The angular distribution of the reaction $\bar{\nu}_e + p \to e^+ + n$

TL;DR

This paper calculates the angular distribution of positrons in low-energy antineutrino-proton reactions, highlighting the effects of weak magnetism and recoil corrections, which are crucial for neutrino detection and source localization.

Contribution

It provides an analytical calculation of the angular distribution including recoil effects, improving understanding of event separation and source localization in neutrino experiments.

Findings

Weak magnetism and recoil make the distribution isotropic at 15 MeV

Angular distribution is slightly forward at higher energies

Neutron emission is strongly forward-peaked

Abstract

The reaction $\bar{\nu}_e + p \to e^+ + n$ is very important for low-energy ($E_\nu \lesssim 60$ MeV) antineutrino experiments. In this paper we calculate the positron angular distribution, which at low energies is slightly backward. We show that weak magnetism and recoil corrections have a large effect on the angular distribution, making it isotropic at about 15 MeV and slightly forward at higher energies. We also show that the behavior of the cross section and the angular distribution can be well-understood analytically for $E_\nu \lesssim 60$ MeV by calculating to ${\cal O}(1/M)$, where $M$ is the nucleon mass. The correct angular distribution is useful for separating $\bar{\nu}_e + p \to e^+ + n$ events from other reactions and detector backgrounds, as well as for possible localization of the source (e.g., a supernova) direction. We comment on how similar corrections appear for the lepton angular distributions in the deuteron breakup reactions $\bar{\nu}_e + d \to e^+ + n + n$ and $\nu_e + d \to e^- + p + p$. Finally, in the reaction $\bar{\nu}_e + p \to e^+ + n$, the angular distribution of the outgoing neutrons is strongly forward-peaked, leading to a measurable separation in positron and neutron detection points, also potentially useful for rejecting backgrounds or locating the source direction.