Higgs lepton flavor violating decays in Two Higgs Doublet Models

Avelino Vicente

REVIEW 3 major objections 3 minor 153 references

Higgs lepton flavor violating decays in Two Higgs Doublet Models

T0 review · 3 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A type-III two-Higgs-doublet model can produce Higgs decays to a tau and a muon at rates near the current experimental limits while remaining compatible with existing flavor constraints.

desk verdict Useful mini-review of h→τμ in the type-III 2HDM, but the central numerical evidence is an unpublished personal scan and the quoted benchmark region appears to conflict with the paper's own h→ττ constraint. read the letter →

arxiv 1908.07759 v2 pith:LYPB7VLP submitted 2019-08-21 hep-ph hep-ex

Avelino Vicente This is my paper · ORCID

classification hep-phhep-ex

keywords Higgsleptonflavorviolationtwodoubletmodeltype-III2HDMhtotaumudecaygammatwo-loopradiativecorrectionschargedZee

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the general 'type-III' two-Higgs-doublet model is a strong candidate for producing Higgs lepton flavor violation, in particular for the decay $h\to\tau\mu$. It claims this model can produce $h\to\tau\mu$ rates close to the current experimental upper bounds while respecting the much stronger limits from $\tau\to\mu\gamma$ and other flavor observables. The structural reason is that the operator driving the Higgs flavor-violating decay is generated at tree level, while the dipole operator behind $\tau\to\mu\gamma$ is suppressed by one loop and by chirality flips. The paper reviews the effective-field-theory reasoning, lists the dominant one- and two-loop contributions to $\tau\to\mu\gamma$, and presents a parameter scan in which the allowed region reaches near the present LHC sensitivity. If the claim is right, an observation of $h\to\tau\mu$ would be a realistic discovery channel for new physics.

What carries the argument

The load-bearing mechanism is the hierarchy between two effective operators. The Higgs lepton-flavor-violating operator $Q_{e\phi}=\bigl(\phi^\dagger\phi\bigr)\bigl(\overline{\ell}\, e\,\phi\bigr)$ is generated at tree level in the type-III 2HDM by a diagram with two scalar doublets both coupling to leptons, giving $C_{e\phi}/\Lambda^2 \sim \lambda\, y_\Phi / m_\Phi^2$. The photonic dipole operator $O_{e\gamma}$ responsible for $\tau\to\mu\gamma$ is instead induced only at one loop with two charged-lepton mass insertions, so the paper's estimate gives $(L_{e\gamma})_{ij}\sim (m_i/v)^2/(16\pi^2)\,(C_{e\phi})_{ij}$, which the author explicitly warns is a poor estimate. The full $\tau\to\mu\gamma$ amplitude is then computed from one-loop neutral-scalar diagrams and two-loop diagrams with an internal photon and a $W$ boson or a third-generation quark, following Ref. [19]; the $W$-boson two-loop contribution generally dominates. This suppression of the dipole relative to the Yukawa operator is what lets large $h\to\tau\mu$ rates escape the $\tau\to\mu\gamma$ bound.

What would settle it

Measure $\tau\to\mu\gamma$ with sensitivity around $10^{-9}$ and look for the correlation: if no $\tau\to\mu\gamma$ events appear, the parameter points in the paper that predict BR($h\to\tau\mu$) near $10^{-3}$ would be excluded, because those points sit close to the current $\tau\to\mu\gamma$ bound.

Watch

Extended reading notes

Core claim

The paper's central claim is that the general 'type-III' two-Higgs-doublet model can produce Higgs lepton flavor violating decays, in particular $h\to\tau\mu$, at rates close to the current experimental upper bounds while remaining compatible with all direct and low-energy flavor constraints. In the Higgs basis, the off-diagonal entries of the Yukawa matrix $\rho_e$ generate the flavor-changing Higgs couplings; with a mass-proportional ansatz, the relevant parameter is $\kappa_{\tau\mu}\,\tan\beta_\tau\,\sqrt{2 m_\tau m_\mu}/v^2$. The numerical scan shows that for $\tan\beta_\tau\gtrsim 2$, $\sin(\beta-\alpha)\simeq 0.9$ and $\kappa_{\tau\mu}\gtrsim 0.1$, one obtains BR($h\to\tau\mu$) near $2.5\times10^{-3}$ while BR($\tau\to\mu\gamma$) stays below $4.4\times10^{-8}$. In this regime the two-loop diagrams with an internal photon and a $W$ boson dominate the $\tau\to\mu\gamma$ amplitude, and partial cancellations between the various contributions weaken the naive correlation between the two observables.

