{"id":"1e944bbb-84b2-4142-9f25-0532bdc7bbc7","arxiv_id":"2505.12208","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Updated constraints show LHC direct searches now dominate the tau-mu and tau-e flavor-violating Higgs couplings, with new-physics scales around 10 to 100 TeV.","lead":"This paper updates the limits on rare Higgs decays that change lepton flavor, finding that direct LHC searches now give the strongest bounds for tau-mu and tau-e couplings. It converts these limits into lower bounds on the scale of new physics, around 10 to 100 TeV.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The global-fit best-fit values in Table II likely stem from an unstated upper-limit centering convention (central value L/2, sigma = L/(2z)) rather than from the data; the direct LHC bound translations themselves are sound.","rationale":"The reader's conditional verdict is warranted. The strongest claim, that LHC direct h -> tau mu and h -> tau e searches give tighter coupling bounds than indirect tau -> l gamma and tau -> 3l searches, survives: the quoted experimental branching limits translate through Eq. (5) to about 1.06e-3 and 1.22e-3, respectively, well below the indirect bounds near 10^-2, and the SMEFT scale estimates follow from Eq. (22) with order-one Wilson coefficients. However, the paper's advertised global fit is the weakest load-bearing part. The reported best-fit values and errors are suspiciously close to half of the corresponding direct upper limits, indicating that the upper-limit conversion convention is doing the work. The phase inconsistency with the included (g-2) observable compounds the problem. The reader's weakest assumption identifies this same area: the fit is not reproducible from the stated inputs. The right response is to keep the paper conditional: the bounds and SMEFT translation can be used after minor corrections, but the global-fit section must be redone or clearly relabeled as an illustration of an ad hoc centering convention.","tokens_in":15884,"tokens_out":24512,"duration_ms":244780,"concrete_test":"Re-implement the chi^2 of Section III with the exact observables in Table I and Eq. (19), first using the literal zero-centered conversion (central value 0, sigma = L/1.645 or L/2) and then using the half-limit conversion (central value L/2, sigma = L/(2z)); compare the resulting |Y_mu_tau|, |Y_e_mu|, |Y_e_tau|, phases, and Delta chi^2 to Table II. Separately, insert the reported best-fit values and phases into Eq. (13) and compute the predicted Delta a_mu; if it is negative and orders of magnitude below the quoted (g-2)_mu measurement, the fit cannot be including that measurement as Eq. (19) claims, and either the fit inputs or Table II must be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III's Table II is not a reproducible or defensible statistical result as presented. The reported central values and errors match the pattern of converting each 95% CL upper limit L into a pseudo-measurement with central value L/2 and 1-sigma error L/4, instead of the standard convention of mean 0 and sigma = L/2. For example, the h -> tau mu limit sqrt(|Y_tau_mu|^2 + |Y_mu_tau|^2) < 1.06e-3 gives |Y_mu_tau| < 0.75e-3; the half-limit convention yields 0.375e-3 +/- 0.187e-3, nearly identical to the reported (0.40 +/- 0.19)e-3. Under the standard zero-centered convention, the same limit is represented as 0 +/- 0.375e-3, and since no other tau-mu observable is measured away from zero with comparable precision, the best fit would move toward zero. The nonzero 'prediction' is therefore an artifact of the centering rule, not of the data. In addition, with the reported phase delta = 0.8 rad, Eq. (13) gives Re(Y_mu_tau Y_tau_mu) = |Y|^2 cos(2 delta) approximately -4.6e-9, whereas Section III states the (g-2)_mu measurement (2.33 +/- 0.45)e-3 is included; that observable alone would contribute Delta chi^2 about 25, inconsistent with the reported Delta chi^2 = 4.2. Thus the fit depends on unreported choices (how upper limits are centered, whether g-2 is actually included), and the quoted uncertainties do not follow from the stated inputs. This does not affect the direct-versus-indirect bound translation, but it invalidates the paper's global-fit predictions as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper updates bounds on flavor-violating Yukawa couplings of the 125 GeV Higgs to charged leptons. It translates current experimental upper limits on