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Five W-boson amplitude is equal to near-null decagon

A. V. Belitsky1, L. V. Bork2, R. N. Lee3,4, A. I. Onishchenko4, and V. A. Smirnov5

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Phys. Rev. D 113, 086003 – Published 6 April, 2026

DOI: https://doi.org/10.1103/5sf8-fhmt

Abstract

We study a five-leg scattering amplitude on the special Coulomb branch of planar N=4 super Yang-Mills theory. We reach this point of the moduli space of scalar vacuum expectation values by considering six-dimensional N=(1,1) super Yang-Mills theory and reducing it down to four space-time dimensions with extradimensional momenta being nonvanishing. This branch is characterized by massive external W-bosons and massless internal gluons propagating in loops. We analyze the five W-boson amplitude in the kinematics when their masses are much smaller than all Mandelstam-like invariants. This is what we dub the near mass-shell limit. We perform calculations to two-loop order in ’t Hooft coupling, making use of recent advances in analytic calculations of required Feynman integrals. Our findings confirm exponentiation of infrared logarithms and enable us to conjecture a concise all-order expression for the amplitude in question. We further analyze its duality to the square root of a five-point correlation function of infinitely heavy half-BPS (Bogomol’nyi–Prasad–Sommerfield) operators, known as the decagon. By considering the near-null limit for inter-operators distances, we verify that the two objects coincide. This observation corroborates the novel Coulomb amplitudes/heavy correlator duality previously observed for four W-boson amplitudes and Sudakov form factors.

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Phys. Rev. D 113, 086003– Published 6 April, 2026
  • Received 2 December 2025
  • Accepted 30 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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