Multiscale pentagon integrals to all orders

TL;DR

This paper derives analytical solutions for complex one-loop five-point integrals with multiple off-shell legs using advanced differential equations, providing explicit results in terms of Goncharov Polylogarithms up to weight six.

Contribution

It introduces a novel application of canonical differential equations and the Simplified Differential Equations approach to compute five-point master integrals analytically.

Findings

Explicit boundary terms in closed form.

Solutions expressed in Goncharov Polylogarithms up to weight six.

Method applicable to complex multi-leg integrals.

Abstract

We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary boundary terms are given in closed form, resulting to solutions in terms of Goncharov Polylogarithms of arbitrary weight. Explicit results up to weight six will be presented.