Combined explanations of $(g-2{)}_{\mu ,e}$ 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, $a_{\mu }=(g-2{)}_{\mu }/2$, at the level of 3-4$\sigma$, it is natural to ask if there could be a sizable effect in the electric dipole moment (EDM) $d_{\mu }$ 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 $d_{\mu }$. However, the recently observed 2.5$\sigma$ tension in $a_e=(g-2{)}_e/2$, if confirmed, requires that the muon and electron sectors effectively decouple to avoid constraints from $\mu \to e\gamma$. We briefly discuss UV complete models that possess such a decoupling, which can be enforced by an Abelian flavor symmetry $L_{\mu }-L_{\tau }$. 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 $d_{\mu }$ improved by up to two orders of magnitude are expected from the upcoming $(g-2{)}_{\mu }$ 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 $a_e$, $a_{\mu }$, as well as the fine-structure constant $\alpha$ 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.

12 pages, 7 figures; journal version

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