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REVIEW 4 major objections 3 minor 55 references

Search for pseudoscalar Higgs boson $A_0$ of the Bestest Little Higgs model at the LHC and FCC-hh

T0 review · 4 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper argues that the BLHM pseudoscalar Higgs A0 is most reachable at future hadron colliders through its one-loop WW and gg decays, yielding tens of events at mA0=500 GeV.

desk verdict Useful loop-decay compendium for the BLHM pseudoscalar, but the event-rate tables rest on a partonic narrow-width cross section treated as a hadronic cross section, so the headline numbers are not reliable. read the letter →

arxiv 2506.23500 v1 pith:4ISSV2AD submitted 2025-06-30 hep-ph

Y. Cervantes-Baltazar , E. Cruz-Albaro , A. Gutiérrez-Rodríguez , M. A. Hernández-Ruíz , D. Espinosa-Gómez This is my paper · ORCID
classification hep-ph PACS 12.60.-i14.80.Cp13.87.Ce
keywords BestestLittleHiggsmodelpseudoscalarbosongluonfusionone-loopdecaywidthsHL-LHCFCC-hheventratesA0
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 tries to establish that the pseudoscalar Higgs boson A0 of the Bestest Little Higgs model could be discovered at the LHC and at the proposed FCC-hh through gluon-fusion production followed by decay into WW, gg, ZZ, γγ, or γZ. It computes the relevant tree-level and one-loop decay widths and converts them into event counts using a narrow-resonance formula. If the central claim is right, the cleanest search channels are A0→WW and A0→gg, with about 10, 32, and 98 WW events at the HL-LHC, HE-LHC, and FCC-hh for mA0=500 GeV and tanβ=6.

What carries the argument

The load-bearing object is the narrow-resonance formula of Eq. (14), σ(gg→A0→Y) = (π/36) Γ(A0→gg) Γ(A0→Y) / ($mA0^{2}$ $Γ_A0^{2}$), which turns the computed partial decay widths into a production cross section at the resonance peak. The one-loop widths for A0→γγ, γZ, ZZ, gg, and WW are obtained by reducing the fermion-loop diagrams to scalar integrals using a standard loop-reduction scheme, with effective couplings listed in the appendix.

What would settle it

Recompute the hadronic cross section by convolving the partonic gg→A0 rate with a gluon density at μ=mA0 for center-of-mass energies of 14, 27, and 100 TeV; if the resulting WW event counts differ substantially from Tables I–VI, the missing density factor is the reason.

Watch

Extended reading notes

Core claim

The paper's central numerical claim is that, within the Bestest Little Higgs model at mA0=500 GeV and tanβ=6, the one-loop decays A0→WW and A0→gg give the largest gluon-fusion production rates, producing roughly 10, 32, and 98 WW events and 5, 16, and 48 gg events at the HL-LHC, HE-LHC, and FCC-hh, with little dependence on the new-physics scale f. At mA0=1000 GeV, the pseudoscalar would be within reach only at the FCC-hh, with about one event or fewer in the WW, gg, and ZZ channels. The tree-level decays A0→tt and A0→γtt dominate the branching ratio, while the one-loop gauge-boson modes that drive the search are rare but cleaner.

Load-bearing premise

The event counts depend on treating the resonance formula as the full proton–proton cross section, with no factor for the probability of finding a gluon inside a proton.

Editorial extensions

If this is right

  • At mA0=500 GeV and tanβ=6, the A0→WW channel yields about 10, 32, and 98 events at the HL-LHC, HE-LHC, and FCC-hh for f=1000 GeV.
  • The A0→gg channel yields about 5, 16, and 48 events at the same colliders and parameters.
  • At mA0=1000 GeV, only the FCC-hh appears within reach of discovery, through A0→WW, A0→gg, or A0→ZZ.
  • The gluon-fusion cross sections grow by up to two orders of magnitude as tanβ approaches 6, so larger tanβ improves discovery prospects.
  • The branching ratios are dominated by tree-level A0→tt and A0→γtt, while the one-loop gauge-boson branching ratios sit around 10^-4 to 10^-7.

Reading between the lines

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

  • If the missing gluon-density factor is supplied, all quoted event counts would rescale by the gluon luminosity at the pseudoscalar mass; the ranking of the WW and gg channels might survive, but the absolute numbers would shift.
  • Because A0→tt dominates the branching ratio, associated production with a top-quark pair, which the paper mentions as ongoing work, is a natural complement to the gluon-fusion channels.
  • The γZ final state stays at zero events in all benchmark tables, so it will not serve as a discovery channel at any of the considered colliders.
  • The same one-loop machinery could be applied to the charged Higgs states of the model, where W-associated final states would play a similar role.
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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

4 major / 3 minor

Summary. The paper studies the decays of the pseudoscalar Higgs boson A0 in the Bestest Little Higgs Model (BLHM), including two- and three-body tree-level decays and one-loop decays to γγ, γZ, ZZ, gg, and WW. It then estimates resonant production via gluon fusion and, using the integrated luminosities of the HL-LHC, HE-LHC, and FCC-hh, computes expected event counts for several decay channels as a function of f, tanβ, and mA0. The central quantitative claims are the event counts in Tables I-VI, with the A0→WW and A0→gg channels said to be the most promising.

