{"id":"1d4b1f6c-a04f-47ef-8e95-2b51aeaeeaa8","arxiv_id":"2610.17801","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"The one-loop branching ratio for A to Z Z gamma reaches 10^-4 in the 2HDM, with up to 5% corrections from Vector-Like Quarks, offering a potential observable signature at future colliders.","lead":"This paper computes the one-loop decay width for A to Z Z gamma in the Two-Higgs-Doublet Model and its extension with Vector-Like Quarks. The results provide a new probe of extended Higgs sectors and could be tested at future multi-TeV muon colliders.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"Omission of VLQ light-heavy interactions may affect the reported ~5% correction from VLQs.","rationale":"The omission of light-heavy interactions is a deliberate but untested simplification. The claimed 5% VLQ effect is small, and missing contributions of similar size could change the conclusion. A check on one benchmark would determine whether the omission is safe. The paper's own statements are not limitations but scope restrictions; they do not provide evidence that the omitted terms are negligible. Therefore the central claim rests on an unverified assumption that light-heavy interactions do not alter the 5% result.","tokens_in":38144,"tokens_out":2357,"duration_ms":28024,"concrete_test":"Recompute the branching ratio for the benchmark point MA=600 GeV, tβ=6, mT=800 GeV, s_uR=0.2 (as in Table 5) including the full set of light-heavy interaction couplings for top–T mixing in all fermion loop diagrams. Compare the resulting total width and VLQ-induced fractional change to the values in Table5. If the VLQ contribution changes by more than 1 percentage point (e.g., from 5% to 4% or 6%), then the claimed central estimate is materially incomplete.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's calculation of VLQ contributions (Tables 4-5, 7-8) explicitly omits all light-heavy interaction couplings (e.g., t–T mixing in the loop) at the level of the one-loop amplitude [b95, b145]. The authors state that because these are not included, gamma5 structures do not appear, but they provide no estimate of their numerical impact. The central claim that VLQs modify total rates by approximately 5% is based solely on heavy-heavy and light-light contributions. Light-heavy couplings could introduce additional diagrams and alter the interference pattern, potentially shifting the 5% figure by an amount comparable to or larger than the claimed effect. Since the analysis scans only the XT doublet scenario, the robustness of the 5% claim is not established for other representations either.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"This paper presents a one-loop calculation of the decay A → ZZγ in the Type-II Two-Higgs-Doublet Model (2HDM) and its extension with Vector-Like Quarks (VLQs). Using standard computational tools (FeynArts, FeynCalc, LoopTools, Collier) and the on-shell renormalization scheme, the authors compute partial decay widths and branching ratios for both unpolarized and polarized final-state Z bosons. Numerical results are given for several benchmark points in the 2HDM parameter space (tβ = 2, 6; MA = 300–1000 GeV; sβ−α = 0.98). For the 2HDM+VLQ, they focus on the XT doublet scenario with mT = 800, 1200 GeV and suR = 0.2, considering only light-light and heavy-heavy couplings while explicitly omitting light-heavy (t–T mixing) interactions. They report branching ratios of order 10⁻⁵–10⁻⁴ and find that VLQ contributions modify the total rates by approximately 5%.","tokens_in":38475,"tokens_out":2770,"duration_ms":29125,"significance":"If correct, this work would provide the first explicit calculation of A → ZZγ beyond the Standard Model, potentially offering a new probe of extended Higgs sectors and VLQs at future multi-TeV muon colliders. The inclusion of polarization information and the verification of UV cancellation and Ward identities are assets. However, the significance is reduced by the omission of light-heavy VLQ interactions, which could alter the reported 5% correction, and by the restriction to a single VLQ representation (XT doublet). The claimed branching ratio range also conflicts with some of the tabulated results.","major_comments":[{"comment":"The paper explicitly states that light-heavy interactions (e.g., t–T mixing) are not included in the VLQ loop contributions. The central numerical claim that 'Vector-Like Quarks can modify the total rates by approximately 5%' is based solely on heavy-heavy and light-light contributions. No estimate or argument is given for the size of the omitted terms. Since t–T mixing could introduce new diagrams and alter interference patterns, the robustness of the 