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

by Prof. Hui Luo (Graduate School of China Academy of Engineering Physics)

Thursday 14 Nov 2019, 12:00 → 13:00 Asia/Shanghai

B105 (CHEP)

We present analytic forms of three-loop four-gluon planar amplitudes in pure Yang-Mills theory in our recent work. 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. After renormalizing the ultraviolet divergences, remaining divergences of the amplitudes agree with known infrared divergence structures exactly. Our results provide an essential piece of three-loop amplitudes required for the ${\rm N^3LO}$ order corrections to the production of dijet at hadron colliders.