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Chiral enhancement in soft-photon bremsstrahlung and charge asymmetry in low-energy lepton-proton scattering

Bhoomika Das1,*, Rakshanda Goswami1,†, Pulak Talukdar2,‡, Udit Raha1,§, and Fred Myhrer3,∥

  • *Contact author: bhoomika.das@iitg.ac.in
  • †Contact author: r.goswami@iitg.ac.in
  • ‡Contact author: pulaktalukdar45@gmail.com
  • §Contact author: udit.raha@iitg.ac.in
  • ∥Contact author: myhrer@mailbox.sc.edu
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Phys. Rev. D 113, 033007 – Published 24 February, 2026

DOI: https://doi.org/10.1103/6396-twj8

Abstract

We perform a Lorentz gauge evaluation of the single soft-photon bremsstrahlung radiative corrections to the unpolarized elastic lepton-proton scattering cross section at low energies, using the framework of heavy baryon chiral perturbation theory (HBχPT). We systematically incorporate all next-to-leading-order [i.e., O(α3/M)] contributions to the cross section arising from radiative and proton’s low-energy recoil effects. An important component of the soft-photon bremsstrahlung corrections arises from the interference between lepton and proton bremsstrahlung processes, which are characterized as charge-odd. We identify a class of Feynman diagrams involving the final-state radiating proton that induces a chiral enhancement, thereby modifying the naive amplitude hierarchy based on the standard chiral power-counting scheme. The recently derived HBχPT result for the analytically computed exact two-photon exchange counterpart at next-to-leading order is combined with our charge-odd soft-photon bremsstrahlung contribution to yield the complete charge-odd radiative correction. By incorporating the leading hadronic correction to the one-photon exchange process within the charge-even radiative correction, we obtain a prediction for the charge asymmetry observable, which can be compared with forthcoming MUon Scattering Experiment data on elastic lepton-antilepton scattering off the proton. In all our calculations, we use finite lepton masses.

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Phys. Rev. D 113, 033007– Published 24 February, 2026
  • Received 18 August 2025
  • Accepted 19 November 2025
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