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Recently, the ATLAS and CMS Collaborations measured the 125 GeV Higgs bosondecay to a pair of muons $h\rightarrow \mu \bar{\mu}$, which reported thesignal strength relative to the standard model (SM) prediction is $1.2\pm0.6$and $1.19^{+0.40+0.15}_{-0.39-0.14}$, respectively. In this work, weinvestigate the 125 GeV Higgs boson decay $h\rightarrow \mu \bar{\mu}$ atone-loop level in the $\mu$ from $\nu$ Supersymmetric Standard Model($\mu\nu$SSM). Compared to the SM prediction, the decay width of $h\rightarrow\mu \bar{\mu}$ in the $\mu\nu$SSM can boost up about 10\%, considering theconstraint from the muon anomalous magnetic dipole moment.

125 GeV Higgs boson decay to a pair of muons in the $\mu\nu$SSM