Can Electron and Muon $$G-2$$ Anomalies Be Jointly Explained in SUSY?

The FNAL+BNL measurements for muon g-2 is 4.2σ above the SM prediction, and the Berkeley ^133 Cs measurement for the fine-structure constant α _em leads to the SM prediction for electron g-2 which is 2.4σ above the experimental value. Hence, a joint explanation of both anomalies requires a positive contribution to muon g-2 and a negative contribution to electron g-2 , which is rather challenging. In this work we explore the possibility of such a joint explanation in the minimal supersymmetric standard model (MSSM). Assuming no universality between smuon and selectron soft masses, we find out a part of parameter space for a joint explanation at 2σ level, i.e., μ M_1,μ M_2<0 , m_L1, m_E2<200 GeV, m_L2 being much larger than the soft masses of other sleptons, |M_1|<125 GeV and μ <400 GeV. This part of parameter space can survive LHC and LEP constraints, but gives an over-abundance for dark matter if the bino-like lightest neutralino is assumed to be the dark matter candidate. With the assumption that the dark matter candidate is a superWIMP (say a pseudo-goldstino in multi-sector SUSY breaking scenarios, whose mass can be as light as GeV and produced from the late-decay of the thermally freeze-out lightest neutralino), the dark matter problem can be avoided. So, we conclude that the MSSM may give a joint explanation for the muon and electron g-2 anomalies at 2σ level (the muon g-2 anomaly can be even ameliorated to 1σ ).