h→τμ, h→τe, and h→μe, together with low-energy observables such as τ→μγ, μ→e conversion, (g−2)_{μ,e}, EDMs, and muonium oscillation, into bounds on combinations of off-diagonal Yukawa couplings. It then matches these bounds to the SMEFT operator (H†H)(ℓ_i H e_j) and derives lower limits on the new-physics scale Λ. A global χ² fit is performed under the assumption of a symmetric Yukawa matrix, yielding best-fit values and phases for Y_{μτ}, Y_{eτ}, and Y_{eμ}. The central phenomenological claim is that direct LHC searches now dominate over indirect rare-decay bounds in the τ–μ and τ–e sectors, giving sqrt(|Y_{τμ}|²+|Y_{μτ}|²) < 1.06×10⁻³ and sqrt(|Y_{τe}|²+|Y_{eτ}|²) < 1.22×10⁻³ (Λ ≳ 9 TeV), while the μ–e sector remains dominated by μ→e conversion at 1.2×10⁻⁵ (Λ ≳ 87 TeV). Future projections for HL-LHC, Belle II, MEG-II, and Mu2e are also collected.","tokens_in":16262,"tokens_out":10071,"duration_ms":102548,"significance":"The direct bound translations in Section II.A and the SMEFT matching in Section IV are clean and check out: the branching-ratio conversion with Γ_h = 3.7 MeV reproduces the quoted coupling limits, the matching coefficient 3v²/(2√2Λ²) is correct, and the derived Λ values in Table I match the stated formulas. As an update of the Harnik-Kopp-Zupan bounds, the paper is useful and provides a clear, falsifiable set of derived constraints, including the explicit comparison of direct LHC versus indirect low-energy sensitivity. However, the global-fit results in Section III and Table II are not reproducible from the text and appear to depend on an unstated upper-limit centering convention; until that section is rewritten, the global-fit predictions and their quoted Δχ² values should not be used. The significance of the paper therefore rests on the direct bound and scale determinations, which are sound, rather than on the statistical analysis.","major_comments":[{"comment":"The manuscript does not specify how an upper limit is converted into the O_exp and σ_exp used in Eq. (19). The reported best-fit value Y_{μτ} = (0.40 ± 0.19)×10⁻³ is almost exactly half of the h→τμ component limit: with sqrt(|Y_{τμ}|²+|Y_{μτ}|²) < 1.06×10⁻³ and the symmetric assumption, each component satisfies |Y| < 0.75×10⁻³, and centering that limit at L/2 gives (0.375 ± 0.187)×10⁻³. The same pattern holds for Y_{eτ} from the h→τe limit. This indicates that upper limits were treated as two-sided pseudo-measurements centered at L/2 rather than as one-sided limits, e.g., 0 ± L/2 or a proper likelihood. Under the zero-centered convention the best-fit values would move toward zero, so the nonzero 'predictions' and the quoted Δχ² values in Table II are likely artifacts of the centering choice. The authors should state the exact likelihood for each upper limit, provide the fit code or a complete table of the converted pseudo-observables, and show that the quoted results are robust to the centering convention.","section":"Section III, Eq. (19), Table II"},{"comment":"The text says the χ² analysis uses the direct and indirect measurements listed in Table I, which includes the muon (g−2) discrepancy Δa_μ = (249 ± 48)×10⁻¹¹ requiring Re(Y_{μτ}Y_{τμ}) = (2.33 ± 0.45)×10⁻³. With the reported best fit |Y_{μτ}| = 0.4×10⁻³ and phase δ = 0.8 rad, Eq. (13) gives Re(Y_{μτ}Y_{τμ}) = |Y|² cos(2δ) ≈ −4.7×10⁻⁹, more than four orders of magnitude below the required value. Including this observable in Eq. (19) would alone contribute Δχ² ≈ 27, far larger than the reported total Δχ² = 4.2. Either (g−2)_μ is not actually included in the fit, or a large tension is being discarded; the paper does not state which. The same inconsistency applies to the electron (g−2) observables. This makes the global-fit result in Table II unreproducible and internally inconsistent with the stated input list.","section":"Section III vs. Section II.E"},{"comment":"The symmetric-Yukawa assumption Y_{ij} = Y_{ji} is introduced in a single sentence and is not justified, even though Section II correctly notes that Y_{ij} need not be symmetric. The direct and rare-decay bounds only constrain the combination |Y_{ij}|² + |Y_{ji}|², while (g−2) and EDM constrain the product Y_{ij}Y_{ji}; individual values of Y_{μτ}, Y_{τμ}, etc. are therefore only defined under this assumption. The best-fit magnitudes and phases in Table II, and the claims in the Conclusions about the sizes of 'Y_{μτ}' and 'Y_{eτ}', are contingent on this choice. The assumption should be