epsilon: A tool to find a canonical basis of master integrals

TL;DR

The paper introduces epsilon, a computational tool implementing Lee's algorithm to efficiently find canonical bases of master integrals, facilitating their expression in terms of iterated integrals in quantum field theory calculations.

Contribution

The paper presents epsilon, a new software tool that automates the process of finding canonical bases of master integrals using Lee's algorithm, enhancing computational efficiency.

Findings

Epsilon successfully implements Lee's algorithm within Fermat.

The tool streamlines the process of identifying canonical master integral bases.

Epsilon improves efficiency in calculating integrals in dimensional regularization.

Abstract

In 2013, Henn proposed a special basis for a certain class of master integrals, which are expressible in terms of iterated integrals. In this basis, the master integrals obey a differential equation, where the right hand side is proportional to $\epsilon$ in $d=4-2\epsilon$ space-time dimensions. An algorithmic approach to find such a basis was found by Lee. We present the tool epsilon, an efficient implementation of Lee's algorithm based on the Fermat computer algebra system as computational backend.