Abstract
In this paper we provide a detailed account of our calculation, briefly reported in arXiv:2209.09263, of a two-particle form factor of the lowest components of the stress-tensor multiplet in \( \mathcal{N} \) = 4 sYM theory on its Coulomb branch, which is interpreted as an off-shell kinematical regime. We demonstrate that up to three-loop order, both its infrared-divergent as well as finite parts do exponentiate in the Sudakov regime, with the coefficient accompanying the double logarithm being determined by the octagon anomalous dimension Γoct. We also observe that up to this order in ’t Hooft coupling the logarithm of the Sudakov form factor is identical to twice the logarithm of the null octagon, which was introduced within the context of integrability-based computation of four point correlators with infinitely large R-charges. The null octagon is known in a closed form for all values of the ’t Hooft coupling constant and kinematical parameters. We conjecture that the relation between the former and the off-shell Sudakov form factor holds to all loop orders.
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Acknowledgments
We are grateful to A.F. Pikelner for collaboration. L.B. is grateful to A.I. Onishchenko for useful discussions and to A.V. Bednyakov, N.B. Muzhichkov and E.S. Sozinov for collaboration at early stages of the project. The work of A.B. was supported by the U.S. National Science Foundation under the grant No. PHY-2207138. The work of L.B. was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”.
The work of V.S. was supported by the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the Agreement No. 075-15-2022-284 (evaluating Mellin-Barnes integrals contributions by the code MBcreate) and by the Russian Science Foundation, agreement no. 21-71-30003 (evaluating three-loop vertex Feynman integrals by expansion by regions).
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Belitsky, A.V., Bork, L.V. & Smirnov, V.A. Off-shell form factor in \( \mathcal{N} \)=4 sYM at three loops. J. High Energ. Phys. 2023, 111 (2023). https://doi.org/10.1007/JHEP11(2023)111
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DOI: https://doi.org/10.1007/JHEP11(2023)111