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Improved Bounds and Global Fit of Flavor-Violating Charged Lepton Yukawa Couplings post LHC

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2505.12208 v2 pith:3MPZDAOE submitted 2025-05-18 hep-ph hep-ex

Fayez Abu-Ajamieh , Suman Kumbhakar , Ratan Sarkar , Sudhir Vempati This is my paper · ORCID
classification hep-phhep-ex
keywords flavor-violatingHiggscouplingschargedleptonflavorviolationLHCsearchesSMEFTnewphysicsscalemuong-2raredecaysYukawa
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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [Section III, Eq. (19), Table II] 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.
  2. [Section III vs. Section II.E] 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.
  3. [Section III, Table II] 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.
minor comments (4)
  1. [Section II.A] 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.
  2. [Section II.G] 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.
  3. [Abstract, Section V, Table I] 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.
  4. [Fig. 1] 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.

Circularity Check

1 steps flagged · score 6.0 of 10

The direct h→τμ/h→τe bound translations are honest arithmetic, but the Section III global-fit 'predictions' are the same 95% CL upper limits rebuilt as pseudo-measurements with an arbitrary L/2 centering; the fit output reduces by construction to its input limits.

  1. fitted input called prediction [Section III, Eq. (19) and Table II; Section V conclusions]
    "In order to include an upper limit in the fit, we convert it to a central value plus an error so that we can reproduce the upper limit value at a levels of 1.645σ (or 90% CL) and 2σ (or 95% CL). ... Yµτ (0.40± 0.19)× 10−3 ... Yeτ (0.46± 0.22)× 10−3."

    The h→τμ 95% CL bound is sqrt(|Yτμ|^2+|Yμτ|^2)<1.06e-3; under the paper's symmetric assumption this is |Y|<7.5e-4. Converting that upper limit into a pseudo-measurement with central value L/2 and sigma L/4 (so that L is reproduced at 2σ) gives 0.375e-3±0.187e-3, matching Table II's 0.40±0.19e-3; the same construction gives Yeτ=0.43e-3±0.22e-3 versus the reported 0.46±0.22e-3. The 'best-fit prediction' is therefore the arbitrary centering convention imposed on the input upper limit, not an inference from an independent signal; a standard zero-centered upper-limit treatment would return a fit consistent with zero. The conclusion that 'the χ2 analysis suggests sizes ... O(10−3)' restates the input upper limits through the paper's own conversion rule.

full rationale

The two headline results—direct LHC bounds and their translation to Yukawa couplings via Eq. (5)—are self-contained and not circular: they are direct conversions of CMS Br(h→τμ), Br(h→τe), and Br(h→μe) upper limits using the tree-level width Γ=m_h/(8π)(|Yij|^2+|Yji|^2). The SMEFT scale limits are likewise explicit recastings of those bounds through the stated matching condition Y=3v^2 C/(2√2 Λ^2) and make no separate predictive claim. The circularity is confined to Section III's global fit. There, the 'most likely values' of |Yμτ| and |Yeτ| are not determined by any measured nonzero signal; they coincide with the half-limit pseudo-measurements constructed from the identical 95% CL upper limits listed in Table I. The paper's own Eq. (19) defines χ2 against an Oexp that, for an upper limit, is the converted central value, so the minimization output is the input convention by construction. In addition, the reported Δχ2=4.2 is incompatible with the stated inclusion of (g−2)μ: the best-fit |Yμτ|=0.40e-3 with δ=0.8 gives Re(YμτYτμ)=|Y|^2 cos(2δ)≈−5e-9, a ~5σ discrepancy from (2.33±0.45)e-3; this is a reproducibility/correctness defect rather than a circularity, but it reinforces that Table II does not follow from the stated observables. No load-bearing self-citation or imported uniqueness theorem appears. Overall, the direct-versus-indirect bound comparison stands independently, but the paper's 'predictions' from the global fit reduce by construction to the input upper limits, giving partial circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central bounds rest on experimental inputs and standard formulas from ref. [42]; the main added assumptions are the choice of dimension-6 operator for SMEFT matching, the symmetric-Yukawa assumption in the fit, and the treatment of the (g-2) discrepancy as real. No new particles or entities are introduced.

free parameters (3)
  • SMEFT Wilson coefficient Cij = 1 (set by hand)
    Section IV sets Cij = Cji = 1 to convert each bound into a lower limit on Lambda; any other value rescales the quoted new-physics scale.
  • Muonium state splitting factor S_B = 0.35
    Section II.D quotes S_B = 0.35 from ref. [42] to convert the MACS bound on P(M -> Mbar) into a bound on |Y_mu_e + Y*_e_mu|.
  • Two-loop Wilson coefficient prefactor = 0.055
    Eq. (8) uses c2loop = 0.055 Y/(125 GeV)^2 from ref. [42], which enters the tau -> mu gamma and mu -> e gamma bounds.
assumptions (4)
  • domain assumption The (g-2) anomalies are treated as real and given by eqs. (14) and (15), despite the authors noting lattice QCD reduces the significance.
    Footnote 2 explicitly assumes the discrepancy is real; this enters the fit and the statement that FV Higgs couplings cannot explain the anomalies.
  • ad hoc to paper The Yukawa matrix is symmetric in the chi2 fit (Yij = Yji).
    Section III imposes this symmetry, reducing the parameter space, after the general discussion allowed Yij != Yji; this affects the translation of direct bounds to individual couplings.
  • domain assumption Only the dimension-6 operator (20) contributes to FV Higgs couplings at tree level.
    Section IV matches the bounds to SMEFT using a single operator; other operators could modify the NP scale limits.
  • standard math The Higgs decay width is Gamma_h = 3.7 MeV.
    Used in converting Br(h -> l_i l_j) to Yukawa couplings in Section II.A; standard PDG input.

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Cite this review

Pith. "Pith review of Improved Bounds and Global Fit of Flavor-Violating Charged Lepton Yukawa Couplings post LHC." pith.science (2026). https://pith.science/paper/3MPZDAOE

@misc{pith2026250512208,
  author       = {Pith},
  title        = {Pith review of: Improved Bounds and Global Fit of Flavor-Violating Charged Lepton Yukawa Couplings post LHC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3MPZDAOE}},
  note         = {Machine review of arXiv:2505.12208}
}
abstract

Higgs couplings to charged leptons form an important measurement to understand not only the Standard Model (SM), but also physics Beyond Standard Models (BSM). In this work, we update the bounds on the Flavor-Violating (FV) Higgs couplings to charged leptons. We find that the bounds on the size of the couplings could range between $\sim \mathcal{O}(10^{-3}) - \mathcal{O}(10^{-6})$. In fact, the direct constraints from LHC are much stronger than those inferred indirectly from rare decays in the $\tau$-$\mu$ and $\tau$-$e$ sector. We also match these bounds to the SM Effective Field Theory (SMEFT) and find lower limits on the scale of New Physics (NP). We find that the scale of NP ranges between $\sim \mathcal{O}(10) - \mathcal{O}(100)$ TeV. We also present future projections for some upcoming experiments. We find that the current bounds on the couplings to $\mu$-$e$ are stronger than all future projections.

Figures

Figures reproduced from arXiv: 2505.12208 by the authors.

Figure 1
Figure 1. FIG. 1: Summary of the experimental limits on the FV couplings of the Higgs to charged leptons. The [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The 68%, 90% and 99% CL ellipses of [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

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