Combined explanations of $(g-2{)}_{\mu }$, $(g-2{)}_e$ and implications for a large muon EDM

We consider possible beyond-the-Standard-Model (BSM) effects that can accommodate both the long-standing tension in the anomalous magnetic moment of the muon, $a_{\mu }=(g-2{)}_{\mu }\mathrm{/}2$, as well as the emerging $2.5\sigma$ deviation in its electron counterpart, $a_e=(g-2{)}_e\mathrm{/}2$. After performing an EFT analysis, we consider BSM physics realized above the electroweak scale and find that a simultaneous explanation becomes possible in models with chiral enhancement. However, this requires a decoupling of the muon and electron BSM sectors to avoid the strong constraints from $\mu \to e\gamma$. In particular, this decoupling implies that there is no reason to expect the muon electric dipole moment (EDM) $d_{\mu }$ to be correlated with the electron EDM $d_e$, avoiding the very stringent limits for the latter. While some of the parameter space for $d_{\mu }$ favored by $a_{\mu }$ could be tested at the $(g-2{)}_{\mu }$ experiments at Fermilab and J-PARC, a dedicated muon EDM experiment at PSI would be able to probe most of this region.