QED radiative corrections in inverse beta decay from virtual pions

A bstract Inverse beta decay (IBD), $$ {\overline{\nu}}_ep\to {e}^{+}n\left(\gamma \right) $$ ν ¯ e p → e + n γ , is the main detection channel for reactor and supernova antineutrinos. To provide precise IBD cross sections at antineutrino energies $$ {E}_{{\overline{\nu}}_e} $$ E ν ¯ e ≳ 10 MeV, we evaluate radiative corrections from virtual pions within the framework of heavy baryon chiral perturbation theory. At leading order, only the pion isospin-breaking contributions are not suppressed by the electron mass. At next-to-leading order, besides recoil effects, only the Wilson coefficient c 4 contributes to the kinematic dependence. However, its precise value is not relevant for IBD at relatively low energies since all next-to-leading order radiative corrections are relatively small. We find the kinematic dependence of the pion-induced QED radiative corrections at the level and below the uncertainty from the momentum dependence of the nucleon form factors. Our results enable sub-permille theoretical precision of charged-current elastic (anti)neutrino-nucleon scattering at (anti) neutrino energies E ν ≳ 10 MeV.