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  • Open Access

Off-shell form factor: Factorization is violated

A. V. Belitsky1 and V. A. Smirnov2

  • 1Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA
  • 2Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia and Moscow Center for Fundamental and Applied Mathematics, 119992 Moscow, Russia

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Phys. Rev. D 113, 036022 – Published 24 February, 2026

DOI: https://doi.org/10.1103/mz4b-k6m6

Abstract

We study the Sudakov form factor on the Coulomb branch of N=4 sYM which endows only external states with masses, and implies that the former is off-shell in the traditional sense. Our consideration is performed at three-loop order in the near mass-shell limit. We use a combination of tools to perform required calculations centered around the method of regions as the main go-to formalism for the asymptotic expansion of emerging parametric Feynman integrals. Explicit separation of quantum loops in terms of hard, collinear, and ultrasoft modes allows us to explore the factorization properties of this infrared-sensitive quantity. While the hard region is cleanly separated from the rest, the ultrasoft-collinear modes remain intertwined. We exhibit effects of factorization violation explicitly in the momentum space making use of the infrared power counting.

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Phys. Rev. D 113, 036022– Published 24 February, 2026
  • Received 11 December 2025
  • Accepted 21 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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