{"id":"883387b2-db70-454a-8b64-d5dd77f82301","arxiv_id":"2506.23500","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Within the Bestest Little Higgs model, a 500 GeV pseudoscalar A0 produced by gluon fusion is estimated to yield about 10 to 100 events in the WW and gg channels at the HL-LHC and FCC-hh for the chosen benchmarks.","lead":"This paper computes decay widths and expected gluon-fusion production rates for the pseudoscalar Higgs boson A0 of the Bestest Little Higgs model at the HL-LHC, HE-LHC, and FCC-hh. The claimed event counts are small, at most about 100 events, but the production cross section is estimated with a simplified formula that omits the gluon parton luminosity.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (14) is an on-peak partonic Breit-Wigner cross section, not a proton-proton cross section; multiplying it by integrated luminosity in Tables I-VI skips the gluon-PDF convolution, so the event-count predictions are not grounded.","rationale":"The paper's useful content is the compendium of decay widths and branching ratios for the BLHM pseudoscalar, and the relative ordering of channels may be informative. However, the central claim is the expected number of signal events at hadron colliders, and every event count in Tables I-VI is obtained by multiplying an integrated luminosity by sigma from Eq. (14). That formula, as written, is an on-peak partonic cross section in the narrow-width approximation and is missing the convolution with the gluon parton distributions. This is not a minor normalization issue: the missing factor contains the gluon luminosity tau dL_gg/dtau, which is substantial, and the order of magnitude of the correction is controlled by Gamma_A0/m_A0, a small parameter that the paper's own branching-ratio analysis determines to be roughly 1e-3. The correction factor can therefore be as large as an order of magnitude at some of the colliders discussed. The reader's weakest_assumption identifies exactly this issue, and my independent check of the derivation agrees. I also note that even after correcting the cross section, the paper does not include backgrounds, detector acceptances, or selection efficiencies, so the sensitivity statements would still need additional work; but the first and most load-bearing break in the argument is Eq. (14) and its use in Tables I-VI. I therefore agree with the reader's REJECT verdict, and my assessment does not change it.","tokens_in":16903,"tokens_out":10880,"duration_ms":112767,"concrete_test":"Recompute Tables I-VI with the standard LO narrow-width hadronic formula sigma(pp -> A0 -> Y) = (pi^2/(8 m_A0^3)) Gamma(A0 -> gg) BR(A0 -> Y) [tau dL_gg/dtau], evaluated with NNPDF4.0 at factorization scale mu_F = m_A0 for sqrt(s) = 14, 27, and 100 TeV, using the same BLHM partial widths and total widths as in the paper. If any table entry changes by more than a factor of about 2, or if the recomputed HL-LHC A0 -> WW count drops below one event, then the paper's event-count claims and the conclusion that these channels are 'very promising' are unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is the expected number of signal events at the HL-LHC, HE-LHC, and FCC-hh, obtained as integrated luminosity times the cross section from Eq. (14). But Eq. (14) is the on-peak partonic gg -> A0 -> Y Breit-Wigner expression: it contains no gluon parton distribution functions and no gg luminosity factor. The correct hadronic narrow-width cross section requires a convolution with the gluon PDF luminosity, sigma(pp -> A0 -> Y) = (pi^2/(8 m_A0^3)) Gamma(A0 -> gg) BR(A0 -> Y) [tau dL_gg/dtau](tau, mu_F) with tau = m_A0^2/s, plus appropriate scale choice. Relative to Eq. (14), the missing factor is (9 pi/2)(Gamma_A0/m_A0) tau dL_gg/dtau. For the benchmark mA0 = 500 GeV, the authors' own numbers imply Gamma_A0 ~ 0.4 GeV (from Br(A0 -> tt) ~ 0.892 and Gamma(tt) around 0.34 GeV at tan beta = 6), so Gamma_A0/m_A0 ~ 8e-4. Multiplying by tau dL_gg/dtau, which is O(10) at 14 TeV and larger at higher energies, gives a correction factor of order 0.1-1, not an O(1) factor. Thus the event counts in Tables I-VI are not reliable hadron-collider predictions as stated; the claim of approximately 10, 32, and 98 A0 -> WW events at the three colliders is not established by the calculation presented.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":17269,"tokens_out":9716,"duration_ms":116525,"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":[{"comment":"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.","section":"III.A, Eq. (14)"},{"comment":"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.","section":"III and Tables I-VI, Eq. (13)"},{"comment":"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.","section":"II.B and Figs. 4-5"},{"comment":"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.","section":"IV and Tables I-VI"}],"minor_comments":[{"comment":"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.","section":"Appendix A, Table IX"},{"comment":"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.","section":"III, Fig. 7"},{"comment":"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.","section":"Eq. (14) reference"}],"recommendation":"major_revision","confidential_remarks":"The PDF-luminosity omission is a genuine, load-bearing error: it changes the central numerical predictions by a large factor and would require recomputation of all event tables. The tanβ=6 benchmark is also outside the paper's own bound in Eq. (13). I nevertheless chose major_revision rather than reject because these issues can in principle be corrected within the scope of the paper, though the corrected conclusions may be weaker than those advertised. The reliance on the authors' previous papers for the effective couplings and the lack of independent numerical validation for the three-body widths also make the calculation difficult to reproduce."