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arXiv · 2510.16471

Five W-boson amplitude = near-null decagon

A. V. Belitsky·L. V. Bork·R. N. Lee·A. I. Onishchenko·V. A. Smirnov
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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 extra-dimensional 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 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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A. V. Belitsky, L. V. Bork, R. N. Lee, A. I. Onishchenko, V. A. Smirnov. 2025-10-18. Five W-boson amplitude = near-null decagon. https://arxiv.org/abs/2510.16471

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