The Two-Higgs Doublet Model beyond tree-level: A gauge-invariant formalism

I. Schienbein; L. Sartore; M. Maniatis; T. Guerandel

REVIEW 2 major objections 5 minor 34 references

The Two-Higgs Doublet Model beyond tree-level: A gauge-invariant formalism

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read One-loop corrections to the two-Higgs-doublet scalar masses can be computed in a manifestly gauge-invariant way, using bilinears and the $\hbar$-expansion, without fixing the Higgs gauge or dealing with Goldstone mixing.

desk verdict A genuinely useful gauge-invariant one-loop THDM toolkit, but the Goldstone-IR cancellation is asserted rather than demonstrated and the numerical example has no independent cross-check. read the letter →

arxiv 2505.12564 v1 pith:ZGEEXHOU submitted 2025-05-18 hep-ph

T. Guerandel , M. Maniatis , L. Sartore , I. Schienbein This is my paper · ORCID

classification hep-ph PACS 12.60.Fr11.30.Qc14.80.Cp

keywords two-Higgs-doubletmodelbilinearformalismgaugeinvarianceone-loopcorrectionshbar-expansioneffectivepotentialGoldstoneinfrareddivergencesscalarmassspectrum

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 establishes that one-loop corrections to the scalar mass spectrum of the general two-Higgs-doublet model (THDM) can be computed while keeping electroweak gauge invariance manifest at every step. Its method combines the bilinear formalism, four real gauge-invariant combinations of the two Higgs doublets, with the $\hbar$-expansion, an iterative solution of the stationarity conditions around the tree-level vacuum. The payoff is that no gauge choice for the Higgs fields is needed, and the problematic Goldstone-sector mixings and infrared divergences are avoided or cancel explicitly. If correct, this gives a compact set of analytic formulas, equations (7.5) and (7.6), applicable to any THDM and useful for precision tests such as the electroweak $\rho$ parameter.

What carries the argument

The central object is the $2\times 2$ positive-semidefinite bilinear matrix $K = \psi\psi^\dagger$, whose four real components $K_0, K_1, K_2, K_3$ are gauge-invariant bilinears. At a charge-conserving minimum $K$ has rank 1, which encodes correct electroweak symmetry breaking and makes the neutral mass matrix expressible as $\gamma_3(M - 2u\,\tilde{g})\gamma_3^T$. The second ingredient is the $\hbar$-expansion with $\kappa = 1/(16\pi^2)$: the potential and vacuum are expanded around their tree-level values, and the stationarity conditions are solved order by order, with derivatives $D_a = \gamma_{a\nu}\partial_\nu$ projecting onto the neutral mass eigenstates. These two ingredients turn the one-loop calculation into a small set of algebraic formulas involving tree-level masses, Yukawa bilinears, and gauge-boson bilinears.

What would settle it

For a fixed benchmark of a CP-conserving THDM, compute the one-loop pole masses through the secular equation (6.22) with explicit self-energies in a general $R_\xi$ gauge and compare with equations (7.5)--(7.6). Residual dependence of the physical masses on the gauge-fixing parameter, or non-vanishing Goldstone masses, would falsify the paper's claim.

Watch

Extended reading notes

Core claim

The central claim is that the one-loop corrected charged and neutral Higgs masses are given by $m^2_{H^\pm} = (m^2_{H^\pm})^{(0)} + \kappa (m^2_{H^\pm})^{(1)} + O(\kappa^2)$ and $m_a^2 = (m_a^2)^{(0)} + \kappa (m_a^2)^{(1)} + O(\kappa^2)$, where the first-order shifts follow from gauge-invariant derivatives of the one-loop effective potential evaluated at the tree-level minimum. Writing the full THDM Lagrangian in terms of bilinears makes the all-order scalar mass matrix block-diagonal in a canonical basis, with the charged-pair mass equal to $4uK_0$ at every order; the $\hbar$-expansion then converts the one-loop stationarity condition into simple algebraic equations for the vacuum shifts and mass corrections. The paper provides explicit closed-form expressions for the gauge, fermion, and scalar contributions to these shifts in Sec. 7.

Load-bearing premise

The load-bearing premise is that quantum corrections shift the vacuum only by small perturbative steps away from the tree-level, electrically neutral minimum; a true one-loop minimum of a different character, such as charge-breaking or far away, would be missed.

