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REVIEW 3 major objections 6 minor 56 references

Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Two parameters control the off-shell Higgs signal in gluon fusion

desk verdict Sound leading-order HEFT result for gg→Z_LZ_L, but the claim that subleading corrections are small is not quantitatively supported. read the letter →

arxiv 2507.23658 v1 pith:ZTPYTFDC submitted 2025-07-31 hep-ph

Gerhard Buchalla , Florian Pandler This is my paper
classification hep-ph
keywords electroweakchiralLagrangiananomalousHiggscouplingsggtoZLoff-shellpowercountinggluonfusionlongitudinalZbosons
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

The paper claims that new-physics contributions to gluon-fusion production of longitudinal $Z$-boson pairs, the channel in which the Higgs boson is highly off shell, are fixed at leading order by just two independent parameters built from three anomalous Higgs couplings. This matters because this channel can expose Higgs couplings that are hard to separate in on-shell Higgs production, and the leading effect at high energies has a distinctive energy-growing signature. Working in the electroweak chiral Lagrangian, the authors show that the leading-order amplitude depends on the products $c_t c_V$ and $c_{ggh} c_V$, where $c_t$ is the top-Yukawa coupling, $c_V$ the Higgs-$Z$ coupling, and $c_{ggh}$ the local Higgs-gluon coupling. They argue that subleading corrections stay small within the EFT's domain of validity, so this compact two-parameter description is the robust prediction to test.

What carries the argument

The machinery is the chiral power counting $d_\chi = 2L+2$ of the electroweak chiral Lagrangian, a loop-counting scheme in which the one-loop order of $gg\to ZZ$ is promoted to leading EFT order and the local Higgs-gluon coupling $c_{ggh}$ enters at that same order. The argument is carried by the two form factors $A_1$ and $A_2$ for gluon helicities ($++/--$) and ($+-/-+$), with $A_1$ receiving the leading anomalous couplings; in the Goldstone limit the longitudinal $Z$ bosons are replaced by the neutral Goldstone $\varphi^0$, and the asymptotic form of $A_1$ is where the $\log^2 s$ and linear-in-$s$ terms appear. The key result is that $A_1$ depends on the anomalous couplings only through the products $c_t c_V$ and $c_{ggh} c_V$.

What would settle it

Measure the partonic differential cross section for $gg\to Z_L Z_L$ as a function of $\sqrt{s}$ in the TeV range and fit the two helicity form factors separately. If the extracted coefficient of the energy-linear term in $A_1$ does not track the product $c_{ggh} c_V$ while a $\log^2 s$ term remains, the promoted leading-order counting is wrong. A cleaner test is to compare the two-parameter fit against a strict chiral-dimension calculation in which $c_{ggh}$ is treated as next-to-leading order, since the two predictions differ in the high-energy slope.

Watch

Extended reading notes

Core claim

Using the chiral (loop) counting of the electroweak chiral Lagrangian, the process $gg\to Z_L Z_L$ is induced at one loop, so the one-loop topologies together with a single insertion of the local $hgg$ vertex define the leading EFT order. At that order the amplitude for two longitudinal $Z$ bosons, computed via Goldstone-boson equivalence, depends on the anomalous couplings only through the two combinations $c_t c_V$ and $c_{ggh} c_V$. In the large-energy limit the form factor $A_1$ contains a $\log^2 s$ term proportional to $(1-c_t c_V)$ and a term linear in $s$ proportional to $c_{ggh} c_V$, so the local Higgs-gluon coupling dominates the new-physics signal at high off-shell energy. The paper further shows that next-to-leading-order local operators and renormalization-group running of $c_V$ and $c_t$ give only parametrically suppressed corrections within the EFT's range of validity, and that modelling $c_{ggh}$ as a local coupling from heavy resonances is an excellent approximation.

Load-bearing premise

The two-parameter claim rests on treating the one-loop order of $gg\to ZZ$ as the leading EFT order and thereby promoting the local Higgs-gluon coupling $c_{ggh}$ to leading order; if the EFT were instead ordered purely by the chiral dimension of operators, $c_{ggh}$ would be a next-to-leading-order effect and the parameter reduction, together with the dominance of the linear-in-$s$ term, would not hold.

