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

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 ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>HB</a:mi> <a:mi>χ</a:mi> <a:mi>PT</a:mi> </a:mrow> </a:math> ). We systematically incorporate all next-to-leading-order [i.e., <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi mathvariant="script">O</c:mi> <c:mo stretchy="false">(</c:mo> <c:msup> <c:mi>α</c:mi> <c:mn>3</c:mn> </c:msup> <c:mo>/</c:mo> <c:mi>M</c:mi> <c:mo stretchy="false">)</c:mo> </c:math> ] 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 <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mrow> <h:mi>HB</h:mi> <h:mi>χ</h:mi> <h:mi>PT</h:mi> </h:mrow> </h:math> 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.