsheet correlators factorize into spacetime three-point functions, which is non-trivial due to the integration over the moduli space. We then restrict to the extremal case and compare our results with the four-point correlators recently computed in the dual boundary theory. We also discuss a particular non-extremal correlator involving two chiral and two anti-chiral operators. (orig)

The soft-gluon current at one-loop order

CERN Document Server

Catani, S

2000-01-01

We study the soft limit of one-loop QCD amplitudes and we derive the process-independent factorization formula that controls the singular behaviour in this limit. This is obtained from the customary eikonal factorization formula valid at tree (classical) level by introducing a generalized soft-gluon current that embodies the quantum corrections. We compute the explicit expression of the soft-gluon current at one-loop order. It contains purely non-abelian correlations between the colour charges of each pair of hard-momentum partons in the matrix element. This leads to colour correlations between (two and) three hard partons in the matrix element squared. Exploiting colour conservation, we recover QED-like factorization for the square of the matrix elements with two and three hard partons.

Higgs mass prediction in the MSSM at three-loop level in a pure DR context

Energy Technology Data Exchange (ETDEWEB)

Harlander, Robert V.; Klappert, Jonas; Voigt, Alexander [RWTH Aachen University, Institute for Theoretical Particle Physics and Cosmology, Aachen (Germany)

2017-12-15

The impact of the three-loop effects of order α{sub t}α{sub s}{sup 2} on the mass of the light CP-even Higgs boson in the MSSM is studied in a pure DR context. For this purpose, we implement the results of Kant et al. (JHEP 08:104, 2010) into the C++ module Himalaya and link it to FlexibleSUSY, a Mathematica and C++ package to create spectrum generators for BSM models. The three-loop result is compared to the fixed-order two-loop calculations of the original FlexibleSUSY and of FeynHiggs, as well as to the result based on an EFT approach. Aside from the expected reduction of the renormalization scale dependence with respect to the lower-order results, we find that the three-loop contributions significantly reduce the difference from the EFT prediction in the TeV-region of the SUSY scale M{sub S}. Himalaya can be linked also to other two-loop DR codes, thus allowing for the elevation of these codes to the three-loop level. (orig.)

Automated one-loop calculations with GOSAM

International Nuclear Information System (INIS)

Cullen, Gavin; Greiner, Nicolas; Heinrich, Gudrun; Reiter, Thomas; Luisoni, Gionata

2011-11-01

We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the loop. (orig.)

Automated one-loop calculations with GOSAM

Energy Technology Data Exchange (ETDEWEB)

Cullen, Gavin [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Deutsches Elektronen-Synchrotron, Zeuthen [DESY; Germany; Greiner, Nicolas [Illinois Univ., Urbana-Champaign, IL (United States). Dept. of Physics; Max-Planck-Institut fuer Physik, Muenchen (Germany); Heinrich, Gudrun; Reiter, Thomas [Max-Planck-Institut fuer Physik, Muenchen (Germany); Luisoni, Gionata [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology; Mastrolia, Pierpaolo [Max-Planck-Institut fuer Physik, Muenchen (Germany); Padua Univ. (Italy). Dipt. di Fisica; Ossola, Giovanni [New York City Univ., NY (United States). New York City College of Technology; New York City Univ., NY (United States). The Graduate School and University Center; Tramontano, Francesco [European Organization for Nuclear Research (CERN), Geneva (Switzerland)

2011-11-15

We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the loop. (orig.)

Three loop anomalous dimensions of higher moments of the non-singlet twist-2 Wilson and transversity operators in the M-bar S-bar and RI' schemes

International Nuclear Information System (INIS)

Gracey, John A.

2006-01-01

We compute the anomalous dimension of the third and fourth moments of the flavour non-singlet twist-2 Wilson and transversity operators at three loops in both the M-bar S-bar and RI' schemes. To assist with the extraction of estimates of matrix elements computed using lattice regularization, the finite parts of the Green's function where the operator is inserted in a quark 2-point function are also provided at three loops in both schemes

Charm Penguin in B± → K±K+K-: Partonic and hadronic loops

Science.gov (United States)

Bediaga, I.; Frederico, T.; Magalhães, P. C.

2018-05-01

Charm penguin diagrams are known to be the main contribution to charmless B decay process with strangeness variation equal to minus one, which is the case of B± →K±K+K- decay. The large phase space available in this and other B three-body decays allows non trivial final state interactions with all sort of rescattering processes and also access high momentum transfers in the central region of the Dalitz plane. In this work we investigate the charm Penguin contribution to B± →K±K+K-, described by a hadronic triangle loop in nonperturbative regions of the phase space, and by a partonic loop at the quasi perturbative region. These nonresonant amplitudes should have a particular structure in the Dalitz plane and their contributions to the final decay amplitude can be confirmed by a data amplitude analysis in this channel. In particular, the hadronic amplitude has a changing sign in the phase at D D bar threshold which can result in a change of sign for the CP asymmetry.

Comment on the prediction of two-loop standard chiral perturbation theory for low-energy ππ scattering

International Nuclear Information System (INIS)

Girlanda, L.; Moussallam, B.; Stern, J.; Knecht, M.

1997-03-01

Four of the six parameters defining the two-loop ππ scattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard χ PT expressions, the threshold parameters, low-energy phases and the O(p 4 ) constants l 1 r , l 2 r are obtained. The result reproduces the correct D-waves but it is incompatible with existing Standard χ PT analyses of K 14 form factors beyond one loop. (author)

Mirror symmetry, toric branes and topological string amplitudes as polynomials

Energy Technology Data Exchange (ETDEWEB)

Alim, Murad

2009-07-13

The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)

Mirror symmetry, toric branes and topological string amplitudes as polynomials

International Nuclear Information System (INIS)

Alim, Murad

2009-01-01

The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)

Flat-Cladding Fiber Bragg Grating Sensors for Large Strain Amplitude Fatigue Tests

Directory of Open Access Journals (Sweden)

Xijia Gu

2010-08-01

Full Text Available We have successfully developed a flat-cladding fiber Bragg grating sensor for large cyclic strain amplitude tests of up to ±8,000 με. The increased contact area between the flat-cladding fiber and substrate, together with the application of a new bonding process, has significantly increased the bonding strength. In the push-pull fatigue tests of an aluminum alloy, the plastic strain amplitudes measured by three optical fiber sensors differ only by 0.43% at a cyclic strain amplitude of ±7,000 με and 1.9% at a cyclic strain amplitude of ±8,000 με. We also applied the sensor on an extruded magnesium alloy for evaluating the peculiar asymmetric hysteresis loops. The results obtained were in good agreement with those measured from the extensometer, a further validation of the sensor.

One-loop transition amplitudes in the D1D5 CFT

Energy Technology Data Exchange (ETDEWEB)

Carson, Zaq; Hampton, Shaun; Mathur, Samir D. [Department of Physics, The Ohio State University,191 West Woodruff Ave, Columbus, OH 43210 (United States)

2017-01-02

We consider the issue of thermalization in the D1D5 CFT. Thermalization is expected to correspond to the formation of a black hole in the dual gravity theory. We start from the orbifold point, where the theory is essentially free, and does not thermalize. In earlier work it was noted that there was no clear thermalization effect when the theory was deformed off the orbifold point to first order in the relevant twist perturbation. In this paper we consider the deformation to second order in the twist, where we do find effects that can cause thermalization of an initial perturbation. We consider a 1-loop process where two untwisted copies of the CFT are twisted to one copy and then again untwisted to two copies. We start with a single oscillator excitation on the initial CFT, and compute the effect of the two twists on this state. We find simple approximate expressions for the Bogoliubov coefficients and the behavior of the single oscillator excitation in the continuum limit, where the mode numbers involved are taken to be much larger than unity. We also prove a number of useful relationships valid for processes with an arbitrary number of twist insertions.

One-loop transition amplitudes in the D1D5 CFT

Science.gov (United States)

Carson, Zaq; Hampton, Shaun; Mathur, Samir D.

2017-01-01

We consider the issue of thermalization in the D1D5 CFT. Thermalization is expected to correspond to the formation of a black hole in the dual gravity theory. We start from the orbifold point, where the theory is essentially free, and does not thermalize. In earlier work it was noted that there was no clear thermalization effect when the theory was deformed off the orbifold point to first order in the relevant twist perturbation. In this paper we consider the deformation to second order in the twist, where we do find effects that can cause thermalization of an initial perturbation. We consider a 1-loop process where two untwisted copies of the CFT are twisted to one copy and then again untwisted to two copies. We start with a single oscillator excitation on the initial CFT, and compute the effect of the two twists on this state. We find simple approximate expressions for the Bogoliubov coefficients and the behavior of the single oscillator excitation in the continuum limit, where the mode numbers involved are taken to be much larger than unity. We also prove a number of useful relationships valid for processes with an arbitrary number of twist insertions.

