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REVIEW 3 major objections 6 minor 25 references

In a two-Higgs-doublet model with a Z3 flavor symmetry, the charged Higgs can decay predominantly to bottom and charm quarks (branching ratio ≈70%), and two benchmark points at 130 GeV reproduce the ATLAS 2.5σ excess and would be visible at

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2026-08-02 21:24 UTC pith:FDWXLP7B

load-bearing objection A solid existence proof for a Z3-flavored 2HDM with dominant H±→cb, but the claimed ATLAS excess 'reproduction' is a postdiction from two selected scan points, so the LHeC projections are illustrative, not robust predictions. the 3 major comments →

arxiv 2602.20244 v2 pith:FDWXLP7B submitted 2026-02-23 hep-ph

Charged Higgs Decay to Bottom and Charm Quarks from Z₃-Flavored Two Higgs Doublet Models

Alfredo Aranda , J. Hern\'andez-S\'anchez , Andrea Montiel , R. Noriega-Papaqui This is my paper
classification hep-ph
keywords charged Higgstwo Higgs doublet modelZ3 flavor symmetryH±→cb decayflavor-changing couplingsATLAS 2.5σ excessLHeC prospectsParticle Swarm Optimization
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 argues that a Z3 flavor symmetry in a two-Higgs-doublet model can naturally produce a large flavor-changing charged-Higgs coupling to bottom and charm quarks, making H±→cb the dominant decay with branching ratio around 70%. Two benchmark parameter points with mH±=130 GeV sit inside the ATLAS 2.5σ excess in BR(t→H±b)×BR(H±→cb), and the same points give signal-to-background ratios of 4.8 and 7.04 in e−p collisions at the proposed LHeC with 100 fb−1. If correct, this is a proof of concept that a discrete flavor symmetry, rather than ad hoc alignment, can account for the observed cb excess and point to a concrete search channel for a light charged Higgs.

Core claim

The paper's central claim is that the Z3-flavored two-Higgs-doublet model can generate an enhanced flavor-changing coupling between the charged Higgs, charm, and bottom quarks. In the Type-A configuration with tanβ=10, the coupling X23 reaches values around 4 while the competing coupling Y23 stays near 0.1, so H±→cb dominates with branching ratios of 68% and 61% for the two benchmark points at mH±=130 GeV. These two points reproduce the observed ATLAS 2.5σ excess in BR(t→H±b)×BR(H±→cb), and a parton-level simulation of e−p→H−νb followed by H−→bc yields signal-to-background ratios of 4.8 and 7.04 at 100 fb−1 at the LHeC. The enhancement is traced to the Z3 charge assignments, which give the q

What carries the argument

The central object is the Z3 flavor symmetry acting on the quark sector, whose charge assignments force the Yukawa matrices into block textures with zeros wherever the Z3 charge is not conserved. After electroweak symmetry breaking, the quark mass matrices display a flipped vev structure: tanβ multiplies complementary blocks in the up and down sectors. A Particle Swarm Optimization algorithm fits the arbitrary texture coefficients aij and bij so that the model reproduces the measured quark masses and CKM mixing; the rotated couplings Xij and Yij then control the charged-Higgs decays. The argument's load-bearing hierarchy is X23≈4 at tanβ=10 in the Type-A configuration, which makes H±→cb the

Load-bearing premise

The argument depends on an unforced technical assumption — that the Yukawa coupling matrices are Hermitian — and on the freedom of a numerical fit to choose the texture coefficients; if either is relaxed, the benchmark points that sit on the ATLAS excess need not survive.

What would settle it

An updated ATLAS or CMS measurement of BR(t→H±b)×BR(H±→cb) at mH±=130 GeV that shows no excess would remove the main experimental anchor of the paper. Alternatively, re-running the parameter scan with non-Hermitian Yukawa matrices (or different PSO weighting) and finding no benchmark point in the ATLAS-allowed region would show the result is an artifact of those assumptions.

