Pentagon Functions for Scattering of Five Massless Particles

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.

Comments: 50 pages, 4 figures; v2: updated references and minor text changes, matches the published version; v3: fixed minor typo in equation (3.2); analytic results at https://gitlab.com/pentagon-functions/PentagonMI ; C++ code at https://gitlab.com/pentagon-functions/PentagonFunctions-cpp