Higgs boson decays $h\rightarrow Z γ$ and $h\rightarrow m_V Z$ in the $U(1)_X$SSM
We present a detailed analysis of the Higgs boson decays $h\rightarrow Z γ$ and $h\rightarrow m_V Z$ in the $U(1)_X$SSM, with $m_V$ denoting the meson ($ω,ρ,ϕ,J/ψ,Υ$). Using the effective Lagrangian method, we calculate the effective constants $C_{γZ}$ (CP-even) and $\tilde{C}_{γZ}$ (CP-odd) for the vertex $h γZ$, which are corrected by the new particle loop diagrams. Numerically, the ratio $Γ_{U(1)_X}(h\rightarrow Z γ)/Γ_{SM}(h\rightarrow Z γ)$ is between $1.02-1.35$. For the vector mesons $ω,ρ,ϕ$ and $J/ψ$, the ratios $Γ_{U(1)_X}(h\rightarrow m_V Z )/Γ_{SM}(h\rightarrow m_V Z)$ are mainly distributed in the range of ($1.01-1.45$). When $m_V$ represents $Υ$, the larger value of the ratio $Γ_{U(1)_X}(h\rightarrow ΥZ )/Γ_{SM}(h\rightarrow ΥZ)$ is mostly located in the range of ($1.002-1.30$). This work can provide a reference for specific types of decay processes which can be searched in LHC.