Improved pion pion scattering amplitude from dispersion relation formalism

International Nuclear Information System (INIS)

Cavalcante, I.P.; Coutinho, Y.A.; Borges, J. Sa

2005-01-01

Pion-pion scattering amplitude is obtained from Chiral Perturbation Theory at one- and two-loop approximations. Dispersion relation formalism provides a more economic method, which was proved to reproduce the analytical structure of that amplitude at both approximation levels. This work extends the use of the formalism in order to compute further unitarity corrections to partial waves, including the D-wave amplitude. (author)

Two-loop planar master integrals for Higgs →3 partons with full heavy-quark mass dependence

International Nuclear Information System (INIS)

Bonciani, Roberto; Duca, Vittorio Del; Frellesvig, Hjalte; Henn, Johannes M.; Moriello, Francesco; Smirnov, Vladimir A.

2016-01-01

We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs→3 partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic integrals. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kernels. We express the result for the elliptic sectors in terms of two and three-fold iterated integrals, which we find suitable for numerical evaluations. This is the first time that four-point multiscale Feynman integrals have been computed in a fully analytic way in terms of elliptic integrals.

Two-loop planar master integrals for Higgs →3 partons with full heavy-quark mass dependence

Energy Technology Data Exchange (ETDEWEB)

Bonciani, Roberto [Dipartimento di Fisica, Sapienza - Università di Roma,Piazzale Aldo Moro 5, 00185, Rome (Italy); INFN Sezione di Roma, Piazzale Aldo Moro 2, 00185, Rome (Italy); Duca, Vittorio Del [ETH Zurich, Institut fur theoretische Physik, Wolfgang-Paulistr. 27, 8093, Zurich (Switzerland); INFN Laboratori Nazionali di Frascati, 00044 Frascati, Roma (Italy); Frellesvig, Hjalte [Institute of Nuclear and Particle Physics, NCSR Demokritos, Agia Paraskevi, 15310 (Greece); Henn, Johannes M. [PRISMA Cluster of Excellence, Johannes Gutenberg University, 55099 Mainz (Germany); Moriello, Francesco [Dipartimento di Fisica, Sapienza - Università di Roma,Piazzale Aldo Moro 5, 00185, Rome (Italy); INFN Sezione di Roma, Piazzale Aldo Moro 2, 00185, Rome (Italy); ETH Zurich, Institut fur theoretische Physik, Wolfgang-Paulistr. 27, 8093, Zurich (Switzerland); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics of Moscow State University, 119991 Moscow (Russian Federation)

2016-12-19

We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs→3 partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic integrals. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kernels. We express the result for the elliptic sectors in terms of two and three-fold iterated integrals, which we find suitable for numerical evaluations. This is the first time that four-point multiscale Feynman integrals have been computed in a fully analytic way in terms of elliptic integrals.

MHV amplitudes for 3→3 gluon scattering in Regge limit

International Nuclear Information System (INIS)

Bartels, J.; Prygarin, A.

2010-12-01

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. (orig.)

MHV amplitudes for 3{yields}3 gluon scattering in Regge limit

Energy Technology Data Exchange (ETDEWEB)

Bartels, J.; Prygarin, A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Lipatov, L.N. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; St. Petersburg Nuclear Physics Institute (Russian Federation)

2010-12-15

We calculate corrections to the BDS formula for the six-particle planar MHV amplitude for the gluon transition 3 {yields} 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. (orig.)

Wrox SharePoint 2010 SharePoint911 three-pack

CERN Document Server

Klindt, Todd; Mason, Jennifer; Rogers, Laura; Drisgill, Randy; Ross, John; Riemann, Larry; Perran, Amanda; Perran, Shane; Sanford, Jacob J; Stubbs, Paul; Caravajal, Steve

2012-01-01

The Wrox SharePoint 2010 SharePoint911 Three-Pack combines the contents of three full e-books written by the experts from SharePoint911.  That's over 1800 pages of hands-on advice from Todd Klindt, Shane Young, Laura Rogers, Randy Drisgill, Jennifer Mason, John Ross, and Larry Riemann, among others. In Beginning SharePoint 2010: Building Business Solutions with SharePoint (ISBN 978-0-470-61789-2) by Amanda Perran, Shane Perran, Jennifer Mason, and Laura Rogers, readers learn the core concepts, terminology, and features of SharePoint 2010. In Professiona

Automorphic properties of low energy string amplitudes in various dimensions

International Nuclear Information System (INIS)

Green, Michael B.; Russo, Jorge G.; Vanhove, Pierre

2010-01-01

This paper explores the moduli-dependent coefficients of higher-derivative interactions that appear in the low-energy expansion of the four-supergraviton amplitude of maximally supersymmetric string theory compactified on a d torus. These automorphic functions are determined for terms up to order ∂ 6 R 4 and various values of d by imposing a variety of consistency conditions. They satisfy Laplace eigenvalue equations with or without source terms, whose solutions are given in terms of Eisenstein series, or more general automorphic functions, for certain parabolic subgroups of the relevant U-duality groups. The ultraviolet divergences of the corresponding supergravity field theory limits are encoded in various logarithms, although the string theory expressions are finite. This analysis includes intriguing representations of SL(d) and SO(d,d) Eisenstein series in terms of toroidally compactified one and two-loop string and supergravity amplitudes.

Experimental and numerical approach on fracture behaviour of four inches diameter carbon-manganese cracked welded pipes in four point bending

International Nuclear Information System (INIS)

Semete, P.; Faidy, C.; Lautier, J.L.

2001-01-01

EDF has conducted a research programme to demonstrate the fracture resistance of carbon-manganese welded pipes. The main task of this programme consisted of testing three four inches diameter (114.3 mm O.D.) thin welded pipes (8.56 mm thick) which are representative of those of the sites. The three pipes were loaded under four point bending at a quasi-static rate at -20 C till their maximum bending moment was reached. This paper presents the experimental results, finite element calculations and their comparison with the simplified fracture assessment method of the RSE-M Code. (author)

The Inverse Optimal Control Problem for a Three-Loop Missile Autopilot

Science.gov (United States)

Hwang, Donghyeok; Tahk, Min-Jea

2018-04-01

The performance characteristics of the autopilot must have a fast response to intercept a maneuvering target and reasonable robustness for system stability under the effect of un-modeled dynamics and noise. By the conventional approach, the three-loop autopilot design is handled by time constant, damping factor and open-loop crossover frequency to achieve the desired performance requirements. Note that the general optimal theory can be also used to obtain the same gain as obtained from the conventional approach. The key idea of using optimal control technique for feedback gain design revolves around appropriate selection and interpretation of the performance index for which the control is optimal. This paper derives an explicit expression, which relates the weight parameters appearing in the quadratic performance index to the design parameters such as open-loop crossover frequency, phase margin, damping factor, or time constant, etc. Since all set of selection of design parameters do not guarantee existence of optimal control law, explicit inequalities, which are named the optimality criteria for the three-loop autopilot (OC3L), are derived to find out all set of design parameters for which the control law is optimal. Finally, based on OC3L, an efficient gain selection procedure is developed, where time constant is set to design objective and open-loop crossover frequency and phase margin as design constraints. The effectiveness of the proposed technique is illustrated through numerical simulations.

Oscillation damping of chiral string loops

International Nuclear Information System (INIS)

Babichev, Eugeny; Dokuchaev, Vyacheslav

2002-01-01

Chiral cosmic string loops tend to the stationary (vorton) configuration due to energy loss into gravitational and electromagnetic radiation. We describe the asymptotic behavior of near stationary chiral loops and their fading to vortons. General limits on the gravitational and electromagnetic energy losses by near stationary chiral loops are found. For these loops we estimate the oscillation damping time. We present solvable examples of gravitational radiation energy loss by some chiral loop configurations. The analytical dependence of string energy with time is found in the case of the chiral ring with small amplitude radial oscillations

Recursion rules for scattering amplitudes in non-Abelian gauge theories

International Nuclear Information System (INIS)

Kim, C.; Nair, V.P.

1997-01-01

We present a functional derivation of recursion rules for scattering amplitudes in a non-Abelian gauge theory in a form valid to arbitrary loop order. The tree-level and one-loop recursion rules are explicitly displayed. copyright 1997 The American Physical Society

Recurrence relations for three-loop prototypes of bubble diagrams with a mass

International Nuclear Information System (INIS)

Avdeev, L.V.