Editorial extensions

If this is right

The one-loop shifted masses in (7.5) and (7.6) are direct analytic predictions for any THDM once the tree-level vacuum and masses are known.
The charged-Higgs mass relation $m^2_{H^\pm} = 4uK_0$ holds at every perturbative order, so its one-loop correction is fixed entirely by the shifts in $u$ and $K_0$.
Goldstone bosons stay massless order by order and never mix with physical scalars, and the usual IR-divergent Goldstone contributions cancel when physical pole masses are extracted through the secular equation.
The gauge, fermion, and scalar contributions to the shifts separate into modular closed-form expressions involving the integrals $A$ and $B$, making phenomenological scans straightforward.
The method applies to any THDM, including models with explicit or softly broken $Z_2$ symmetries and different Yukawa types, once the parameters are expressed in bilinear form.

Reading between the lines

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

Beyond the paper: the same vacuum-shift formulas should feed directly into gauge-invariant one-loop predictions for the electroweak oblique parameters $S$, $T$, $U$, which are not computed here.
Beyond the paper: the rank-1 vacuum condition gives a built-in consistency check for numerical implementations, since physical masses must stay gauge-independent and Goldstone modes must remain massless.
Beyond the paper: because the $\hbar$-expansion is iterative, the structure carries to two loops whenever a two-loop effective potential in bilinears becomes available, with no new gauge-fixing step required.
Beyond the paper: one could test the method's reach by benchmarking it against conventional diagrammatic one-loop calculations for non-CP-conserving or type-II Yukawa scenarios, where the $|\xi_{ud}|^2$ terms are active.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper does what it says: it extends the bilinear formalism to one loop using the ℏ-expansion and packages the results as compact, ready-to-use formulas. If you work in the THDM, having the scalar mass corrections in gauge-invariant bilinear form is a real convenience, and the authors deserve credit for carrying the algebra through and collecting it cleanly in Sec. 7. The tree-level masses are used as inputs, not fitted to the output, so there is no circularity problem.

The structure is coherent and the internal derivations are careful. The weak points are exactly where the stress-test note lands. First, the cancellation of the B(0,0) Goldstone divergences is argued by citing the general secular-equation logic of Denner, but the paper never shows, for its own ℏ-expanded mass matrix and couplings, that the divergent terms in Eq. (5.82) actually drop out of the physical masses. That is not a fatal flaw -- the argument is plausible and the mechanism is standard -- but it is a gap, and an explicit check in this formalism would close it.

Second, the numerical example in Sec. 8 has no comparison to any existing one-loop THDM calculation. Since the algebraic expressions are long, a systematic sign or factor error could easily hide. A single benchmark compared against, say, a conventional diagrammatic one-loop calculation would substantially raise confidence. Without that, the central claim rests on internal consistency, which is good but not conclusive.

One more thing: the paper overstates the novelty a little. The components -- bilinears, ℏ-expansion, gauge-invariant effective potential -- all exist. What is new is the combination and the explicit formulas, which is enough to justify publication but not to call it a breakthrough.

Overall: the framework is plausible, the formulas are likely correct, and the paper deserves refereeing. A serious referee should ask for two additions: an explicit demonstration of the Goldstone cancellation and an independent numerical comparison. If those are provided, I would be comfortable with the result. Who is this for? THDM phenomenologists doing precision studies -- they will want the formulas in Sec. 7. I would not cite it in my own work right now, but I would bring it to the attention of people who might.

Referee Report

2 major / 5 minor

Summary. The manuscript develops a gauge-invariant, bilinear-formalism treatment of one-loop corrections in the general Two-Higgs-Doublet Model (THDM). The authors review the bilinear formulation of the THDM potential, gauge sector, and Yukawa sector, then combine it with the ℏ-expansion (Sec. 4) to solve the one-loop stationary-point equations iteratively around the tree-level vacuum. Sections 5 and 6 derive the gauge, fermionic, and scalar contributions to the one-loop effective potential and its first and second bilinear-field derivatives, and express the one-loop shifts of the charged and neutral scalar masses in terms of these quantities. The central results are Eqs. (7.5) and (7.6), which give m_H±^2 and m_a^2 at next-to-leading order, together with the collection of all required derivatives and couplings in Sec. 7. The method is applied in Sec. 8 to a CP-conserving type-I THDM, with a numerical spectrum shown in Fig. 1 as a function of tanβ.

