Study muon g-2 at two loop level in the $U(1)_X$SSM

The new experiment data of muon g-2 is consistent with the previous data of Fermion lab, and the departure from SM prediction is about 4.2 $sigma$. It strengthens our faith in the new physics. $U(1)_X$SSM is the U(1) extension of the minimal supersymmetric standard model, where we study the electroweak corrections to the anomalous magnetic dipole moment of muon from the one loop diagrams and some two loop diagrams possessing important contributions. These two loop diagrams include Barr-Zee type, rainbow type and diamond type. The virtual supersymmetric particles in these two loop diagrams are chargino, scalar neutrino, neutralino, scalar lepton, which are supposed not very heavy to make relatively large corrections. We obtain the Wilson coefficients of the dimension 6 operators inducing the anomalous magnetic dipole moment of muon. The numerical results can reach $25times 10^{-10}$ and even larger.