Radiative corrections to anti-neutrino proton scattering

TL;DR

This paper provides analytic calculations of radiative and recoil corrections for low-energy anti-neutrino proton scattering, crucial for precise neutrino measurements, revealing that recoil effects are significant and energy-dependent.

Contribution

It derives next-to-leading order analytic expressions for radiative and recoil corrections in inverse beta decay within heavy-baryon chiral perturbation theory, including the weak magnetism effect.

Findings

Recoil corrections are comparable to radiative corrections at typical reactor neutrino energies.

Recoil and radiative corrections have distinct energy dependences.

Recoil corrections are small for neutron beta decay but significant for inverse beta decay.

Abstract

The inverse $\beta$-decay reaction, $ \bar{\nu}_e p \to e^+ n$, for low-energy anti-neutrinos coming from nuclear reactors is of great current interest in connection with high-precision measurements of the neutrino mixing angle $\theta_{13}$. We have derived analytic expressions, up to next-to-leading order in heavy-baryon chiral perturbation theory, for the radiative corrections (RCs) and the nucleon-recoil corrections both for this reaction and for the related neutron $\beta$-decay process. We show that the recoil corrections, which include the "weak magnetism" contribution, are small for neutron $\beta$-decay, but for inverse $\beta$-decay, the recoil corrections are comparable in size to the RCs for typical energies of reactor anti-neutrinos, and they have opposite signs. The RCs and the recoil corrections exhibit very different dependences on the neutrino energy.