Top-quark flavor-changing neutral currents and charged-lepton flavor violation in a generational three-Higgs-doublet model

Abstract

In this work, we systematically investigate top-quark flavor-changing neutral-current decays, charged-lepton flavor-violating processes, and coherent $\mu -e$ conversion in the CP-conserving generational three-Higgs-doublet model (G3HDM), including the relevant tree-level and one-loop contributions. The 4839-point sample passes conservative sufficient vacuum-stability conditions, necessary perturbative-unitarity preselection cuts, Higgs-mass and signal-strength constraints, electroweak precision data, the UTfit 2025 neutral-meson-mixing ranges, $\overline{B}\to X_s\gamma$, and $B_s\to {\mu }^{+}{\mu }^{-}$. In the scanned region, $\mathrm{Br}(t\to c{h}_1)\le 1.04\times 10^{-5}$ and $\mathrm{Br}(h_1\to \mu \tau )\le 4.83\times 10^{-4}$, while the maximal conversion rates are $\mathrm{CR}(\mu \mathrm{Al}\to e\mathrm{Al})\approx 4.95\times 10^{-15}$ and $\mathrm{CR}(\mu \mathrm{Au}\to e\mathrm{Au})\approx 1.05\times 10^{-14}$. The dominant collider signals are mainly driven by tree-level flavor-changing neutral-Higgs couplings, which determine the relative strengths of these processes and induce the pronounced enhancement of $t\to c{h}_1$ and $h_1\to \mu \tau$. Meanwhile, the upper range of the predicted $\mu -e$ conversion rate in aluminum lies within the sensitivity reach of next-generation $\mu -e$ conversion experiments.