5% figure is not established. This omission also contradicts the claim in the abstract of a 'complete' one-loop calculation. The authors should either include these contributions or provide a quantitative estimate of their expected impact.","section":"§2.3, §3, sentence b95, b145","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The numerical analysis is restricted to the XT doublet scenario. Singlet, (TB) doublet, and triplet VLQ representations are not considered (the text says they are 'temporarily neglected' without justification that the XT case is representative). The claim that VLQ contributions modify rates by ~5% may be representation-dependent. The authors should extend the scan to other representations or discuss the expected variation.","section":"§4, Tables 4-5, 7-8","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract states that branching ratios can reach 10⁻⁵–10⁻⁴, but Table 3 (tβ = 6, MA = 600 GeV) shows an unpolarized branching ratio of 1.677 × 10⁻³, an order of magnitude larger. This discrepancy should be corrected or clarified.","section":"Abstract, §4","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The paper contains several typographical issues, including inconsistent spacing in tables and the use of 'sβ−α' as a subscript without clarification. A careful proofreading pass is recommended.","section":"General","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The notation for polarization modes (λ2 = 0, L, R) is introduced in §4, but the detailed definition and relations are deferred to Appendix B. Cross-referencing the appendix earlier would improve readability.","section":"§4, Appendix B","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The vertical axis labels read 'dΓ_{A→ZZγ}/dm_{Zγ} × 10⁻⁴', which is potentially confusing. Consider normalizing the differential rate and removing the explicit factor, or clarifying that the scale includes a multiplicative factor.","section":"Fig. 2 and 3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The phrase 'temporarily consider' (e.g., 'we do not temporarily consider these light-heavy interactions') is awkward. 'Presently' or 'in this work' would be clearer.","section":"Throughout","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The paper is technically sound in its computational approach, but the omission of light-heavy VLQ interactions is a significant gap given that the central claim (5% VLQ correction) rests on a partial calculation. The authors should either complete the calculation or provide a quantitative bound. The branching ratio discrepancy between the abstract and Table 3 also needs attention. The paper may be suitable for the journal after these issues are addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"This paper gives the first one-loop treatment of A→ZZγ in the 2HDM and the 2HDM extended with vector-like quarks. The calculation uses standard renormalization and computational tools (FeynArts, FeynCalc, Collier) and checks UV cancellation and Ward identities. The branching ratios (10⁻⁵–10⁻⁴) in the 2HDM part are solid, and the polarization analysis (longitudinal/transverse) is a nice addition. The authors also provide differential distributions for the Zγ invariant mass, which is useful for collider studies.\n\nThe main advertised result—that VLQs modify the total rate by about 5%—rests on a narrower basis than the abstract suggests. The authors explicitly omit all light-heavy interaction couplings (t–T mixing vertices etc.) from the one-loop amplitude, including only light-light and heavy-heavy contributions. They note this omission but give no estimate of its numerical impact. If VLQ mixing is at the level assumed (s_uR=0.2), light-heavy loops could alter the interference pattern and shift the 5% number by an unknown amount. The parameter scan is also limited: fixed s_β-α=0.98, one VLQ mixing angle, and only the XT doublet representation. The authors are upfront about these choices, but the robustness of the VLQ result is therefore untested.\n\nWho should read this: anyone working on Higgs phenomenology in 2HDM or VLQ models who wants a concrete prediction for this decay mode. The pure 2HDM predictions are the more reliable part; the VLQ correction should be treated as indicative rather than definitive.