Significance. If the central formulas (7.5)–(7.6) are correct, the paper provides a compact and manifestly gauge-invariant route to one-loop THDM scalar masses that avoids gauge-fixing of the Higgs fields and Goldstone-sector mixing, and it is directly applicable to any THDM. The manuscript has genuine strengths: the derivations are detailed and systematic; the summary section (Sec. 7) is self-contained; the approach is parameter-free in the sense that no parameter is fitted to the one-loop output (tree-level masses, tanβ, and cos(α−β) are used as inputs); and the appendices provide the nontrivial second-derivative formulae. The main unresolved points concern the infrared behaviour of the final mass formula and the absence of an external numerical validation, both of which are load-bearing for the paper's central claim.

major comments (2)

[Secs. 5.3, 6, 7 (Eqs. (5.82), (6.22)-(6.27), (7.6), (7.28))] The cancellation of the spurious Goldstone-boson divergences is asserted but not demonstrated for the specific formula that is the paper's main result. In Eq. (5.82) (reproduced in Eq. (7.19)) the terms proportional to B(0,0) have coefficients (1/2)(λ̄_{aG0G0}λ̄_{bG0G0} + λ̄_{aG±G±}λ̄_{bG±G±}); using the couplings of Eq. (7.20), λ̄_{aG0G0} and λ̄_{aG±G±} are each proportional to m_a^2 k̄_a / √(2K0), so this coefficient is generically nonzero at a charge-conserving vacuum. The remaining contributions to (m_a^2)^(1) in Eq. (7.6) — the vacuum-shift terms (K_0^(1)/K_0^(0))(m_a^2)^(0) and f̄^±_a δ̄^(1)_a — depend on D̄_a V^(1) through Eq. (7.1) and involve only the A-functions, so they cannot cancel the B(0,0) divergence. The discussion in Sec. 6 (Eqs. (6.22)–(6.27)) is the standard argument, following Ref. [34], that on-shell pole masses are IR finite once the momentum-dependent self-energy combination Π(p^2)−Π(0) is included; it does not show that the zero-momentum object (7.6) is that pole mass. In the computational flow the divergence is instead disposed of by Eq. (7.28), which sets Bs(0,0)=0 — a prescription that conflicts with the definition B(x,x)=log(x/µ^2) in (5.18) and that changes the numerical result by the finite part of the Goldstone loop unless an independent cancellation is proved. As written, (7.6) is an MS-bar zero-momentum curvature mass, and its IR finiteness and gauge invariance do not follow from the arguments given. The authors should either provide the explicit pole-mass formula, including the Π(p^2)−Π(0) contributions that replace B(0,0) by the finite B(p^2,0,0), or prove that the B(0,0) coefficients in the final combination (7.6) vanish identically.
[Sec. 8.2, Fig. 1] The numerical application is not validated against any independent one-loop THDM calculation. The one-loop masses in Fig. 1 follow from many pages of algebraic expressions (Secs. 5–7 and Appendices A–B), and internal consistency cannot detect a global sign error or a missing factor in, for example, the scalar couplings of Eq. (7.20) or the fermionic coefficients of Eq. (5.70). I recommend adding a comparison with an existing THDM one-loop spectrum for a benchmark point — for instance by recomputing the same type-I scenario with a public code or with the one-loop formulae of an independent calculation (see Ref. [5] and references therein) — and reporting the numerical one-loop shifts, not only the plot, so that the central claim of Eqs. (7.5)–(7.6) can be checked.

minor comments (5)

[Sec. 7, Eq. (7.19)] The third displayed equation of (7.19) has unbalanced braces and a stray period, and the quantities λ0aa and λ0H±H± are written without the bar used in Eq. (5.85); please align the notation with (5.85)–(5.86).
[Sec. 7, Eq. (7.28)] The value Bs(0,0)=0 should be introduced as an explicit regularization prescription with a justification, rather than as a value that follows from Eqs. (5.18)–(5.19), since the limit x→0 of log(x/µ^2) is not defined there.
[Sec. 8.1, Eqs. (8.20) and (8.22)] The constraint |α|=|β|=π/2 combined with cos(α−β)=1 is confusing, since the latter relation already suggests α=β; moreover the barred four-vector f̄K in Eq. (8.22) is used before it is defined. Please clarify the alignment conditions and the rotation that defines f̄K.
[Secs. 6–8, Fig. 1] The manuscript explains that results are first obtained in the MS-bar scheme and that one should switch to the on-shell scheme for pole masses, but Fig. 1 does not state which scheme the plotted curves correspond to; please specify the scheme, the renormalization scale, and the scale dependence of the one-loop shifts.
[Title and general text] The running title contains 'T wo-Higgs' with an extra space, and there are a few similar formatting artifacts; these should be cleaned up before submission.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular reduction found; the one-loop mass shifts are computed from tree-level inputs via the hbar-expansion and are not fitted to the target quantities, while the heavy self-citations to [7,19] provide prior established derivations rather than presupposing the present results.