Editorial extensions

If this is right

  • In $gg\to Z_L Z_L$ at leading EFT order, only $c_t c_V$ and $c_{ggh} c_V$ are measurable; the three underlying couplings cannot be individually disentangled from this process alone.
  • The $c_{ggh} c_V$ contribution grows linearly with partonic energy at the amplitude level, so the high-off-shell-energy region is where new physics in the Higgs-gluon coupling shows up most cleanly.
  • On-shell $gg\to h$ production cannot separate $c_t$ from $c_{ggh}$, but combining it with the off-shell $gg\to Z_L Z_L$ measurement can break that degeneracy.
  • Next-to-leading-order operators such as $hZ_{\mu\nu}Z^{\mu\nu}$, $\bar t t Z_\mu Z^\mu$, modified $\bar t t Z$ couplings, and local $ggZZ$ contact terms are parametrically suppressed by $\xi/16\pi^2$ or $s/M^2$ inside the EFT's validity range, so the leading two-parameter description is stable against NLO contamination.
  • Renormalization-group running between the TeV scale and the 8 TeV cutoff can shift $c_V$ and $c_t$ by amounts of order 0.1 to 0.3 through top-mass-enhanced terms, so a fit must state the scale at which the couplings are defined.

Reading between the lines

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

  • If the two-parameter reduction is correct, a global fit combining on-shell $gg\to h$ with off-shell $gg\to Z_L Z_L$ should constrain $c_t$, $c_V$, and $c_{ggh}$ separately, because the two processes weight the products differently; the paper does not perform that fit.
  • The same loop-counting logic likely applies to other loop-induced Higgs processes such as $gg\to hh$ or $gg\to H\to WW$, where a local $hgg$-type coupling would likewise be promoted to leading order; this generalization is not pursued in the paper.
  • Because the linear-in-$s$ growth formally violates perturbative unitarity above the EFT cutoff, matching the two-parameter amplitude to a unitary ultraviolet completion should set an upper bound on $\sqrt{s}$ where the leading-order description can be trusted; the paper only notes that unitarity is preserved within the EFT's range.
  • A testable consequence of the factorization structure is that the helicity amplitude $A_2$ remains Standard-Model-like at leading order; observing a deviation in $A_2$ comparable to one in $A_1$ would indicate a breakdown of the leading-order chiral counting.
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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

3 major / 6 minor

Summary. The paper investigates gluon-fusion production of longitudinal Z-boson pairs, gg → Z_L Z_L, in the electroweak chiral Lagrangian (HEFT), with emphasis on the off-shell Higgs region. The authors present the leading-order amplitude in the chiral counting, showing that new-physics effects at that order are controlled by two independent parameters that depend on three EFT couplings (c_t, c_V, c_ggh). They then survey next-to-leading-order contributions from dχ=4 and dχ=6 operators, estimate their coefficients through toy models and power-counting arguments, discuss renormalization-group running, and illustrate the phenomenology with partonic cross-section plots. The formal leading-order derivation is explicit and cross-checked against [43] and Package-X, while the NLO analysis is acknowledged in the paper to be incomplete, resting on toy models and order-of-magnitude estimates.

Significance. If the two-parameter leading-order statement is correct, it is a useful simplification for Higgs EFT studies of gg → ZZ. The paper supplies explicit form factors, validates the SM limit against an independent calculation, and includes a discussion of c_ggh, which is absent from the earlier HEFT treatment [30]. The power-counting logic that intertwines the loop order of the process with the chiral dimension of the EFT is clearly presented and is a genuine methodological contribution. The paper is also transparent about the incompleteness of the NLO analysis, presenting it as an overview with representative estimates rather than a full calculation. However, the quantitative claim that NLO corrections are subdominant for experimentally allowed parameter values is not robust, as the paper's own equations show; this affects the abstract and the conclusions and needs to be addressed.

