Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory

Understand

We present analytic forms of three-loop four-gluon planar amplitudes in pure Yang-Mills theory in this letter.

• Gauge invariant bases and a set of proper master integrals are chosen such that the amplitudes are explicitly invariant under cyclic permutations of external particles.
• The $D$-dimensional unitarity method and integration-by-parts reductions with cut conditions are performed to determine the coefficients of the master integrals.
• Helicity amplitudes in the conventional dimension regularization scheme are obtained by setting gauge invariant bases to helicity configurations.