QED radiative corrections for accelerator neutrinos

Neutrino oscillation experiments at accelerator energies aim to establish charge-parity violation in the neutrino sector by measuring the energy-dependent rate of $\nu_e$ appearance and $\nu_\mu$ disappearance in a $\nu_\mu$ beam. These experiments can precisely measure $\nu_\mu$ cross sections at near detectors, but $\nu_e$ cross sections are poorly constrained and require theoretical inputs. In particular, quantum electrodynamics radiative corrections are different for electrons and muons. These corrections are proportional to the small quantum electrodynamics coupling $\alpha \approx 1/137$; however, the large separation of scales between the neutrino energy and the proton mass ($\sim{\rm GeV}$), and the electron mass and soft-photon detection thresholds ($\sim{\rm MeV}$) introduces large logarithms in the perturbative expansion. The resulting flavor differences exceed the percent-level experimental precision and depend on nonperturbative hadronic structure. We establish a factorization theorem for exclusive charged-current (anti)neutrino scattering cross sections representing them as a product of two factors. The first factor is flavor universal; it depends on hadronic and nuclear structure and can be constrained by high-statistics $\nu_\mu$ data. The second factor is non-universal and contains logarithmic enhancements, but can be calculated exactly in perturbation theory. For charged-current elastic scattering, we demonstrate the cancellation of uncertainties in the predicted ratio of $\nu_e$ and $\nu_\mu$ cross sections. We point out the potential impact of non-collinear energetic photons and the distortion of the visible lepton spectra and provide precise predictions for inclusive observables.