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We perform an analytical four loop calculation of exponent $z$ in model A of critical dynamics in $d=4-2\varepsilon$ dimensions. This is the first time such a large order of perturbation theory has been calculated analytically for models of…

Statistical Mechanics · Physics 2025-12-12 Loran Ts. Adzhemyan , Diana A. Davletbaeva , Daniil A. Evdokimov , Mikhail V. Kompaniets

We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar $n$-point integral as a cyclicly symmetric combination of $(n-1)$-point integrals. The computation of such…

High Energy Physics - Phenomenology · Physics 2008-11-26 Z. Bern , L. Dixon , D. A. Kosower

We describe in some detail the present features of an automatic loop calculation program as well as the integration techniques that go into it. The program, called XLOOPS 1.0, allows one to calculate massive one- and two-loop Feynman…

High Energy Physics - Phenomenology · Physics 2009-09-25 A. Frink , J. G. Körner , J. B. Tausk

We evaluate the massless one-loop hexagon integral in six dimensions. The result is given in terms of standard polylogarithms of uniform transcendental weight three, its functional form resembling the one of the remainder function of the…

High Energy Physics - Theory · Physics 2015-05-27 Vittorio Del Duca , Claude Duhr , Vladimir A. Smirnov

The objective of this short note is to provide two closed-form evaluations for the generalized hypergeometric function $_4F_3$ of the argument $\frac1{16}$. This is achieved by means of separating a generalized hypergeometric function…

Classical Analysis and ODEs · Mathematics 2025-01-14 Arjun K. Rathie , Mykola A. Shpot

We evaluate one-loop partition functions of higher-spin fields in thermal flat space with angular potentials; this computation is performed in arbitrary space-time dimension, and the result is a simple combination of Poincar\'e characters.…

High Energy Physics - Theory · Physics 2016-05-04 Andrea Campoleoni , Hernan A. Gonzalez , Blagoje Oblak , Max Riegler

It is demonstrated that the well-regularized hypergeometric functions can be evaluated directly and numerically. The package NumExp is presented for expanding hypergeometric functions and/or other transcendental functions in a small…

Computational Physics · Physics 2013-05-14 Zhi-Wei Huang , Jueping Liu

In this work, we compute one-loop planar five-point functions in $\mathcal{N}$=4 super-Yang-Mills using integrability. As in the previous work, we decompose the correlation functions into hexagon form factors and glue them using the weight…

High Energy Physics - Theory · Physics 2018-04-04 Thiago Fleury , Shota Komatsu

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…

High Energy Physics - Phenomenology · Physics 2016-01-12 Zhao Li , Jian Wang , Qi-Shu Yan , Xiaoran Zhao

We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Huber

We present master formulas for the divergent part of the one-loop effective action for an arbitrary (both minimal and nonminimal) operators of any order in the 4-dimensional curved space. They can be considered as computer algorithms,…

High Energy Physics - Theory · Physics 2009-10-30 P. Pronin , K. Stepanyantz

Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Hahn , M. Perez-Victoria

An overview is presented on the current status of main mathematical computation methods for the multi-loop corrections to single scale observables in quantum field theory and the associated mathematical number and function spaces and…

High Energy Physics - Phenomenology · Physics 2018-09-19 Johannes Blümlein , Carsten Schneider

Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared…

High Energy Physics - Phenomenology · Physics 2010-04-06 Z. Bern , G. Chalmers

In this paper, we present HyperPrecision, a Mathematica package for high-precision numerical evaluation of general Horn-type multivariate hypergeometric functions and their Laurent expansions in a small parameter $\epsilon$. Such functions…

High Energy Physics - Phenomenology · Physics 2026-05-29 Sumit Banik , Souvik Bera

We present formulas for the coefficients of 2-, 3-, 4- and 5-point master integrals for one-loop massive amplitudes. The coefficients are derived from unitarity cuts in D dimensions. The input parameters can be read off from any…

High Energy Physics - Phenomenology · Physics 2008-11-26 Ruth Britto , Bo Feng , Pierpaolo Mastrolia

We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The…

High Energy Physics - Phenomenology · Physics 2011-09-13 Andre van Hameren , Jens Vollinga , Stefan Weinzierl

We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the…

High Energy Physics - Phenomenology · Physics 2010-12-09 Sebastian Becker , Christian Reuschle , Stefan Weinzierl

The overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector \lambda \phi^4 Euclidean field theory are written down up…

Statistical Mechanics · Physics 2008-11-26 A. I. Sokolov

We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…

High Energy Physics - Phenomenology · Physics 2011-04-20 L. Brücher , J. Franzkowski , D. Kreimer