Probing a 146 GeV cLFV scalar using the LHC and low-energy experiments

Abstract: The CMS Collaboration reported a local excess at $146~\mathrm{GeV}$ in the search for the lepton-flavor-violating decay of the Higgs boson and additional Higgs bosons in the $eμ$ final state at $\sqrt{s}= 13~\mathrm{TeV}$. If confirmed, this would constitute a major piece of evidence of charged lepton flavor violation (cLFV). We investigate the compatibility of the claimed signal with the full suite of existing low-energy cLFV constraints in a bottom-up effective description: a single real scalar of mass $146~\mathrm{GeV}$ coupled to gluons and to all charged-lepton bilinears, with seven free parameters that simultaneously control the LHC production cross section, every di-lepton decay channel, and every low-energy cLFV observable. A Bayesian MCMC analysis against $μ-e$ conversion, muonium-antimuonium oscillation, three-lepton and radiative LFV decays, semileptonic $τ$ LFV decays, and LHC di-lepton searches yields a preferred mode with peaked value $Y_{eμ} \sim 10^{-4.09}$, already cut into by the current $μ-e$ conversion limits. The projected sensitivities of Mu2e, COMET, Mu3e, MACE, MEG~II, Belle~II, STCF, and the HL-LHC directly probe the region of coupling space selected by the CMS excess, so the complementarity between high-energy and low-energy cLFV probes will either corroborate or decisively exclude the scalar interpretation of the anomaly within the next decade.

• The paper introduces a model-agnostic effective Lagrangian for a 146 GeV scalar mediating charged lepton flavor violation.
• It employs Bayesian MCMC to extract posterior distributions for seven couplings, reconciling the CMS LHC excess with stringent low-energy bounds.
• The analysis outlines experimental prospects from Mu2e, COMET, and HL-LHC to decisively probe the parameter space of the scalar mediator.

Charged Lepton Flavor Violation from a 146 GeV Scalar: Bayesian Analysis and Experimental Prospects

Motivation and Model Construction

Charged lepton flavor violation (cLFV) is a clear signal of physics beyond the Standard Model (SM), as the SM's contributions are suppressed to negligible levels by the GIM mechanism. CMS reported a local excess at $146~\mathrm{GeV}$ in searches for lepton-flavor-violating (LFV) decays into $e\mu$, with global significance $2.8\sigma$ and a cross-section $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$, but no analogous signal in $h \to e\mu$ or from ATLAS.

To probe the compatibility of this anomaly with stringent constraints from low-energy cLFV experiments, the paper formulates a model-agnostic effective Lagrangian for a real scalar mediator $\phi$ (mass $M_\phi = 146~\mathrm{GeV}$) with seven couplings: $\kappa_{gg}$ (gluons), three diagonal Yukawas ($Y_{ee}$, $Y_{\mu\mu}$, $e\mu$0), and three off-diagonal Yukawas ($e\mu$1, $e\mu$2, $e\mu$3). This parameterization encompasses ggF production, all di-lepton decay modes at the LHC, and low-energy observables, enabling a global consistency test independent of UV completion.

Observable Channels and Effective Operators

The scalar $e\mu$4 mediates cLFV in two distinct regimes:

• LHC Production via Gluon Fusion: The cross section is determined by $e\mu$5 and partial widths (all Yukawa couplings contribute through the total width). The CMS anomaly constrains the combination $e\mu$6.
• Low-Energy cLFV Processes:
  • $e\mu$7 conversion in nuclei (Figure 1): tree-level via the effective $e\mu$8 operator, sensitive to $e\mu$9.
  • Muonium-antimuonium oscillation (Figure 2): tree-level exchange, $2.8\sigma$0.
  • Three-lepton decays ($2.8\sigma$1, $2.8\sigma$2): off-diagonal × diagonal Yukawa.
  • Radiative LFV decays ($2.8\sigma$3, $2.8\sigma$4): loop-level, mixing products ($2.8\sigma$5).
  • Semileptonic $2.8\sigma$6 LFV: $2.8\sigma$7, hadronic matrix element.

The constraints from experiments such as MEG II, Mu3e, Mu2e, COMET, Belle II, STCF, and HL-LHC cover several orders of magnitude, demanding a specific arrangement of couplings to reconcile the CMS excess with null results elsewhere.

Figure 1: Diagram for $2.8\sigma$8 conversion via scalar exchange, illustrating the effective $2.8\sigma$9 operator's contribution to cLFV.

Figure 2: Diagram for scalar-mediated $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$0 oscillation via tree-level $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$1 exchange.

