The paper examines the radiative decay of one charged lepton into another, both with an emitted photon and through a three-lepton final state. Such processes are forbidden in the Standard Model, where lepton-flavor number is conserved, so their experimental detection would provide evidence of physics beyond the Standard Model. The authors also study the muon anomalous magnetic dipole moment, a precisely measured quantity that constrains possible contributions from new interactions.

The FDM extends the Standard Model gauge group with a local U(1) symmetry whose charges are associated with fermion flavor. It also introduces two additional scalar doublets and one scalar singlet. The third generation of fermions obtains mass through tree-level couplings to the Standard Model Higgs doublet, while the first two generations are linked to the third through tree-level mixings. A Type-I seesaw mechanism generates small Majorana neutrino masses and neutrino flavor mixings. The source describes the framework as addressing fermion flavor mixing, the fermion mass hierarchy and neutrino-mass generation within a single model.

Because the additional U(1) charges depend on flavor, the model’s new gauge interactions and Yukawa couplings can produce charged-lepton flavor violation. The particle content includes only two right-handed neutrinos with nonzero U(1) charge, leaving one active neutrino massless at tree level as a characteristic feature of the framework. The scalar sector contains two neutral Goldstone modes and one singly charged Goldstone mode, while the fermion mass matrices are constructed so that the measured quark and charged-lepton masses can be reproduced within the approximation used by the authors.

For the muon anomalous magnetic moment, the study calculates one-loop contributions from two dominant types of diagrams: loops containing neutrinos and charged Higgs bosons, and loops containing charged leptons with neutral scalar or pseudoscalar particles. The numerical analysis uses the reported experimental difference between the measured muon magnetic moment and the Standard Model prediction of 26(66) × 10^−11, corresponding to a 0.5-standard-deviation difference. This is substantially below the five-standard-deviation discovery threshold and therefore places strict limits on new-physics contributions.

The authors scan a parameter space subject to constraints on vacuum stability, perturbativity, Higgs signal strengths at the two-standard-deviation level and direct searches for additional scalars. The scan also imposes a lower limit of 4.05 TeV on the mass of the additional Z′ boson at 95% confidence level and requires M_Z′/g_F to exceed 6 TeV at 99% confidence level. The analysis finds that the predicted muon correction generally decreases as the charged Higgs mass increases, with a wider spread of values for charged Higgs masses below 100 GeV. The charged-Higgs-mediated loop gives the strongest effect among the contributions examined.

For charged-lepton flavor violation, the authors compute branching ratios for the radiative modes l_j^− → l_i^−γ and the three-lepton modes l_j^− → l_i^−l_i^−l_i^+. The dominant contributions to the latter include photon-, Z- and Z′-penguin diagrams, together with box diagrams containing fermions and scalar particles. The numerical calculation fixes several scalar, gauge and neutrino-sector parameters at values compatible with the measured Higgs mass and the latest muon g−2 result, then varies the first scalar doublet’s vacuum expectation value v_1, an electron-mass-matrix element m_e,13 and flavor-mixing phases.

The predicted branching ratios decrease as v_1 increases, showing that a larger vacuum expectation value suppresses lepton-flavor violation in the analyzed setup. At small v_1, the predictions for μ → eγ and μ → 3e exceed the corresponding present experimental upper bounds, while remaining potentially accessible to future experiments. Increasing m_e,13 strongly reduces the two muon-to-electron channels; it causes slower decreases for τ → eγ and τ → 3e, while the τ → μγ and τ → 3μ rates depend only weakly on that element. The flavor-mixing phases affect the muon-to-electron and tau-to-electron rates through their influence on mixing strength, but have a negligible effect on the two tau-to-muon channels in the reported scans.

The study’s conclusions are conditional on the model, its parameter choices and the one-loop treatment of the relevant observables. Its numerical results indicate that the FDM can reproduce current muon g−2 data over much of the scanned viable parameter space and can generate rare-decay rates within the reach of next-generation experiments. The authors did not calculate coherent μ → e conversion rates in nuclei, although they note that the model’s dipole, photon-penguin and Z/Z′-penguin contributions could also contribute to that complementary observable.

Subject of Research: Theoretical predictions for muon g−2 and charged-lepton flavor-violating decays in a flavor-dependent U(1) gauge model

Article Title: Lepton-flavor violation and muon \((g-2)\) in the flavor-dependent \(U(1)_F\) model

Article References: Peng, Y.-J., Niu, F.-Y., Qin, Q.-Z., Cao, Z., & Yang, J.-L. (2026). Lepton-flavor violation and muon $$(g-2)$$ in the flavor-dependent $$U(1)_F$$ model. The European Physical Journal C, 86(10), Article 1184. https://doi.org/10.1140/epjc/s10052-026-16457-7

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DOI: 10.1140/epjc/s10052-026-16457-7

Keywords: lepton flavor violation, muon g−2, flavor-dependent U(1), rare lepton decays, muon-to-electron gamma, tau decays, Z′ boson, new physics, theoretical physics, Lepton-flavor, violation, muon