Inclusive Neutrino and Antineutrino Scattering on the $^{12}$C Nucleus Within the Coherent Density Fluctuation Model

Abstract: We investigate quasielastic (anti)neutrino scattering on the $^{12}$C nucleus utilizing a novel scaling variable, $\psi^*$. This variable is derived from the interacting relativistic Fermi gas model, which incorporates both scalar and vector interactions, leading to a relativistic effective mass for the interacting nucleons. For inclusive lepton scattering from nuclei, we develop a new scaling function, denoted as $f^\text{QE}(\psi^*)$, based on the coherent density fluctuation model (CDFM). This model serves as a natural extension of the relativistic Fermi gas (RFG) model applicable to finite nuclei. In this study, we compute theoretical predictions and compare them with experimental data from Miner$\nu$a and T2K for inclusive (anti)neutrino cross-sections. The scaling function is derived within the CDFM framework, employing a relativistic effective mass of $m_N^*$ = 0.8 $m_N$. The findings demonstrate a high degree of consistency with experimental data across all (anti)neutrino energy ranges.