major comments (3)
  1. [Abstract; §3.3.2, Eqs. (27), (34), (36), (71); Figs. 5–6] The central phenomenological claim that c_ggh dominates at high energy and that NLO corrections are subdominant is contradicted by the numbers in the paper itself. Using Eq. (27) for the leading c_ggh term and Eqs. (34) and (36) for the QψS1 correction, with ξ=0.1 and c_ggh=0.01 (which is inside the 68% interval of Eq. (71)), one obtains at √s=2 TeV ΔA1 ≈ −0.40 from QψS1 versus about −0.33 from the c_ggh term; at √s=3 TeV the QψS1 correction is about −1.3 whereas the c_ggh term is about −0.75. The parametric suppression ξ/16π^2 is offset by the s ln^2(s) growth and by the experimentally allowed smallness of c_ggh. This directly undermines the abstract's statement that 'Subleading effects can be expected to be small within the range of validity of the EFT' and the corresponding claim in Section 5. The authors should either add a quantitative validity condition for c_ggh (for example, a lower bound on c_ggh for the stated energies and ξ values) or soften the claim to reflect that the dominance of c_ggh holds only when c_ggh is near its power-counting size.
  2. [§3.3.2 and §3.4, Eq. (59)] The argument that c_ggh is a leading-order effect of size O(√ξ) and that NLO effects are therefore subleading implicitly assumes that c_ggh is not much smaller than its power-counting estimate. However, the global fit quoted in Eq. (71) gives c_ggh ≈ −0.01 ± 0.08, which is an order of magnitude below √ξ for ξ=0.1. The paper's own discussion in Section 3.3.2 acknowledges that c_ggh is taken to be smaller than its power-counting value due to experimental constraints, but it does not translate this into a quantitative condition for the validity of the two-parameter leading-order dominance. Without such a condition, the conclusion that the two-parameter parametrization is self-consistently the dominant new-physics effect is not established for the experimentally preferred values.
  3. [§3.3.3, Eq. (39)] The statement that the QψV correction is 'numerically negligible' because δV ∼ ξ/16π^2 while 1−c_t c_V ∼ ξ is only valid if 1−c_t c_V is of order ξ. But the global fit in Eq. (71) allows c_t c_V to be close to 1 to within about 10%, in which case 1−c_t c_V could be much smaller than ξ and the comparison would not hold. A quantitative bound on δV relative to the actual allowed range of c_t c_V is needed before concluding that these operators are always subdominant.
minor comments (6)
  1. [§3.2] The word 'calclulation' should be 'calculation'.
  2. [Figs. 4–8] The axis label 'f b' should be 'fb'; the current form is likely a typographical artifact.
  3. [Eq. (13)] The symbol '⊇' in Eq. (13) is unclear; the text should say explicitly that only the terms relevant for gg → ZZ are retained, rather than using a set-theoretic notation.
  4. [Table 1 and Ref. [49]] The caption says the input parameters are 'taken from [49]', but [49] is the PDG review; please specify which PDG values are used and whether the top-quark mass is the pole mass or an MS-bar value.
  5. [Eq. (2)] The Yukawa part of the Lagrangian is typeset in a way that makes the expansions in M^(n) hard to read; a clearer presentation would help the reader verify the coupling conventions.
  6. [§2.3] The comparison with the operator basis of [30] would be easier to follow if the correspondence were presented in a table rather than in prose.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation found: the leading-order amplitude is a direct one-loop calculation, and its two-parameter form follows from the Feynman rules rather than from fitted inputs or self-citations.

full rationale

The central result of the paper, the leading-order amplitude for gg -> Z_L Z_L in Eqs. (25)-(26), is obtained from an explicit one-loop diagrammatic calculation. The couplings c_t, c_V, and c_ggh are free parameters of the electroweak chiral Lagrangian, not fitted to the process being studied; no parameter is extracted from gg -> ZZ data and then presented as a prediction. The claim that only two combinations (c_t c_V and c_ggh c_V) enter at leading order is a direct algebraic consequence of the amplitude structure, not an input. The SM limit is cross-checked against the independent calculation of Glover and van der Bij [43], and the Goldstone-boson equivalence is validated numerically in Fig. 8. The power-counting choice that promotes c_ggh to leading order because the process is one-loop induced is an explicit organizational assumption stated in Section 2.2; it is not circular, though it is a substantive assumption about how to order the EFT expansion. The NLO operator classification and beta functions are taken from the authors' earlier papers [21, 51], which is self-citation, but these are framework inputs applied to a new amplitude rather than the load-bearing target of the paper; the leading-order result does not reduce to those citations. The abstract's statement that subleading effects are small is explicitly conditional on power-counting-sized NLO coefficients, and the reviewer's numerical comparison with experimentally allowed small c_ggh values shows this claim may be quantitatively fragile; however, that is a correctness/robustness concern, not evidence of circularity. Overall, the derivation is self-contained and no circular step can be exhibited.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central result rests on the HEFT operator basis and power counting developed in earlier work by Buchalla et al., plus standard perturbative QCD and Goldstone equivalence. The amplitude coefficients c_V, c_t, and c_ggh are free EFT parameters, not fitted here; the NLO estimates additionally depend on the chosen toy-model scales f and M.

