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 $qoverline{q}h$ and $ u overline{ u}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.
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