Chasing the muon EDM to constrain the SMEFT and UV models

Abstract

Following a proposal for an experiment with sensitivity to an electric dipole moment (EDM) of the muon $d_μ$ 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 $d_μ$ 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 $d_μ$ experiment. In case of VLLs, we also find measurements of $Γ(h \rightarrow μμ)$ 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.

Figures (3)

• Figure 1: Constraints on the VLL model parameters $(\lambda_L\bar{\lambda}\lambda_E)/(M_LM_E)$ from the current ranges of $\Delta a_\mu$, $d_e$, ${\rm BR}(\mu\to e\gamma)$ and ${\rm BR}(h\to\mu^+\mu^-)$, and the projected reach of $d_\mu$. (Left) The $e-\mu$ plane. For $\text{BR}(\mu\to e\gamma)$, we assume $\lambda_L^e\lambda_E^e = \lambda_L^\mu\lambda_E^\mu$. (Right) The ${\rm Re}\frac{\lambda_L^\mu\bar{\lambda}\lambda_E^\mu}{M_LM_E}-{\rm Im}\frac{\lambda_L^\mu\bar{\lambda}\lambda_E^\mu}{M_LM_E}$ plane.
• Figure 2: Exclusion regions from current bounds on $d_e$, BR($\mu\to e\gamma$) and $\Delta a_\mu$, and the region covered by the projected $d_\mu$, in the plane of lepton flavor changing couplings of a heavy vector boson $Z^\prime$. The $Z^\prime$ couplings to a pair of charged leptons $\overline{\ell}_i\ell_j$ of chirality $M$ is given by $g_{Z^\prime}s_{ij}^M$. The ratio $M_{Z^\prime}/g_{Z^\prime}$ is fixed at 10 TeV.
• Figure 3: 2HDM: Constraints from $d_e$, ${\rm BR}(\mu\to e\gamma)$, $\Delta a_\mu$ and (the projected) $d_\mu$ in the plane of $S=A,H$ couplings vs. $M_S$. (Left) Only $\rho_{i\tau},\rho_{\tau j}\neq0$. (Right) $\rho_{i\tau},\rho_{\tau j}=0$, $\varepsilon\neq0$.