Study the Higgs mass with the effective potential and Higgs decays in the $U(1)_X$SSM

As the U(1) extension of the minimal supersymmetric standard model, the $U(1)_X$SSM has new super fields such as right-handed neutrinos and three Higgs singlets. In the $U(1)_X$SSM, the lightest CP-even Higgs mass $m_{h^0}$ is researched through the Higgs effective potential with one loop corrections. We also calculate the Higgs decays $h^0\rightarrow\gamma\gamma$, $h^0\rightarrow VV~(V=W,~Z)$, $h^0\rightarrow l\bar{l}Z$ and $h^0\rightarrow \nu\bar{\nu}Z$. The obtained results are reasonable, which are in favour of the study of the Higgs characteristic and the phenomenology of the $U(1)_X$SSM.