Modeling quasielastic interactions of monoenergetic kaon decay-at-rest neutrinos

TL;DR

This paper calculates quasielastic cross sections for 236 MeV monoenergetic muon neutrinos from kaon decay at rest, using a mean-field and CRPA nuclear model, aiding neutrino interaction studies.

Contribution

It introduces a detailed nuclear model combining Hartree-Fock and CRPA to predict neutrino-nucleus quasielastic scattering at specific energies, validated against electron scattering data.

Findings

Model accurately describes ($e,e'$) data for $^{12}$C and $^{40}$Ca.

Provides cross section predictions for neutrino interactions relevant to KDAR neutrinos.

Discusses future experimental applications and precision measurements.

Abstract

Monoenergetic muon neutrinos at 236 MeV are readily produced in intense medium-energy proton facilities ($\gtrsim$2-3~GeV) when a positive kaon decays at rest (KDAR; $K^+ \rightarrow \mu^+ \nu_\mu$). These neutrinos provide a unique opportunity to both study the neutrino interaction and probe the nucleus with a monoenergetic weak-interaction-only tool. We present cross section calculations for quasielastic scattering of these 236~MeV neutrinos off $^{12}$C and $^{40}$Ar, paying special attention to low-energy aspects of the scattering process. Our model takes the description of the nucleus in a mean-field (MF) approach as the starting point, where we solve Hartree-Fock (HF) equations using a Skyrme type nucleon-nucleon interaction. Thereby, we introduce long-range nuclear correlations by means of a continuum random phase approximation (CRPA) framework where we solve the CRPA equations using a Green's function method. The model successfully describes ($e,e'$) data on $^{12}$C and $^{40}$Ca in the kinematic region that overlaps with the KDAR $\nu_\mu$ phase space. In addition to these results, we present future prospects for precision KDAR cross section measurements and applications of our calculations in current and future experiments that will utilize these neutrinos.