Global Lepton Flavour Violating Constraints on New Physics

TL;DR

This study performs a comprehensive global analysis of charged lepton flavour violation (cLFV) within effective field theory, contrasting low-energy LEFT and high-energy SMEFT frameworks to constrain the full operator space beyond one-operator-at-a-time approaches. It shows that fully leptonic four-fermion operators have no flat directions in LEFT, allowing robust global bounds, while semileptonic operators exhibit flat directions that are only partially lifted by SMEFT matching and are highly sensitive to nuclear uncertainties in μ–e conversion. The authors map operator constraints across τ–ℓ and μ–e sectors, quantify flat directions, and provide correlation matrices to facilitate UV completion studies, including a scenario with only first-generation quarks where near-complete global constraints emerge. The results highlight the pivotal role of nuclear overlap uncertainties and suggest additional observables (e.g., τ decays to KK) to close remaining degeneracies, offering practical tools for interpreting cLFV bounds in UV models.

Abstract

We perform a global analysis of the bounds from charged lepton flavour violating observables to new physics. We parametrize generic new physics through the Effective Field Theory formalism and perform global fits beyond the common one-operator-at-a-time analyses to investigate how much present data is able to constrain the full parameter space. We particularly focus on leptonic and semileptonic operators with light quarks, identifying unbounded flat directions, detailing how many are present and which operators are involved. The analysis is performed in the general LEFT formalism, which contains all possible low-energy effective operators relevant for lepton flavour violation, as well as in more restricted scenarios, when operators come from a SMEFT completion. We find that flat directions play no role in the fully leptonic four-fermion operators. Conversely, they significantly hinder the ability to derive global bounds on semileptonic operators, with several flat or at least very poorly constrained directions preventing to fully constrain the parameter space. These results are particularly affected by the proper inclusion of uncertainties in the parameters describing $μ-e$ conversion, which decrease the number of well-constrained directions in operator space when treated as nuisance parameters in the fit. While present data is able to provide global constraints on all operators only in the more restricted scenarios we investigated, very strong correlations among the parameters must exist to avoid conflict with the different observables. We provide correlation matrices approximating our full results as a useful tool to compare present data with particular UV completions.

Figures (8)

• Figure 1: Current 95% CL upper bounds on 4-lepton and dipole LEFT operators. The same bounds hold for the corresponding $(L \longleftrightarrow R)$ operators. In the case in which the LEFT is matched as the low-energy realisation of the SMEFT, the bounds on scalar operators do not apply, since they are not generated, but the rest still hold. The bounds shown in the plot are collected in appendix \ref{['app:dipole_4l_bounds']}.
• Figure 2: Current $95\%$ CL bounds on LEFT cLFV operators with quarks considering only one operator at a time (see Fig. \ref{['fig:circular_barplot']} for the rest of operators). Missing bars indicate that there is no (relevant) bound for those operators at present.
• Figure 3: Current 95% CL global bounds on LEFT cLFV operators involving the three lightest quarks. All operators are considered at the same time and their WCs are profiled over to obtain individual bounds. Missing bars indicate that there is no (relevant) global bound for those WCs. For easier comparison, we depict as empty bars the one-at-a-time constraints of Fig. \ref{['fig:one-at-a-time_bounds']}.
• Figure 4: Current 95% CL global bounds on the cLFV LEFT operators with the three lightest quarks induced by $d=6$ SMEFT at low energies. Color code as in Fig. \ref{['fig:LEFT_global_bounds']}, but now darker red bars show the effects of including nuclear uncertainties in the $\mu-e$ analysis. Bounds on pseudoscalar operators are equal to the scalar ones due to the correlations in Eqs. \ref{['eq:SMEFTcorrelationsU']}-\ref{['eq:SMEFTcorrelationsS']}. These global bounds, along with their correlations, are collected in appendix \ref{['App:results']}.
• Figure 5: Current 95% CL global bounds on the cLFV LEFT operators with only first generation quarks induced by $d=6$ SMEFT at low energies . Color code as in Fig. \ref{['fig:SMEFT_global_uds_bounds']}. Bounds on pseudoscalar operators are equal to the scalar ones due to the correlations in Eqs. \ref{['eq:SMEFTcorrelationsU']}-\ref{['eq:SMEFTcorrelationsS']}. These global bounds, along with their correlations, are collected in appendix \ref{['App:results']}.