Global analysis of $\mu \to e$ interactions in the SMEFT

We study current experimental bounds on charged lepton flavor violating (CLFV) $\mu$-$e$ interactions in the model-independent framework of the Standard Model Effective Field Theory (SMEFT). Assuming a generic flavor structure in the quark sector, we consider the contributions of CLFV operators to low-energy observables, including $\mu\to e\gamma$ and $\mu\to e$ conversion for quark-flavor conserving operators and CLFV meson decays for quark-flavor violating operators. At high energy, we consider limits on CLFV decays of the Higgs and Z bosons and of the top quark, and obtain bounds on operators with light quarks by recasting searches for production of $e\mu$ pairs in $pp$ collisions at the Large Hadron Collider (LHC). We connect observables at low- and high-energy by taking into account renormalization group running and matching between CLFV operators. We also discuss the sensitivity of the future Electron-Ion Collider, where the prospective bounds are derived by imposing simple cuts on final state particles. We find that, in a single operator scenario, bounds on purely leptonic operators are dominated by $\mu \rightarrow e \gamma$ and $\mu \rightarrow e$ conversion. Semileptonic operators with down-type quarks are also dominantly constrained by low-energy observables, while LHC searches lead the bounds on up-type quark-flavor violating operators. Taking simplified multiple-coupling scenarios, we show that it is easy to evade the strongest low-energy bounds from spin-independent $\mu \rightarrow e$ conversion, and that collider searches are competitive and complementary to constraints from spin-dependent $\mu \rightarrow e$ conversion and other low-energy probes.