Load-bearing premise

The whole conclusion rests on the $\tau\to\mu\gamma$ decay-rate calculation being complete and correct; if it misses a significant contribution, the large $h\to\tau\mu$ rates shown could already be ruled out by the measured upper bound.

Editorial extensions

If this is right

The type-III 2HDM can keep BR($h\to\tau\mu$) within a factor of a few of the current upper bound, so a dedicated run at the LHC could discover the decay in the near term.
A future measurement of $\tau\to\mu\gamma$ near $10^{-9}$ would strongly compress the allowed parameter region, because the same off-diagonal coupling $\rho_e^{\tau\mu}$ controls both processes.
Planned $e^+e^-$ Higgs factories could probe BR($h\to\tau\mu$) down to about $10^{-5}$--$10^{-4}$, roughly an order of magnitude better than current LHC limits.
In the Zee-model extension, the measured neutrino mixing angles force both $\rho_e^{\tau\mu}$ and $\rho_e^{\tau e}$ to be nonzero, giving the lower bound BR($h\to\tau\mu$) $\gtrsim 10^{-6}$ for normal neutrino mass ordering.
Any observed HLFV decay would be an unambiguous signal of physics beyond the Standard Model, and in this framework it would directly measure the off-diagonal entries of the $\rho_e$ matrix.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the paper's effective-field-theory logic is right, the same tree-level/dipole hierarchy should apply to $h\to\tau e$, so future lepton colliders reaching $10^{-5}$ in both channels could map the flavor structure of the $\rho_e$ matrix; the paper focuses on the $\tau\mu$ channel only.
The scan fixes the quark Yukawa sectors to type-II textures; relaxing that choice would add new quark-loop contributions to $\tau\to\mu\gamma$, so the permitted $h\to\tau\mu$ region is tied to that simplifying assumption.
A percent-level measurement of the Higgs couplings to taus, muons, and $W$ bosons would indirectly probe $\sin(\beta-\alpha)$ and could corroborate or exclude the preferred region ($\sin(\beta-\alpha)\simeq 0.9$) even before a direct $h\to\tau\mu$ observation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague — quick take on arXiv:1908.07759. It is a mini-review, not a new result. The physics content is mostly imported: Section 3 follows Herrero-Garcia et al., Section 4.4 reproduces the scan from the author's own Ref. [9], and Section 5 draws on the Zee-model paper. There is no new computation, parameter point, or released code/data.

That said, the paper does several things well. The EFT motivation is clean and correct: the type-III 2HDM generates Qeϕ at tree level while Oeγ is loop- and mass-suppressed, which is exactly the right way to explain why h→τμ can be large when τ→μγ is not killing it. The Higgs-basis notation is carefully set up, the summary of experimental bounds is handy, and the Appendix collects the relevant τ→μγ loop functions in one place. The brief survey of neutrino-mass connections (Zee, left-right) is a useful addition.

The soft spots are in the evidence for the headline claim. Fig. 3 is reproduced from Ref. [9] and no scan data are provided, so the reader cannot audit it. More worrying, the region described as giving large h→τμ — tanβτ ≳ 2, sin(β−α) ≈ 0.9, κτμ ≳ 0.1 — looks inconsistent with the h→ττ constraint the scan says it enforces. Using the paper's own equations with κττ = 1, the hττ coupling is proportional to sin(β−α) − tanβτ cos(β−α). For tanβτ = 2 and sin(β−α) = 0.9, that is about 0.02, so μ(h→ττ) ≈ 4×10^-4, nowhere near any CMS 1σ interval. Either the surviving points sit much closer to alignment, in which case h→τμ is simultaneously suppressed and the quoted benchmark region is wrong, or the constraint implementation needs checking. I also note that Eq. (36) as printed looks dimensionally off: ρ should be dimensionless, so the Cheng-Sher factor should be /v, not /v^2. That may be a typographical issue, but it makes the equations hard to audit.

