We have carried out $ u_{mu}$ charged-current interaction measurement on iron using an emulsion detector exposed to the T2K neutrino beam in the J-PARC neutrino facility. The data samples correspond to 4.0$times$10$^{19}$ protons on target, and the neutrino mean energy is 1.49$,$GeV. The emulsion detector is suitable for precision measurements of charged particles produced in neutrino-iron interactions with a low momentum threshold thanks to thin-layered structure and sub-$mu$m spatial resolution. The charged particles are successfully detected, and their multiplicities are measured using the emulsion detector. The cross section was measured to be $sigma^{mathrm{Fe}}_{mathrm{CC}} = (1.28 pm 0.11({mathrm{stat.}})^{+0.12}_{-0.11}({mathrm{syst.}})) times 10^{-38} , {mathrm{cm}}^{2}/{mathrm{nucleon}}$. The cross section in a limited kinematic phase space of induced muons, $theta_{mu} < 45^{circ}$ and $p_{mu} > 400 , {rm MeV}/c$, on iron was $sigma^{mathrm{Fe}}_{mathrm{CC hspace{1mm} phase hspace{0.5mm} space}} = (0.84 pm 0.07({mathrm{stat.}})^{+0.07}_{-0.06}({mathrm{syst.}})) times 10^{-38} , {mathrm{cm}}^{2}/{mathrm{nucleon}}$. The cross-section results are consistent with previous values obtained via different techniques using the same beamline, and they are well reproduced by current neutrino interaction models. These results demonstrate the capability of the detector towards the detailed measurements of the neutrino-nucleus interactions around the 1$,$GeV energy region.
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