Combinatorics

Physics

Loop (graph theory)

Mathematics

Mathematical physics

Particle physics

Algorithm

Quantum chromodynamics

Computer graphics (images)

Gluon

Unitarity

Numerical integration

Mathematical analysis

Planar

Amplitude

Helicity

Quantum electrodynamics

Computer science

Computation

Quantum mechanics

Physical review. D/Physical review. D.

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.

Planar two-loop five-gluon amplitudes from numerical unitarity