ftint: Calculating gradient-flow integrals with pySecDec

TL;DR

The paper introduces ftint, a numerical tool that uses sector decomposition and pySecDec to evaluate gradient-flow integrals in quantum field theory, enabling calculations up to three loops with potential for broader applications.

Contribution

It presents ftint, a new program that automates the numerical evaluation of gradient-flow integrals using sector decomposition and pySecDec, extending computational capabilities in quantum field theory.

Findings

Successfully evaluates integrals up to three loops

Handles massive and massless integrals with zero external momenta

Provides a extendable framework for more general cases

Abstract

The program ftint is introduced which numerically evaluates dimensionally regulated integrals as they occur in the perturbative approach to the gradient-flow formalism in quantum field theory. It relies on sector decomposition in order to determine the coefficients of the individual orders in $\epsilon=(4-D)/2$, where $D$ is the space-time dimension. For that purpose, it implements an interface to the public library pySecDec. The current version works for massive and massless integrals up to three-loop level with vanishing external momenta, but the underlying method is extendable to more general cases.