Comparing radiative and recoil corrections in neutron beta-decay and inverse beta-decay

TL;DR

This paper compares radiative and recoil corrections in neutron beta-decay and inverse beta-decay, showing that recoil corrections are significant for inverse beta-decay and differ notably from radiative corrections in energy dependence.

Contribution

The study provides a detailed numerical analysis of radiative and recoil corrections in inverse beta-decay, highlighting their relative sizes and energy dependencies, which was not previously quantified.

Findings

Recoil corrections are small in neutron beta-decay.

Recoil corrections are comparable to radiative corrections in inverse beta-decay.

Radiative and recoil corrections have different energy dependences.

Abstract

The inverse $\beta$-decay reaction, anti-nu_e + p --> 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 previously 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 investigate here the numerical consequences of these analytic expressions. We show that the recoil corrections 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. It turns out that the RCs and the recoil corrections exhibit very different dependences on the neutrino energy.