I would not call this fatal — the qualitative model-viability claim is independently supported in the literature — but the paper's own numerical demonstration is not reproducible as written. Section 6's phrase "arbitrarily close to the current limits" overstates what the scan shows; "close" would be defensible.

Who should read this: someone new to HLFV who wants a compact map of the 2HDM landscape and the constraints. Experts should cite the original papers, not this review. If the venue wants a review article, it deserves a serious referee — mainly to force a corrected Eq. (36), a reproducibility statement or scan data, and a recheck of the allowed region against h→ττ. I would not accept it as is, and I would not cite it in my own work.

Best, [Your name]

Referee Report

3 major / 3 minor

Summary. This paper is a minireview of Higgs lepton-flavor-violating (HLFV) decays, specifically h→τμ, in the general (type-III) Two Higgs Doublet Model. It motivates the model with an effective-field-theory argument based on the Qeϕ operator, introduces the 2HDM in the Higgs basis, presents the main contributions to τ→μγ (including two-loop Barr-Zee diagrams), and shows a numerical scan, reproduced from Ref. [9], in which BR(h→τμ) can approach the CMS bound while BR(τ→μγ) is compatible with experiment. The paper also discusses the connection between HLFV and neutrino masses, focusing on the Zee model.

Significance. If the central claim is correct, the type-III 2HDM is a viable and simple framework for observable Higgs lepton-flavor-violating decays, which is an important target for LHC and future e+e− colliders. The paper usefully collects the constraints, summarizes the relevant loop contributions, and gives a clear EFT motivation for why the 2HDM can have a hierarchy between the operators controlling h→τμ and τ→μγ. However, the numerical evidence is a random scan reproduced from a previous publication, and the manuscript does not provide the scan data or code. There are no machine-checked proofs or new analytic results; the main independent value is the synthetic review of existing constraints and formulas.

major comments (3)

[Sec. 4.4, Eqs. (26), (34), (35)] The claimed region of large h→τμ rates, characterized as tanβτ ≳ 2 with sin(β−α) ∼ 0.9 and κτμ ≳ 0.1, is incompatible with the stated h→ττ constraint. With κττ = 1, Eq. (26) gives g_{hττ} = (mτ/v)[sin(β−α) − tanβτ cos(β−α)], and for tanβτ = 2 and sin(β−α) = 0.9 the τ-Yukawa strength is κτ ≈ 0.9 − 2×0.44 = 0.02, implying μ(h→ττ) ≈ κτ² ≈ 4×10⁻⁴, far below any 1σ interval around the measured value near unity. The same suppression affects h→bb through the type-II quark texture in Eq. (37). Consequently the scan as described cannot have passed the quoted CMS 1σ constraints; because the scan data and code are not provided, Fig. 3 does not support the central claim that rates arbitrarily close to the CMS bound survive all constraints.
[Sec. 4.2, Eqs. (34) and (36)] Equations (34) and (36) are mutually inconsistent as written. Equation (34) defines tanβτ = −ρττ v/(√2 mτ), while Eq. (36) with κττ = 1 gives ρττ = −tanβτ √2 mτ²/v²; substituting the latter into the former yields tanβτ = (mτ/v) tanβτ, which is not an identity and indicates a missing or extra power of v. Since Eq. (36) is the input for the numerical scan, the values of ρe and hence both BR(h→τμ) and BR(τ→μγ) are ambiguous by powers of v or mτ, and Fig. 3 cannot be reproduced from the manuscript as it stands.
[Sec. 6, final paragraph] The statement that 'the 2HDM can accommodate HLFV rates arbitrarily close to the current limits' is stronger than what a finite random scan can establish. Figure 3 shows a sparse scattering of points with only a few entries near the CMS bound; it does not demonstrate that the allowed region extends continuously up to the bound. The claim should be downgraded to the existence of points with rates at the level of a few×10⁻⁴–10⁻³, or be supported by a dedicated parameter scan that quantifies how close to the bound the allowed region actually reaches.

