Electron and Muon Anomalous Magnetic Moments in the Inverse Seesaw Extended NMSSM

The recently improved observation of the fine structure constant has led to a negative $2.4\sigma$ anomaly of electron $g-2$. Combined with the long-existing positive $4.2\sigma$ discrepancy of the muon anomalous magnetic moment, it is interesting and difficult to explain these two anomalies with a consistent model without introducing flavor violations. We show that they can be simultaneously explained in the inverse seesaw extended next-to-minimal supersymmetric standard model (ISS-NMSSM) by the Higgsino--sneutrino contributions to $(g-2)_e$ and $(g-2)_\mu$. The spectrum features prefer light $\mu$, which can predict $m_Z$ naturally, and it is not difficult to obtain a $\tau$-type sneutrino dark matter candidate that is compatible with the observed dark matter relic density and the bounds from dark matter direct detection experiments. Due to the compressed spectra and the undetectable decay mode of selectrons, they can evade the current Large Hadron Collider (LHC) constraints.