\n\nRecommendation: this deserves a serious referee. The core 2HDM calculation is new and competently done. I would ask the authors to provide at least an order-of-magnitude estimate of the omitted light-heavy contributions, or a discussion of why they can be safely neglected in the considered parameter region. Without that, the headline \"5% VLQ effect\" is not substantiated.","headline":"First one-loop calculation of A→ZZγ in 2HDM and with VLQs; the 5% VLQ effect is based on partial contributions only.","tokens_in":38985,"tokens_out":1881,"would_cite":false,"duration_ms":22448,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek/deepseek-v4-flash","headline":"This paper presents the first complete one-loop calculation of the CP-odd Higgs decay A→ZZγ in the Two-Higgs-Doublet Model and its extension with Vector-Like Quarks, finding branching ratios of order 10⁻⁵–10⁻⁴ and VLQ corrections of…","keywords":["A→ZZγ","one-loop decay","Two-Higgs-Doublet Model","Vector-Like Quarks","branching ratio","polarization","muon collider"],"falsifier":"A multi- TeV muon collider that measures the A→ZZγ branching ratio to 10% precision at a mass A of 600 GeV would find no signal; this would falsify the prediction that the branching ratio reaches 10⁻⁴ for the chosen benchmark parameters, assuming the 2HDM Type‑ I with VLQs exists in that mass range.","tokens_in":39688,"feed_emoji":"","tokens_out":2343,"duration_ms":31485,"temperature":0.7,"pith_summary":"The authors compute the one-loop partial decay width and branching ratio for A→ZZγ in the Type-II 2HDM and in a version extended by a doublet of Vector-Like Quarks (VLQs) of the XT type. They find that for viable parameter points near the alignment limit, the branching ratio reaches 10⁻⁵–10⁻⁴, and the VLQ loops modify the total unpolarized rate by roughly 5% relative to the 2HDM alone. The decay is dominated by longitudinal Z-boson polarizations, and the invariant-mass distribution shows peaks from the light and heavy CP-even Higgs poles. The result suggests that this rare decay could serve as a complementary probe of extended Higgs sectors and VLQ effects at future multi-TeV muon colliders.","feed_headline":"Rare Higgs decay A→ZZγ reaches 10⁻⁴ branching ratio","feed_subtitle":"First complete one-loop calculation in 2HDM plus vector-like quarks predicts 5% VLQ shift, testable at future muon colliders.","key_machinery":"The central object is the one-loop amplitude for A→ZZγ, decomposed into six independent form factors after applying the Ward identity for the photon. The calculation uses FeynArts to generate the diagrams, FeynCalc and Package-X to perform the Passarino–Veltman reduction, and the Collier library for numerical evaluation of the scalar integrals. The dominant contributions come from triangle and box diagrams with the heaviest fermions (top quark and VLQ T) and from reducible diagrams with the neutral Higgs poles h and H. The Narrow Width Approximation is used when kinematically allowed (M_A ≥ M_φ + M_Z), and a full three-body integration is performed otherwise.","core_discovery":"The paper establishes the first complete one-loop calculation of the process A → ZZγ in both the Type-II Two-Higgs-Doublet Model and its extension with Vector-Like Quarks in the XT doublet scenario. It demonstrates that the branching ratios lie in the range 10⁻⁵–10⁻⁴ for CP-odd Higgs masses between 300 and 1000 GeV and that the VLQ contributions—dominated by the top partner T—modify the total decay rates by approximately 5%. The longitudinal polarization mode of one Z boson dominates the rate by a factor of about 4 over the transverse modes, and the differential rates reveal distinct structures from the h(125) and H(500) poles.","pith_inferences":["Because the VLQ contribution is only ~5% and depends on the mixing angle s_uR (set to 0.2 here), a non-observation of this deviation would not rule out VLQs; it would only exclude the specific XT doublet with that mixing angle and mass.","The same one-loop formalism can be extended to other rare A → VV'γ decays (V = W, Z) in the 2HDM-VLQ, providing a systematic programme to test the Higgs sector.","The paper's parameter choices (sβ−α=0.98, MH=500 GeV, M_{H±}=650 GeV) are motivated by current constraints, but these values are not uniquely fixed; a scan over the full allowed space would show whether larger VLQ corrections are possible in other regions.","If future colliders measure the A→ZZγ branching ratio and its polarization fractions, one could disentangle the 2HDM Yukawa type (Type-II vs Type-I, X, Y) by comparing the ratio of longitudinal to transverse rates, as those depend on the φ t\\bar{t} and φ b\\bar{b} couplings."],"forward_implications":["The predicted branching ratios of 10⁻⁵–10⁻⁴ are within reach of future multi-TeV muon colliders with high integrated luminosity, offering a new channel to probe the CP-odd Higgs boson A.","The approximately 5% shift from VLQ contributions could be distinguished from the pure 2HDM rate if the experimental precision reaches the few-percent level, thereby constraining VLQ scenarios.","The strong dominance of longitudinal Z polarization (a factor