English

Numerical calculation of one-loop integration with hypergeometric functions

High Energy Physics - Phenomenology 2011-05-12 v1

Abstract

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 FDF_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 FDF_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 FDF_D is known, information about the stabilities in the numerical calculation is obtained. We have developed a numerical library calculating FDF_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.

Keywords

Cite

@article{arxiv.1105.2080,
  title  = {Numerical calculation of one-loop integration with hypergeometric functions},
  author = {Toshiaki Kaneko},
  journal= {arXiv preprint arXiv:1105.2080},
  year   = {2011}
}

Comments

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

R2 v1 2026-06-21T18:05:27.766Z