{"id":"00b7d243-d221-4291-9d1c-94196b700226","arxiv_id":"1908.07759","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":1.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A mini-review explaining that the type-III two Higgs doublet model can produce h to tau mu branching ratios near the present CMS bound while remaining compatible with tau to mu gamma and related flavor constraints.","lead":"This review examines how a general Two Higgs Doublet Model could make the Higgs boson decay into a tau and a muon at rates close to the current LHC limits, while staying below the strict bound from tau to mu gamma. It gathers the model arguments, the relevant loop calculations, and the connections to neutrino mass models in one report.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Stated allowed region (tanβτ≈2, sin(β-α)≈0.9) appears to violate the h→ττ constraint the scan claims to enforce, so the large-h→τμ evidence needs reproduction.","rationale":"The paper's central claim—that the type-III 2HDM can yield h→τμ rates close to the current LHC limits while evading τ→μγ and other constraints—rests on the random scan shown in Fig. 3, taken from Ref. [9]. The reader's weakest point was the dependence of the τ→μγ bound on the Appendix A loop formulas. That is a legitimate concern, but it is a generic check on an external calculation. I think a sharper, internal consistency check is available. The text describes the allowed large-h→τμ region as tanβτ≳2, sin(β−α)∼0.9. From Eq. (26) and the Cheng-Sher ansatz (34)-(36), the hττ coupling is exactly (mτ/v)(sin(β−α) − tanβτ cos(β−α)). For tanβτ=2 and sin(β−α)=0.9 this yields |κτ| ≈ 0.02, which gives a h→ττ signal strength of order 10^-4—far outside the CMS 1σ constraint that the scan says it applies. Either the scan does not actually contain the points described, or the quoted '1σ ranges' were applied very loosely. In either case, the existence of points with large h→τμ is not established by the text. The test I propose is to recompute μ(h→ττ) for a representative claimed point and to verify whether any point reaching BR(h→τμ) ≈ 10^-3 and satisfying BR(τ→μγ) < 4.4×10^-8 also passes the h→ττ constraint. This directly checks the internal consistency of the numerical evidence. I therefore do not change the overall CONDITIONAL verdict, but I would place the condition on reproducing the scan with the h→ττ constraint applied consistently.","tokens_in":23019,"tokens_out":35907,"duration_ms":337159,"concrete_test":"Recompute μ(h→ττ) for the representative point (tanβτ = 2, sin(β−α) = 0.9, κττ = 1, κτμ = 3) using Eqs. (26), (34) and (36) and compare with the CMS 1σ ranges in Ref. [129]. Then repeat for a point with BR(h→τμ) ≈ 10^-3 and BR(τ→μγ) < 4.4×10^-8, and check whether its h→ττ coupling lies within the 1σ band. If no point with BR(h→τμ) at the current limit passes the h→ττ constraint, the stated allowed region is not valid.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Sec. 4.4 states that the scan imposes CMS 1σ ranges for h→ττ, h→bb, h→WW and h→ZZ (Ref. [129]) and identifies the large-h→τμ region as tanβτ ≳ 2, sin(β−α) ≈ 0.9, κτμ ≳ 0.1. Using the paper's own definitions, the hττ coupling from Eq. (26) with ρττ from Eqs. (34) and (36), and κττ = 1, is g_{hττ} = (mτ/v)[sin(β−α) − tanβτ cos(β−α)]. For tanβτ = 2 and sin(β−α) = 0.9 (cos = 0.44), this gives κτ = g_{hττ}/(mτ/v) ≈ 0.9 − 0.88 = 0.02, so μ(h→ττ) ≈ κτ^2 ≈ 4×10^-4, far outside any 1σ interval around the measured μττ ≈ 0.9–1.1. The same cancellation occurs for tanβτ up to O(few) unless cos(β−α) is much smaller than 0.44. Thus the points described as giving large h→τμ appear to fail the very h→ττ constraint the scan claims to apply; the actual allowed points must be much closer to alignment, where g_{hτμ} = ρτμ cos(β−α)/√2 is suppressed. Without access to the scan data, the central claim that BR(h→τμ) can approach the current CMS limit is not independently supported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":23381,"tokens_out":12247,"duration_ms":511579,"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":[{"comment":"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.","section":"Sec. 4.4, Eqs. (26), (34), (35)"},{"comment":"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.","section":"Sec. 4.2, Eqs. (34) and (36)"},{"comment":"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.","section":"Sec. 6, final