The two-loop contributions to muon MDM in $$U(1)_X$$ SSM

The MSSM is extended to the $U(1)_X$SSM, whose local gauge group $SU(3)_C \times SU(2)_L U(1)_Y U(1)_X$. To obtain we add new superfields MSSM, namely: three Higgs singlets $\hat{\eta},~\hat{\bar{\eta}},~\hat{S}$ and right-handed neutrinos $\hat{\nu}_i$. It can give light neutrino tiny mass at tree level through seesaw mechanism. study of contribution two-loop diagrams MDM muon under $U(1)_X$SSM provides possibility for us search physics. In analytical calculation loop (one-loop diagrams), effective Lagrangian method used derive MDM. Here, considered include Barr-Zee type rainbow diagrams, especially Z-Z diagram taken into account. obtained numerical results reach $7.4\times10^{-10}$, which remedy deviation between SM prediction experimental data some extent.