1995-01-01

Recurrence relations derived via the Chetyrkin-Tkachev method of integration by parts are applied to reduce scalar three-loop bubble (vacuum) diagrams with a mass to a limited number of master integrals. The reduction is implemented as a package of computer programs for analytic evaluation in FORM. The algorithms are applicable to diagrams with any integer powers on the lines in an arbitrary dimension. A physical application is the evaluation of the three-loop QCD correction to the electroweak ρ-parameter. 8 refs., 1 fig

Tree-level amplitudes and dual superconformal symmetry

Energy Technology Data Exchange (ETDEWEB)

Drummond, J M, E-mail: drummond@lapp.in2p3.fr [PH-TH Division, CERN, CH-1211, Geneva 23 (Switzerland); LAPTH, Universite de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux Cedex (France)

2011-11-11

We review the structure of gauge theory scattering amplitudes at tree level and describe how a compact expression can be found which encodes all the tree-level amplitudes in the maximally supersymmetric N=4 theory. The expressions for the amplitudes reveal a dual superconformal symmetry. We describe how these ideas can be extended to leading singularities and the loop integrand in the planar theory and discuss the appearance of dual conformal symmetry in higher-dimensional gauge theories. 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)

Inductive Loops for Sensing Position as Signature Signals

International Nuclear Information System (INIS)

Larbani, Sofiane; Malik, Noreha Abdul; Nordin, Anis Norashikin; Khan, Sheroz; Shobaki, Mohammad

2013-01-01

In this paper, an inductive sensing technique made of a special shaped inductive loop is proposed. The inductive loop has an inner turn fitted within an outer turn, making a total inductance value 100μH. This loop is made to be shown with balanced response using three capacitance values of 0.068μF each when a sinusoidal voltage source of 5V peak-to-peak is applied. The variation of the relative permeability of the inductance of the inductive loop (AL) results in a variation of the overall inductance value (L+AL), that causes the output signal to change in term of shape and amplitude for variation of total inductance sweep over a given period of time. As a result of change in inductance value (lμH) there is a correspondence increase of 300mV. Theoretical derivations have showed in close agreement with the simulation plots obtained using Multisim software

Inductive Loops for Sensing Position as Signature Signals

Science.gov (United States)

Larbani, Sofiane; Malik, Noreha Abdul; Norashikin Nordin, Anis; Khan, Sheroz; Shobaki, Mohammad

2013-12-01

In this paper, an inductive sensing technique made of a special shaped inductive loop is proposed. The inductive loop has an inner turn fitted within an outer turn, making a total inductance value 100μH. This loop is made to be shown with balanced response using three capacitance values of 0.068μF each when a sinusoidal voltage source of 5V peak-to-peak is applied. The variation of the relative permeability of the inductance of the inductive loop (AL) results in a variation of the overall inductance value (L+AL), that causes the output signal to change in term of shape and amplitude for variation of total inductance sweep over a given period of time. As a result of change in inductance value (lμH) there is a correspondence increase of 300mV. Theoretical derivations have showed in close agreement with the simulation plots obtained using Multisim software.

Three-dimensional closed-loop control of self-propelled microjets

NARCIS (Netherlands)

Khalil, I.S.M.; Magdanz, Veronika; Schmidt, Oliver S.; Sanchez, Samuel; Misra, Sarthak

2013-01-01

We demonstrate precise closed-loop control of microjets under the influence of the magnetic fields in three-dimensional (3D) space. For this purpose, we design a magnetic-based control system that directs the field lines towards reference positions. Microjets align along the controlled field lines

Higgs mass prediction in the MSSM at three-loop level in a pure \\overline{{ {DR}}} context

Science.gov (United States)

Harlander, Robert V.; Klappert, Jonas; Voigt, Alexander

2017-12-01

The impact of the three-loop effects of order α _tα _s^2 on the mass of the light CP-even Higgs boson in the { {MSSM}} is studied in a pure \\overline{{ {DR}}} context. For this purpose, we implement the results of Kant et al. (JHEP 08:104, 2010) into the C++ module Himalaya and link it to FlexibleSUSY, a Mathematica and C++ package to create spectrum generators for BSM models. The three-loop result is compared to the fixed-order two-loop calculations of the original FlexibleSUSY and of FeynHiggs, as well as to the result based on an EFT approach. Aside from the expected reduction of the renormalization scale dependence with respect to the lower-order results, we find that the three-loop contributions significantly reduce the difference from the EFT prediction in the TeV-region of the { {SUSY}} scale {M_S}. Himalaya can be linked also to other two-loop \\overline{{ {DR}}} codes, thus allowing for the elevation of these codes to the three-loop level.

Automated one-loop calculations with GoSam

International Nuclear Information System (INIS)

Cullen, Gavin; Greiner, Nicolas; Heinrich, Gudrun; Reiter, Thomas; Luisoni, Gionata; Mastrolia, Pierpaolo; Ossola, Giovanni; Tramontano, Francesco

2012-01-01

We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the loop. (orig.)

Automated One-Loop Calculations with GoSam

CERN Document Server

Cullen, Gavin; Heinrich, Gudrun; Luisoni, Gionata; Mastrolia, Pierpaolo; Ossola, Giovanni; Reiter, Thomas; Tramontano, Francesco

2012-01-01

We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the loop.

Temperature Oscillations in Loop Heat Pipes - A Revisit

Science.gov (United States)

Ku, Jentung

2018-01-01

Three types of temperature oscillation have been observed in the loop heat pipes. The first type is an ultra-high frequency temperature oscillation with a period on the order of seconds or less. This type of temperature oscillation is of little significance in spacecraft thermal control because the amplitude is in the noise level. The second type is a high frequency, low amplitude temperature oscillation with a period on the order of seconds to minutes and an amplitude on the order of one Kelvin. It is caused by the back-and-forth movement of the vapor front near the inlet or outlet of the condenser. The third type is a low frequency, high amplitude oscillation with a period on the order of hours and an amplitude on the order of tens of Kelvin. It is caused by the modulation of the net heat load into the evaporator by the attached large thermal mass which absorbs and releases energy alternately. Several papers on LHP temperature oscillation have been published. This paper presents a further study on the underlying physical processes during the LHP temperature oscillation, with an emphasis on the third type of temperature oscillation. Specifically, equations governing the thermal and hydraulic behaviors of LHP operation will be used to describe interactions among LHP components, heat source, and heat sink. The following sequence of events and their interrelationship will also be explored: 1) maxima and minima of reservoir and thermal mass temperatures; 2) the range of the vapor front movement inside the condenser; 3) rates of change of the reservoir and thermal mass temperatures; 4) the rate of heat absorption and heat release by the thermal mass and the rate of vapor front movement; and 5) inflection points of the reservoir and thermal mass temperatures.

Preparation of three- and four-qubit decoherence-free states via Zeno-like measurements

International Nuclear Information System (INIS)

Shao, Xiao-Qiang; Zhang, Shou; Zhao, Yong-Fang; Chen, Li; Yeon, Kyu-Hwang

2010-01-01

Enlightened by the idea of purification through Zeno-like measurements (Nakazato et al 2003 Phys. Rev. Lett. 90 060401), we propose a scheme for generating three- and four-qubit decoherence-free states with respect to collective amplitude damping. The whole system is in a star configuration of a spin network and the outer spin qubits construct the decoherence-free state via measuring the state of central spin qubit at intervals of τ repeatedly. An interesting feature is found: namely, that in order to prepare the three-qubit decoherence-free state successfully, the value of τ for the projected time-evolution operator must be set definitely, while this restrictive condition is relaxed for achieving the four-qubit decoherence-free state. The simulation results reveal that the fidelity approaches one asymptotically, and the corresponding success probability reaches a stable value by increasing the number of measurements N.

On the unfolding of the fundamental region in integrals of modular invariant amplitudes

International Nuclear Information System (INIS)

Trapletti, Michele

2003-01-01

We study generic one-loop (string) amplitudes where an integration over the fundamental region F of the modular group is needed. We show how the known lattice-reduction technique used to unfold F to a more suitable region S can be modified to rearrange generic modular invariant amplitudes. The main aim is to unfold F to the strip and, at the same time, to simplify the form of the integrand when it is a sum over a finite number of terms, like in one-loop amplitudes for closed strings compactified on orbifolds. We give a general formula and a recipe to compute modular invariant amplitudes. As an application of the technique we compute the one-loop vacuum energy ρ n for a generic Z n freely acting orbifold, generalizing the result that this energy is less than zero and drives the system to a tachyonic divergence, and that ρ n m if n>m. (author)

Automated one-loop calculations with GoSam

International Nuclear Information System (INIS)

Cullen, G.; Greiner, N.; Heinrich, G.; Reiter, T.; Luisoni, G.; Mastrolia, P.; Padua Univ.; Ossola, G.; Tramontano, F.

2012-01-01

In this talk, the program package GOSAM is presented which can be used for the automated calculation of one-loop amplitudes for multi-particle processes. The integrands are generated in terms of Feynman diagrams and can be reduced by d-dimensional integrand-level decomposition, or tensor reduction, or a combination of both. Through various examples we show that GOSAM can produce one-loop amplitudes for both QCD and electroweak theory; model files for theories Beyond the Standard Model can be linked as well. (orig.)

