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

TL;DR

This paper presents a high-precision computation of the three-loop three-point form factor in ${ m N}=4$ SYM, revealing an analytic form of a previously numerical constant and providing detailed integral results.

Contribution

It introduces a high-precision calculation of three-loop form factors in ${ m N}=4$ SYM, enabling analytic determination of a key constant and supplying comprehensive integral data.

Findings

Analytic form of a numerical constant in the three-loop BDS ansatz.

High-precision values for non-leading-color finite remainder.

Complete set of integrals at a special kinematic point.

Abstract

We perform a high-precision computation of the three-loop three-point form factor of the stress-tensor supermultiplet in ${\cal N}=4$ SYM. Both the leading-color and non-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 $\mathtt{AMFlow}$. 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.