REVIEW
Top-quark flavor-changing neutral currents and charged-lepton flavor violation in a generational three-Higgs-doublet model
High Energy Physics - Phenomenology · Submitted 8 Sep 2026 · 80 references
Pith's verdict: Solid G3HDM flavor paper whose headline upper bounds are scan-range artifacts, not true model maxima; the factorization correlations are the real result.
T0 · AI review
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Referee report
The paper
The paper claims
After the paper's full set of constraints, the generational three-Higgs-doublet model still allows $t\to c h_1$ near $10^{-5}$, $h_1\to\mu\tau$ near $10^{-4}$, and muon-to-electron conversion within next-generation reach.
The reading
What carries the argument
The central object is the scalar misalignment $\Delta_{23}=|Z^h_{12}/v_2-Z^h_{13}/v_3|$, the difference between how the lightest neutral scalar couples to the second and third Higgs doublets, normalized by their vacuum expectation values. It is the common driver of the factorized leading-order rates $\mathrm{Br}(t\to c h_1)\propto(y_{ct}^2+y_{tc}^2)\Delta_{23}^2$ and $\mathrm{Br}(h_1\to\mu\tau)\propto(y_{\mu\tau}^2+y_{\tau\mu}^2)\Delta_{23}^2$, where the $y$'s are $O(1)$ second--third generation texture parameters from the rank-one Yukawa construction. The mechanism is that the tree-level flavor-changing neutral-Higgs couplings are proportional to this misalignment and vanish in the alignment limit; its scale is approximated by $v|2\lambda_3-\lambda_6-\lambda_9|/M^2_{H^\pm_\mathrm{min}}$, which is why the light charged-Higgs mass and the quartic combinations $\lambda_3$ and $\lambda_6+\lambda_9$ largely control the rates.
Extended reading notes
Core claim
The central claim is that the leading flavor-changing rates of the CP-conserving G3HDM factorize into a fermion-generation texture factor and a single scalar-misalignment factor. In the accepted sample, $\mathrm{Br}(t\to c h_1)\propto (y_{ct}^2+y_{tc}^2)\Delta_{23}^2$ and $\mathrm{Br}(h_1\to\mu\tau)\propto (y_{\mu\tau}^2+y_{\tau\mu}^2)\Delta_{23}^2$, where $\Delta_{23}=|Z^h_{12}/v_2-Z^h_{13}/v_3|$ measures how the physical 125 GeV scalar overlaps the second and third Higgs doublets relative to their vacuum values. Because the two modes share $\Delta_{23}$, their branching-ratio ratio $\mathrm{Br}(h_1\to\mu\tau)/\mathrm{Br}(t\to c h_1)\simeq 34.26(y_{\mu\tau}^2+y_{\tau\mu}^2)/(y_{ct}^2+y_{tc}^2)$ is nearly independent of the scalar sector. The dominant collider signals are generated by tree-level flavor-changing neutral-Higgs couplings rather than by loop enhancement, and both rates vanish in the alignment limit.
Load-bearing premise
The quoted ceilings and correlations assume all complex phases in the Yukawa couplings are turned off and that each Higgs doublet couples to exactly one combination of fermion families; if those phases are switched on or that coupling pattern is relaxed, the rates and correlation structure can change.
Editorial extensions
If this is right
- Both $\mathrm{Br}(t\to c h_1)$ and $\mathrm{Br}(h_1\to\mu\tau)$ grow with the product of the appropriate second--third generation texture factor and $\Delta_{23}^2$, and both vanish in the alignment limit; the enhancement is tree level, not a loop effect.
- The ratio $\mathrm{Br}(h_1\to\mu\tau)/\mathrm{Br}(t\to c h_1)\simeq 34.26(y_{\mu\tau}^2+y_{\tau\mu}^2)/(y_{ct}^2+y_{tc}^2)$ cancels the dominant scalar-sector dependence, giving a diagnostic that isolates the fermion texture structure.
- First-generation modes are suppressed at amplitude level by $m_u/m_c$ for quarks and $m_e/m_\mu$ for leptons, which is why $h_1\to\mu\tau$ dominates $h_1\to e\mu$ and $t\to c h_1$ dominates $t\to u h_1$.
- The maximal aluminum $\mu\to e$ conversion rate sits between the single-event and projected upper-limit benchmarks of the next-generation conversion experiments, while the gold rate remains roughly a factor of 67 below the current experimental bound.
- Radiative and three-body charged-lepton modes stay far below current limits, with $\mathrm{Br}(\mu\to 3e)$ tracking approximately the dipole-dominance value $6.13\times10^{-3}\mathrm{Br}(\mu\to e\gamma)$.
Reading between the lines
- Editorial inference: because both rates share $\Delta_{23}$, measuring $\mathrm{Br}(t\to c h_1)$ and $\mathrm{Br}(h_1\to\mu\tau)$ together tests the fermion texture ratio while cancelling the scalar sector, so the pair is a sharper experimental target than either channel alone.
- Editorial inference: restoring the CP-violating texture phases that the paper sets to zero could enlarge the maximal $\mu\to e$ conversion or $h_1\to\mu\tau$ rates through constructive interference, so the quoted ceilings are best read as CP-conserving ceilings rather than full-model bounds.
- Editorial inference: the same second--third doublet misalignment should also feed $b\to s$ flavor transitions in this construction, so combining $t\to c h_1$ with rare $B$ measurements would stress-test the generational ansatz across quark sectors.
Original 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, $\mathrm{Br}(t\to c h_1)\leq 1.04\times10^{-5}$ and $\mathrm{Br}(h_1\to\mu\tau)\leq 4.83\times10^{-4}$, while the maximal conversion rates are $\mathrm{CR}(\mu\mathrm{Al}\to e\mathrm{Al})\approx 4.95\times10^{-15}$ and $\mathrm{CR}(\mu\mathrm{Au}\to e\mathrm{Au})\approx 1.05\times10^{-14}$. 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.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
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, $\mathrm{Br}(t\to c h_1)\leq 1.04\times10^{-5}$ and $\mathrm{Br}(h_1\to\mu\tau)\leq 4.83\times10^{-4}$, while the maximal conversion rates are $\mathrm{CR}(\mu\mathrm{Al}\to e\mathrm{Al})\approx 4.95\times10^{-15}$ and $\mathrm{CR}(\mu\mathrm{Au}\to e\mathrm{Au})\approx 1.05\times10^{-14}$. 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 1.00 | 0.92 | 0.08 | asserted 0.89 |
| s1 | 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 $B_s\to\mu^+\mu^-$. | method 0.94 | 0.84 | 0.05 | asserted 1.00 |
| s2 | In the scanned region, $\mathrm{Br}(t\to c h_1)\leq 1.04\times10^{-5}$ and $\mathrm{Br}(h_1\to\mu\tau)\leq 4.83\times10^{-4}$, while the maximal conversion rates are $\mathrm{CR}(\mu\mathrm{Al}\to e\mathrm{Al})\approx 4.95\times10^{-15}$ and $\mathrm{CR}(\mu\mathrm{Au}\to e\mathrm{Au})\approx 1.05\times10^{-14}$. | result 1.00 | 0.92 | 0.30 | asserted 1.00 |
| s3 | 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 $h_1\to\mu\tau$. | interpretation 0.98 | 0.83 | 0.25 | asserted 1.00 |
| s4 | 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. | interpretation 0.95 | 0.84 | 0.25 | asserted 0.84 |
What was examined, and what was not
- arXiv listing abstract v1
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- references and citing sentences
- relations to other papers
- P abstract
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Figures
Figures reproduced from arXiv:2609.08350 by the authors.
References
Discussion
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