Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity

TL;DR

This paper computes planar two-loop five-gluon scattering amplitudes using a novel numerical unitarity method combined with finite field arithmetic, enabling exact rational coefficient calculations for the first time.

Contribution

It introduces a new approach for generating unitarity-compatible IBP identities and extends numerical unitarity to efficiently compute five-gluon amplitudes at two loops.

Findings

All helicity amplitudes reduced to master integrals.

Exact rational coefficients obtained at phase-space points.

Amplitudes computed with arbitrary precision.

Abstract

We present a calculation of the planar two-loop five-gluon amplitudes. The amplitudes are obtained in a variant of the generalized unitarity approach suitable for numerical computations, which we extend for use with finite field arithmetics. Employing a new method for the generation of unitarity-compatible integration-by-parts identities, all helicity amplitudes are reduced to a linear combination of master integrals for the first time. The approach allows us to compute exact values for the integral coefficients at rational phase-space points. All required master integrals are known analytically, and we obtain arbitrary-precision values for the amplitudes.