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.

22 pages, 18 figures, final version to appear in EPJC

References in corpus (5)

• OneLOop: for the evaluation of one-loop scalar functions
• Collider Physics at the Precision Frontier
• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• Higgs-Pair Production via Gluon Fusion at Hadron Colliders: NLO QCD Corrections
• A four-dimensional approach to quantum field theories

Cited by in corpus (4)

• 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