Automated one-loop calculations with GoSam

Energy Technology Data Exchange (ETDEWEB)

Cullen, G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Greiner, N.; Heinrich, G.; Reiter, T. [Max-Planck-Institut fuer Physik, Muenchen (Germany); Luisoni, G. [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology; Mastrolia, P. [Max-Planck-Institut fuer Physik, Muenchen (Germany); Padua Univ. (Italy). Dipt. di Fisica; Ossola, G. [City Univ. of New York, NY (United States). New York City College of Technology; Tramontano, F. [CERN, Geneva (Switzerland). AS Div.

2012-01-15

In this talk, the program package GOSAM is presented which can be used for the automated calculation of one-loop amplitudes for multi-particle processes. The integrands are generated in terms of Feynman diagrams and can be reduced by d-dimensional integrand-level decomposition, or tensor reduction, or a combination of both. Through various examples we show that GOSAM can produce one-loop amplitudes for both QCD and electroweak theory; model files for theories Beyond the Standard Model can be linked as well. (orig.)

K0-anti K0 mixing at three loops

International Nuclear Information System (INIS)

Eeg, J.O.

1987-01-01

We consider diagrams of order α s 2 G F 2 for the K 0 -anti K 0 mixing, topologically different from the gluon-corrected standard box. The treatment of three-loop diagrams is simplified by factorizing them in terms of momentum-dependent effective vertices for s → dG and s → dGG transitions. An enhancement from the remaining loop-momentum integration compensates for the extra powers of the strong coupling. This gives a significant contribution to the CP-violating part (-15% to -40% of the standard-box value). The dependence of the results on the involved mass parameters is illustrated by LEGO plots for both the CP-conserving and CP-violating parts. (orig.)

N-point g-loop vertex for free bosonic theory with vacuum charge Q

International Nuclear Information System (INIS)

Di Vecchia, P.; Pezzella, F.; Frau, M.; Hornfeck, K.

1988-12-01

Starting from the N-Point Vertex on the sphere and using the sewing procedure we construct the N-Point g-Loop Vertex for a free bosonic theory with vacuum charge Q. We then show that, when this vertex is saturated with N highest weight states, it gives their correlation function on an arbitrary Riemann surface of genus g. We also extend our formalism to the case of a free scalar field compactified on a circle, which is related to the Coulomb gas description of minimal models. (orig.)

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.

Employing optical code division multiple access technology in the all fiber loop vibration sensor system

Science.gov (United States)

Tseng, Shin-Pin; Yen, Chih-Ta; Syu, Rong-Shun; Cheng, Hsu-Chih

2013-12-01

This study proposes a spectral amplitude coding-optical code division multiple access (SAC-OCDMA) framework to access the vibration frequency of a test object on the all fiber loop vibration sensor (AFLVS). Each user possesses an individual SAC, and fiber Bragg grating (FBG) encoders/decoders using multiple FBG arrays were adopted, providing excellent orthogonal properties in the frequency domain. The system also mitigates multiple access interference (MAI) among users. When an optical fiber is bent to a point exceeding the critical radius, the fiber loop sensor becomes sensitive to external physical parameters (e.g., temperature, strain, and vibration). The AFLVS involves placing a fiber loop with a specific radius on a designed vibration platform.

Junction leakage measurements with micro four-point probes

DEFF Research Database (Denmark)

Lin, Rong; Petersen, Dirch Hjorth; Wang, Fei

2012-01-01

We present a new, preparation-free method for measuring the leakage current density on ultra-shallow junctions. The junction leakage is found by making a series of four-point sheet resistance measurements on blanket wafers with variable electrode spacings. The leakage current density is calculated...... using a fit of the measured four-point resistances to an analytical two-sheet model. The validity of the approximation involved in the two-sheet model is verified by a comparison to finite element model calculations....

Genetic diversity of mtDNA D-loop sequences in four native Chinese chicken breeds.

Science.gov (United States)

Guo, H W; Li, C; Wang, X N; Li, Z J; Sun, G R; Li, G X; Liu, X J; Kang, X T; Han, R L

2017-10-01

1. To explore the genetic diversity of Chinese indigenous chicken breeds, a 585 bp fragment of the mitochondrial DNA (mtDNA) region was sequenced in 102 birds from the Xichuan black-bone chicken, Yunyang black-bone chicken and Lushi chicken. In addition, 30 mtDNA D-loop sequences of Silkie fowls were downloaded from NCBI. The mtDNA D-loop sequence polymorphism and maternal origin of 4 chicken breeds were analysed in this study. 2. The results showed that a total of 33 mutation sites and 28 haplotypes were detected in the 4 chicken breeds. The haplotype diversity and nucleotide diversity of these 4 native breeds were 0.916 ± 0.014 and 0.012 ± 0.002, respectively. Three clusters were formed in 4 Chinese native chickens and 12 reference breeds. Both the Xichuan black-bone chicken and Yunyang black-bone chicken were grouped into one cluster. Four haplogroups (A, B, C and E) emerged in the median-joining network in these breeds. 3. It was concluded that these 4 Chinese chicken breeds had high genetic diversity. The phylogenetic tree and median network profiles showed that Chinese native chickens and its neighbouring countries had at least two maternal origins, one from Yunnan, China and another from Southeast Asia or its surrounding area.

Massive three-loop form factor in the planar limit

Energy Technology Data Exchange (ETDEWEB)

Henn, Johannes [PRISMA Cluster of Excellence, Johannes Gutenberg University,Staudingerweg 9, 55099 Mainz (Germany); Smirnov, Alexander V. [Research Computing Center, Moscow State University,119991 Moscow (Russian Federation); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics of Moscow State University,119991 Moscow (Russian Federation); Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT),Wolfgang-Gaede Straße 1, 76128 Karlsruhe (Germany); Steinhauser, Matthias [Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT),Wolfgang-Gaede Straße 1, 76128 Karlsruhe (Germany)

2017-01-17

We compute the three-loop QCD corrections to the massive quark-anti-quark-photon form factors F{sub 1} and F{sub 2} in the large-N{sub c} limit. The analytic results are expressed in terms of Goncharov polylogarithms. This allows for a straightforward numerical evaluation. We also derive series expansions, including power suppressed terms, for three kinematic regions corresponding to small and large invariant masses of the photon momentum, and small velocities of the heavy quarks.

Leptonic contributions to the effective electromagnetic coupling at four-loop order in QED

International Nuclear Information System (INIS)

Sturm, Christian

2013-01-01

The running of the effective electromagnetic coupling is for many electroweak observables the dominant correction. It plays an important role for deriving constraints on the Standard Model in the context of electroweak precision measurements. We compute the four-loop QED corrections to the running of the effective electromagnetic coupling and perform a numerical evaluation of the different gauge invariant subsets

Properties of the twisted Polyakov loop coupling and the infrared fixed point in the SU(3) gauge theories

Science.gov (United States)

Itou, Etsuko

2013-08-01

We report the nonperturbative behavior of the twisted Polyakov loop (TPL) coupling constant for the SU(3) gauge theories defined by the ratio of Polyakov loop correlators in finite volume with twisted boundary condition. We reveal the vacuum structures and the phase structure for the lattice gauge theory with the twisted boundary condition. Carrying out the numerical simulations, we determine the nonperturbative running coupling constant in this renormalization scheme for the quenched QCD and N_f=12 SU(3) gauge theories. First, we study the quenched QCD theory using the plaquette gauge action. The TPL coupling constant has a fake fixed point in the confinement phase. We discuss this fake fixed point of the TPL scheme and obtain the nonperturbative running coupling constant in the deconfinement phase, where the magnitude of the Polyakov loop shows the nonzero values. We also investigate the system coupled to fundamental fermions. Since we use the naive staggered fermion with the twisted boundary condition in our simulation, only multiples of 12 are allowed for the number of flavors. According to the perturbative two-loop analysis, the N_f=12 SU(3) gauge theory might have a conformal fixed point in the infrared region. However, recent lattice studies show controversial results for the existence of the fixed point. We point out possible problems in previous work, and present our careful study. Finally, we find the infrared fixed point (IRFP) and discuss the robustness of the nontrivial IRFP of a many-flavor system under the change of the analysis method. Some preliminary results were reported in the proceedings [E. Bilgici et al., PoS(Lattice 2009), 063 (2009); Itou et al., PoS(Lattice 2010), 054 (2010)] and the letter paper [T. Aoyama et al., arXiv:1109.5806 [hep-lat

Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions

CERN Document Server

Cornalba, L; Penedones, J; Schiappa, R; Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo

2007-01-01

We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ . This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function _{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.

Effective string theory and QCD scattering amplitudes

International Nuclear Information System (INIS)

Makeenko, Yuri

2011-01-01

QCD string is formed at distances larger than the confinement scale and can be described by the Polchinski-Strominger effective string theory with a nonpolynomial action, which has nevertheless a well-defined semiclassical expansion around a long-string ground state. We utilize modern ideas about the Wilson-loop/scattering-amplitude duality to calculate scattering amplitudes and show that the expansion parameter in the effective string theory is small in the Regge kinematical regime. For the amplitudes we obtain the Regge behavior with a linear trajectory of the intercept (d-2)/24 in d dimensions, which is computed semiclassically as a momentum-space Luescher term, and discuss an application to meson scattering amplitudes in QCD.