of 4 over transverse modes) provides a polarization-dependent observable that could be measured in future detectors.","The differential distribution in m(Zγ) shows clear peaks from the light h(125) and heavy H(500) Higgs poles, allowing a direct determination of the CP-even Higgs masses and couplings if the decay is observed.","The results for the doublet XT representation give a concrete benchmark; other VLQ representations (singlets, triplets) would produce similar but distinguishable corrections, enabling model discrimination."],"supporting_citations":[{"why":"Provides the standard review of the 2HDM potential, parameters, and mass eigenstates that the paper adopts.","marker":"[25]"},{"why":"Supplies the general Lagrangian and couplings for all VLQ representations (singlets, doublets, triplets) used in the paper's model.","marker":"[27]"},{"why":"Same as [27] but provides additional detail on the XT doublet scenario and the coupling coefficients needed in the calculation.","marker":"[28]"},{"why":"The previous work by some of the same authors on A→Zγγ; the present paper extends the method to the ZZγ final state and compares results.","marker":"[32]"},{"why":"Reference for the LoopTools package used to evaluate the Passarino–Veltman scalar integrals numerically.","marker":"[35]"},{"why":"The FeynArts package was used to generate the one-loop Feynman diagrams for the process.","marker":"[38]"}],"fun_headline_variants":["Rare A→ZZγ decay reaches 10⁻⁴ branching in 2HDM with vector-like quarks","First one-loop A→ZZγ calculation in 2HDM+VLQ predicts 5% shift","A→ZZγ one-loop rates in 2HDM+VLQ reach 10⁻⁵–10⁻⁴","CP-odd Higgs A→ZZγ: first complete one-loop rates with VLQ effects"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The numerical results depend on fixing sβ−α = 0.98 (the alignment limit), s_uR = 0.2, m_T = 800 eV (or 1200 eV), and other scalar masses to representative values; small deviations in these parameters could alter the branching ratios and the size of the VLQ contribution significantly.","fun_headline_variants_meta":{"raw":{"variants":["Rare A→ZZγ decay reaches 10⁻⁴ branching in 2HDM with vector-like quarks","First one-loop A→ZZγ calculation in 2HDM+VLQ predicts 5% shift","A→ZZγ one-loop rates in 2HDM+VLQ reach 10⁻⁵–10⁻⁴","CP-odd Higgs A→ZZγ: first complete one-loop rates with VLQ effects"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000114,"raw_usage":{"cost":0.0001135134,"is_byok":false,"cost_details":{"upstream_inference_cost":0.0001135134,"upstream_inference_prompt_cost":2.87014e-05,"upstream_inference_completions_cost":8.4812e-05},"total_tokens":1403,"prompt_tokens":937,"completion_tokens":466,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":777,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":364}},"tokens_in":937,"tokens_out":466,"cost_source":"openrouter_usage","duration_ms":15577,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":364,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-14T14:50:46.905889+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"A multi- TeV muon collider that measures the A→ZZγ branching ratio to 10% precision at a mass A of 600 GeV would find no signal; this would falsify the prediction that the branching ratio reaches 10⁻⁴ for the chosen benchmark parameters, assuming the 2HDM Type‑ I with VLQs exists in that mass range.","supporting_citations":[{"cited_title":"Theory and phenomenology of two-Higgs-doublet models","cited_arxiv_id":"1106.0034","evidence_quote":"Provides the standard review of the 2HDM potential, parameters, and mass eigenstates that the paper adopts."},{"cited_title":"Arhrib, R","cited_arxiv_id":null,"evidence_quote":"Supplies the general Lagrangian and couplings for all VLQ representations (singlets, doublets, triplets) used in the paper's model."},{"cited_title":"Arhrib, R","cited_arxiv_id":null,"evidence_quote":"Same as [27] but provides additional detail on the XT doublet scenario and the coupling coefficients needed in the calculation."},{"cited_title":"General Formulas for Loop-Induced Decays of $A \\to Z\\gamma\\gamma$ and Their Applications","cited_arxiv_id":"2503.22974","evidence_quote":"The previous work by some of the same authors on A→Zγγ; the present paper extends the method to the ZZγ final state and compares results."},{"cited_title":"Hahn and M","cited_arxiv_id":null,"evidence_quote":"Reference for the LoopTools package used to evaluate the Passarino–Veltman scalar integrals numerically."},{"cited_title":"Generating Feynman Diagrams and Amplitudes with FeynArts 3","cited_arxiv_id":"hep-ph/0012260","evidence_quote":"The FeynArts package was used to generate the one-loop Feynman diagrams for the process."}],"review_version":1}