free parameters (6)
  • c_V = SM=1; plots use c_t c_V = 1.05, 1.1
    Leading-order hZZ coupling modifier; central two-parameter result depends on it through products c_t c_V and c_ggh c_V.
  • c_t = SM=1; enters as c_t c_V
    Leading-order top-Yukawa modifier; affects the hgg top loop and the triangle contribution.
  • c_ggh = SM=0; plots use 0.01, 0.02, 0.05
    Local hgg coupling promoted to leading order in the paper's counting; dominates high-energy behavior.
  • C_psiS1 = C_psiS1/m_t = -1/(2 M^2) ~ - xi/(16 pi^2 v^2)
    NLO operator coefficient estimated from a heavy-scalar toy model; used for subleading corrections in Section 3.3.2.
  • C_GU1 = c_gghH/(32 pi^2 M^2)
    NNLO local ggZZ coefficient estimated from a heavy-scalar model; used for subleading corrections in Section 3.3.4.
  • xi = v^2/f^2 and M = 4 pi f = xi=0.05, 0.1; f~0.7 TeV, M~8 TeV
    Power-counting inputs used to estimate the size of NLO coefficients in Section 3.3.
assumptions (6)
  • standard math Perturbative QFT and one-loop scalar integrals (C and D) as defined in Appendix A
    The central form factors are built from these loop functions.
  • domain assumption Goldstone boson equivalence for longitudinal Z at high energy
    Used in Section 3.1 to replace Z_L by phi^0; validity checked in Fig. 8.
  • domain assumption Top-quark loop dominance in gg to ZZ; light quark contributions neglected
    Amplitudes (25) and (26) contain only the top-quark mass scale; stated in Section 2.2.
  • domain assumption The one-loop order of the gg to ZZ amplitude defines the leading order of the EFT, so the L4 hgg coupling c_ggh enters at leading order
    Section 2.2; this power-counting choice is load-bearing for the two-parameter conclusion.
  • domain assumption CP conservation in the operator set
    Section 2.1 states operators are listed assuming CP conservation.
  • domain assumption The EFT is valid for sqrt(s) below the cutoff M ~ 4 pi f ~ 8 TeV
    Used in Section 3.3 to argue that subleading s-growing terms remain small within the EFT range.

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Cite this review

Pith. "Pith review of Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$." pith.science (2026). https://pith.science/paper/ZTPYTFDC

@misc{pith2026250723658,
  author       = {Pith},
  title        = {Pith review of: Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZTPYTFDC}},
  note         = {Machine review of arXiv:2507.23658}
}
abstract

We investigate the production of (longitudinal) $Z$-boson pairs in gluon fusion as a probe of anomalous Higgs couplings. Of particular interest is the kinematic region of large center-of-mass energy, where the Higgs-boson is highly off-shell. We employ the electroweak chiral Lagrangian with a light Higgs, which is the most natural effective field theory (EFT) for this process. We demonstrate this by a detailed analysis of the leading and next-to-leading EFT contributions to the amplitude, at leading order in QCD, emphasizing the role of power counting for a systematic application of the EFT. We show that at leading order the new-physics contributions are described by only two parameters, which depend on three EFT couplings. Subleading effects can be expected to be small within the range of validity of the EFT. Phenomenological implications are briefly discussed.

Figures

Figures reproduced from arXiv: 2507.23658 by the authors.

Figure 1
Figure 1. Diagrams for gg → ZZ at leading order in the chiral counting. Curly, wavy, dashed and full lines refer to gluons, Z bosons, Higgs bosons and quarks, respectively. Black circles and black squares denote anomalous couplings from the LO and NLO Lagrangian, respectively. Additional diagrams with permutations of the external legs are not explicitly shown. 2.2 EFT applied to gg → ZZ: Overview It is important to note that … view at source ↗
Figure 2
Figure 2. Representative diagrams for gg → ZZ at next-to-leading order in the chiral counting. Black circles, black squares and crossed squares denote anomalous couplings from the LO, NLO and NNLO Lagrangian, respectively [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Sample diagrams for gg → ZZ with operators from the Lagrangian at chiral dimension 4, which would only contribute at next-to-next-to-leading (3-loop) order to this process. Black squares denote vertices from the NLO Lagrangian. of class ψ 4Uh (c). All graphs in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Energy dependence of the scattering cross section at cos [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: Energy dependence of the scattering cross section at cos [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]
Figure 6
Figure 6. Figure 6: Energy dependence of the scattering cross section at cos [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: Energy dependence of the scattering cross section at cos [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: Energy dependence of the scattering cross section at cos [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]

