Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow *

Abstract

Abstract We extend the auxiliary-mass-flow (AMF) method originally developed for Feynman loop integration to calculate integrals which also involve phase-space integration. The flow of the auxiliary mass from the boundary ( ) to the physical point ( ) is obtained by numerically solving differential equations with respective to the auxiliary mass. For problems with two or more kinematical invariants, the AMF method can be combined with the traditional differential-equation method, providing systematic boundary conditions and a highly nontrivial self-consistency check. The method is described in detail using a pedagogical example of at NNLO. We show that the AMF method can systematically and efficiently calculate integrals to high precision.