Regular Article - Theoretical Physics
Direct numerical evaluation of multi-loop integrals without contour deformation
Departamento de Física Teórica y del Cosmos and CAFPE, Universidad de Granada, 18071, Granada, Spain
2 Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
3 University of Cambridge, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge, UK
Accepted: 6 January 2022
Published online: 20 January 2022
We propose a method for computing numerically integrals defined via 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.
© The Author(s) 2022
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