Numerical calculation of one-loop integration with hypergeometric functions

الأصل · EN

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