Extending BLMSSM with exotic Higgs superfields $(Phi_{NL},varphi_{NL})$ and superfields ($Y,Y^prime$), one obtains the new model called as EBLMSSM, where exotic leptons are heavy and have tree level couplings with SM lepton. In this model, some new parameters with CP-violating phases are considered, so there are new contributions to lepton anomalous magnetic dipole moments (MDMs) and electric dipole moments (EDMs). Therefore, we study the one-loop, two-loop Barr-Zee and two-loop Rainbow type corrections to lepton MDMs and EDMs in the EBLMSSM. Considering the constraints from the lightest CP-even Higgs mass and decays, we calculate the corresponding numerical results. In our used parameter space, the new physics contributions to lepton MDMs are large, which can remedy the deviation between the SM prediction and experimental result well. New introduced CP-violating phases also affect the lepton EDMs in a certain degree.
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