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The paper shows that a benchmark model generating the bottom, charm, tau, and tau-neutrino masses at one loop remains viable under current constraints, and that future Yukawa measurements cannot rule it out—only raise its required mass scal

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2026-08-03 22:43 UTC pith:66VENTB7

load-bearing objection A competent benchmark extension of the Baker-Cox-Volkas radiative mass framework to charm and tau-neutrino, but the 'viable regions' claim is conditional on an unspecified seesaw completion. the 2 major comments →

arxiv 2511.08924 v2 pith:66VENTB7 submitted 2025-11-12 hep-ph

Higgs Yukawa coupling constraints on a benchmark one-loop radiative mass model for the bottom, charm and tau

Lucia Stockdale , Raymond R. Volkas This is my paper
classification hep-ph
keywords radiative mass generationone-loop fermion massesHiggs Yukawa couplingsHiggs signal strengthst→ch flavour-changing decaydark matter relic densityvectorlike fermionsfermion mass hierarchy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to show that the Standard Model's tree-level Higgs mechanism is not uniquely verifiable by measuring Higgs Yukawa couplings, because a concrete radiative alternative can still fit the data. It constructs a benchmark model where only the top quark gets its mass at tree level, while the bottom, charm, tau, and tau-neutrino masses all arise at one loop through two vectorlike fermions and two scalars. After checking perturbative unitarity, fine-tuning, Higgs decay signal strengths, electroweak oblique corrections, the rare t→ch decay, and dark matter relic density, the authors find viable regions of parameter space today. They further argue that future collider precision, even if it perfectly matches Standard Model predictions, will only push the required new-physics scale higher and increase fine-tuning, not exclude the model. The paper also flags that the physical tau-neutrino mass needs a further, unspecified seesaw mechanism, leaving that part of the construction incomplete.

Core claim

The paper's central claim is that a benchmark extension in which the bottom, charm, tau, and tau-Dirac-neutrino masses are all generated at one loop—while the top mass stays at tree level—passes every current constraint that can be brought to bear: Higgs decay signal strengths, electroweak T parameter, rare top decay bounds, perturbativity, fine-tuning, and dark matter relic abundance. Because the same loop function that generates a fermion mass also generates its effective Yukawa coupling, and because that function is strictly positive, the model always predicts a Yukawa coupling larger than the Standard Model value for a given mass. Current measurements are still loose enough to accommodat

What carries the argument

The machinery is a pair of one-loop diagrams—one for mass generation and one for the effective Yukawa coupling—sharing the same loop function F(x, y). The soft trilinear coupling a mixes the real scalar φ with the lower component of the doublet η, producing two scalar mass eigenstates with mixing angle given by sin2θ_s = 2av/(m_2^2 − m_1^2). Positivity of F(x, y) is what turns every mass-generation diagram into a strictly positive shift in the effective Yukawa coupling, which is what gives Higgs decay signal strengths their constraining power. The top-quark couplings also induce one-loop t–c mixing, producing a calculable t→ch flavour-changing decay as a complementary probe.

Load-bearing premise

The load-bearing premise is that an unspecified seesaw can supply the physical neutrino mass without disturbing the one-loop sector whose formulas drive every constraint in the paper.

