Numerical evaluation of loop integrals

Abstract

We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to extract the divergent parts in the epsilon->0 limit. We then perform an epsilon-expansion and evaluate the integral coefficients of the expansion numerically. The method yields stable results in physical kinematic regions avoiding intricate analytic continuations. It can also be applied to evaluate both scalar and tensor integrals without employing reduction methods. We demonstrate our method with specific examples of infrared divergent integrals with many kinematic scales, such as two-loop and three-loop box integrals and tensor integrals of rank six for the one-loop hexagon topology.