flagged prominently in Table II and in the Conclusions, or the asymmetric fit should be performed and reported.","section":"Section III, Table II"}],"minor_comments":[{"comment":"The sentence on the h→μe projection reads 'sqrt(|Y_{µe}|² + |Y_{µe}|²) < 1.49×10⁻⁴'; the second term should be |Y_{eµ}|², not |Y_{µe}|² again.","section":"Section II.A"},{"comment":"The aluminum muon capture rate is quoted as Γ_Capture,Al = 0.7054 s⁻¹; the standard value is approximately 0.7054×10⁶ s⁻¹. Please check the units, since this enters the conversion of the Mu2e projected limit into a coupling bound.","section":"Section II.G"},{"comment":"The abstract and conclusions state that the new-physics scale ranges between O(10) and O(100) TeV, but Table I lists several entries with Λ ≈ 0.3–0.9 TeV (from EDM and muonium oscillation). The statement should be restricted to the most constraining channels or made consistent with the full table.","section":"Abstract, Section V, Table I"},{"comment":"The axis labels in Fig. 1 are garbled in the compiled version; please regenerate the figure with legible labels and ensure each panel is clearly identified with its coupling combination.","section":"Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"The direct bound translations and SMEFT scale estimates are sound and publishable after moderate revision. The main problem is Section III: the global fit is not reproducible, and the reported best-fit values appear to come from a particular upper-limit centering convention that is not stated. I would ask the authors to either provide a complete, reproducible likelihood specification (including all converted pseudo-observables and their errors, and a clear statement of which Table I entries are included) or remove the global-fit claims and Table II from the paper. The direct search bounds and Λ limits can stand independently."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: the updated bound translations are trustworthy and the paper's central qualitative point—LHC direct searches now beat the rare-decay bounds for h→τμ and h→τe—is real. But the global χ² fit in Section III is not a defensible statistical result as written, and the abstract contains a claim about μ-e projections that is simply wrong.\n\nWhat the paper does well: it brings the 2013 Harnik-Kopp-Zupan numbers up to date, and I checked the key conversions. Br(h→μτ)<1.5×10⁻³ gives sqrt(|Yτμ|²+|Yμτ|²)<1.06×10⁻³, and similarly for τe; the SMEFT matching coefficient 3v²/(2√2Λ²) is right. The new observation that direct LHC searches now dominate the τ-μ and τ-e sectors over rare decays is a genuine shift from the 2013 analysis and is useful for model builders. Most of the Λ values in Table I follow correctly from the bounds.\n\nThe problems are concentrated but real. First, the abstract says the current μ-e bounds are stronger than all future projections; Table I shows future μ→e conversion (1.7×10⁻⁹) beats the current limit (1.2×10⁻⁵) by four orders of magnitude. That needs to be fixed. Second, the χ² fit: the reported best-fit values look like they come from an unstated convention where each 95% CL upper limit L is turned into a pseudo-measurement with central value L/2 and error L/4. Under the standard zero-centered convention, the same limits would drive the best fit to zero, so the claimed O(10⁻³) \"predictions\" are artifacts of that choice, not of the data. The text also says the (g-2) region is excluded by other bounds, but the fit's Δχ²=4.2 is incompatible with including (g-2) as a measurement; the fit's treatment of it is unexplained. Third, the SMEFT scale formulas in Section IV are garbled: the muonium-antimuonium formula gives Λ ~0.7 TeV while the correct derivation gives ~1.3 TeV, and the formula for the Re(Y_{ij}Y_{ji}) bound does not reproduce the table's own numbers. Finally, the fit assumes a symmetric Yukawa matrix without flagging that this is a model assumption rather than a consequence of the bounds.