What would settle it

Measure the exotic spectra and the t→ch rate: the model fixes effective Yukawas strictly above the Standard Model line, so if future collider data pin κ_τ, κ_b, and κ_c all to unity at the projected sensitivities while direct searches exclude the colour-triplet χ below the required TeV scale and push scalar masses beyond a ≃ O(1) m_1, the benchmark parameter space closes; likewise, a t→ch branching fraction that violates the predicted quadratic relation in the effective bottom Yukawa coupling would disprove the assumed coupling structure.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the central claim is correct, current and projected Higgs signal-strength measurements for h→ττ, h→bb, and h→cc do not exclude loop-generated masses for these fermions; they only restrict the underlying mass scale.
  • Future measurements that agree perfectly with the Standard Model will not falsify the model; they will push its required scalar and fermion masses higher and increase the fine-tuning needed, making it less theoretically compelling without being ruled out.
  • The model predicts a t→ch branching fraction that depends quadratically on the effective bottom Yukawa coupling; the current bound is not yet competitive with the mu_tau signal strength in the parameter space studied.
  • The dark matter candidate in the model, the upper component of the vectorlike fermion ψ, can reproduce the observed relic density through annihilation into tau leptons and neutrinos for TeV-scale masses.
  • A full three-generation extension would face a rank-one mass-matrix structure, meaning only one fermion of each type can gain mass without additional structure; this makes non-SM flavour-changing processes like t→ch a potentially central probe of complete radiative models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if a pattern of equal enhancements in κ_τ, κ_b, and κ_c were observed together with a t→ch signal, it would be a distinctive fingerprint of this class of one-loop models, since the model predicts equal deviations when the two vectorlike fermion masses are equal.
  • Beyond the paper: the unspecified neutrino seesaw is the soft spot; any concrete completion that adds new fields or couplings will feed back into the same one-loop diagrams, so the quoted viable regions should be read as conditional on that sector remaining inert.
  • Beyond the paper: the same logic—that loop-generated small masses always imply Yukawa couplings above the Standard Model line—extends naturally to the muon and lighter generations, so a systematic multi-family version could turn precision Higgs measurements into a monotonic probe of loop order.
  • Beyond the paper: a decisive test would be to look for the coloured exotic χ: if direct searches exclude it below roughly a TeV while the scalar sector is pushed toward the perturbative unitarity bound, the benchmark parameter space shown in the paper would close.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper constructs a benchmark radiative mass model in which the top quark mass is tree-level while the bottom, charm, tau, and tau-Dirac-neutrino masses are generated at one loop. The model extends the earlier framework of Baker, Cox and Volkas by adding a second quark generation and a neutrino Dirac mass term, using two vectorlike fermions, a complex scalar doublet, and a real scalar singlet, with three softly broken U(1) symmetries and an exact Z2. The authors compute one-loop effective Yukawa couplings (Eq. (6)), study constraints from Higgs signal strengths, electroweak T parameter, and the flavour-changing t→ch decay, and present current and projected exclusion plots (Figs. 2 and 3). They also show that a pseudo-Dirac fermion ψ_up can account for the observed dark matter relic density (Fig. 4). The central claim is that viable parameter space exists now, and that future Higgs/Yukawa and EW precision measurements cannot exclude the model but only push the new-physics scale higher.

Significance. If the result holds, the paper makes a useful and timely point: precision Higgs Yukawa measurements, often viewed as a way to verify the SM mass mechanism, may be unable to distinguish the SM from loop-level alternatives in this class of models. The paper is transparent about its assumptions, uses current PDG data and future projections, and includes a dark matter candidate, making it a concrete benchmark for further study. The loop calculations follow the established framework of Ref. [16] and appear internally consistent. The main strengths are the explicit treatment of the t–c mixing and t→ch constraint, the use of actual projected collider sensitivities, and the recognition that the predicted κ_f > 1 is a structural consequence of the loop origin of the mass, not an independent fit. However, the completeness of the model and the reach of the central 'cannot rule out' claim are limited by (i) the unspecified neutrino-mass completion, which can feed back into the very loop formulas used, and (ii) the restriction of the future-exclusion analysis to selected benchmark slices of parameter space. These issues are fixable but currently leave the central claim only partially supported.

major comments (2)
  1. [Sec. II, Eq. (6), Fig. 1, footnote 1] The model is not a complete fermion-mass model because the physical neutrino mass is deferred to an unspecified seesaw. As the authors note in footnote 1, ν_R couples to ψ_L through yν_R, and a heavy Majorana ν_R generates a one-loop Majorana mass for ψ_L. This splits the would-be pseudo-Dirac ψ, modifying the mτ and yeff_τ loop relations of Eq. (6), the T-parameter calculation, and the dark matter relic cross-section of Eq. (17). Since no concrete seesaw is specified, the viable regions in Figs. 2 and 3 are defined only under the ad hoc assumption that neutrino physics decouples without feedback. This is load-bearing for the claim that the model explains the fermion masses; the authors should either supply a minimal seesaw completion and show that the feedback is negligible, or explicitly state and quantitatively justify the decoupling limit.
  2. [Sec. VI, Figs. 2–3] The central abstract and conclusion claim that future improvements 'will not be able to rule out the model, only increase the scale of new physics required.' The evidence presented for this is limited to two benchmark slices in Fig. 2 and the special slice m2_ϕ = m2_η, mψ = mχ = m2 in Fig. 3. No scan over the full parameter space is shown, and no argument is given that the surviving regions in these slices are representative. To support the strong claim, the authors should either extend the scan over the full parameter space or qualify the statement to 'for the benchmark slices considered here' throughout the abstract and conclusions.
minor comments (4)
  1. [Sec. III, around Eq. (13)] The notation 'cosθ_i = θ_i' is presumably a typo for c_i; as written it is dimensionally inconsistent. Please correct.
  2. [Sec. III, Eqs. (10), (14)–(16)] The t→ch branching fraction is computed using the ad hoc ansatz y3_L = yb_R and y2_L = yc_R. The conclusion that projected t→ch bounds are weaker than the μτ constraint is stated for 'the parameter space considered,' which is appropriate, but it would be helpful to state how the off-diagonal entry depends on this flavour assumption.
  3. [Sec. IV, Eq. (17)] The relic-density calculation considers only ψ_up annihilation and neglects possible coannihilations and the scalar dark matter candidate φ1. The authors acknowledge this is a preliminary treatment, but a sentence on the size of expected corrections would improve the reliability of the 'viable dark matter candidate' statement.
  4. [Fig. 2 caption] The caption says 'Shaded regions are excluded, except for the case of Δ>100 where they are disfavoured.' Please make the colour/hatching distinction clearer in the figure or caption, since the same shading is used for both.

