Study on muon MDM and lepton EDM in BLMSSM via the mass insertion approximation

In the framework of the MSSM extension with local gauged baryon and lepton numbers (BLMSSM), we calculate the muon anomalous magnetic dipole moment (MDM) and lepton $(e, \mu, \tau)$ electric dipole moment (EDM), and discuss how the muon MDM and lepton EDM depend on the parameters within the mass insertion approximation. Among many parameters, $\tan{\beta}$,~$g_L$,~$m_L$ and $\mu_H$ are more sensitive parameters for $a^{BL}_{\mu}$. Considering the experimental limitations, our best numerical result of $a^{BL}_{\mu}$ is around $2.5 \times 10^{-9}$, which can well compensate the departure between the experiment data and Standard Model (SM) prediction. The CP violating phases in BLMSSM are more than those in the MSSM, including new parameters $\theta_{\mu_L}$ and $\theta_{L}$. They can give large contributions, which play an important role in exploring the source of CP violation and probing new physics beyond SM.