Significance. If the results were correct, the paper would provide useful collider phenomenology for the BLHM pseudoscalar, extending earlier work by the same group and covering a broad set of final states. A strength is the inclusion of explicit one-loop amplitudes and the use of Package-X for the Passarino-Veltman reductions, which allows the loop-induced widths to be checked in principle. The paper also explores the dependence of the widths and branching ratios on the model parameters f and tanβ. However, the main production predictions are obtained from a partonic Breit-Wigner formula without gluon luminosity convolution, so the hadronic cross sections and all event counts derived from them are not physical predictions as they stand. The benchmark choice tanβ=6 also lies outside the bound given in Eq. (13). These issues affect the central claims of the paper.

major comments (4)
  1. [III.A, Eq. (14)] The expression σ(gg→A0→Y) = (π/36) Γ(A0→gg) Γ(A0→Y)/(mA0^2 ΓA0^2) is an on-peak partonic Breit-Wigner cross section for an initial gg state. It contains no gluon parton distribution function and no gg luminosity factor, yet in Tables I-VI it is multiplied directly by proton-proton integrated luminosity to obtain event counts. The correct hadronic cross section requires a convolution with the gluon-gluon luminosity, e.g., σ(pp→A0→Y) = (π^2/(8 mA0^3)) Γ(A0→gg) BR(A0→Y) τ dL_gg/dτ(τ, μF) with τ=mA0^2/s. Relative to Eq. (14), the missing factor is (9π/2)(ΓA0/mA0) τ dL_gg/dτ; for the mA0=500 GeV, tanβ=6 benchmark, with ΓA0≈0.4 GeV, this factor is of order 0.1 rather than 1 at 14 TeV. The event counts in Tables I-VI are therefore not reliable hadron-collider predictions.
  2. [III and Tables I-VI, Eq. (13)] The benchmark tanβ=6 used in Tables I-VI exceeds the upper bound given by Eq. (13). Using mA0=500 GeV, mh0=125 GeV and v=246 GeV, Eq. (13) gives tanβ_max≈5.9. The quoted event counts at tanβ=6 are therefore outside the theoretically allowed parameter space stated in the same paper. This should be corrected before any numerical conclusions are drawn.
  3. [II.B and Figs. 4-5] The three-body decay widths that determine ΓA0 and the branching ratios in Figs. 4 and 5 are computed numerically, but the manuscript provides only the generic phase-space formula Eq. (3) and the amplitudes Eqs. (4)-(7). No numerical integration method, phase-space cuts, or validation is described. Since ΓA0 enters the denominator of Eq. (14), the cross-section predictions depend on this undocumented numerical step, which makes the results difficult to reproduce or assess.
  4. [IV and Tables I-VI] The conclusion that the A0→WW and A0→gg channels are 'very promising scenarios' is based solely on expected signal event counts. No background estimates, selection efficiencies, or statistical significance are provided, so the stated discovery potential is not supported. This is particularly important because the corrected event rates after including the gluon luminosity factor are likely to be substantially lower.
minor comments (3)
  1. [Appendix A, Table IX] There are several typographical issues in the effective-coupling tables, for example the expression for gA^ZT6T6 appears to contain an extra factor of g, and some entries mix sβ/cβ with s2β/c2β without consistent notation. These should be cleaned up and each coupling checked for dimensional consistency.
  2. [III, Fig. 7] The horizontal axis of Fig. 7 is labelled in TeV while the text quotes mass values in GeV (mA0 ∈ [500, 2000] GeV); the units should be made consistent to avoid ambiguity.
  3. [Eq. (14) reference] The Breit-Wigner formula is attributed to Ref. [41] (PDG), but the reference does not by itself justify the use of the formula as a hadronic cross section. The paper should provide a proper derivation or cite a source that includes the PDF luminosity factor.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the A0 widths, cross sections, and event counts are computed from stated BLHM couplings and luminosities; the Eq. (14) PDF omission is a numerical-approximation concern, not a constructional reduction.

full rationale

The derivation chain is not circular. The partial widths in Eqs. (1)-(12) are functions of the effective couplings tabulated in Appendix A; the production cross section in Eq. (14) is the standard on-peak Breit-Wigner expression built from those widths; and the event counts in Tables I-VI are L*sigma. No parameter is fitted to the predicted counts, and no equation equals its input by construction. The paper's reliance on earlier work by the same group for BLHM Feynman rules and couplings (e.g., Refs. [16-18,38-40]) is a self-citation, but the couplings are also displayed and trace to the external BLHM, so it is not load-bearing. The genuine weakness is physical, not circular: Eq. (14) is a partonic on-resonance formula with no gluon PDF luminosity convolution, so the hadron-level event numbers may be unreliable; the paper itself labels it "an approximate description... just at the resonance." An incorrect or over-simplified approximation is a correctness risk and does not make the derivation equivalent to its inputs.

