The two-loop scalar and tensor pentabox graph with light-like legs

TL;DR

This paper analyzes two-loop pentabox integrals with light-like legs, providing explicit analytic expressions and algorithms for scalar and tensor integrals using integration-by-parts identities.

Contribution

It introduces a method to express tensor integrals in terms of two master integrals and provides explicit formulas for these master integrals in arbitrary dimensions.

Findings

Explicit series expansion for scalar pentabox integral

Algorithm for reducing tensor integrals to master integrals

General formulas for master integrals in arbitrary dimensions

Abstract

We study the scalar and tensor integrals associated with the pentabox topology: the class of two-loop box integrals with seven propagators - five in one loop and three in the other. We focus on the case where the external legs are light-like and use integration-by-parts identities to express the scalar integral in terms of two master-topology integrals and present an explicit analytic expression for the pentabox scalar integral as a series expansion in ep = (4-D)/2. We also give an algorithm based on integration by parts for relating the generic tensor integrals to the same two master integrals and provide general formulae describing the master integrals in arbitrary dimension and with general powers of propagators.