Branching ratio measurement of $h \to \mu ^+ \mu ^-$ at the ILC

We study the prospects of measurement of the branching ratio of $h \to \mu ^+ \mu ^-$ at the International Linear Collider (ILC). The study is performed at center-of-mass energies of 250 GeV and 500 GeV, using fully-simulated MC samples with the International Large Detector (ILD) model. For both center-of-mass energies, the two final states $q\overline{q}h$ and $\nu \overline{\nu}h$ have been analyzed. For an integrated luminosity of 2000 fb$^{-1}$ at 250 GeV and 4000 fb$^{-1}$ at 500 GeV, corresponding to the H20 running scenario as well as its staged version, the precision on $\sigma \times \mathrm{BR}(h \to \mu ^+ \mu ^-)$ is estimated.