Measurement of ${\bar{\nu }}_{\mu }$ and ${\nu }_{\mu }$ charged current inclusive cross sections and their ratio with the T2K off-axis near detector

We report a measurement of cross section $\sigma(\nu_{\mu}+{\rm nucleus}\rightarrow\mu^{-}+X)$andthefirstmeasurementsofthecrosssection$\sigma(\bar{\nu}_{\mu}+{\rm nucleus}\rightarrow\mu^{+}+X)$andtheirratio$R(\frac{\sigma(\bar \nu)}{\sigma(\nu)})$ at (anti-)neutrino energies below 1.5 GeV. We determine the single momentum bin cross section measurements, averaged over the T2K $\bar{\nu }\mathrm{/}\nu$-flux, for the detector target material (mainly Carbon, Oxygen, Hydrogen and Copper) with phase space restricted laboratory frame kinematics of ${\theta }_{\mu }<{32}^{\circ }$ and $p_{\mu }>$500 MeV/c. The results are $\sigma(\bar{\nu})=\left( 0.900\pm0.029{\rm (stat.)}\pm0.088{\rm (syst.)}\right)\times10^{-39}$and$\sigma(\nu)=\left( 2.41
\pm0.022{\rm{(stat.)}}\pm0.231{\rm (syst.)}\ \right)\times10^{-39}$ in units of cm${}^2$/nucleon and $R\left(\frac{\sigma(\bar{\nu})}{\sigma(\nu)}\right)= 0.373\pm0.012{\rm (stat.)}\pm0.015{\rm (syst.)}$.