KDAR neutrino scattering for $^{12}$C target via charged current and muon angular distribution

Abstract

We calculate muon-neutrino ($\nu_{\mu}$) scattering off $^{12}$C via charged current (CC) by exploiting the 236 MeV ${\nu_{\mu}}$ from the kaon-decay-at-rest (KDAR). In this energy region, since both inelastic scattering below the quasielastic (QE) region and the QE scattering contribute simultaneously, we combine the inelastic scattering obtained by the QRPA and the QE scattering obtained by distorted wave born approximation (DWBA) based on the relativistic mean field (RMF) theory. We compare the results to the data from MiniBooNE. Further, since the KDR $\nu_{\mu}$ CC scattering may have angle dependence of outgoing muon, we investigate the differential angular dependent cross section in the ${\nu_{\mu}}$-$^{12}$C scattering and compare to the results by $\nu_e$-$^{12}$C scattering. These results could be useful for the calibration of the forthcoming KDAR neutrino cross section experiments.