The minimal supersymmetric standard model (MSSM) with complex parameters can contribute sizably to muon/electron anomalous magnetic dipole momemnt ($g-2$) and electric dipole moment (EDM). The electron $g-2$ interplays with electron EDM; the muon $g-2$ can also interplay with electron EDM assuming the universality between smuon and selectron masses, either of which can constrain the relevant CP-phases in the MSSM. In this work, we first use such an interplay to derive an approximate analytical upper limit on the relevant CP-phase. Then we extensively scan the parameter space to obtain more accurate upper limits. We obtain the following observations: (i) The muon $g-2$ in the $2sigma$ range combined with the electron EDM upper limit (assuming the universality between smuon and selectron masses) typically constrains the relevant CP-phase under $1.9times 10^{-5} (text{rad})$; (ii) The electron $g-2$ in the $2sigma$ range (Berkeley) interplays with the electron EDM upper limit (without assuming the universality between smuon and selectron masses) constrains the relevant CP-phase under $3.9times 10^{-6}(text{rad})$ (also requiring muon $g-2$ in the allowed $2sigma$ range). We also find some special cancellations in the parameter space which can relax the constraints by a couple of orders. Such stringent limits on CP-phases may pose a challenge for model building of SUSY, i.e., how to naturally suppress these phases.
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