Monte Carlo evaluation of divergent one-loop integrals without contour deformation

TL;DR

This paper extends a numerical method for evaluating multi-loop integrals without contour deformation to massless scalar one-loop integrals in dimensional regularization, and discusses a two-loop example.

Contribution

It introduces an extension of a contour deformation-free numerical evaluation method to massless one-loop integrals and explores its application to a two-loop case.

Findings

Successfully applied to massless scalar one-loop integrals

Demonstrated potential for simplifying multi-loop integral computations

Provides a foundation for further multi-loop numerical evaluations

Abstract

Reference [1] introduces a method for computing numerically four-dimensional multi-loop integrals without performing an explicit analytic contour deformation around threshold singularities. In this paper, we extend such a technique to massless scalar one-loop integrals regularized in the framework of dimensional regularization. A two-loop example is also discussed.