Pentagon functions for massless planar scattering amplitudes

TL;DR

This paper analyzes pentagon functions arising in massless five-particle scattering amplitudes, studying their analytic properties, classifying basis functions, and providing explicit expressions and evaluation routines for practical use.

Contribution

It offers a detailed classification and computation of pentagon functions up to two loops, including their analytic structure and explicit formulas in terms of polylogarithms.

Findings

Classified minimal basis of pentagon functions.

Derived analytical expressions for pentagon functions.

Provided numerical routines for all relevant kinematics.

Abstract

Loop amplitudes for massless five particle scattering processes contain Feynman integrals depending on the external momentum invariants: pentagon functions. We perform a detailed study of the analyticity properties and cut structure of these functions up to two loops in the planar case, where we classify and identify the minimal set of basis functions. They are computed from the canonical form of their differential equations and expressed in terms of generalized polylogarithms, or alternatively as one-dimensional integrals. We present analytical expressions and numerical evaluation routines for these pentagon functions, in all kinematical configurations relevant to five-particle scattering processes.