Advanced methods for scattering amplitudes in gauge theories

International Nuclear Information System (INIS)

Peraro, Tiziano

2014-01-01

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.

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.

Spectator scattering at NLO in non-leptonic B decays: Leading penguin amplitudes

International Nuclear Information System (INIS)

Beneke, M.; Jaeger, S.

2007-01-01

We complete the computation of the 1-loop (α s 2 ) corrections to hard spectator scattering in non-leptonic B decays at leading power in Λ/m b by evaluating the penguin amplitudes. This extends the knowledge of these next-to-next-to-leading-order contributions in the QCD factorization formula for B decays to a much wider class of final states, including all pseudoscalar-pseudoscalar, pseudoscalar-vector, and longitudinally polarized vector-vector final states, except final states with η or η ' mesons. The new 1-loop correction is significant for the colour-suppressed amplitudes, but turns out to be strongly suppressed for the leading QCD penguin amplitude α 4 p . We provide numerical values of the phenomenological P/T and C/T amplitude ratios for the ππ, πρ and ρρ final states, and discuss corrections to several relations between electroweak penguin and tree amplitudes

The three-point function as a probe of models for large-scale structure

International Nuclear Information System (INIS)

Frieman, J.A.; Gaztanaga, E.

1993-01-01

The authors analyze the consequences of models of structure formation for higher-order (n-point) galaxy correlation functions in the mildly non-linear regime. Several variations of the standard Ω = 1 cold dark matter model with scale-invariant primordial perturbations have recently been introduced to obtain more power on large scales, R p ∼20 h -1 Mpc, e.g., low-matter-density (non-zero cosmological constant) models, open-quote tilted close-quote primordial spectra, and scenarios with a mixture of cold and hot dark matter. They also include models with an effective scale-dependent bias, such as the cooperative galaxy formation scenario of Bower, et al. The authors show that higher-order (n-point) galaxy correlation functions can provide a useful test of such models and can discriminate between models with true large-scale power in the density field and those where the galaxy power arises from scale-dependent bias: a bias with rapid scale-dependence leads to a dramatic decrease of the hierarchical amplitudes Q J at large scales, r approx-gt R p . Current observational constraints on the three-point amplitudes Q 3 and S 3 can place limits on the bias parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that scale-dependent bias is responsible for the extra power observed on large scales

Engineering topological phases with a three-dimensional nodal-loop semimetal

Science.gov (United States)

Li, Linhu; Yap, Han Hoe; Araújo, Miguel A. N.; Gong, Jiangbin

2017-12-01

A three-dimensional (3D) nodal-loop semimetal phase is exploited to engineer a number of intriguing phases featuring different peculiar topological surface states. In particular, by introducing various two-dimensional gap terms to a 3D tight-binding model of a nodal-loop semimetal, we obtain a rich variety of topological phases of great interest to ongoing theoretical and experimental studies, including a chiral insulator, degenerate-surface-loop insulator, and second-order topological insulator, as well as a Weyl semimetal with tunable Fermi arc profiles. The unique concept underlying our approach is to engineer topological surface states that inherit their dispersion relations from a gap term. The results provide one rather unified principle for the creation of novel topological phases and can guide the search for new topological materials. Two-terminal transport studies are also carried out to distinguish the engineered topological phases.

Renormalization of loop functions for all loops

International Nuclear Information System (INIS)

Brandt, R.A.; Neri, F.; Sato, M.

1981-01-01

It is shown that the vacuum expectation values W(C 1 ,xxx, C/sub n/) of products of the traces of the path-ordered phase factors P exp[igcontour-integral/sub C/iA/sub μ/(x)dx/sup μ/] are multiplicatively renormalizable in all orders of perturbation theory. Here A/sub μ/(x) are the vector gauge field matrices in the non-Abelian gauge theory with gauge group U(N) or SU(N), and C/sub i/ are loops (closed paths). When the loops are smooth (i.e., differentiable) and simple (i.e., non-self-intersecting), it has been shown that the generally divergent loop functions W become finite functions W when expressed in terms of the renormalized coupling constant and multiplied by the factors e/sup -K/L(C/sub i/), where K is linearly divergent and L(C/sub i/) is the length of C/sub i/. It is proved here that the loop functions remain multiplicatively renormalizable even if the curves have any finite number of cusps (points of nondifferentiability) or cross points (points of self-intersection). If C/sub γ/ is a loop which is smooth and simple except for a single cusp of angle γ, then W/sub R/(C/sub γ/) = Z(γ)W(C/sub γ/) is finite for a suitable renormalization factor Z(γ) which depends on γ but on no other characteristic of C/sub γ/. This statement is made precise by introducing a regularization, or via a loop-integrand subtraction scheme specified by a normalization condition W/sub R/(C-bar/sub γ/) = 1 for an arbitrary but fixed loop C-bar/sub γ/. Next, if C/sub β/ is a loop which is smooth and simple except for a cross point of angles β, then W(C/sub β/) must be renormalized together with the loop functions of associated sets S/sup i//sub β/ = ]C/sup i/ 1 ,xxx, C/sup i//sub p/i] (i = 2,xxx,I) of loops C/sup i//sub q/ which coincide with certain parts of C/sub β/equivalentC 1 1 . Then W/sub R/(S/sup i//sub β/) = Z/sup i/j(β)W(S/sup j//sub β/) is finite for a suitable matrix Z/sup i/j

A general reduction method for one-loop N-point integrals

International Nuclear Information System (INIS)

Heinrich, G.; Binoth, T.

2000-01-01

In order to calculate cross sections with a large number of particles/jets in the final state at next-to-leading order, one has to reduce the occurring scalar and tensor one-loop integrals to a small set of known integrals. In massless theories, this reduction procedure is complicated by the presence of infrared divergences. Working in n = 4 - 2ε dimensions, it will be outlined how to achieve such a reduction for diagrams with an arbitrary number of external legs. As a result, any integral with more than four propagators and generic 4-dimensional external momenta can be reduced to box integrals

A Three Level Framework for Closed-Loop Supply Chain Management—Linking Society, Chain and Actor Level

Directory of Open Access Journals (Sweden)

Stefan Seuring

2011-04-01

Full Text Available Supply chain management and closed-loop supply chain management (CLSCM have developed into established concepts in recent years. The related material cycles and product returns form an important part of all related processes with high potential for reducing environmental burden. The paper proposes a framework for (environmentally triggered closed-loop supply chain management, spanning three different levels: the societal or governance, the chain and the actor level. Within each level, a set of activities or processes can be identified. Taken together, the levels allow a comprehensive analysis of a closed-loop supply chain system. This is illustrated building on two case studies in the textile and apparel industry, where closed-loop supply chains have been designed to take specific apparel products back. The case studies are analyzed against all three levels and allow exemplification of related challenges and interrelations among the three levels. The three levels contribute to the further comprehension of the multiple issues having to be taken into account for successfully implementing closed-loop supply chains.

Results from GRACE/SUSY at one-loop

International Nuclear Information System (INIS)

Fujimoto, J.; Ishikawa, T.; Kurihara, Y.; Jimbo, M.; Yasui, Y.; Kaneko, T.; Kon, T.; Kuroda, M.; Shimizu, Y.

2007-01-01

We report the recent development on the SUSY calculations with the help of GRACE system. GRACE/SUSY/1LOOP is the computer code which can generate Feynman diagrams in the MSSM automatically and compute one-loop amplitudes in the numerical way. We present new results of various two-body widths and chargino pair production at ILC (international linear collider) at one-loop level. (author)

On Fine Structure of Strings: The Universal Correction to the Veneziano Amplitude

CERN Multimedia

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.

2D quantum gravity at three loops: A counterterm investigation

Directory of Open Access Journals (Sweden)

Lætitia Leduc

2016-02-01

Full Text Available We analyze the divergences of the three-loop partition function at fixed area in 2D quantum gravity. Considering the Liouville action in the Kähler formalism, we extract the coefficient of the leading divergence ∼AΛ2(ln⁡AΛ22. This coefficient is non-vanishing. We discuss the counterterms one can and must add and compute their precise contribution to the partition function. This allows us to conclude that every local and non-local divergence in the partition function can be balanced by local counterterms, with the only exception of the maximally non-local divergence (ln⁡AΛ23. Yet, this latter is computed and does cancel between the different three-loop diagrams. Thus, requiring locality of the counterterms is enough to renormalize the partition function. Finally, the structure of the new counterterms strongly suggests that they can be understood as a renormalization of the measure action.