minor comments (3)

[General] There are several typographical errors, including 'He have introduced' for 'We have introduced' in Sec. 4.2, 'phemenological' for 'phenomenological' in Sec. 4.3, and 'proporcionalities' for 'proportionalities' after Eq. (29).
[Sec. 5, Eq. (39)] The parentheses in the sentence following Eq. (39) are misleading: as printed, 'BR(h→τμ) & 10⁻⁶(10⁻⁷)' does not clearly attach the normal/inverted ordering labels to the two limits; rephrase as 'BR(h→τμ) ≳ 10⁻⁶ for normal ordering and ≳ 10⁻⁷ for inverted ordering.'
[Fig. 3 caption and Sec. 4.4] The caption of Fig. 3 should state explicitly whether the plotted points are required to satisfy all quoted constraints (h→ττ, h→bb, h→WW, h→ZZ, and τ→μγ) simultaneously or only the τ→μγ and h→τμ limits; the text says the scan imposes more constraints, but the figure alone does not indicate which points pass all of them.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation chain; the central claim is an externally checkable model scan, with self-citations used transparently.

full rationale

The paper's chain is not circular. The EFT argument (Secs. 3 and 4.1, based on independent Ref. [72]) identifies Q_eφ as the only HLFV operator and explains why a type-III 2HDM may have L_eγ much smaller than C_eφ. The model setup (Sec. 4.2) and the τ→μγ amplitudes (Appendix A) are taken from independent literature (Refs. [19], [120], [123]) and are written out explicitly, so the numerical relation between BR(h→τμ) and BR(τ→μγ) is checkable from the displayed equations. The scan in Sec. 4.4 follows Ref. [9], co-authored by the present author, and the DsixTools notation [111] also includes him; these are transparent self-citations, but no load-bearing argument reduces to an unverified self-citation. No parameter is defined in terms of the predicted branching ratios, and κτμ is scanned rather than fitted to the output, so the 'close to current limits' statement is a viability demonstration, not a fit renamed as a prediction. The h→ττ consistency of the stated region (tanβτ ≳ 2, sin(β−α) ∼ 0.9) is a separate correctness concern — Eq. (26) with Eq. (36) gives κτ proportional to s_{β−α} − tanβτ c_{β−α}, which would suppress h→ττ for those nominal values — but an internal inconsistency of a constraint application is not a circular definition or self-citation reduction. Accordingly, no circular step is identified.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper's claim that the type-III 2HDM gives large yet allowed h to tau mu rates depends on a scanned set of model parameters and on imported loop calculations. The only genuinely new ingredients are the choices of Yukawa textures and the random scan ranges; no new particles are invented, since the second doublet and the Zee singlet exist in prior literature.

free parameters (4)

kappa_tau_mu (LFV Yukawa texture) = not fixed; scanned magnitude in [0.1, 3.0]
Defines the off-diagonal tau-mu Higgs coupling via Eq. (36); the h to tau mu and tau to mu gamma rates scale as |kappa_tau_mu|^2.
tan beta_tau = scanned in [0.1, 40]
Physical ratio of the tau Yukawa coupling to its SM value, Eq. (34); controls the tau coupling and the quark textures in Eq. (37), and affects the tau to mu gamma two-loop contributions.
sin(beta - alpha) = scanned in [0.7, 1.0]
Mixing between the CP-even scalars, controls the SM-likeness of the observed Higgs couplings via Eqs. (26)-(29); must deviate from 1 to allow flavor-violating h couplings.
Heavy scalar masses m_H, m_A, m_H+ = m_H in 200-1000 GeV, m_A in 400-1000 GeV, m_H+ within 5 GeV of m_A
Scanned within ranges motivated by perturbativity, electroweak precision, and B physics; the tau to mu gamma loop amplitudes depend on these masses.