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

If this is right

  • A 130 GeV charged Higgs in this model would show up mainly through H±→cb, so LHC and LHeC searches that tag a bottom and a charm jet are the right place to look.
  • The two benchmark points lie inside the ATLAS 2.5σ excess window, meaning the Z3-flavored 2HDM is one of the few parameterizations that can match that anomaly without violating existing flavor and Higgs constraints.
  • At the LHeC with 100 fb−1, the predicted significance (4.8 and 7.04) is at or near the common 5σ discovery threshold, so the channel is testable in a single run.
  • For Type-A, the branching ratio to cb is about 70% or higher for tanβ=5,10, while Type-B also gives cb dominance with 60–90%, so the cb final state is a robust signature of the Z3 texture rather than a single fine-tuned point.

Where Pith is reading between the lines

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

  • Strictly, the Z3 symmetry alone does not force X23≈4; the Hermiticity assumption and the PSO-fitted coefficients do. So the paper demonstrates that such a coupling can arise in this symmetry setting, not that the symmetry predicts it.
  • A natural next step is to repeat the fit without Hermiticity or with different random seeds to see how often points in the ATLAS excess region appear; that fraction would measure how robust the benchmark points are.
  • Because the leptons are assigned trivial Z3 charges, extending the symmetry to the lepton sector could connect the cb-enhanced charged Higgs to neutrino mixing and lepton-flavor violation, possibly yielding correlated predictions for H±→τν and μ→eγ.
  • The LHeC significance numbers come from a parton-level selection; a full detector-level analysis with systematic uncertainties could shift the projected 4.8 and 7.04 values, so those numbers are a first estimate rather than a guaranteed discovery.

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

3 major / 6 minor

Summary. The paper analyzes a two-Higgs-doublet model with a Z3 flavor symmetry acting on the quark sector and two Higgs doublets. The charge assignments force a 'flipped' texture in the Yukawa matrices, so that the charged-Higgs couplings to down-type quarks can be enhanced. The authors use Particle Swarm Optimization to fit the Yukawa texture coefficients to quark masses and the CKM matrix, then impose flavor constraints (b→sγ, B0–B0 mixing, neutron EDM), Higgs coupling constraints (κ-framework), and existing ATLAS limits on BR(t→H±b)×BR(H±→cb). For THDMZ3 Type-A with tanβ=10 and mH±=130 GeV, they identify two benchmark points (BP-I, BP-II in Table 2) that sit on the 2.5σ ATLAS excess. For these points they simulate e−p→H−ν¯q at the LHeC with 100 fb−1 and report S/√B = 4.8 and 7.04. The central claim is that in this Z3-flavored 2HDM the charged Higgs can have a dominant H±→cb decay and that the model can reproduce the ATLAS excess while remaining consistent with a wide set of low-energy constraints.

Significance. If the result is robust, the paper provides an interesting existence proof: a discrete flavor symmetry can yield a large flavor-changing H±cb coupling without immediate conflict with flavor constraints, and the LHeC could discover a light charged Higgs in the cb channel. The authors have also made their PSO code publicly available, which is a strength. However, the central phenomenological claim—'reproduction' of the ATLAS excess—is a postdiction from two hand-picked benchmark points, and the Hermiticity assumption on the Yukawa matrices is an extra input not required by the Z3 symmetry. The paper would be significantly strengthened by quantifying how much of the allowed parameter space actually predicts the excess, and by assessing the sensitivity to the Hermiticity assumption. The LHeC projection is a useful addition, but the quoted S/√B values carry no systematic uncertainties and should be interpreted cautiously.

