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

TL;DR

This work constructs a complete SMEFT-based framework to analyze μ–e charged lepton flavor violation across low- and high-energy frontiers. By cataloging leptonic, semileptonic, and quark-flavor–changing operators, performing leading-log RG evolution and SMEFT-to-LEFT matching, the authors translate a wide array of experimental bounds into bounds on 126 Wilson coefficients. They demonstrate that μ→eγ and μ→e conversion dominate many leptonic and down-type semileptonic constraints, while LHC Drell–Yan and LFV decays constrain up-type semileptonic operators, with EIC offering complementary sensitivity for light-quark couplings. In multi-operator scenarios with flavor symmetries, cancellations can relax low-energy bounds, elevating collider and SD constraints to comparable levels, underscoring the importance of a global, multi-channel approach for CLFV phenomenology. The study highlights the power and limitations of current and future experiments (μ→eγ, μ→e conversion, meson decays, LHC, and EIC) in probing the SMEFT parameter space for μ–e transitions.

Abstract

We study current experimental bounds on charged lepton flavor violating (CLFV) $μ$-$e$ 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 $μ\to eγ$ and $μ\to e$ 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 $eμ$ 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 $μ\rightarrow e γ$ and $μ\rightarrow e$ 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 $μ\rightarrow e$ conversion, and that collider searches are competitive and complementary to constraints from spin-dependent $μ\rightarrow e$ conversion and other low-energy probes.

Figures (11)

• Figure 1: Differential branching ratio distributions for the decays $B^{+}\to\pi^{+}e^{\pm}\mu^{\mp}$ (solid black) and $B^{+}\to K^{+}e^{-}\mu^{+}$ (dashed red) as a function of the dilepton invariant mass ($q^{2}$) assuming one single vector (left) and scalar (right) operator from Table \ref{['Table:DownTypeLimits_flavor']} is turned on, with the others set to zero. Here $C_V$ and $C_S$ denote the combination $C^{ed}_{\rm VLR} + C^{ed}_{\rm VLL}$ and $C^{ed}_{\rm SRR} + C^{ed}_{\rm SRL}$, respectively.
• Figure 2: Differential branching ratio distribution (top) and Dalitz plot (in arbitrary units) in the $(q^{2},\cos\theta)$ variables (bottom) for the decay $D^{+}\to\pi^{+}e^{+}\mu^{-}$ assuming one single vector, scalar or tensor operator from Table \ref{['Table:UpTypeLimits_flavor']} is turned on, with the others set to zero. Here $C_V$, $C_S$ and $C_T$ denote the combinations $C^{eu}_{\rm VLR} + C^{eu}_{\rm VLL}$, $C^{eu}_{\rm SRR} + C^{eu}_{\rm SRL}$ and $C^{eu}_{\rm TRR}$, respectively.
• Figure 3: Muon transverse momentum distribution (left) and azimuthal separation between the muon and the hardest jet (right) in the SM and in the presence of three LFV SMEFT operators, $\left[C_{Lu}\right]_{uu}$, $\left[C_{Ld}\right]_{dd}$ and $\left[C_{Ld}\right]_{bb}$, with their coefficients set to 1.
• Figure 4: Dependence of the bounds on the effective coefficients $\left[C_{Lu}\right]_{uu}$ and $\left[C_{Ld}\right]_{bb}$ on the kinematics cuts summarized in Table \ref{['table:eic1']}. The cut denoted by 0 indicates the idealized situation in which $\epsilon_{\rm SM} = 0$ and $\epsilon_{uu} = \epsilon_{bb} = 1$.
• Figure 5: Upper bounds (leftmost axis) on $C_{Ld}$ (top) and $C_{Lu}$ (bottom) and lower bounds on new physics scale $\Lambda$ (rightmost axis) from the EIC (left), LHC (middle) and low-energy observables (right).