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

The paper introduces no new particles; A0 is a preexisting prediction of the BLHM. The free parameters are the model inputs scanned or fixed as benchmarks. The most consequential assumption is that Eq. (14) can be used as a hadronic cross section without PDFs, which is effectively an ad hoc modeling choice.

free parameters (4)
  • f (new physics scale) = scanned 1000-2000 GeV
    Controls the masses of new heavy quarks and gauge bosons; central input for all widths and cross sections.
  • tan beta = scanned 1-6
    Ratio of Higgs doublet vevs; the paper notes cross sections grow by up to two orders of magnitude as beta approaches 1.4 rad.
  • mA0 (pseudoscalar mass) = 500 GeV for event tables; scanned 500-2000 GeV
    Sets the resonance mass; event counts are quoted for 500 and 1000 GeV benchmarks.
  • Yukawa couplings y1, y2, y3 = 0.61, 0.84, 0.35
    Enter the effective couplings such as gA0tt and gA0bb; values are taken from prior BLHM papers.
assumptions (3)
  • domain assumption The BLHM effective couplings are correctly given by Refs. 16-18, 38-40 and Appendix A.
    All decay widths and cross sections are computed from these couplings, which the paper does not rederive.
  • standard math The one-loop amplitudes for A0 to gamma-gamma, gamma-Z, ZZ, gg, WW are UV finite and correctly evaluated with Package-X.
    The paper states the diagrams are free of ultraviolet divergences, but provides no independent verification or cross-check against published results.
  • ad hoc to paper Eq. (14), sigma(gg to A0 to Y) = (pi/36) Gamma_gg Gamma_Y / (mA0^2 Gamma_A0^2), gives the hadronic production cross section without any gluon PDF convolution.
    This formula is used directly with integrated luminosities to produce event tables; it contains no parton luminosity factor, which is the load-bearing assumption of the quantitative results.

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Cite this review

Pith. "Pith review of Search for pseudoscalar Higgs boson $A_0$ of the Bestest Little Higgs model at the LHC and FCC-hh." pith.science (2026). https://pith.science/paper/4ISSV2AD

@misc{pith2026250623500,
  author       = {Pith},
  title        = {Pith review of: Search for pseudoscalar Higgs boson $A_0$ of the Bestest Little Higgs model at the LHC and FCC-hh},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4ISSV2AD}},
  note         = {Machine review of arXiv:2506.23500}
}
abstract

We analyse the sensitivity of the Large Hadron Collider (LHC) and the Future Circular Collider-hadron-hadron (FCC-hh) to the existence of pseudoscalar Higgs boson $A_0$ predicted by the Bestest Little Higgs model. We study the tree-level (two and three body) and one-loop decays of the pseudoscalar, $A_0 \to b\bar b, t \bar t, \gamma t\bar t, \gamma b \bar b, Zt\bar t, Zb \bar b, Wt\bar b, h_0 t \bar t, h_0 b \bar b$, and $A_0 \to \gamma\gamma, \gamma Z, ZZ, gg, WW$, respectively. In addition, we perform a phenomenological study of the production of the pseudoscalar $A_0$ via gluon fusion $gg \to A_0 \to Y$ processes, where $Y \equiv \gamma\gamma, \gamma Z, ZZ, gg, WW$. From the cross section of the processes of interest and the expected integrated luminosity of the LHC and FCC-hh, we determined the number of events that could be produced in both colliders.

Figures

Figures reproduced from arXiv: 2506.23500 by the authors.

Figure 1
Figure 1. FIG. 1: Feynman diagrams corresponding to the tree-level two-b [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Feynman diagrams corresponding to the tree-level three [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Feynman diagrams corresponding to the two-body decays [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Decay widths for the [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: , in this scenario we generate curves by varying the β parameter while keeping the other parameter, f, fixed at 1000 GeV. In the corresponding figure, we see that the two main contributions are Br(A0 → tt¯) ≈ 8.92×10−1 and Br(A0 → γtt¯) = [9.80, 9.81]×10−2 when β ∈ [ta…
Figure 6
Figure 6. Figure 6: FIG. 6: Production cross section of the pseudoscalar [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Production cross section of the pseudoscalar [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

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Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.