Quantum mechanics

Theoretical physics

Massless particle

Mathematical physics

Scattering amplitude

Planar

Computer graphics (images)

Scattering

Economics

Computer science

Classical mechanics

Physics

Amplitude

Mathematics

Quantum electrodynamics

Feynman diagram

Mathematical analysis

Geometry

Momentum (technical analysis)

Finance

Pentagon

Journal of High Energy Physics

A bstract 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.

Pentagon functions for massless planar scattering amplitudes