CO-ANALYSIS OF SOLAR MICROWAVE AND HARD X-RAY SPECTRAL EVOLUTIONS. II. IN THREE SOURCES OF A FLARING LOOP

International Nuclear Information System (INIS)

Huang Guangli; Li Jianping

2011-01-01

Based on the spatially resolvable data of the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and Nobeyama Radio Heliograph (NoRH), co-analysis of solar hard X-ray and microwave spectral evolution is performed in three separate sources located in one looptop (LT) and two footpoints (FPs) of a huge flaring loop in the 2003 October 24 flare. The RHESSI image spectral evolution in 10-100 keV is always fitted by the well-known soft-hard-soft (SHS) pattern in the three sources. When the total energy is divided into four intervals similar to the Yohkoh/Hard X-ray Telescope, i.e., 12.5-32.5 keV, 32.5-52.5 keV, 52.5-72.5 keV, and 72.5-97.5 keV, the SHS pattern in lower energies is converted gradually to the hard-soft-hard (HSH) pattern in higher energies in all three sources. However, the break energy in the LT and the northeast FP (∼32.5 keV) is evidently smaller than that in the southwest FP (∼72.5 keV). Regarding microwave spectral evolution of the NoRH data, the well-known soft-hard-harder pattern appeared in the southwest FP, while the HSH pattern coexisted in the LT and the northeast FP. The different features of the hard X-ray and microwave spectral evolutions in the three sources may be explained by the loop-loop interaction with another huge loop in the LT and with a compact loop in the northeast FP, where the trapping effect is much stronger than that in the southwest FP. The comparison between the LT and FP spectral indices suggests that the radiation mechanism of X-rays may be quite different in different energy intervals and sources. The calculated electron spectral indices from the predicted mechanisms of X-rays gradually become closer to those from the microwave data with increasing X-ray energies.

Computational stability appraisal of rectangular natural circulation loop: Effect of loop inclination

International Nuclear Information System (INIS)

Krishnani, Mayur; Basu, Dipankar N.

2017-01-01

Highlights: • Computational model developed for single-phase rectangular natural circulation loop. • Role of loop inclination to vertical on thermalhydraulic stability is explored. • Inclination has strong stabilizing effect due to lower effective gravitation force. • Increase in tilt angle reduces settling time and highest amplitude of oscillation. • An angle of 15° is suggested for the selected loop geometry. - Abstract: Controlling stability behavior of single-phase natural circulation loops, without significantly affecting its steady-state characteristics, is a topic of wide research interest. Present study explores the role of loop inclination on a particular loop geometry. Accordingly a 3D computational model of a rectangular loop is developed and transient conservation equations are solved to obtain the temporal variation in flow parameters. Starting from the quiescent state, simulations are performed for selected sets of operating conditions and also with a few selected inclination angles. System experiences instability at higher heater powers and also with higher sink temperatures. Inclination is found to have a strong stabilizing influence owing to the reduction in the effective gravitational acceleration and subsequent decline in local buoyancy effects. The settling time and highest amplitude of oscillations substantially reduces for a stable system with a small inclination. Typically-unstable systems can also suppress the oscillations, when subjected to tilting, within a reasonable period of time. It is possible to stabilize the loop within shorter time span by increasing the tilt angle, but at the expense of reduction in steady-state flow rate. Overall a tilt angle of 15° is suggested for the selected geometry. Results from the 3D model is compared with the predictions from an indigenous 1D code. While similar qualitative influence of inclination is observed, the 1D model predicts early appearance of the stability threshold and hence hints

Renormalization of three-quark operators for baryon distribution amplitudes

Energy Technology Data Exchange (ETDEWEB)

Gruber, Michael

2017-07-01

In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI{sup '}/SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.

Renormalization of three-quark operators for baryon distribution amplitudes

International Nuclear Information System (INIS)

Gruber, Michael

2017-01-01

In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI ' /SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.

Electrical conduction through surface superstructures measured by microscopic four-point probes

DEFF Research Database (Denmark)

Hasegawa, S.; Shiraki, I.; Tanabe, F.

2003-01-01

For in-situ measurements of the local electrical conductivity of well-defined crystal surfaces in ultra-high vacuum, we have developed two kinds of microscopic four-point probe methods. One involves a "four-tip STM prober," in which four independently driven tips of a scanning tunneling microscope...... (STM) are used for measurements of four-point probe conductivity. The probe spacing can be changed from 500 nm to 1 mm. The other method involves monolithic micro-four-point probes, fabricated on silicon chips, whose probe spacing is fixed around several mum. These probes are installed in scanning...

Conformal higher spin scattering amplitudes from twistor space

Energy Technology Data Exchange (ETDEWEB)

Adamo, Tim [Blackett Laboratory, Imperial College, London, SW7 2AZ (United Kingdom); Hähnel, Philipp; McLoughlin, Tristan [School of Mathematics, Trinity College Dublin, College Green, Dublin 2 (Ireland)

2017-04-04

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 (MHV)-bar 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.

Conformal higher spin scattering amplitudes from twistor space

International Nuclear Information System (INIS)

Adamo, Tim; Hähnel, Philipp; McLoughlin, Tristan

2017-01-01

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 (MHV)-bar 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.

Design of four-point SENB specimens with stable crack growth

DEFF Research Database (Denmark)

Jørgensen, Jeppe Bjørn; Kildegaard, Casper; Sørensen, Bent F.

2018-01-01

A four-point single-edge-notch-beam (SENB) test specimen loaded in displacement control (fixed grip) is proposed for studying crack deflection at bi-material interfaces. In order to ensure stable crack growth, a novel analytical model of the four-point SENB specimen in fixed grip is derived...... and compared with numerical models. Model results show that the specimen should be short and thick, and the start-crack length should be deep for the crack to propagate stable towards the bi-material interface. Observations from experimental tests of four-point SENB specimens with different start-crack lengths...

A solution for tensor reduction of one-loop N-point functions with N{>=}6

Energy Technology Data Exchange (ETDEWEB)

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

2011-11-15

Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N{>=}6. A general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N-1)-point Feynman integrals of rank (R-1) (for N{>=}6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization. (orig.)

N=4 supersymmetric Yang Mills scattering amplitudes at high energies. The Regge cut contribution

International Nuclear Information System (INIS)

Bartels, J.; Sabio Vera, A.

2008-07-01

We further investigate, in N=4 supersymmetric Yang Mills theories, the high energy Regge behavior of six-point scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two loop corrections to the discontinuities of the amplitudes for the transitions 2→4 and 3→3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. (orig.)

Flexural strength and behaviour of SFRSCC ribbed slab under four point bending

Science.gov (United States)

Ahmad, Hazrina; Hashim, Mohd Hisbany Mohd; Bakar, Afidah Abu; Hamzah, Siti Hawa; Rahman, Fadhillah Abdul

2017-11-01

An experimental investigation was carried out to study the ultimate strength and behaviour of SFRSCC ribbed slab under four point bending. Comparison was been made between ribbed slab that was fully reinforced with steel fibres (SFWS) with conventionally reinforced concrete ribbed slab (CS and CRC). The volume fraction of the 35 mm hooked end steel fibres used in the mix was 1% (80 kg/m3) with the aspect ratio of 65. Three full scale slab samples with the dimension of 2.8 x 1.2 m with 0.2 m thickness was constructed for the purpose of this study. The slab samples was loaded until failure in a four point bending test. As a whole, based on the results, it can be concluded that the performance of the steel fiber reinforced samples (SFWS) was found to be almost equivalent to the conventionally reinforced concrete ribbed slab sample (CRC).

Tree-level disk amplitude of three closed strings

Science.gov (United States)

Mousavi, Sepideh; Velni, Komeil Babaei

2018-05-01

It has been shown that the disk-level S-matrix elements of one Ramond-Ramond (RR) and two Neveu-Schwarz-Neveu-Schwarz (NSNS) states could be found by applying the Ward identity associated with the string duality and the gauge symmetry on a given component of the S matrix. These amplitudes have appeared as the components of six different T-dual multiplets. It is predicted in the literature that there are some nonzero disk-level scattering amplitudes, such as one RR (p -1 ) form with zero transverse index and two N S N S states, could not be captured by the T-dual Ward identity. We explicitly find this amplitude in terms of a minimal context of the integral functions by the insertion of one closed string RR vertex operator and two NSNS vertex operators. From the amplitude invariance under the Ward identity associated with the NSNS gauge transformations and T-duality, we also find some integral identities.

Loop integration results using numerical extrapolation for a non-scalar integral

International Nuclear Information System (INIS)

Doncker, E. de; Shimizu, Y.; Fujimoto, J.; Yuasa, F.; Kaugars, K.; Cucos, L.; Van Voorst, J.

2004-01-01

Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar four-point diagram. Extensions to accommodate loop integration by existing integration packages are also discussed. These include: using previously generated partitions of the domain and roundoff error guards

Results from GRACE/SUSY at one-loop

Indian Academy of Sciences (India)

We report the recent development on the SUSY calculations with the help of GRACE system. GRACE/SUSY/1LOOP is the computer code which can generate Feynman diagrams in the MSSM automatically and compute one-loop amplitudes in the numerical way. We present new results of various two-body decay widths ...

