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We report a measurement of the $\nu_{\mu}$-nucleus inclusive charged currentcross section (=$\sigma^{cc}$) on iron using data from exposed to the J-PARCneutrino beam. The detector consists of 14 modules in total, which are spreadover a range of off-axis angles from 0$^\circ$ to 1.1$^\circ$. The variation inthe neutrino energy spectrum as a function of the off-axis angle, combined withevent topology information, is used to calculate this cross section as afunction of neutrino energy. The cross section is measured to be$\sigma^{cc}(1.1\text{ GeV}) = 1.10 \pm 0.15$$(10^{-38}\text{cm}^2/\text{nucleon})$, $\sigma^{cc}(2.0\text{ GeV}) = 2.07 \pm0.27$ $(10^{-38}\text{cm}^2/\text{nucleon})$, and $\sigma^{cc}(3.3\text{ GeV})= 2.29 \pm 0.45$ $(10^{-38}\text{cm}^2/\text{nucleon})$, at energies of 1.1,2.0, and 3.3 GeV, respectively. These results are consistent with the crosssection calculated by the neutrino interaction generators currently used byT2K. More importantly, the method described here opens up a new way todetermine the energy dependence of neutrino-nucleus cross sections.

Measurement of the muon neutrino inclusive charged-current cross section in the energy range of 1-3 GeV with the T2K INGRID detector