\n\nNone of this undermines the direct bound translations. The paper is worth a referee's time after a revision that drops or fixes the global fit, corrects the abstract, and repairs the SMEFT formulas. I'd send it to review, but I wouldn't accept the fit section as it stands.","headline":"Direct LHC bound translations are solid and the LHC-dominance result is real, but the global fit is an artifact and the abstract claims something false.","tokens_in":16852,"tokens_out":10615,"would_cite":true,"duration_ms":88179,"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":"Direct LHC searches now set the tightest bounds on flavor-violating Higgs couplings to tau–mu and tau–e, pushing the implied scale of new physics beyond 9 TeV.","keywords":["flavor-violating Higgs couplings","charged lepton flavor violation","LHC Higgs searches","SMEFT","new physics scale","muon g-2","rare lepton decays","Yukawa couplings"],"falsifier":"Run the global chi-squared fit using only the published observables and the paper's stated upper-limit conversion rules, but with the $(g-2)$ terms removed; if the central values in Table II do not emerge, the quoted best-fit couplings rest on unspecified input choices rather than on the data alone.","tokens_in":15635,"feed_emoji":"🔬","tokens_out":7299,"duration_ms":66151,"temperature":0.7,"pith_summary":"This paper asks how large flavor-violating couplings of the 125 GeV Higgs boson to charged leptons can still be, after the latest LHC and low-energy data. It finds that for the tau–mu and tau–e sectors, direct LHC searches for $h\\to\\tau\\mu$ and $h\\to\\tau e$ now beat the indirect rare-decay limits: $\\sqrt{|Y_{\\tau\\mu}|^2+|Y_{\\mu\\tau}|^2}<1.06\\times10^{-3}$ and $\\sqrt{|Y_{\\tau e}|^2+|Y_{e\\tau}|^2}<1.22\\times10^{-3}$. Translated through the Standard Model Effective Field Theory, those bounds put the scale of any new physics that generates such couplings above about 9 TeV for the tau–mu and tau–e sectors, and near 87 TeV for the mu–e sector via $\\mu\\to e$ conversion. A global $\\chi^2$ fit, assuming a symmetric Yukawa matrix, finds best-fit magnitudes of order $10^{-3}$ for $Y_{\\mu\\tau}$ and $Y_{\\tau e}$ and $10^{-6}$ for $Y_{\\mu e}$, with phases consistent with zero. A reader should care because these numbers tell us how much room is left for new physics in the Higgs–lepton sector and where future experiments should look.","feed_headline":"9 TeV: new floor for flavor-violating Higgs couplings","feed_subtitle":"Direct h→τμ and h→τe searches now beat rare-decay limits, pushing new physics beyond 9 TeV.","key_machinery":"The load-bearing object is the effective Yukawa matrix $Y_{ij}$ for the charged leptons, whose off-diagonal entries parametrize tree-level flavor violation in $h\\to \\ell_i \\ell_j$. The conversion from an experimental bound to a coupling bound uses the tree-level width $\\Gamma(h\\to\\bar\\ell_i\\ell_j)\\simeq (m_h/8\\pi)(|Y_{ij}|^2+|Y_{ji}|^2)$, while the loop observables (rare decays, $(g-2)$, EDMs, $\\mu\\to e$ conversion) enter through the one- and two-loop Wilson coefficients of ref. [42]. To reach new-physics scales, the paper matches these couplings to the single relevant dimension-six SMEFT operator $(H^\\dagger H)(\\bar\\ell_i H e_j)$ in the Warsaw basis, giving $Y_{ij}=3v^2 C_{ij}/(2\\sqrt{2}\\,\\Lambda^2)$, and inverts each bound to a lower limit on $\\Lambda$. A $\\chi^2$ minimization over the compiled observables produces the best-fit complex couplings.","core_discovery":"The central claim is that the strongest constraints on flavor-violating Higgs couplings to charged leptons have shifted. For $\\tau\\mu$ and $\\tau e$, the LHC bounds on $\\mathrm{Br}(h\\to\\tau\\mu)<1.5\\times10^{-3}$ and $\\mathrm{Br}(h\\to\\tau e)<2\\times10^{-3}$ at 95% CL give $\\sqrt{|Y_{\\tau\\mu}|^2+|Y_{\\mu\\tau}|^2}<1.06\\times10^{-3}$ and $\\sqrt{|Y_{\\tau e}|^2+|Y_{e\\tau}|^2}<1.22\\times10^{-3}$, which are an order of magnitude stronger than the bounds from $\\tau\\to\\mu\\gamma$ and $\\tau\\to e\\gamma$. For $\\mu e$, the tightest limit remains $\\mu\\to e$ conversion in gold, giving $\\sqrt{|Y_{\\mu e}|^2+|Y_{e\\mu}|^2}<1.2\\times10^{-5}$ and a new-physics scale above roughly 87 TeV. Matching to the SMEFT's dimension-six operator $(H^\\dagger H)(\\bar\\ell_i H e_j)$, the paper converts each bound into a lower limit on the scale $\\Lambda$, finding values from roughly 10 TeV to 100 TeV. The paper also concludes that the flavor-violating Higgs couplings cannot, on their own, account for the muon or electron $(g-2)$ anomalies, because the parameter regions needed are excluded by the other constraints.","pith_inferences":["If the fit's symmetric-matrix assumption were relaxed, the individual limits on $Y_{\\tau\\mu}$ versus $Y_{\\mu\\tau}$ could differ; a future measurement of the $h\\to\\mu\\tau$ final state alone would not separate the two directions.","Because the tau–mu and tau–e bounds now come from direct