Motivic amplitudes and cluster coordinates

International Nuclear Information System (INIS)

Golden, J.K.; Goncharov, A.B.; Spradlin, M.; Vergu, C.; Volovich, A.

2014-01-01

In this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic configuration space Conf n (ℙ 3 ) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the two-loop seven-particle MHV motivic amplitude A 7,2 M and find that like the previously known six-particle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster X-coordinates on Conf n (ℙ 3 ). We also find intriguing relations between motivic amplitudes and the geometry of generalized associahedrons, to which cluster coordinates have a natural combinatoric connection. For example, the obstruction to A 7,2 M being expressible in terms of classical polylogarithms is most naturally represented by certain quadrilateral faces of the appropriate associahedron. We also find and prove the first known functional equation for the trilogarithm in which all 40 arguments are cluster X-coordinates of a single algebra. In this respect it is similar to Abel’s 5-term dilogarithm identity

Relationship between the Amplitude and Phase of a Signal Scattered by a Point-Like Acoustic Inhomogeneity

Science.gov (United States)

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.

Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions

International Nuclear Information System (INIS)

Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo

2007-01-01

We introduce the impact parameter representation for conformal field theory correlators of the form A∼ 1 O 2 O 1 O 2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function 1 O 1 > shock in the presence of a shock wave in anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch cut, we find the high spin and dimension conformal partial wave decomposition of all tree-level anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high spin O 1 O 2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling

Four-junction superconducting circuit

Science.gov (United States)

Qiu, Yueyin; Xiong, Wei; He, Xiao-Ling; Li, Tie-Fu; You, J. Q.

2016-01-01

We develop a theory for the quantum circuit consisting of a superconducting loop interrupted by four Josephson junctions and pierced by a magnetic flux (either static or time-dependent). In addition to the similarity with the typical three-junction flux qubit in the double-well regime, we demonstrate the difference of the four-junction circuit from its three-junction analogue, including its advantages over the latter. Moreover, the four-junction circuit in the single-well regime is also investigated. Our theory provides a tool to explore the physical properties of this four-junction superconducting circuit. PMID:27356619

SEISMOLOGY OF A LARGE SOLAR CORONAL LOOP FROM EUVI/STEREO OBSERVATIONS OF ITS TRANSVERSE OSCILLATION

International Nuclear Information System (INIS)

Verwichte, E.; Van Doorsselaere, T.; Foullon, C.; Nakariakov, V. M.; Aschwanden, M. J.

2009-01-01

The first analysis of a transverse loop oscillation observed by both Solar TErrestrial RElations Observatories (STEREO) spacecraft is presented, for an event on the 2007 June 27 as seen by the Extreme Ultraviolet Imager (EUVI). The three-dimensional loop geometry is determined using a three-dimensional reconstruction with a semicircular loop model, which allows for an accurate measurement of the loop length. The plane of wave polarization is found from comparison with a simulated loop model and shows that the oscillation is a fundamental horizontally polarized fast magnetoacoustic kink mode. The oscillation is characterized using an automated method and the results from both spacecraft are found to match closely. The oscillation period is 630 ± 30 s and the damping time is 1000 ± 300 s. Also, clear intensity variations associated with the transverse loop oscillations are reported for the first time. They are shown to be caused by the effect of line-of-sight integration. The Alfven speed and coronal magnetic field derived using coronal seismology are discussed. This study shows that EUVI/STEREO observations achieve an adequate accuracy for studying long-period, large-amplitude transverse loop oscillations.

Off-Shell Green Functions: One-Loop with Growing Legs

International Nuclear Information System (INIS)

Bashir, A.; Concha-Sanchez, Y.; Delbourgo, R.; Tejeda-Yeomans, M. E.

2008-01-01

One loop calculations in gauge theories in arbitrary gauge and dimensions become exceedingly hard with growing number of external off-shell legs. Let alone higher point functions, such a calculation for even the three point one-loop vertices for quantum electrodynamics (QED) and quantum chromodynamics (QCD) has been made available only recently. In this article, we discuss how Ward-Fradkin-Green-Takahashi identities (WFGTI) may provide a helpful tool in these computations. After providing a glimpse of our suggestion for the case of the 3-point vertex, we present our preliminary findings towards our similar efforts for the 4-point function. We restrict ourselves to the example of scalar quantum electrodynamics (SQED)

Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity

International Nuclear Information System (INIS)

Chiodaroli, Marco; Günaydin, Murat; 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 through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at tree-level and one loop. The double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.

On Resumming Inflationary Perturbations beyond One-loop

DEFF Research Database (Denmark)

Riotto, Antonio; Sloth, Martin Snoager

2008-01-01

It is well known that the correlation functions of a scalar field in a quasi-de Sitter space exhibit at the loop level cumulative infra-red effects proportional to the total number of e-foldings of inflation. Using the in-in formalism, we explore the behavior of these infra-red effects in the large...... N limit of an O(N) invariant scalar field theory with quartic self-interactions. By resumming all higher-order loop diagrams non-perturbatively, we show that the connected four-point correlation function, which is a signal of non-Gaussianity, is non-perturbatively enhanced with respect to its tree-level...

Light-like Wilson Loops and Cusp Anomalous Dimensions in Nonconformal Gauge Theories

International Nuclear Information System (INIS)

Pando Zayas, Leopoldo A.; Phalen, Daniel J.; Terrero-Escalante, Cesar A.

2008-01-01

We emphasize that nonconformal theories provide a natural playground for the ideas of the Maldacena conjecture opening the possibility of exploring properties that could potentially be in the same universality class as QCD. In particular, we discuss in detail how light-like Wilson loops, an important ingredient in the prescription for scattering amplitudes, can be described in a number of gravity duals of nonconformal gauge theories. We point out to a few universal properties and the prominent role of the strong scale

Experimental and Theoretical Deflections of Hybrid Composite Sandwich Panel under Four-point Bending Load

Directory of Open Access Journals (Sweden)

Jauhar Fajrin

2017-03-01

Full Text Available This paper presents a comparison of theoretical and experimental deflection of a hybrid sandwich panel under four-point bending load. The paper initially presents few basic equations developed under three-point load, followed by development of model under four-point bending load and a comparative analysis between theoretical and experimental results. It was found that the proposed model for predicting the deflection of hybrid sandwich panels provided fair agreement with the experimental values. Most of the sandwich panels showed theoretical deflection values higher than the experimental values, which is desirable in the design. It was also noticed that the introduction of intermediate layer does not contribute much to reduce the deflection of sandwich panel as the main contributor for the total deflection was the shear deformation of the core that mostly determined by the geometric of the samples and the thickness of the core.

Nonlinear (super)symmetries and amplitudes

Energy Technology Data Exchange (ETDEWEB)

Kallosh, Renata [Physics Department, Stanford University,382 Via Pueblo Mall, Stanford, CA 94305-4060 (United States)

2017-03-07

There is an increasing interest in nonlinear supersymmetries in cosmological model building. Independently, elegant expressions for the all-tree amplitudes in models with nonlinear symmetries, like D3 brane Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the generalized background field method we show how, in general, nonlinear symmetries of the action, bosonic and fermionic, constrain amplitudes beyond soft limits. The same identities control, for example, bosonic E{sub 7(7)} scalar sector symmetries as well as the fermionic goldstino symmetries. We present a universal derivation of the vanishing amplitudes in the single (bosonic or fermionic) soft limit. We explain why, universally, the double-soft limit probes the coset space algebra. We also provide identities describing the multiple-soft limit. We discuss loop corrections to N≥5 supergravity, to the D3 brane, and the UV completion of constrained multiplets in string theory.

Low-mass Higgs decays to four leptons at one loop and beyond

Energy Technology Data Exchange (ETDEWEB)

Kniehl, Bernd A.; Veretin, Oleg L. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik

2012-06-15

The ongoing searches for Higgs-boson signals in data taken at the CERN LHC and the Fermilab Tevatron crucially rely on the decay channels H{yields}Zll and H{yields}Wl{nu}{sub l}. We present a precision study of the partial widths of these decay channels including the full one-loop electroweak corrections and the dominant contributions at two and three loops, of O(G{sub F}{sup 2}m{sub t}{sup 4}), O(G{sub F}m{sub t}{sup 2}{alpha}{sub s}), and O(G{sub F}m{sub t}{sup 2}{alpha}{sub s}{sup 2}). Since the invariant mass of the off-shell intermediate boson is relatively low in the mass window 115 GeV< m{sub H}<129 GeV of current interest, lepton mass effects are relevant, especially for the {tau} lepton. (orig.)

