One-loop pentagon integral in $d$ dimensions from differential equations in $\epsilon$-form

TL;DR

This paper presents a method to compute the one-loop pentagon integral in arbitrary dimensions using differential equations in epsilon-form, resulting in a simple integral representation and discussing epsilon expansion and analytical continuation.

Contribution

The authors apply the differential equation technique in epsilon-form to derive a simple, exact integral representation for the one-loop pentagon integral in arbitrary dimensions.

Findings

Derived a one-fold integral representation exact in space-time dimensionality

Provided epsilon expansion of the integral

Discussed analytical continuation to physical regions

Abstract

We apply the differential equation technique to the calculation of the one-loop massless diagram with five onshell legs. Using the reduction to $\epsilon$-form, we manage to obtain a simple one-fold integral representation exact in space-time dimensionality. The expansion of the obtained result in $\epsilon$ and the analytical continuation to physical regions are discussed.