Chasing the muon EDM to constrain the SMEFT and UV models

Following a proposal for an experiment with sensitivity to an electric dipole moment (EDM) of the muon $d_\mu$ of order $6\times10^{-23}\ e$ cm, three to four orders of magnitude below the current bound, but still seven orders of magnitude above the current bound on the EDM of the electron $d_e$, we explore the discovery potential of such an experiment. Within the dimension-six CP violating operators of the Standard Model effective field theory (SMEFT), we identify two dipole operators where $d_\mu$ has the strongest sensitivity, and four classes of four-fermion operators where it has the best sensitivity for regions of parameter space that are far from minimal flavor violation. We further consider three UV completions: vector-like leptons (VLLs), heavy vector boson with off-diagonal leptonic couplings, and two Higgs doublet model. For each, we identify the region in parameter space that will be uniquely explored by the proposed $d_\mu$ experiment. In case of VLLs, we also find measurements of $\Gamma (h \rightarrow \mu \mu)$ offer competitive sensitivity, highlighting the complementary role of collider observables. Generically, the potential reach is to ${\cal O}(10\ {\rm TeV})$ scale of new physics.