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Works this paper leans on

56 extracted references · 9 canonical work pages

  1. [43]

    E. W. N. Glover and J. J. van der Bij, Nucl. Phys. B 321 (1989), 561

    work page 1989

  2. [30]

    Englert, R

    Anisha, C. Englert, R. Kogler and M. Spannowsky, Phys. Rev. D 109 (2024) no.9, 095033 [arXiv:2402.06746 [hep-ph]]

    arXiv 2024

  3. [1]

    Feruglio, Int

    F. Feruglio, Int. J. Mod. Phys. A 08 (1993) 4937 [hep-ph/9301281]

    arXiv 1993

  4. [2]

    The Strongly Interacting $WW$ System: Gold--Plated Modes

    J. Bagger et. al., Phys. Rev. D 49 (1994) 1246 [hep-ph/9306256]

    work page Pith review arXiv 1994

  5. [3]

    Koulovassilopoulos and R

    V. Koulovassilopoulos and R. S. Chivukula, Phys. Rev. D 50 (1994) 3218 [hep- ph/9312317]

    work page arXiv 1994

  6. [4]

    C. P. Burgess, J. Matias and M. Pospelov, Int. J. Mod. Phys. A 17 (2002) 1841 [hep-ph/9912459]

    arXiv 2002

  7. [5]

    L. M. Wang and Q. Wang, [arXiv:hep-ph/0605104 [hep-ph]]

    arXiv

  8. [6]

    Grinstein and M

    B. Grinstein and M. Trott, Phys. Rev. D 76 (2007) 073002 [arXiv:0704.1505 [hep- ph]]

    arXiv 2007

Show all 56 references
  1. [7]

    Contino, C

    R. Contino, C. Grojean, M. Moretti, F. Piccinini and R. Rattazzi, JHEP 1005 (2010) 089 [arXiv:1002.1011 [hep-ph]]

    2010 arXiv

  2. [8]

    Contino, arXiv:1005.4269 [hep-ph]

    R. Contino, arXiv:1005.4269 [hep-ph]

    arXiv

  3. [9]

    Buchalla and O

    G. Buchalla and O. Cat` a, JHEP07 (2012) 101 [arXiv:1203.6510 [hep-ph]]

    2012 arXiv

  4. [10]

    Alonso, M

    R. Alonso, M. B. Gavela, L. Merlo, S. Rigolin and J. Yepes, Phys. Lett. B 722 (2013) 330 Erratum: [Phys. Lett. B 726 (2013) 926] [arXiv:1212.3305 [hep-ph]]

    2013 arXiv

  5. [11]

    Alonso, M

    R. Alonso, M. B. Gavela, L. Merlo, S. Rigolin and J. Yepes, Phys. Rev. D 87 (2013) no. 5, 055019 [arXiv:1212.3307 [hep-ph]]

    2013 arXiv

  6. [12]

    A. Pich, I. Rosell and J. J. Sanz-Cillero, Phys. Rev. Lett. 110 (2013), 181801 [arXiv:1212.6769 [hep-ph]]. 22

    2013 arXiv

  7. [13]

    Buchalla, O

    G. Buchalla, O. Cat` a and C. Krause, Nucl. Phys. B880 (2014) 552 Erratum: [Nucl. Phys. B 913 (2016) 475] [arXiv:1307.5017 [hep-ph]]

    2014 arXiv

  8. [14]

    A. Pich, I. Rosell and J. J. Sanz-Cillero, JHEP 01 (2014), 157 [arXiv:1310.3121 [hep-ph]]

    2014 arXiv

  9. [15]

    R. L. Delgado, A. Dobado, M. J. Herrero and J. J. Sanz-Cillero, JHEP 07 (2014) 149 [arXiv:1404.2866 [hep-ph]]

    2014 arXiv

  10. [16]

    Buchalla, O

    G. Buchalla, O. Cat` a, A. Celis and C. Krause, Phys. Lett. B 750 (2015) 298 [arXiv:1504.01707 [hep-ph]]

    2015 arXiv

  11. [17]

    Buchalla, O

    G. Buchalla, O. Cat` a, A. Celis and C. Krause, Eur. Phys. J. C 76 (2016) no.5, 233 [arXiv:1511.00988 [hep-ph]]

    2016 arXiv

  12. [18]