Circularity Check

0 steps flagged

No significant circularity: the mass–Yukawa relation is a genuine model prediction, external constraints are independent, and the reliance on Ref. [16] is a normal citation rather than a circular load-bearing step.

full rationale

The derivation chain fixes the products yf_L yf_R by requiring the observed fermion masses to be reproduced (Sec. III) and then computes the effective Yukawa couplings from Eq. (6). The prediction κ_f > 1 is not equal to the fitted input: it is the ratio of the two loop functions in Eq. (6), which depends only on scalar/fermion mass ratios and the mixing angle, not on the fitted product yf_L yf_R. Hence no fitted quantity is renamed as a prediction. The constraints (signal strengths, T parameter, t→ch, relic density) are external data or standard calculations, not outputs of the fit. The one-loop expressions are imported from Ref. [16], a prior published calculation by one of the present authors; this is a legitimate reliance on prior work and does not incorporate the target conclusion, so it is not a circular self-citation. Sec. II explicitly leaves the physical neutrino mass to an unspecified seesaw ('The physical neutrino mass then must arise from further suppression, for example through a seesaw effect, though we do not consider any specific implementation'); this is a genuine incompleteness/risk for a fully defined model, but it does not make the τ/b/c Yukawa predictions equivalent to their inputs. Overall the central claim is conditional on the stated benchmark assumptions and is not forced by construction.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 4 invented entities

The model introduces four new exotic fields (ψ, χ, η, ϕ) and three softly broken U(1)s plus an exact Z2. The free parameters (masses, a, individual Yukawas) are scanned rather than fitted to data, but several ad hoc choices (the y3^L=yb^R ansatz, unspecified seesaw, DM-scan consistency) are load-bearing. The external benchmarks (PDG signal strengths, T parameter, CMS/ATLAS searches) are genuine constraints, so the central viability claim is not circular, even though the core loop formulas come from the authors' earlier paper [16].

