Direct numerical evaluation of multi-loop integrals without contour deformation

Abstract

We propose a method for computing numerically integrals defined via $i\epsilon$ 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 four-dimensional regularization techniques, our treatment can be extended to ultraviolet and infrared divergent integrals.

arXiv comment22 pages, 18 figures, final version to appear in EPJC

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• Tropical Feynman integration in the Minkowski regime
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Towards a Localised S-Matrix Theory
• Monte Carlo evaluation of divergent one-loop integrals without contour deformation