major comments (3)
  1. [Section 3.1, after Eq. (10)] The Hermiticity assumption on the Yukawa matrices Y^q_i is an ad hoc input, not a consequence of the Z3 flavor symmetry. The large X23~4 and small Y23~0.1 values in Table 2—which are essential for H±→cb dominance and for reproducing the ATLAS excess—arise from this assumption together with the unrestricted coefficients a_ij, b_ij in Eq. (12). The paper does not test how the benchmark points or the branching ratios change if Hermiticity is relaxed, nor does it provide a symmetry argument for why Hermiticity should hold. This is a load-bearing assumption for the central claim, and the robustness of the result needs to be demonstrated (e.g., by a scan over non-Hermitian textures or a stability analysis around the benchmark points).
  2. [Section 3.3, Figure 6] The two benchmark points are selected post hoc from a PSO scan because they lie within the ATLAS 2.5σ excess at mH±=130 GeV. The paper does not report the total number of scanned parameter sets, the number of points that survive all constraints, or the fraction of those points that predict the observed excess. Without this information, the 'reproduction' is a fit rather than a robust prediction. The authors should provide a coverage statement: for example, how many of the tanβ=10 Type-A survivors give BR(t→H±b)×BR(H±→cb) within the 2.5σ band, and what the distribution looks like. This is essential to assess whether the agreement with ATLAS is a meaningful test of the model or an artifact of the selection.
  3. [Section 4, Tables 3–4] The LHeC S/√B values of 4.8 and 7.04 are computed for only the two selected benchmark points and do not include systematic uncertainties. The simulation relies on a specific set of selection efficiencies (b-tagging, jet reconstruction, mass-window cuts) taken from Ref. [20]. To support the claim that the signal is 'viable', the authors should include realistic systematic uncertainties (e.g., PDF, scale, b-tagging efficiencies) and show how the significance changes. Without this, the quoted S/√B values are optimistic and do not yet establish discovery potential.
minor comments (6)
  1. [Section 2, charge assignments] The assignment reads '[d1] = 1, [d2] = [d1] = 2'. This is likely a typo for '[d2] = [d3] = 2'. Please correct and verify the consistency of the textures in Eqs. (9)–(10).
  2. [Section 3.1, after Eq. (10)] Typo: 'ad additional assumption' should be 'an additional assumption'. Also, in Eq. (8) 'Yuakawa' should be 'Yukawa'.
  3. [References] Reference [10] is malformed: it contains an unexplained 'Phys. Lett. B 742 (2015), 347-352 ...' entry that appears to be a separate citation inserted into the middle of the PSO reference. Please clean up the bibliography.
  4. [Section 3.2, Eq. (27)] The constraint in Eq. (27) is applied at mH±=100 GeV, while the benchmark points are at 130 GeV. Clarify whether the bound is taken to be mH±-independent or whether the analysis was repeated at the benchmark mass.
  5. [Abstract] The abstract states the model can 'reproduce the ATLAS excess'. Given the post-hoc selection of benchmark points, I recommend softening this to something like 'can accommodate the reported excess' and to state in the abstract that this is achieved in a specific benchmark scenario.
  6. [Figure 5] The captions for the Type-A and Type-B panels are not clearly distinguished in the text; the reader must infer that the colored curves correspond to different tanβ values. Please label the curves or add a legend.

Circularity Check

1 steps flagged

The 'reproduction' of the ATLAS 130 GeV excess is a selection effect: the two benchmark points are chosen because they sit on the excess, and the LHeC signal significance is then quoted at exactly those pre-selected points.

specific steps
  1. fitted input called prediction [Section 3.3, paragraph after Fig. 5; Table 2; Section 4, Tables 3-4]
    "In particular, focusing on the largest excess in the data for mH ± = 130 GeV reported by ATLAS [6] (with a global significance around 2.5σ ...), only two points with tan β = 10 can reproduce this slight excess, as shown in Figure 6. These benchmark points are taken as prospect for discovering a light charged Higgs boson in the future Large Hadron electron Collider (LHeC)"

    The benchmark points are not derived from the Z3 texture alone; they are defined as the two PSO/constraint survivors that sit on the ATLAS 130 GeV excess. Thus the paper's statement that the model 'reproduces' the excess is the selection rule, not an independent model prediction. The Table 2 couplings X23≈4.33/3.39 and Y23≈0.087/0.019, and the consequent BR(H±→cb)≈60-70%, are properties of those selected points, where aij, bij are arbitrary coefficients subject only to quark-mass/CKM constraints plus an extra Hermiticity assumption. The LHeC S/√B=4.8 and 7.04 in Table 4 are computed at exactly the two points chosen to match the ATLAS input, so the claimed LHeC 'viability' is conditional on that fitted/selected input rather than being a robustness prediction of the symmetry model.