full rationale

Walking the derivation chain: Secs. 3-4 establish the gauge-invariant mass matrices and the hbar-expansion; Secs. 5-6 derive one-loop derivatives of the effective potential; Sec. 7 collects the final formulas; Sec. 8 fixes potential parameters from tree-level inputs (8.1)-(8.22) and then evaluates the one-loop corrections (7.5)-(7.6). The one-loop masses are not set equal to the inputs by construction: m^(1)_H+ and m^(1)_a are explicit functions of one-loop potential derivatives, the tree-level vacuum, and the shift of the Lagrange multiplier u^(1), with no parameter fitted to absorb the one-loop result. The self-citations to [19] for the scalar mass-matrix formalism and to [7] for stability and electroweak-symmetry-breaking conditions are load-bearing, but they are prior published derivations with stated assumptions that do not include the one-loop predictions made here; they therefore count as independent support rather than circularity. The main technical caveat is that the cancellation of the B(0,0) Goldstone-boson infrared divergences is argued through the general secular-equation identity (6.22)-(6.23) from [34] and is not explicitly exhibited inside the final MS-scheme formula (7.6). This is an omitted demonstration and a correctness risk, but not a circular reduction, since the divergent terms are not used as inputs to define the predicted masses.

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

The derivation itself introduces no fitted parameters. The benchmark application in Sec. 8.2 fixes scalar masses, tanβ, cos(α−β), and fermion masses by hand as illustrative inputs; these do not enter the formal derivation. The axioms are standard perturbative QFT assumptions plus the imported bilinear formalism from the authors' earlier work.

free parameters (4)

Benchmark tree-level scalar masses (m_h^(0), m_A^(0), m_H^(0), m_H±^(0)) = 125.25, 190, 300, 200 GeV
Chosen by hand in Sec. 8.2 as inputs to define the example model; not fitted to data and not part of the formal derivation.
tanβ = scanned from 0 to 10
Scanned input parameter in Sec. 8.2 to produce the one-loop spectrum in Fig. 1.
cos(α−β) = 1
Alignment-limit choice in Sec. 8.2 for the illustrative CP-conserving benchmark.
Fermion masses m_b, m_t, m_tau = 4.18, 172.5, 1.777 GeV
Standard PDG inputs used in Sec. 8.2 for the numerical example.

assumptions (4)

domain assumption The quantum corrections to the potential and vacuum can be expanded perturbatively in powers of κ=1/(16π²) around the tree-level solution
Section 4 states this assumption explicitly. If the true one-loop minimum were of a different character, for example charge-breaking, the iterative ℏ-expansion would not converge to it.
domain assumption The Landau-gauge, MS-bar one-loop effective potential with the Coleman-Weinberg formula is sufficient to compute gauge-invariant physical masses
Section 5 uses this standard result; the paper argues that the ℏ-expansion and on-shell scheme remove gauge artefacts, but does not give a general proof of gauge invariance of the final masses.
domain assumption The bilinear formalism results of Refs. [7] and [19], including the one-to-one correspondence, canonical rotation, and tree-level mass matrices, are valid
Sections 2 and 3 import the central machinery from earlier work by overlapping authors without reproving it. The scalar mass matrix expressions (3.27) to (3.32) are taken from Ref. [19].
standard math Standard eigenvalue perturbation formulas for field-dependent mass matrices, equations (5.10) and (5.13)
Appendix A derives these from non-degenerate perturbation theory; degenerate cases are handled by a basis choice, as stated in Section 5.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The Two-Higgs Doublet Model beyond tree-level: A gauge-invariant formalism." pith.science (2026). https://pith.science/paper/ZGEEXHOU

@misc{pith2026250512564,
  author       = {Pith},
  title        = {Pith review of: The Two-Higgs Doublet Model beyond tree-level: A gauge-invariant formalism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZGEEXHOU}},
  note         = {Machine review of arXiv:2505.12564}
}

abstract

Employing the gauge-invariant formalism in the two-Higgs-doublet model (THDM) offers profound insights into the model's fundamental structure. A specific set of gauge-invariant bilinear combinations, constructed from the Higgs doublets, establishes a one-to-one correspondence between the components of the doublet fields and real-valued bilinears. This formalism provides a compact and consistent framework to study various aspects of the THDM, including stability, electroweak symmetry breaking, basis transformations, and general symmetries of the Higgs potential. Recently, the bilinear formalism has been extended beyond the Higgs potential to encompass the full THDM, including the gauge and Yukawa sectors, all in gauge-invariant terms. In this work, we advance the formalism further by incorporating quantum corrections. Specifically, we show how bilinears, combined with the $\hbar$-expansion, can be used to compute one-loop corrections. We provide concise, gauge-invariant expressions for these corrections, which are directly applicable to the THDM.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references · 12 canonical work pages