Bayesian MCMC Analysis: Likelihood Construction and Results

The analysis utilizes a Bayesian Markov Chain Monte Carlo (MCMC) scan over log-uniform priors for all seven couplings, maximizing sensitivity to potential parameter regions. The likelihood incorporates both the CMS $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$2 signal and all current low-energy cLFV constraints with their respective uncertainties. The result is a multidimensional posterior that exposes distinct preference modes for the model parameters.

Figure 3: Numerical results of the MCMC analysis, showing the corner plot for seven parameters. Two modes for $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$3 (one near zero, one peaked) reflect the competing effects of the CMS excess and low-energy exclusions.

Key findings from the posterior:

• Bimodality in $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$4: Regions include a tiny-coupling mode favored by null cLFV searches and a non-zero mode around $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$5 dictated by the CMS anomaly.
• Preferred Gluon Coupling: $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$6, with $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$7 HPD interval $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$8.
• Tight Upper Bounds on Off-Diagonal Yukawas: $$\sigma(pp \to \phi \to e\mu) \simeq 3.89~\mathrm{fb}$$9 (95% C.L.), dominated by $h \to e\mu$0.
• Loose Constraints on Diagonal Yukawas: $h \to e\mu$1 bounded by total width effects and resonance searches.
• Posterior Weight: The tiny-coupling regime still dominates ($h \to e\mu$2 at $h \to e\mu$3 credibility); current CMS excess is insufficiently significant ($h \to e\mu$4) to favor genuine cLFV.

Complementarity and Future Experimental Reach

The interplay between high-energy (LHC) and low-energy (cLFV) constraints results in complementarity: the CMS cross-section fixes $h \to e\mu$5, while low-energy bounds cut along other axes. The projected sensitivity of Mu2e, COMET, Mu3e, MACE, MEG II, Belle II, STCF, and HL-LHC will directly probe the signal-preferred region, potentially distinguishing between the two posterior modes.

Figure 4: Constraints for $h \to e\mu$6 in the $h \to e\mu$7 plane, overlaid with current and future experimental exclusion lines.

Figure 5: Constraints for $h \to e\mu$8 and their interplay with semileptonic and radiative LFV channels.

Figure 6: Constraints for $h \to e\mu$9, showing the dominance of $\phi$0 bounds in shaping the credible region.

Experimental prospects are strong:

• Mu2e and COMET: Will tighten $\phi$1 conversion limits toward the signal-preferred $\phi$2 region.
• Mu3e: Future three-lepton decays will offer complementary coverage.
• MEG II: Targets loop-induced $\phi$3, extending constraints by an order of magnitude.
• Belle II and STCF: Improve direct $\phi$4 LFV searches.
• HL-LHC: Expands reach for diagonal Yukawas.

Statistical Robustness and Prior Sensitivity

Upper limits on couplings not directly fixed by the LHC signal exhibit mild prior dependence. Variation of the prior lower boundary shifts the limits by less than $\phi$5, confirming stability of the bounds. Highest posterior density (HPD) intervals for bimodal distributions (e.g. $\phi$6) are correctly computed as disconnected regions.

Figure 7: The sensitivity of 95% credible upper limit to the prior lower limit.

Figure 8: Unimodal HPD intervals in Bayesian analysis for $\phi$7 and $\phi$8.

Figure 9: Strict, disjoint HPD intervals for $\phi$9, reflecting the physical bifurcation in parameter space.

Implications and Outlook

This comprehensive analysis demonstrates that interpretation of the CMS $M_\phi = 146~\mathrm{GeV}$0 anomaly via a generic cLFV scalar mediator is currently viable but largely contingent on future experimental clarification. The model-independent approach isolates the parameter directions sensitive to each experimental program and provides clear mapping between collider signals and low-energy observables.

The methodology and results are broadly applicable to any cLFV scalar scenario near the electroweak scale, providing a robust framework for interpreting the next decade's data from both colliders and precision muon/taus experiments. Should the anomaly persist and be confirmed, high-energy and low-energy cLFV experiments will either corroborate or exclude the scalar interpretation, regardless of the underlying UV origin. Model-independent constraints and joint Bayesian inference will be critical in ensuring robust interpretation amid multiple experimental sources.

Conclusion

The Bayesian global analysis detailed in "Probing a 146 GeV cLFV scalar using the LHC and low-energy experiments" (2607.03249) establishes a quantitative link between an LHC excess and extensive cLFV constraints, delineating viable parameter space for a scalar mediator. The preferred region is tightly bounded and will be probed decisively by upcoming experiments. The framework provides an essential point of reference for interpreting cLFV anomalies and assessing the interplay between collider and precision probes, highlighting the strategic role of model-agnostic effective approaches in BSM phenomenology for the next decade.