Radiative corrections to antineutrino-proton scattering at low energies

Abstract

For the low-energy antineutrino reaction, ${\overline{\ensuremath{\nu}}}_{e}+p\ensuremath{\rightarrow}{e}^{+}+n$, which is of great current interest in connection with on-going high-precision neutrino-oscillation experiments, we calculate the differential cross section in a model-independent effective field theory (EFT), taking into account radiative corrections of order $\ensuremath{\alpha}$. In EFT, the short-distance radiative corrections are subsumed into well-defined low-energy constants, the values of which can in principle be determined from the available neutron $\ensuremath{\beta}$-decay data. In our low-energy EFT, the order-$\ensuremath{\alpha}$ radiative corrections are considered to be of the same order as the nucleon recoil corrections, which include the ``weak magnetism'' contribution. These recoil corrections have been evaluated as well. We emphasize that EFT allows a systematic evaluation of higher order corrections, providing estimates of theoretical uncertainties in our results.