One loop integration with hypergeometric series by using recursion relations
High Energy Physics - Phenomenology
2015-06-17 v1
Abstract
General one-loop integrals with arbitrary mass and kinematical parameters in -dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects -point to -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.
Cite
@article{arxiv.1309.3118,
title = {One loop integration with hypergeometric series by using recursion relations},
author = {Norihisa Watanabe and Toshiaki Kaneko},
journal= {arXiv preprint arXiv:1309.3118},
year = {2015}
}