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We report a measurement of the flux-integrated $\nu_{\mu}$ charged-currentcross sections on water, hydrocarbon, and iron in the T2K on-axis neutrino beamwith a mean neutrino energy of 1.5 GeV. The measured cross sections on water,hydrocarbon, and iron are $\sigma^{\rm{H_{2}O}}_{\rm{CC}}$ = (0.840$\pm0.010$(stat.)$^{+0.10}_{-0.08}$(syst.))$\times$10$^{-38}$cm$^2$/nucleon,$\sigma^{\rm{CH}}_{\rm{CC}}$ = (0.817$\pm0.007$(stat.)$^{+0.11}_{-0.08}$(syst.))$\times$10$^{-38}$cm$^2$/nucleon, and$\sigma^{\rm{Fe}}_{\rm{CC}}$ = (0.859$\pm 0.003$(stat.)$^{+0.12}_{-0.10}$(syst.))$\times$10$^{-38}$cm$^2$/nucleon respectively, for arestricted phase space of induced muons: $\theta_{\mu}<45^{\circ}$ and$p_{\mu}>$0.4 GeV/$c$ in the laboratory frame. The measured cross sectionratios are ${\sigma^{\rm{H_{2}O}}_{\rm{CC}}}/{\sigma^{\rm{CH}}_{\rm{CC}}}$ =1.028$\pm 0.016$(stat.)$\pm 0.053$(syst.),${\sigma^{\rm{Fe}}_{\rm{CC}}}/{\sigma^{\rm{H_{2}O}}_{\rm{CC}}}$ = 1.023$\pm0.012$(stat.)$\pm 0.058$(syst.), and${\sigma^{\rm{Fe}}_{\rm{CC}}}/{\sigma^{\rm{CH}}_{\rm{CC}}}$ = 1.049$\pm0.010$(stat.)$\pm 0.043$(syst.). These results, with an unprecedented precisionfor the measurements of neutrino cross sections on water in the studied energyregion, show good agreement with the current neutrino interaction models usedin the T2K oscillation analyses.

Measurement of the $\nu_{\mu}$ charged-current cross sections on water, hydrocarbon, iron, and their ratios with the T2K on-axis detectors