Higgs boson decay $h\to Z\gamma$ and muon magnetic dipole moment in the $\mu \nu$SSM

To solve the $\mu$ problem and generate three tiny neutrino masses in the MSSM, the $\mu$ from $\nu$ Supersymmetric Standard Model ($\mu \nu$SSM) introduces three singlet right-handed neutrino superfields, which lead to the mixing of the Higgs doublets with the sneutrinos. The mixing affects the lightest Higgs boson mass and the Higgs couplings. The present observed 95% CL upper limit on signal strength of the 125 GeV Higgs boson decay $h\rightarrow Z\gamma$ is 6.6, which still is plenty of space to prove the existence of new physics. In this work, we investigate the signal strength of the 125 GeV Higgs boson decay channel $h\to Z\gamma$ in the $\mu \nu$SSM. Besides, we consider the two-loop electroweak corrections of muon anomalous magnetic dipole moment (MDM) in the model, which also make important contributions compared with one-loop electroweak corrections.