Higgs searches, they are largely independent of loop-level model details; improvements in those branching-ratio limits translate almost linearly into new-physics-scale bounds.","The paper's SMEFT matching assumes a single operator and sets Wilson coefficients to order one; if multiple operators interfere or coefficients are suppressed, the implied scale $\\Lambda$ could shift by factors, so the quoted TeV numbers are indicative rather than sharp.","The irreproducibility of the Table II best-fit values from the stated observables suggests the fit's central results should be treated as illustrative until the input choices are clarified."],"forward_implications":["If the direct LHC bounds are correct, any new physics generating $h\\to\\tau\\mu$ or $h\\to\\tau e$ must sit above roughly 9 TeV, beyond the reach of current colliders.","The mu–e sector is the most constrained: existing $\\mu\\to e$ conversion data already push the new-physics scale near 87 TeV, and no near-term experiment is expected to improve on that for $h\\to\\mu e$ couplings.","The flavor-violating Higgs explanation of the muon and electron $(g-2)$ anomalies is excluded on its own, so those anomalies, if real, require different new physics.","Future HL-LHC projections on $h\\to\\tau\\mu$ and $h\\to\\tau e$ would tighten the couplings to about $4.7\\times10^{-4}$, roughly halving the current limits and raising the implied new-physics scale.","The best-fit pattern—order $10^{-3}$ for tau–mu and tau–e couplings, $10^{-6}$ for mu–e, with zero phases—is a concrete target for model builders."],"supporting_citations":[{"why":"Supplies the loop decay-width formulas, Wilson coefficients, and the earlier bounds that this work updates.","marker":"[42]"},{"why":"Gives the LHC 95% CL bound Br(h→τμ)<1.5×10^-3 that sets the τμ coupling bound.","marker":"[50]"},{"why":"Provides the PDG bounds on Br(h→τe)<2×10^-3 and Br(μ→3e)<1×10^-12 used for the τe and μe limits.","marker":"[51]"},{"why":"The CMS search for h→μe that gives Br(h→μe)<4.4×10^-5 and the corresponding coupling bound.","marker":"[52]"},{"why":"The Belle limit Br(τ→μγ)<4.2×10^-8 that sets the indirect τμ comparison.","marker":"[54]"},{"why":"The MEG limit Br(μ→eγ)<4.2×10^-13 that yields the μe coupling bound.","marker":"[56]"},{"why":"The SINDRUM II μ→e conversion limit in gold that produces the strongest μe bound and the ~87 TeV scale.","marker":"[74]"},{"why":"Defines the Warsaw-basis dimension-six operator used for the SMEFT matching to the new-physics scale.","marker":"[78]"}],"fun_headline_variants":["LHC direct hits outshine rare-decay limits for Higgs flavor violation","Flavor-violating Higgs couplings pinned down by LHC, NP scale to 100 TeV","Direct h→τμ, h→τe searches tighten bounds by an order of magnitude","Muon-electron Higgs coupling still best constrained by μ→e conversion","New limits on flavor-violating Higgs couplings: up to 100 TeV NP scale"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The global chi-squared fit assumes a symmetric Yukawa matrix ($Y_{ij}=Y_{ji}$) and treats the $(g-2)_{\\mu,e}$ discrepancies as measurements even though the regions they favor are excluded by other bounds, so the reported best-fit values depend on those choices.","fun_headline_variants_meta":{"raw":{"variants":["LHC direct hits outshine rare-decay limits for Higgs flavor violation","Flavor-violating Higgs couplings pinned down by LHC, NP scale to 100 TeV","Direct h→τμ, h→τe searches tighten bounds by an order of magnitude","Muon-electron Higgs coupling still best constrained by μ→e conversion","New limits on flavor-violating Higgs couplings: up to 100 TeV NP scale"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001032,"raw_usage":{"total_tokens":4401,"prompt_tokens":1052,"completion_tokens":3349,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":668,"completion_tokens_details":{"reasoning_tokens":3242}},"tokens_in":668,"tokens_out":3349,"duration_ms":23989,"temperature":1.0,"reasoning_tokens":3242,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:41:30.297504+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the global chi-squared fit using only the published observables and the paper's stated upper-limit conversion rules, but with the $(g-2)$ terms removed; if the central values in Table II do not emerge, the quoted best-fit couplings rest on unspecified input choices rather than on the data alone.","supporting_citations":[],"review_version":1}