paragraph"}],"minor_comments":[{"comment":"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).","section":"General"},{"comment":"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.'","section":"Sec. 5, Eq. (39)"},{"comment":"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.","section":"Fig. 3 caption and Sec. 4.4"}],"recommendation":"major_revision","confidential_remarks":"The manuscript overlaps substantially with the author's own Ref. [9], from which the central numerical figure is reproduced, and it also cites Ref. [111] (DsixTools) co-authored by the author. The overlap is disclosed and the review value is legitimate, but the numerical evidence is not independent. If a corrected reanalysis is provided that resolves the Eq. (34)/(36) inconsistency and the h→ττ constraint conflict, the paper would be a useful review; in its current form, the central claim is not supported by the presented evidence."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThat 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.\n\nThe 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.\n\nI 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.\n\nWho 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.\n\nBest,\n[Your name]","headline":"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.","tokens_in":23949,"tokens_out":9015,"would_cite":false,"duration_ms":179744,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["Higgs lepton flavor violation","two Higgs doublet model","type-III 2HDM","h to tau mu decay","tau to mu gamma","two-loop radiative corrections","charged lepton flavor violation","Zee model"],"falsifier":"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.","tokens_in":22786,"feed_emoji":"⚛️","tokens_out":12002,"duration_ms":115156,"temperature":0.7,"pith_summary":"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.","feed_headline":"Second Higgs doublet can push h→τμ to current limits","feed_subtitle":"The Higgs turning a tau into a muon is forbidden in the Standard Model; this model says it could be found.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the one-loop and two-loop form factors for $\\tau\\to\\mu\\gamma$ in the type-III 2HDM, the key constraint that determines the allowed $h\\to\\tau\\mu$ rates.","marker":"[19]"},{"why":"Provides the phenomenological scan and the mass-proportional parameterisation of $\\rho_e$ that produce the BR($h\\to\\tau\\mu$) versus BR($\\tau\\to\\mu\\gamma$) results shown in the paper.","marker":"[9]"},{"why":"Identifies $Q_{e\\phi}$ as the unique dimension-six operator generating HLFV, the starting point of the effective-field-theory argument.","marker":"[3]"},{"why":"Provides the ultraviolet-completion topology of the $Q_{e\\phi}$ operator and the connection between HLFV and neutrino masses used to motivate the type-III 2HDM.","marker":"[72]"},{"why":"Provides the two-loop radiative computations and loop functions that feed into the $\\tau\\to\\mu\\gamma$ form factors.","marker":"[123]"},{"why":"Sets the current experimental upper bound on BR($h\\to\\tau\\mu$) that defines the horizontal line in the phenomenological plot.","marker":"[95]"},{"why":"Sets the experimental upper limit on BR($\\tau\\to\\mu\\gamma$) that provides the vertical constraint in the scan.","marker":"[98]"},{"why":"Supplies the full parameter scan of the Zee model that yields the lower bounds on $h\\to\\tau\\mu$ from neutrino mixing.","marker":"[83]"}],"fun_headline_variants":["General 2HDM can push Higgs tau-muon decay to limit","Type-III two-Higgs model yields h→τμ near current cap","Flavor-changing Higgs decay to τμ within reach in 2HDM","Higgs flipping tau to muon possible in two-doublet model","Two Higgs doublets bring h→τμ to the edge of detection"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["General 2HDM can push Higgs tau-muon decay to limit","Type-III two-Higgs model yields h→τμ near current cap","Flavor-changing Higgs decay to τμ within reach in 2HDM","Higgs flipping tau to muon possible in two-doublet model","Two Higgs doublets bring h→τμ to the edge of detection"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000303,"raw_usage":{"total_tokens":1699,"prompt_tokens":860,"completion_tokens":839,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":476,"completion_tokens_details":{"reasoning_tokens":740}},"tokens_in":476,"tokens_out":839,"duration_ms":9296,"temperature":1.0,"reasoning_tokens":740,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:57:32.310989+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}