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Relativistic distorted-wave analysis of the missing-energy spectrum measured with monochromatic $ν_μ$-$^{12}$C interactions at JSNS$^{2}$

J. M. Franco-Patino, M. B. Barbaro, G. Co'

Abstract

Recently, the JSNS$^2$ collaboration measured for the first time the missing-energy distribution of $^{12}$C using a monochromatic neutrino beam coming from kaon decays at rest. In this work we present the results of an analysis of this spectrum using the relativistic distorted-wave approach with a new parameterization of the spectral function for neutrons in $^{12}$C, which incorporates detailed information from $\left(e,e'p\right)$ experiments with high missing-energy resolution. The role of the recoil of the residual nucleus in the description of the measured distribution, final-state interactions, and the ability of neutrino event generators to describe low-energy nuclear effects are discussed.

Relativistic distorted-wave analysis of the missing-energy spectrum measured with monochromatic $ν_μ$-$^{12}$C interactions at JSNS$^{2}$

Abstract

Recently, the JSNS collaboration measured for the first time the missing-energy distribution of C using a monochromatic neutrino beam coming from kaon decays at rest. In this work we present the results of an analysis of this spectrum using the relativistic distorted-wave approach with a new parameterization of the spectral function for neutrons in C, which incorporates detailed information from experiments with high missing-energy resolution. The role of the recoil of the residual nucleus in the description of the measured distribution, final-state interactions, and the ability of neutrino event generators to describe low-energy nuclear effects are discussed.
Paper Structure (6 sections, 19 equations, 6 figures, 3 tables)

This paper contains 6 sections, 19 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Kinematics
  3. The relativistic distorted-wave approach
  4. Missing energy profile parameterization
  5. Comparison with experimental data
  6. Summary and conclusions

Figures (6)

  • Figure 1: Charge and neutron radial density calculated with the RMF potential NLSH SHARMA1993377, compared with a fit to elastic electron–nucleus scattering data DEVRIES1987495. The root-mean-square (rms) charge radius obtained with NLSH is $2.46811$ fm, in agreement with the experimental value of $2.4701 \pm 0.0022$ fm ANGELI201369.
  • Figure 2: Missing energy profile of a neutron in a $s$-state of $^{12}$C parameterized with $\mu=37$ MeV and $\sigma=19$ MeV using Gaussian and Maxwell-Boltzmann distributions (see Eq. \ref{['eq:M-B']}). Both distributions are normalized to $n_{1s1/2} =$ 1.74 nucleons.
  • Figure 3: Comparison of our missing energy profile $\rho_\kappa\left(E_m\right)$ of neutrons with that of Ref. PhysRevC.110.054612. A shift of +2.764 MeV has been applied to the results of Ankowski et al. to account for neutron, rather than proton, emission (see text for explanation).
  • Figure 4: Differential cross section as function of the missing energy separated by contributions of the different shells to the QE channel using the ED-RMF model with recoil. The contribution of MEC calculated with a semi-inclusive model based on the Relativistic Fermi gas Belocchi:2024rfpBelocchi:2025eix is also shown separately.
  • Figure 5: Charge-current $\nu_\mu + ^{12}$C cross sections as a function of the missing energy $E_m$ for an incoming neutrino with $E_\nu = 235.5$ MeV. All the theoretical results are normalized to the total strength of the experimental data. In the panel (a), the theoretical results consider the recoil of the residual nucleus in the definition of $E_m$. In the panel (b), this effect is neglected. All the results include both QE and MEC contributions.
  • ...and 1 more figures