GLoop: A Monte Carlo program to construct higher-loop integrals from lower-loop structures

TL;DR

GLoop is a Fortran90 framework that uses Monte Carlo methods to compute higher-loop integrals from lower-loop structures without explicit contour deformation.

Contribution

It introduces a novel numerical approach for higher-loop integrals based on i epsilon deformations and Monte Carlo, with detailed examples and routines.

Findings

Enables numerical computation of integrals with i epsilon deformations

Avoids explicit analytic contour deformation

Provides practical routines for higher-loop integral calculations

Abstract

We present GLoop, a Fortran90 computational framework that allows one to compute by Monte Carlo a certain class of higher-loop integrals in terms of lower-loop building blocks. This is based on a recently introduced method that enables the numerical computation of integrals defined by i epsilon deformations acting on single pole singularities without the need for an explicit analytic contour deformation. We provide detailed, worked-out examples and routines to show how our strategy works. These can be used as a starting point for the reader to develop her/his own calculations.