full rationale

The algebraic core of the paper—the Yukawa textures from the Z3 assignments, the diagonalization in Eq. (8)-(11), and the coupling formulas in Eqs. (16)-(26)—is self-contained and not circular: Xij and Yij are computed from the fitted mass matrices via well-defined formulas, and the PSO fit to quark masses and CKM entries uses external data. The self-citations to [11] and [20] are method/parametrization references by overlapping authors, but they are not the load-bearing evidence for the central excess claim and do not by themselves constitute circularity. The circular element is the benchmark-point selection: BP-I and BP-II are chosen after inspecting the ATLAS 130 GeV excess, then the same selected points are used to demonstrate both the 'reproduction' of the excess and the large LHeC significance. This makes the headline result a postdiction/fit rather than a parameter-free prediction; the model's predictive reach is weakened because the 16 Hermitian coefficients leave a large unconstrained space, and no measure is given of how typical the excess-matching points are. The LHeC simulation itself is a genuine forward calculation for those points, so the circularity is partial, not total.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 1 invented entities

The central claim leans on a large set of fitted Yukawa coefficients, a hand-picked Z3 charge assignment, and an ad hoc Hermiticity assumption. The Z3 symmetry does organizational work, but the numerical enhancement is not a parameter-free prediction.

free parameters (3)
  • Yukawa texture coefficients a_ij, b_ij = not reported directly; PSO output only through couplings such as X22≈126-187, X23≈3.4-4.3, Y23≈0.02-0.09
    In Eq. (12), these arbitrary coefficients are fitted by PSO to reproduce quark masses and the CKM matrix; they directly determine X_ij,Y_ij and therefore the H±→cb branching ratio.
  • tan β = scanned over 1, 2, 5, 10, 20; surviving BPs use tanβ=10
    Chosen by hand; the benchmark-point selection and the resulting BR(H±→cb) ~ 70% depend on tanβ=10.
  • Scalar masses and mixing angles (mH±, mH0, mA0, α/β) = mH±=130 GeV for BPs; 160≤mH0≤260 GeV; mA0>mH±; cos(β−α)≤0.008
    Selected within allowed ranges to target the ATLAS excess; there is no independent determination of these values.
axioms (6)
  • ad hoc to paper Z3 flavor symmetry with specified charge assignments ([Q1]=2, [Q2]=[Q3]=1, [u1]=0, [u2]=[u3]=1, [d1]=1, [d2]=[d3]=2, [H1]=2, [H2]=0)
    Posted without independent motivation; it is engineered to produce the flipped mass-matrix textures in Eq. (7).
  • ad hoc to paper Yukawa matrices Y^q_i are Hermitian
    Assumed after Eq. (10) to simplify diagonalization; not imposed by the Z3 symmetry or any other principle.
  • domain assumption CP conservation in the scalar sector
    Stated in Section 2; restricts the scalar potential but is a standard simplifying assumption.
  • domain assumption Quark Yukawa sector only; leptons are set to Z3-trivial and ignored
    The analysis deliberately omits lepton mixing and neutrino masses, so constraints from lepton flavor are not evaluated.
  • domain assumption The 2HDM scalar potential with soft Z3-breaking term and the chosen mass spectrum satisfies theoretical and electroweak precision constraints
    Used to define mh0=125 GeV, mH0, mA0, mH±, and cos(β−α) ranges in Section 3.1.
  • standard math Trace/determinant eigenvalue relations (Eqs. 13-15) reduce the PSO parameter space
    Algebraic identities for the eigenvalues of M_q†M_q, used to constrain the fitted Yukawa coefficients.
invented entities (1)
  • Z3 flavor symmetry (with assigned charges) no independent evidence
    purpose: Restrict Yukawa textures so that the charged Higgs has an enhanced flavor-changing cb coupling.
    No external evidence for this symmetry; it is introduced to generate the desired mass-matrix textures. It yields a falsifiable H±→cb enhancement, but only after parameter selection.

