Numerical calculation of one-loop integration with hypergeometric functions

Details Numerical calculation of one-loop integration with hypergeometric functions Numerical calculation of one-loop integration with hypergeometric functions

2011-05-11

arxiv.org/abs/1105.2080v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

8 pages, talk given at 3rd Computational Particle Physics Workshop -- CPP2010, September 23-25, 2010, KEK Japan

Scientific paper

One-loop two-, three- and four-point scalar functions are analytically integrated directly such that they are expressed in terms of Lauricella's hypergeometric function $F_D$. For two- and three-point functions, exact expressions are obtained with arbitrary combination of kinematic and mass parameters in arbitrary space-time dimension. Four-point function is expressed in terms of $F_D$ up to the finite part in the expansion around 4-dimensional space-time with arbitrary combination of kinematic and mass parameters. Since the location of the possible singularities of $F_D$ is known, information about the stabilities in the numerical calculation is obtained. We have developed a numerical library calculating $F_D$ around 4-dimensional space-time. The numerical values for IR divergent cases of four-point functions in massless QCD are calculated and agreed with golem95 package.

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