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.
Highlights
Ever since Schwinger’s seminal prediction al 1⁄4 α=ð2πÞ [1], magnetic moments of charged leptons have served as powerful precision tests first of quantum electrodynamics (QED) and later of the full SM
In order to avoid the bound from μ → eγ we assume that these three generations of heavy leptons couple separately to muons and electrons. This flavor conservation can be guaranteed by introducing an Abelian flavor symmetry for the leptons and their vectorlike partners, e.g., Lμ − Lτ [82,83], and other charge assignments are compatible with the observed PMNS matrix [84] and ensure flavor conservations as well
In this article we argued that the recent tension observed in ae, together with the long-standing anomaly in aμ, can be considered an indication that potential beyond the SM (BSM) physics does not respect minimally flavor-violating (MFV)
Summary
Ever since Schwinger’s seminal prediction al 1⁄4 α=ð2πÞ [1], magnetic moments of charged leptons have served as powerful precision tests first of quantum electrodynamics (QED) and later of the full SM. Measurements can be translated directly into yet more stringent SM precision tests From these considerations the emergence of a nonzero Δae, in particular the opposite sign, would be surprising, and a BSM explanation almost necessarily has to violate the quadratic mass scaling. Such a scenario itself is not entirely unexpected [43], given that only one power of the mass is coming from the equations of motions, while the second one results from assuming a SM-like structure of the Yukawa interactions. Such scenarios could be probed at the upcoming ðg − 2Þμ experiments at Fermilab and J-PARC, and, potentially, a dedicated muon EDM experiment at PSI
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