pith-pipeline@v1.3.0-alltime-deepseek · 11696 in / 16725 out tokens · 155213 ms · 2026-08-02T21:24:00.733924+00:00 · methodology

0 comments
read the original abstract

The phenomenology of a charged Higgs present in a model with two Higgs SU(2) doublets and a $Z_3$ flavor symmetry is analyzed. It is shown that it is possible to generate an enhancement of its flavor changing coupling to c and b quarks and also to reproduce the ATLAS excess associated to the process $H^\pm \to bc$ for a charge Higgs mass of $130$~GeV. Furthermore, by considering the possibility of a search at the future LHeC, the analysis suggests viability for its detection.

Figures

Figures reproduced from arXiv: 2602.20244 by Alfredo Aranda, Andrea Montiel, J. Hern\'andez-S\'anchez, R. Noriega-Papaqui.

Figure 1
Figure 1. Figure 1: Left: Values of Vct and Vut for sets of parameters ⃗s = (aij , bij ) that reproduce quark masses values and VCKM entries (other than Vct and Vut) for three values of tan β. The small rectangular area corresponds to the experimentally allowed values of Vct and Vut where only 125 sets remain (25 for each value of tan β). Right: A zoom of the region containing sets consistent with all quark masses and VCKM en… view at source ↗
Figure 2
Figure 2. Figure 2: We apply, to the survivor parameter space, one of the strongest experimental limits at low energies b → sγ and B0 − B0 mixing. The shaded region is the allowed by both constraints. Summarizing: the benchmark points candidates selected are the ones with mh0 = 125 GeV, mA0 > mH± , 160 GeV≤ mH0 ≤ 260 GeV, and 80 GeV ≤ mH± ≤ 160 GeV with cos (β − α) ≤ 0.008 for tan β = 2, 5, 10, and 20. κi CMS or ATLAS Run 2 T… view at source ↗
Figure 3
Figure 3. Figure 3: Considering the points that survive in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: BR(H± → cb, cs, τν) for the benchmark points of the model. The effect of the Z3 flavor symmetry on the quark sector can be seen in the enhancement of the channel decay H± → cb, which is dominant with BR ∼ 70% for tan β = 5, 10, 20. The upper panel shows the THDMZ3 Type-A case while the THDMZ3 Type-B case in shown on the bottom panel. 10, and 20 ), and the BR(cb) > 70% (BR(cb) = 60 − 90% ) can be reached. T… view at source ↗
Figure 5
Figure 5. Figure 5: BR(t → H±b)BR(H± → cb)% vs. tan β, benchmark points of the model are selected. The upper panel shows the THDMZ3 Type-A case while the THDMZ3 Type-B case in shown on the bottom panel. The shaded region is the allowed region for the experimental data of LHC [6]. state topologies, and an improvement of the kinematical reconstruction of observables that involve Higgs-fermion interactions. As such, the LHeC cou… view at source ↗
Figure 6
Figure 6. Figure 6: Contribution to BR(t → H±b)BR(H± → cb)% as a function of mH± for three bench￾mark points of the model (solid lines in orange, blue and red). Only the two benchmark points corresponding to blue and red lines are in agreement with the slight excess for mH± = 130 GeV reported by the ATLAS Collaboration [6]. and mH± = 130 GeV. Following the analysis presented in [20] with the benchmark points in [PITH_FULL_IM… view at source ↗
Figure 7
Figure 7. Figure 7: Distributions for (mH± − 20 GeV) < M((btag, jc)) < mH± , where M((btag, jc)) is the invariant mass of two central jets for mH± = 130 GeV. BP Event (raw) Selection I Selection II Selection III Selection IV S/ √ B BP-I 7643 917 558 412 183 4.8 BP-II 11126 1134 812 600 266 7.04 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗

discussion (0)

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Reference graph

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