assumptions (6)

domain assumption Both Higgs doublets couple generically to leptons (type-III 2HDM without natural flavor conservation).
This defines the model; Sec. 4.1 explicitly excludes type-I/II and other NFC versions.
domain assumption The lepton Yukawa matrix rho_e is Hermitian.
Sec. 4.2 assumes Hermiticity 'for simplicity', leading to |A_L| = |A_R| and reducing degrees of freedom; a non-Hermitian rho_e could alter the tau to mu gamma constraints.
domain assumption Cheng-Sher texture for charged leptons (Eq. 36) with kappa_tau_tau = 1, and type-II textures for quarks (Eq. 37).
This ansatz reduces the free parameters and ensures compatibility with quark Higgs coupling measurements; the claimed large HLFV rates are conditional on this texture.
standard math The dimension-six operator Q_e_phi is the only non-redundant source of HLFV at leading order.
Sec. 3 asserts that other operators reduce to Q_e_phi via equations of motion and field redefinitions; this is a standard SMEFT result but is used without proof.
domain assumption The tau to mu gamma form factors in Appendix A, taken from Ref. [19], are correct.
The claimed compatibility of h to tau mu with tau to mu gamma depends on these published loop expressions, which are not re-derived here.
domain assumption The experimental constraints in Tables 1-2 and the CMS signal strength ranges [129] are complete and up to date.
The scan accepts only points satisfying these bounds; stronger or additional constraints, such as direct heavy scalar searches, would reduce the allowed region.

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Cite this review

Pith. "Pith review of Higgs lepton flavor violating decays in Two Higgs Doublet Models." pith.science (2026). https://pith.science/paper/LYPB7VLP

@misc{pith2026190807759,
  author       = {Pith},
  title        = {Pith review of: Higgs lepton flavor violating decays in Two Higgs Doublet Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LYPB7VLP}},
  note         = {Machine review of arXiv:1908.07759}
}

abstract

The discovery of a non-zero rate for a lepton flavor violating decay mode of the Higgs boson would definitely be an indication of New Physics. We review the prospects for such signal in Two Higgs Doublet Models, in particular for Higgs boson decays into $\tau \mu$ final states. We will show that this scenario contains all the necessary ingredients to provide large flavor violating rates and still be compatible with the stringent limits from direct searches and low-energy flavor experiments.

Figures

Figures reproduced from arXiv: 1908.07759 by the authors.

**Figure 1.** 2HDM ultraviolet completion of the Qeϕ operator. Here Φ is a heavy new scalar SU(2)L doublet. See [72] for details. way. 6 We note that Qeϕ is generated at tree-level in this scenario, thus enhancing the Wilson coefficient Ceϕ. We expect Ceϕ Λ2 ∼ λ yΦ m2 Φ , (14) where λ and yΦ are the quartic scalar and Yukawa couplings involved in the topology shown in [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗

**Figure 2.** Most important contributions to τ → µγ in the 2HDM. Here φ = h, H, A. To the left, 1-loop diagrams with neutral Higgs bosons and charged leptons in the loop. To the right, 2-loop Barr-Zee diagrams with an internal photon and a third generation quark or a W-boson. The LFV vertex proportional to ρ τµ e is explicitly indicated. where f = u, d, e. He have introduced sf = +1 for down-type quarks and charged leptons and s… view at source ↗

**Figure 3.** BR(h → τµ) as a function of BR(τ → µγ) in the type-III 2HDM. The parameters are fixed as explained in the text. The vertical lines correspond to the current bound BR(τ → µγ) < 4.4 × 10−8 [98] and the expected Belle-II sensitivity, estimated to be ∼ 10−9 [99]. Finally, the horizontal line indicates the limit by the CMS collaboration BR(h → τµ) < 0.0025 [95]. This ansatz is particularly convenient since it ensures com… view at source ↗

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Reviewed August 14, 2026 · model on record in the stance chip above.

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