A high-precision result for a full-color three-loop three-point form factor in $$ \mathcal{N} $$ = 4 SYM

Abstract

Abstract We perform a high-precision computation of the three-loop three-point form factor of the stress-tensor supermultiplet in $$ \mathcal{N} $$ N = 4 SYM. Both the leading-color and sub-leading-color form factors are expanded in terms of simple integrals. We compute the complete set of integrals at a special kinematic point with very high precision using AMFlow. The high-precision leading-color result enables us to obtain the analytic form of a numerical constant in the three-loop BDS ansatz, which is previously known only numerically. The high-precision values of the non-leading-color finite remainder as well as all integrals are also presented, which can be valuable for future use.