Pentagon Functions for Scattering of Five Massless Particles

TL;DR

This paper completes the analytic calculation of all two-loop Feynman integrals for massless five-particle scattering using pentagon functions, providing a minimal basis and a numerical library for practical use.

Contribution

It introduces a complete set of pentagon functions for two-loop five-particle scattering, enabling precise amplitude calculations across the physical phase space.

Findings

Derived explicit expressions for pentagon functions.

Constructed a minimal basis of transcendental functions.

Provided a numerical library for phenomenological applications.

Abstract

We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.