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know that the event counts in Tables I-VI are not grounded: Eq. (14) is the on-peak partonic Breit-Wigner cross section for gg -> A0 -> Y, and the authors multiply it directly by integrated luminosity. The hadronic cross section needs a convolution with the gluon PDF luminosity, tau dL_gg/dtau. For mA0 = 500 GeV at 14 TeV that missing factor is O(10), and the correction relative to Eq. (14) is about an order of magnitude down, not an O(1) nuisance. So the headline claim of ~10, 32, 98 A0 -> WW events at HL-LHC, HE-LHC, and FCC-hh is not established by the calculation as presented.\n\nWhat is actually new: the one-loop partial widths for A0 -> gamma-gamma, gamma-Z, ZZ, gg, and WW in the BLHM, computed with Passarino-Veltman reduction and Package-X, appear absent from the cited literature. The branching-ratio curves and the dependence on f, tan(beta), and mA0 are a reasonable first reference. The tree-level three-body amplitudes are written down, and the loop widths are explicitly free of UV divergences.\n\nSoft spots, in proportion. The PDF omission is the load-bearing flaw, and it invalidates the event-rate section, not the decay-width part. A second soft spot: the three-body widths that dominate the branching ratios are shown only as plots; no analytic expressions or numerical tables are given, so those branching ratios are not independently checkable from the paper. Minor: the sensitivity claims are just event-count arithmetic, with no backgrounds or detector effects.\n\nWho this is for: phenomenologists working on Little Higgs models who want a first map of A0 loop-induced decay modes. The loop calculation itself seems substantial and could be salvaged. I would not cite this version, but I would send it to a referee with a clear request to check the cross-section normalization; if the PDF factor is confirmed missing, the event tables need to be redone before the paper can be used for collider studies.","headline":"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.","tokens_in":17872,"tokens_out":4451,"would_cite":false,"duration_ms":46169,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.60.-i","14.80.Cp","13.87.Ce"],"model":"deepseek-v4-flash","headline":"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.","keywords":["Bestest Little Higgs model","pseudoscalar Higgs boson","gluon fusion","one-loop decay widths","HL-LHC","FCC-hh","event rates","A0 boson"],"falsifier":"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.","tokens_in":16685,"feed_emoji":"⚛️","tokens_out":6707,"duration_ms":69233,"temperature":0.7,"pith_summary":"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.","feed_headline":"Tens of pseudoscalar-Higgs events predicted at three colliders","feed_subtitle":"In the Bestest Little Higgs model, A0 to WW gives 10, 32, and 98 events at the HL-LHC, HE-LHC, and FCC-hh.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the Bestest Little Higgs model and its pseudoscalar sector.","marker":"[13]"},{"why":"Sets the Yukawa parameter values used in the numerical benchmarks.","marker":"[16]"},{"why":"Sets the allowed range for the new-physics scale f.","marker":"[17]"},{"why":"Supplies the Feynman rules and effective couplings used for the decay amplitudes.","marker":"[18]"},{"why":"Is the source of the narrow-resonance cross-section formula in Eq. (14).","marker":"[41]"},{"why":"Provides the loop-integral reduction used for the one-loop decay widths.","marker":"[44]"},{"why":"Used to evaluate the scalar loop functions appearing in the one-loop widths.","marker":"[45]"},{"why":"Motivates the mA0=500 GeV benchmark point used for the event counts.","marker":"[47]"}],"fun_headline_variants":["Pseudoscalar Higgs may give ~100 WW events at FCC-hh","WW decays reveal pseudoscalar Higgs at LHC and FCC-hh","Pseudoscalar Higgs: FCC-hh could rack up 98 WW events","WW channel best bet for pseudoscalar Higgs at future colliders","Bestest Little Higgs pseudoscalar: up to 98 WW events"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Pseudoscalar Higgs may give ~100 WW events at FCC-hh","WW decays reveal pseudoscalar Higgs at LHC and FCC-hh","Pseudoscalar Higgs: FCC-hh could rack up 98 WW events","WW channel best bet for pseudoscalar Higgs at future colliders","Bestest Little Higgs pseudoscalar: up to 98 WW events"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001277,"raw_usage":{"total_tokens":5241,"prompt_tokens":985,"completion_tokens":4256,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":601,"completion_tokens_details":{"reasoning_tokens":4155}},"tokens_in":601,"tokens_out":4256,"duration_ms":29443,"temperature":1.0,"reasoning_tokens":4155,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:42:14.508572+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Schmaltz, Nucl","cited_arxiv_id":null,"evidence_quote":"Defines the Bestest Little Higgs model and its pseudoscalar sector."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Sets the Yukawa parameter values used in the numerical benchmarks."},{"cited_title":"Chang and J","cited_arxiv_id":null,"evidence_quote":"Sets the allowed range for the new-physics scale f."},{"cited_title":"Schmaltz, JHEP 08, 056 (2004)","cited_arxiv_id":null,"evidence_quote":"Supplies the Feynman rules and effective couplings used for the decay amplitudes."},{"cited_title":"Aad et al","cited_arxiv_id":null,"evidence_quote":"Is the source of the narrow-resonance cross-section formula in Eq. (14)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the loop-integral reduction used for the one-loop decay widths."},{"cited_title":"Cruz-Albaro, A","cited_arxiv_id":null,"evidence_quote":"Used to evaluate the scalar loop functions appearing in the one-loop widths."},{"cited_title":"New physics search with the new gauge boson $Z'$ of the bestest little Higgs model at the muon collider","cited_arxiv_id":"2312.08560","evidence_quote":"Motivates the mA0=500 GeV benchmark point used for the event counts."}],"review_version":1}