Empirical Reconstruction of the JSNS$^2$ KDAR $\nu_\mu$-$^{12}$C Missing-Energy Spectrum with a Two-Ex-Gaussian and Generalized-Tail Model

Abstract

Recent analyses of the JSNS$^2$ monoenergetic $\nu_\mu$ scattering on $^{12}$C at 235.5~MeV have compared the measured missing-energy spectrum with several nuclear models, including \textsc{NuWro}, \textsc{GiBUU}, and RMF+Achilles. While these models reproduce the overall peak position, their respective $\chi^2$ values of $35.5$, $176.8$, and $58.1$ indicate that none can simultaneously describe the spectral width and the high-energy tail, reflecting limitations in the treatment of binding energy, two-particle--two-hole (2p-2h) excitations, and final-state interactions (FSI). To address these discrepancies, we introduce an empirical yet physically motivated representation of the spectrum based on two exponentially modified Gaussian (ex-Gaussian) components for p- and s-shell knockout and a generalized power-exponential continuum term describing multinucleon and FSI-induced strength. The fit reproduces the JSNS$^2$ data within the fitted energy range with $\chi^2=8.0$ for 6 degrees of freedom. yielding parameters that quantify asymmetric broadening of the s-shell while preserving a narrow quasielastic p-shell response. This compact model demonstrates that a minimal empirical framework can capture key features of the nuclear response and provides a useful reference for phenomenological comparisons and future studies of quasielastic and 2p-2h dynamics in the few-hundred-MeV regime.