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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 $α_{\rm em}$ 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., $μM_1,μM_2<0$, $m_{L1}, m_{E2}<200$ 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 $1σ$).