free parameters (5)
  • mψ and mχ (vectorlike fermion masses) = scanned; e.g. m2_ψ = m2_χ = m2_2 in Fig. 3
    Free mass scales of the new fermions; enter loop functions (eq. 6) and the T parameter. Chosen by hand for benchmark slices.
  • mϕ, mη (or scalar mass eigenvalues m1, m2) = scanned; m2_ϕ = m2_η in Fig. 3
    Scalar masses set the loop suppression and the mass-splitting that controls the κ deviations. Treated as free parameters in the scans.
  • a (trilinear scalar coupling) = indirectly through sin2θ_s = 2av/(m2^2−m1^2); upper bound O(1)·m1 from perturbativity
    Together with v and scalar masses it sets the mixing angle θ_s, which controls the magnitude of the radiative Yukawa correction (eq. 6). Not fitted to data, but scanned within perturbativity.
  • yτ^L and yτ^R (individual third-generation couplings) = not specified; product fixed by mτ via eq. (6), individual values free
    The DM relic cross-section (eq. 17) depends on the sum of fourth powers (yτL)^4 and (yτR)^4, so individual couplings matter for DM even though only their product appears in the mass formula. The paper does not state that the DM-fitted points obey the mτ constraint.
  • y3^L = yb^R and y2^L = yc^R (t–c mixing ansatz) = set equal 'to obtain indicative values' (eq. 10)
    The Y_eff matrix and the t→ch branching ratio (eqs. 10, 14–16) are computed under this ad hoc equality, which is not a general consequence of the model. This is a hand-chosen assumption, not a fit or derivation.
axioms (5)
  • domain assumption The one-loop effective mass and Yukawa formulas of Ref. [16] apply unchanged (eq. 6), including the F(x,y) loop function and its limits.
    The paper states 'Our expressions for the masses and Yukawa couplings are identical to those in [16]' (Sec. II) and does not re-derive them; the extension to charm and ντ assumes these formulas carry over.
  • ad hoc to paper The softly broken U(1)_a, U(1)_ψ, U(1)_χ symmetries forbid tree-level Yukawa terms for τ, ντ, b, c, while the Z2 parity is exact.
    This is the model-building structure that makes the radiative mass mechanism work; it is imposed for this paper and not derived from a more fundamental theory (Sec. II).
  • domain assumption η does not acquire a VEV, and ϕ mixes with Re(η_low) at angle θ_s.
    Assumed to define the scalar mass eigenstates φ1, φ2 and the mixing relations (eqs. 3–4). Standard for this class of models.
  • ad hoc to paper The physical neutrino mass is explained by an unspecified further suppression (e.g., seesaw).
    Sec. II: 'The physical neutrino mass then must arise from further suppression... we do not consider any specific implementation.' The viability claims do not include this extra mechanism.
  • domain assumption Dark matter freeze-out is computed pre-EWSB using only the tree-level cross-section of eq. (17), with ψ_up being pseudo-Dirac and no substantial coannihilation.
    Sec. IV: the relic density uses ⟨σv⟩ from Ref. [37], with the assumption that the pre-EWSB regime dominates for TeV-scale mψ; the paper notes 'A more thorough investigation would be required'. No explicit check that the points also satisfy the τ mass relation.
invented entities (4)
  • ψ (vectorlike SU(2)-doublet fermion) independent evidence
    purpose: Mediates one-loop τ, ντ masses and Yukawa corrections via the yLL, yτR, yνR couplings; the upper component ψ_up is the dark matter candidate.
    Predicts modified κτ and κν (through y_eff), contributes to T, and has a DM relic abundance curve (Fig. 4) plus indirect limits from τ-like collider searches.
  • χ (vectorlike SU(2)-doublet quark, colour triplet) independent evidence
    purpose: Mediates one-loop b, c masses and Yukawa corrections and induces t–c mixing / t→ch.
    Coloured exotic that cannot decay only to SM fields due to Z2; direct searches give mχ ≳ 1 TeV as a typical bound; its loop effects generate the off-diagonal Y_eff (eq. 10).
  • η (complex SU(2) doublet scalar) independent evidence
    purpose: Couples exotics to SM fermions in the loop (yτR, ybR, ycR, yνR terms); mixes with ϕ to split scalar masses.
    Contributes to T and to the κ deviations; resembles a left-handed anti-slepton doublet, yielding collider bounds (mη ≳ 425 GeV when mψ ≪ mη).
  • ϕ (real singlet scalar) independent evidence
    purpose: Mixes with η_low to give φ1, φ2 mass eigenstates; the trilinear coupling a seeds the radiative mass generation.
    Affects T, the κ deviations, and the DM annihilation cross-section; resembles a right-handed anti-sneutrino in collider searches.

pith-pipeline@v1.3.0-alltime-deepseek · 9121 in / 15365 out tokens · 164092 ms · 2026-08-03T22:43:33.617216+00:00 · methodology

0 comments
read the original abstract

Measurements of Higgs boson Yukawa couplings to Standard Model (SM) fermions constrain radiative mass models for those species. Such models, motivated by the observed fermion mass hierarchy, act as foils for the SM tree-level mechanism: we cannot claim to have verified the standard mechanism if other possibilities also fit the data well. We construct a benchmark model which generates the top mass at tree level, and the bottom, charm, tau, and tau Dirac neutrino masses at one-loop level. Current theoretical and experimental constraints on the model, including from Higgs decays, demonstrate it possesses viable regions of parameter space. We show that future improvements to measurements will not be able to rule out the model, only increase the scale of new physics required, illustrating how difficult it will be to verify the SM fermion mass generation mechanism with great precision. As a bonus, a dark matter candidate is shown to be capable of reproducing the correct relic density within the permitted parameter space.

Figures

Figures reproduced from arXiv: 2511.08924 by Lucia Stockdale, Raymond R. Volkas.

Figure 1
Figure 1. Figure 1: FIG. 1. Mass generation (left) and effective Yukawa coupling (right) diagrams for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Theoretical and current 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Projected 2 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Exclusion plot with [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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  2. Probing the imaginary parts and their $q^2$ dependences for the tau $g-2$ and EDM

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