Collider Probes of Four-Lepton Final States in Maximally Flavor-Violating $U(1)_{L_μ-L_τ}$ Model

We investigate the collider signatures of the maximally flavor-violating $U(1){L_μ-L_τ}$ model, where a new gauge boson $Z^\prime$ and scalar triplets induce lepton flavor-changing interactions in the $μ$-$τ$ sector. Focusing on four-lepton final states at multi-TeV lepton colliders, we conduct a detailed analysis of cross sections, asymmetries, and polarization effects. We show that the signal cross section is highly sensitive to $m{Z^\prime}$ and the effective parameters $\tilde{g}/m_{Z^\prime}$, while remaining largely insensitive to the triplet Yukawa couplings within the phenomenologically allowed region. The forward-backward asymmetry exhibits a characteristic monotonic dependence on $m_{Z^\prime}$, and beam polarization can significantly suppress Standard Model backgrounds while enhancing new physics contributions. We find that over the phenomenologically allowed parameter space, the predicted observables remain highly sensitive to the underlying model parameters. These results demonstrate that multi-lepton final states are powerful probes of the $U(1)_{Lμ- L_τ}$ framework and offer valuable guidance for future searches at muon and electron-positron colliders.

💡 Research Summary

This paper presents a comprehensive investigation of collider signatures within a “maximally flavor-violating” extension of the U(1)_{L_μ-L_τ} gauge model, focusing on four-lepton final states at multi-TeV lepton colliders.

The study begins by motivating the search for charged lepton flavor violation (LFV), a phenomenon highly suppressed in the Standard Model (SM) but predicted in many beyond-SM scenarios. The U(1)_{L_μ-L_τ} symmetry, which distinguishes between muon and tau lepton numbers, is a well-motivated framework. While its minimal version features only flavor-conserving couplings, the authors construct a non-minimal, “maximally flavor-violating” realization. This is achieved by introducing an extended Higgs sector, including three scalar triplets (Δ), and imposing a specific exchange symmetry. After symmetry breaking and rotating to the mass eigenbasis, the model yields tree-level flavor-changing couplings of the new Z’ gauge boson between muons and taus (e.g., Z’μτ vertex), alongside interactions from the triplet scalars.

Before the collider analysis, the paper establishes the phenomenologically viable parameter space by imposing constraints from low-energy experiments: the muon anomalous magnetic moment (g-2)_μ, the leptonic tau decay τ → μνν, and neutrino trident production. These constraints are mapped onto the plane of effective parameters: the gauge coupling-to-mass ratio (˜g/m_Z’) and the triplet Yukawa coupling-to-mass ratio (y/m_Δ). Within the allowed region, five benchmark points (B1-B5) with varying ratios of these parameters are selected for detailed study.

The core of the paper is a detailed analysis of the process μ⁻μ⁺ → μ⁺μ⁻τ⁺τ⁻ (or its permutations) at a future muon collider with a center-of-mass energy of √s = 3 TeV and an integrated luminosity of 1 ab⁻¹. The signal, mediated by both the Z’ boson and the charged/ doubly-charged components of the scalar triplets, is calculated. A key finding is that the signal cross-section exhibits a strong, monotonic dependence on the Z’ mass (m_Z’) and the effective gauge coupling (˜g/m_Z’), while remaining largely insensitive to the triplet Yukawa coupling (y/m_Δ) within the allowed region. Among the benchmarks, B1 (with the largest ˜g/m_Z’) predicts the most significant cross-sections, potentially observable over a wide mass range, whereas others like B4 yield much weaker signals.

The SM background, primarily from ZZ* production, is considered. The statistical significance (S/√(B+S)) is evaluated, showing that for benchmark B1, a discovery potential (≥3σ) is achievable for m_Z’ above approximately 400 GeV. The analysis further demonstrates that utilizing polarized muon beams can dramatically enhance sensitivity. Specific polarization configurations (e.g., {P_μ+, P_μ-} = {80%, -80%}) can suppress the SM background and amplify the signal, improving the statistical significance by up to ~64% for some benchmarks. Additionally, the forward-backward asymmetry of the final state leptons is shown to possess a characteristic monotonic dependence on m_Z’, providing a complementary observable for diagnosing the model’s parameters.

In conclusion, the research demonstrates that multi-lepton final states, particularly in the four-lepton channel, serve as powerful and clean probes of the flavor-violating U(1)_{L_μ-L_τ} framework. A multi-TeV muon collider, especially when leveraging beam polarization techniques, offers exceptional sensitivity to the model’s gauge sector, potentially enabling the discovery or exclusion of the Z’ boson over a significant portion of the allowed parameter space. These findings provide valuable guidance for future search strategies at both muon and electron-positron colliders.