JSNS$^2$ KDAR $ν_μ$-$^{12}$C 缺失能谱的双指数修正高斯与广义尾模型经验重建
Empirical Reconstruction of the JSNS$^2$ KDAR $ν_μ$-$^{12}$C Missing-Energy Spectrum with a Two-Ex-Gaussian and Generalized-Tail Model
AI总结：
针对 JSNS$^2$ 单能 $ν_μ$-$^{12}$C 散射能谱现有核模型无法同时描述谱宽与高能尾部的局限，提出基于双指数修正高斯与广义幂指数连续谱项的经验模型，以 6 自由度 $χ^2=8.0$ 精确重现数据，为核响应与准弹性动力学研究提供参考。
摘要：
近期对 JSNS$^2$ 在 235.5 MeV 处单能 $ν_μ$ 在 $^{12}$C 上散射的分析，将测量的缺失能谱与包括 NuWro、GiBUU 和 RMF+Achilles 在内的几种核模型进行了比较。尽管这些模型重现了整体峰位，但它们分别为 35.5、176.8 和 58.1 的 $χ^2$ 值表明，没有模型能同时描述谱宽和高能尾部，反映了对结合能、双粒子-双空穴 (2p-2h) 激发和末态相互作用 (FSI) 处理上的局限。为解决这些差异，我们引入了一个经验且基于物理动机的谱表示，它基于用于 p 壳和 s 壳敲出的两个指数修正高斯 (ex-Gaussian) 分量，以及一个描述多核子与 FSI 诱导强度的广义幂指数连续谱项。该拟合在拟合能区内以 6 个自由度下 $χ^2=8.0$ 重现了 JSNS$^2$ 数据，所得参数量化了 s 壳的不对称展宽，同时保留了窄的准弹性 p 壳响应。这一紧凑模型表明，最小经验框架能捕捉核响应的关键特征，并为几百 MeV 能区的准弹性和 2p-2h 动力学的唯象比较及未来研究提供了有用参考。
英文摘要：
Recent analyses of the JSNS$^2$ monoenergetic $ν_μ$ 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 $χ^2$ 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 $χ^2=8.0$ 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.
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