    Alonso, E

    R. Alonso, E. E. Jenkins and A. V. Manohar, JHEP 08 (2016), 101 [arXiv:1605.03602 [hep-ph]]

    2016 arXiv

  13. [19]

    A. Pich, I. Rosell, J. Santos and J. J. Sanz-Cillero, JHEP 04 (2017), 012 [arXiv:1609.06659 [hep-ph]]

    2017 arXiv

  14. [20]

    A. Pich, I. Rosell and J. J. Sanz-Cillero, Phys. Rev. D 102 (2020) no.3, 035012 [arXiv:2004.02827 [hep-ph]]

    2020 arXiv

  15. [21]

    Buchalla, O

    G. Buchalla, O. Cat` a, A. Celis, M. Knecht and C. Krause, Phys. Rev. D 104 (2021) no.7, 076005 [arXiv:2004.11348 [hep-ph]]

    2021 arXiv

  16. [22]

    Cohen, N

    T. Cohen, N. Craig, X. Lu and D. Sutherland, JHEP 03 (2021) 237 [arXiv:2008.08597 [hep-ph]]

    2021 arXiv

  17. [23]

    G´ omez-Ambrosio, F

    R. G´ omez-Ambrosio, F. J. Llanes-Estrada, A. Salas-Bern´ ardez and J. J. Sanz-Cillero, Phys. Rev. D 106 (2022) no.5, 053004 [arXiv:2204.01763 [hep-ph]]

    2022 arXiv

  18. [24]

    G´ omez-Ambrosio, F

    R. G´ omez-Ambrosio, F. J. Llanes-Estrada, A. Salas-Bern´ ardez and J. J. Sanz-Cillero, Commun. Theor. Phys.75 (2023) no.9, 095202 [arXiv:2207.09848 [hep-ph]]; EPJ Web Conf. 274 (2022) 08013 [arXiv:2211.09605 [hep-ph]]

    2023 arXiv

  19. [25]

    R. L. Delgado, R. G´ omez-Ambrosio, J. Mart ´ ınez-Mart ´ ın, A. Salas-Bern´ ardez and J. J. Sanz-Cillero, JHEP 03 (2024) 037 [arXiv:2311.04280 [hep-ph]]

    2024 arXiv

  20. [26]

    Caola and K

    F. Caola and K. Melnikov, Phys. Rev. D 88 (2013), 054024 [arXiv:1307.4935 [hep- ph]]

    2013 arXiv

  21. [27]

    Cacciapaglia, A

    G. Cacciapaglia, A. Deandrea, G. Drieu La Rochelle and J. B. Flament, Phys. Rev. Lett. 113 (2014) no.20, 201802 [arXiv:1406.1757 [hep-ph]]

    2014 arXiv

  22. [28]

    Azatov, C

    A. Azatov, C. Grojean, A. Paul and E. Salvioni, Zh. Eksp. Teor. Fiz. 147 (2015), 410-425 [arXiv:1406.6338 [hep-ph]]. 23

    2015 arXiv

  23. [29]

    Ghosh, M

    A. Ghosh, M. Griese, U. Haisch and T. H. Park, [arXiv:2507.02032 [hep-ph]]

    arXiv

  24. [31]

    Aad et al

    G. Aad et al. [ATLAS], JHEP 12 (2023), 107 [arXiv:2310.04350 [hep-ex]]

    2023 arXiv

  25. [32]

    Aad et al.[ATLAS], Phys

    G. Aad et al.[ATLAS], Phys. Lett. B843 (2023), 137895 [arXiv:2211.09435 [hep-ex]]

    2023 arXiv

  26. [33]

    Gauld, A

    R. Gauld, A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover and A. Huss, JHEP 11 (2017), 003 [arXiv:1708.00008 [hep-ph]]

    2017 arXiv

  27. [34]

    V. E. Lyubovitskij, A. S. Zhevlakov and I. A. Anikin, [arXiv:2503.16008 [hep-ph]]

    arXiv

  28. [35]

    J. M. Campbell, R. K. Ellis, M. Czakon and S. Kirchner, JHEP 08 (2016), 011 [arXiv:1605.01380 [hep-ph]]

    2016 arXiv

  29. [36]

