The two-loop scalar and tensor Pentabox graph with light-like legs Original Research Article

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 ε=(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.