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arXiv · 2309.04395

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

Xin Guan·Guanda Lin·Xiao Liu·Yan-Qing Ma·Gang Yang
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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.

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Xin Guan, Guanda Lin, Xiao Liu, Yan-Qing Ma, Gang Yang. 2023-09-08. A high-precision result for a full-color three-loop three-point form factor in ${\cal N}=4$ SYM. https://doi.org/10.1007/jhep02(2024)201

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