Direct numerical evaluation of multi-loop integrals without contour deformation

Abstract

We propose a method for computing numerically integrals defined via i deformations acting on single-pole singularities. We achieve this without an explicit analytic contour deformation. Our solution is then used to produce precise Monte Carlo estimates of multi-scale multi-loop integrals directly in Minkowski space. We corroborate the validity of our strategy by presenting several examples ranging from one to three loops. When used in connection with fourdimensional regularization techniques, our treatment can be extended to ultraviolet and infrared divergent integrals.