    Caola, M

    F. Caola, M. Dowling, K. Melnikov, R. R¨ ontsch and L. Tancredi, JHEP 07 (2016), 087 [arXiv:1605.04610 [hep-ph]]

    2016 arXiv

  30. [37]

    Han and W

    Z. Han and W. Skiba, Phys. Rev. D 71 (2005), 075009 [arXiv:hep-ph/0412166 [hep- ph]]

    2005 arXiv

  31. [38]

    Grzadkowski, M

    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, JHEP 10 (2010), 085 [arXiv:1008.4884 [hep-ph]]

    2010 arXiv

  32. [39]

    Buchalla, M

    G. Buchalla, M. Capozi, A. Celis, G. Heinrich and L. Scyboz, JHEP 09 (2018), 057 [erratum: JHEP 06 (2025), 094] [arXiv:1806.05162 [hep-ph]]

    2018 arXiv

  33. [40]

    Buchalla, G

    G. Buchalla, G. Heinrich, C. M¨ uller-Salditt and F. Pandler, SciPost Phys.15 (2023) no.3, 088 [arXiv:2204.11808 [hep-ph]]

    2023 arXiv

  34. [41]

    H. H. Patel, Comput. Phys. Commun. 197 (2015) 276 [arXiv:1503.01469 [hep-ph]]

    2015 arXiv

  35. [42]

    H. H. Patel, Comput. Phys. Commun. 218 (2017) 66 [arXiv:1612.00009 [hep-ph]]

    2017 arXiv

  36. [44]

    Degrande, N

    C. Degrande, N. Greiner, W. Kilian, O. Mattelaer, H. Mebane, T. Stelzer, S. Wil- lenbrock and C. Zhang, Annals Phys. 335 (2013), 21-32 [arXiv:1205.4231 [hep-ph]]

    2013 arXiv

  37. [45]

    Buchalla, O

    G. Buchalla, O. Cat` a, A. Celis and C. Krause, Nucl. Phys. B 917 (2017) 209 [arXiv:1608.03564 [hep-ph]]

    2017 arXiv

  38. [46]

    Ruegg and M

    H. Ruegg and M. Ruiz-Altaba, Int. J. Mod. Phys. A 19 (2004) 3265 [arXiv:hep- th/0304245 [hep-th]]

    2004

  39. [47]

    Carena, A

    M. Carena, A. Daleo, B. A. Dobrescu and T. M. P. Tait, Phys. Rev. D 70 (2004), 093009 [arXiv:hep-ph/0408098 [hep-ph]]. 24

    2004 arXiv

  40. [48]

    Dawson, M

    S. Dawson, M. Forslund and M. Schnubel, Phys. Rev. D 110 (2024) no.1, 015002 [arXiv:2404.01375 [hep-ph]]

    2024 arXiv

  41. [49]

    Navas et al

    S. Navas et al. [Particle Data Group], Phys. Rev. D 110 (2024) no.3, 030001

    2024

  42. [50]

    Djouadi, Phys

    A. Djouadi, Phys. Rept. 457 (2008) 1 [arXiv:hep-ph/0503172 [hep-ph]]

    2008 arXiv

  43. [51]

    Buchalla, O

    G. Buchalla, O. Cata, A. Celis, M. Knecht and C. Krause, Nucl. Phys. B 928 (2018), 93 [arXiv:1710.06412 [hep-ph]]

    2018 arXiv

  44. [52]

    Alonso, K

    R. Alonso, K. Kanshin and S. Saa, Phys. Rev. D 97 (2018) no.3, 035010 [arXiv:1710.06848 [hep-ph]]

    2018 arXiv

  45. [53]

    de Blas, O

    J. de Blas, O. Eberhardt and C. Krause, JHEP 07 (2018) 048 [arXiv:1803.00939 [hep-ph]]

    2018 arXiv

  46. [54]

    Buchalla, M

    G. Buchalla, M. H¨ ofer and C. M¨ uller-Salditt, Phys. Rev. D107 (2023) no.7, 076021 [arXiv:2212.08560 [hep-ph]]

    2023 arXiv

  47. [55]

    Braun, P

    J. Braun, P. Bredt, G. Heinrich and M. H¨ ofer, JHEP07 (2025) 209 [arXiv:2502.09132 [hep-ph]]

    2025 arXiv

  48. [56]

    Hahn and M

    T. Hahn and M. Perez-Victoria, Comput. Phys. Commun. 118 (1999) 153 [arXiv:hep- ph/9807565 [hep-ph]]. 25

    1999

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