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One-loop contributing for $A \rightarrow Z Z \gamma$ in the Two-Higgs-Doublet Model with Vector-Like Quarks

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Dzung Tri Tran (HCMUS, DTU), Vo Quoc Phong (HCMUS), Khiem Hong Phan (EIU)

High Energy Physics - Phenomenology · Submitted 13 Oct 2026 · 63 references

Pith's verdict: First one-loop calculation of A→ZZγ in 2HDM and with VLQs; the 5% VLQ effect is based on partial contributions only.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on October 14, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

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arXiv ID2610.17801 (version 1)
Pith IDOSOZ7KT6, Pith's permanent record of this paper and its review
CitationDTU), Dzung Tri Tran (HCMUS, Khiem Hong Phan (EIU), Vo Quoc Phong (HCMUS). "One-loop contributing for $A \rightarrow Z Z \gamma$ in the Two-Higgs-Doublet Model with Vector-Like Quarks." arXiv:2610.17801 (2026). https://pith.science/paper/OSOZ7KT6
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The paper

The paper claims

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…

The reading

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.

What carries the argument

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.

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
Original abstract

In this paper, we present the first results for the one-loop decay $A \rightarrow ZZ\gamma$ in the Two-Higgs-Doublet Model and its extension with Vector-Like Quarks. We calculate the one-loop partial decay widths and branching ratios for both unpolarized and polarized final-state $Z$ bosons. The effects of Vector-Like Quarks propagating in the loop are also examined in our phenomenological analysis. We find that the branching ratios can reach $10^{-5}-10^{-4}$ for several benchmark points within the viable parameter space of the considered models. The contributions from Vector-Like Quarks can modify the total rates by approximately $5\%$. With the high luminosities expected at future multi-TeV muon colliders, these effects may be experimentally accessible.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-14: 1 request, 4,921 input tokens.

What the abstract itself states, as probabilities: claims first 0.96 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper, we present the first results for the one-loop decay $A \rightarrow ZZ\gamma$ in the Two-Higgs-Doublet Model and its extension with Vector-Like Quarks. We calculate the one-loop partial decay widths and branching ratios for both unpolarized and polarized final-state $Z$ bosons. The effects of Vector-Like Quarks propagating in the loop are also examined in our phenomenological analysis. We find that the branching ratios can reach $10^{-5}-10^{-4}$ for several benchmark points within the viable parameter space of the considered models. The contributions from Vector-Like Quarks can modify the total rates by approximately $5\%$. With the high luminosities expected at future multi-TeV muon colliders, these effects may be experimentally accessible.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we present the first results for the one-loop decay $A \rightarrow ZZ\gamma$ in the Two-Higgs-Doublet Model and its extension with Vector-Like Quarks. contribution 0.99 0.91 0.12 asserted 1.00
s1 We calculate the one-loop partial decay widths and branching ratios for both unpolarized and polarized final-state $Z$ bosons. method 0.50 0.97 0.06 asserted 1.00
s2 The effects of Vector-Like Quarks propagating in the loop are also examined in our phenomenological analysis. contribution 0.83 0.90 0.05 asserted 0.92
s3 We find that the branching ratios can reach $10^{-5}-10^{-4}$ for several benchmark points within the viable parameter space of the considered models. result 1.00 0.96 0.44 asserted 0.92
s4 The contributions from Vector-Like Quarks can modify the total rates by approximately $5\%$. result 1.00 0.92 0.14 asserted 0.86
s5 With the high luminosities expected at future multi-TeV muon colliders, these effects may be experimentally accessible. interpretation 0.99 0.21 0.19 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from simulation or computation 0.93.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. All one-loop Feynman diagrams contributing to the decay p
Figure 2. The differential decay rates as functions of the invariant
Figure 3. Same as Figure
Figure 4. The other distinctive triangle topology relevant to the one
Figure 5. Same as Figure

Figures reproduced from arXiv:2610.17801 by the authors.

References

Discussion

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