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

Abstract

With the long-standing tension between experiment and Standard-Model (SM) prediction in the anomalous magnetic moment of the muon, $a_μ=(g-2)_μ/2$, at the level of 3-4$σ$, it is natural to ask if there could be a sizable effect in the electric dipole moment (EDM) $d_μ$ as well. In this context it has often been argued that in UV complete models the electron EDM, which is very precisely measured, excludes a large effect in $d_μ$. However, the recently observed 2.5$σ$ tension in $a_e=(g-2)_e/2$, if confirmed, requires that the muon and electron sectors effectively decouple to avoid constraints from $μ\to eγ$. We briefly discuss UV complete models that possess such a decoupling, which can be enforced by an Abelian flavor symmetry $L_μ-L_τ$. We show that, in such scenarios, there is no reason to expect a correlation between the electron and muon EDM, so that the latter can be sizable. New limits on $d_μ$ improved by up to two orders of magnitude are expected from the upcoming $(g-2)_μ$ experiments at Fermilab and J-PARC. Beyond, a proposed dedicated muon EDM experiment at PSI could further advance the limit. In this way, future improved measurements of $a_e$, $a_μ$, as well as the fine-structure constant $α$ are not only set to provide exciting precision tests of the SM, but, in combination with EDMs, to reveal crucial insights into the flavor structure of physics beyond the SM.