Relative amplitude preservation processing utilizing surface consistent amplitude correction. Part 4; Surface consistent amplitude correction wo mochiita sotai shinpuku hozon shori. 4

Energy Technology Data Exchange (ETDEWEB)

Saeki, T [Japan National Oil Corp., Tokyo (Japan). Technology Research Center

1997-10-22

Discussions were given on seismic exploration from the ground surface using the reflection method, for surface consistent amplitude correction from among effects imposed from the ground surface and a surface layer. Amplitude distribution on the reflection wave zone is complex. Therefore, items to be considered in making an analysis are multiple, such as estimation of spherical surface divergence effect and exponential attenuation effect, not only amplitude change through the surface layer. If all of these items are taken into consideration, burden of the work becomes excessive. As a method to solve this problem, utilization of amplitude in initial movement of a diffraction wave may be conceived. Distribution of the amplitude in initial movement of the diffraction wave shows a value relatively close to distribution of the vibration transmitting and receiving points. The reason for this is thought because characteristics of the vibration transmitting and receiving points related with waveline paths in the vicinity of the ground surface have no great difference both on the diffraction waves and on the reflection waves. The lecture described in this paper introduces an attempt of improving the efficiency of the surface consistent amplitude correction by utilizing the analysis of amplitude in initial movement of the diffraction wave. 4 refs., 2 figs.

Three-dimensional finite amplitude electroconvection in dielectric liquids

Science.gov (United States)

Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

2018-02-01

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Three Point Functions in Higher Spin AdS3 Holography with 1/N Corrections

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Yasuaki Hikida

2017-10-01

Full Text Available We examine three point functions with two scalar operators and a higher spin current in 2d W N minimal model to the next non-trivial order in 1 / N expansion. The minimal model was proposed to be dual to a 3d higher spin gauge theory, and 1 / N corrections should be interpreted as quantum effects in the dual gravity theory. We develop a simple and systematic method to obtain three point functions by decomposing four point functions of scalar operators with Virasoro conformal blocks. Applying the method, we reproduce known results at the leading order in 1 / N and obtain new ones at the next leading order. As confirmation, we check that our results satisfy relations among three point functions conjectured before.

Trisections in Three and Four Dimensions

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Koenig, Dale R.

Every closed orientable three dimensional manifold has a Heegaard splitting, a decomposition into two handlebodies. Any two Heegaard splittings of the same manifold can be made isotopic after a finite number of stabilization operations. The notion of trisections, developed by Gay and Kirby, provided an analogue in four dimensions. They showed that any closed smooth orientable four dimensional manifold can be broken into three four dimensional handlebodies, with "niceness" conditions on their intersections, and showed that any two trisections are isotopic after stabilizations. In this thesis we investigate the notion of trisections in both three and four dimensions. In dimension three we define trisections of 3-manifolds and stabilization on these trisections. We use this to define the trisection genus of a 3-manifold. We then present several examples, showing among other things that the trisection genus is not additive under connect sum. We prove a stable equivalence theorem for trisections of 3-manifolds, showing that any two trisections of the same three-manifold can be made isotopic after stabilizations. We also show that trisections of S3 can be very complicated, so there is no analogue of Waldhausen's theorem for trisections of three manifolds. We then move on to trisections in four dimensions. We first show that if there exist four manifolds with unbalanced trisection genus lower than their balanced trisection genus, then trisection genus as defined by Gay and Kirby is not additive under connect sum. We produce several new classes of trisections, including several likely such examples. We include a class of examples that are provably minimal genus. We provide trisection diagrams for many of these trisections, and summarize some methods for quickly checking that these diagrams produce valid trisections.

The two Josephson junction flux qubit with large tunneling amplitude

International Nuclear Information System (INIS)

Shnurkov, V.I.; Soroka, A.A.; Mel'nik, S.I.

2008-01-01

In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling amplitude between the two macroscopic states. The latter can be controlled via the height and form of the potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest circuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude between two macroscopically different states can be increased substantially by engineering of the qubit circuit if the tunnel junction is replaced by a ScS contact. However, only Josephson tunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with present-day technology. To overcome this difficulty we consider here a flux qubit with high energy-level separation between the 'ground' and 'excited' states, consisting of a superconducting loop with two low-capacitance Josephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition between the two macroscopic states the tunneling amplitude can reach values greater than 1 K. Analytical results for the tunneling amplitude obtained within the semiclassical approximation by the instanton technique show good correlation with a numerical solution

Color-kinematic duality for form factors

International Nuclear Information System (INIS)

Boels, Rutger H.; Kniehl, Bernd A.; Tarasov, Oleg V.; Yang, Gang

2012-12-01

Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory observables formed by form factors. After a discussion of the general setup the existence of the duality is verified in two and three loop examples in four dimensional maximally supersymmetric Yang-Mills theory which involve the stress energy tensor multiplet. In these cases the duality reproduces known results in a particularly transparent and uniform way. As a non-trivial application we obtain a very simple form of the integrand of the four-loop two-point (Sudakov) form factor which passes a large set of unitarity cut checks.

Color-kinematic duality for form factors

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Boels, Rutger H.; Kniehl, Bernd A.; Tarasov, Oleg V.; Yang, Gang [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2012-12-15

Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory observables formed by form factors. After a discussion of the general setup the existence of the duality is verified in two and three loop examples in four dimensional maximally supersymmetric Yang-Mills theory which involve the stress energy tensor multiplet. In these cases the duality reproduces known results in a particularly transparent and uniform way. As a non-trivial application we obtain a very simple form of the integrand of the four-loop two-point (Sudakov) form factor which passes a large set of unitarity cut checks.

Three ports versus four ports laparoscopic cholecystectomy

International Nuclear Information System (INIS)

Shah, S.F.; Waqar, S.; Chaudry, M.A.; Hameed, S.

2017-01-01

To compare three ports laparoscopic cholecystectomy and four ports laparoscopic cholecystectomy in terms of complications, time taken to complete the procedure, hospital stay and cost effectiveness in local perspective. Methodology: This randomized control trial included 60 patients who underwent elective laparoscopic cholecystectomy at Department of Surgery, Pakistan Institute of Medical Sciences, Islamabad, Pakistan from January 2013 to June 2013. These patients were randomized on computer generated table of random numbers into group A and Group B. In Group A patients four ports were passed to perform laparoscopic cholecystectomy and in Group B patients three ports were passed to perform the procedure. Results: The mean age in both groups was 44 years (range 18-72). Three ports laparoscopic cholecystectomy (43 min) took less time to complete than four ports laparoscopic cholecystectomy (51 min). Patients in three ports laparoscopic cholecystectomy experienced less pain as compared to four ports group. The total additional analgesia requirement in 24 hours calculated in milligrams was less in three port laparoscopic cholecystectomy group as compared four port laparoscopic cholecystectomy group. The mean hospital stay in three port laparoscopic cholecystectomy group is 25 hours while the mean hospital stay in the four port laparoscopic cholecystectomy group is 28 hours. Conclusion: Three ports laparoscopic cholecystectomy is safe and effective procedure and it did not compromise the patient safety. (author)

Generation of high-order Bessel vortex beam carrying orbital angular momentum using multilayer amplitude-phase-modulated surfaces in radiofrequency domain

Science.gov (United States)

Kou, Na; Yu, Shixing; Li, Long

2017-01-01

A high-order Bessel vortex beam carrying orbital angular momentum (OAM) is generated by using multilayer amplitude-phase-modulated surfaces (APMSs) at 10 GHz. The APMS transmitarray is composed of four-layer conformal square-loop (FCSL) surfaces with both amplitude and phase modulation. The APMS can transform a quasi-spherical wave emitted from the feeding source into a pseudo non-diffractive high-order Bessel vortex beam with OAM. The APMS for a second-order Bessel beam carrying OAM in the n = 2 mode is designed, fabricated, and measured. Full-wave simulation and measurement results confirm that Bessel vortex beams with OAM can be effectively generated using the proposed APMS transmitarray.

Shrunk loop theorem for the topology probabilities of closed Brownian (or Feynman) paths on the twice punctured plane

International Nuclear Information System (INIS)

Giraud, O; Thain, A; Hannay, J H

2004-01-01

The shrunk loop theorem proved here is an integral identity which facilitates the calculation of the relative probability (or probability amplitude) of any given topology that a free, closed Brownian (or Feynman) path of a given 'duration' might have on the twice punctured plane (plane with two marked points). The result is expressed as a 'scattering' series of integrals of increasing dimensionality based on the maximally shrunk version of the path. Physically, this applies in different contexts: (i) the topology probability of a closed ideal polymer chain on a plane with two impassable points, (ii) the trace of the Schroedinger Green function, and thence spectral information, in the presence of two Aharonov-Bohm fluxes and (iii) the same with two branch points of a Riemann surface instead of fluxes. Our theorem starts from the Stovicek scattering expansion for the Green function in the presence of two Aharonov-Bohm flux lines, which itself is based on the famous Sommerfeld one puncture point solution of 1896 (the one puncture case has much easier topology, just one winding number). Stovicek's expansion itself can supply the results at the expense of choosing a base point on the loop and then integrating it away. The shrunk loop theorem eliminates this extra two-dimensional integration, distilling the topology from the geometry

CHY loop integrands from holomorphic forms

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