Measurement of the ${\nu }_{\mu }$ charged current quasi-elastic cross-section on carbon with the T2K on-axis neutrino beam

We report a measurement of the ${\nu }_{\mu }$ charged current quasi-elastic cross-sections on carbon in the T2K on-axis neutrino beam. The measured charged current quasi-elastic cross-sections on carbon at mean neutrino energies of 1.94 GeV and 0.93 GeV are $(11.95\pm 0.19(stat.){-1.47}^{+1.82} (syst.))\times 10^{-39}$\mathrm{c}\mathrm{m}$^2/$\mathrm{n}\mathrm{e}\mathrm{u}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}$$and$(10.64\pm 0.37(stat.){-1.65}^{+2.03} (syst.))\times 10^{-39}$\mathrm{c}\mathrm{m}$^2/$\mathrm{n}\mathrm{e}\mathrm{u}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}$$, respectively. These results agree well with the predictions of neutrino interaction models. In addition, we investigated the effects of the nuclear model and the multi-nucleon interaction.