Abstract
We perform a high-precision computation of the three-loop three-point form factor of the stress-tensor supermultiplet in \( \mathcal{N} \) = 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.
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Acknowledgments
We would like to thank Siyuan Zhang for collaboration at the early stage of this project. This work is supported by the National Natural Science Foundation of China (Grants No. 11935013, 11975029, 12047503, 12175291, 12325503). We also thank the support of the HPC Cluster of ITP-CAS and the High-performance Computing Platform of Peking University.
Note added. While our paper was being finalized, we were acknowledged that the constant in f(3) has also been calculated using a different method by Chen et al. [46]. Our results are in full agreement with each other.
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Guan, X., Lin, G., Liu, X. et al. A high-precision result for a full-color three-loop three-point form factor in \( \mathcal{N} \) = 4 SYM. J. High Energ. Phys. 2024, 201 (2024). https://doi.org/10.1007/JHEP02(2024)201
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DOI: https://doi.org/10.1007/JHEP02(2024)201