[34]

Denner,Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch

A. Denner,Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41 (1993) 307 [0709.1075]. – 51 –

arXiv 1993
[5]

Branco, P.M

G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva,Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [1106.0034]

arXiv 2012
[1]

Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01

2022
[2]

Lee,A Theory of Spontaneous T Violation, Phys

T.D. Lee,A Theory of Spontaneous T Violation, Phys. Rev. D8 (1973) 1226

work page 1973
[3]

Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh

A.D. Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz.5 (1967) 32

1967
[4]

Martin,A Supersymmetry primer, Adv

S.P. Martin,A Supersymmetry primer, Adv. Ser. Direct. High Energy Phys.18 (1998) 1 [hep-ph/9709356]

arXiv 1998
[6]

Nagel,New aspects of gauge-boson couplings and the Higgs sector, Ph.D

F. Nagel,New aspects of gauge-boson couplings and the Higgs sector, Ph.D. thesis, Heidelberg U., 2004

work page 2004
[7]

Maniatis, A

M. Maniatis, A. von Manteuffel, O. Nachtmann and F. Nagel,Stability and symmetry breaking in the general two-Higgs-doublet model, Eur. Phys. J.C48 (2006) 805 [hep-ph/0605184]

arXiv 2006

Show all 34 references

[8]

Nishi,CP violation conditions in N-Higgs-doublet potentials, Phys

C.C. Nishi,CP violation conditions in N-Higgs-doublet potentials, Phys. Rev. D74 (2006) 036003 [hep-ph/0605153]

2006 arXiv
[9]

Ivanov,Minkowski space structure of the Higgs potential in 2HDM

I.P. Ivanov,Minkowski space structure of the Higgs potential in 2HDM. II. Minima, symmetries, and topology, Phys. Rev. D77 (2008) 015017 [0710.3490]

2008 arXiv
[10]

Maniatis and O

M. Maniatis and O. Nachtmann,Symmetries and renormalisation in two-Higgs-doublet models, JHEP 11 (2011) 151 [1106.1436]

2011 arXiv
[11]

Ferreira, B

P.M. Ferreira, B. Grzadkowski, O.M. Ogreid and P. Osland,Symmetries of the 2HDM: an invariant formulation and consequences, JHEP 02 (2021) 196 [2010.13698]

2021 arXiv
[12]

Bento, R

M.P. Bento, R. Boto, J.a.P. Silva and A. Trautner,A fully basis invariant Symmetry Map of the 2HDM, JHEP 21 (2020) 229 [2009.01264]. – 49 –

2020 arXiv
[13]

Maniatis, D

M. Maniatis, D. Mehta and C.M. Reyes,Stability and symmetry breaking in a three-Higgs-doublet model with lepton family symmetry O(2)⊗Z2, Phys. Rev. D92 (2015) 035017 [1503.05948]

2015 arXiv
[14]

Maniatis and O

M. Maniatis and O. Nachtmann,Stability and symmetry breaking in the general n-Higgs-doublet model, Phys. Rev. D92 (2015) 075017 [1504.01736]

2015 arXiv
[15]

Maniatis, L

M. Maniatis, L. Sartore and I. Schienbein,Multiple point principle in the general Two-Higgs-Doublet model, JHEP 08 (2020) 158 [2001.10541]

2020 arXiv
[16]

Bennett and H.B

D.L. Bennett and H.B. Nielsen,Predictions for nonAbelian fine structure constants from multicriticality, Int. J. Mod. Phys. A9 (1994) 5155 [hep-ph/9311321]

1994 arXiv
[17]

Bennett,Multiple point criticality, nonlocality, and fine tuning in fundamental physics: Predictions for gauge coupling constants gives alpha**-1 = 136.8 +- 9, hep-ph/9607341

D.L. Bennett,Multiple point criticality, nonlocality, and fine tuning in fundamental physics: Predictions for gauge coupling constants gives alpha**-1 = 136.8 +- 9, hep-ph/9607341

arXiv
[18]

Bennett and H.B

D.L. Bennett and H.B. Nielsen,Gauge couplings calculated from multiple point criticality yield alpha**(-1) = 136.8 +- 9: At last the elusive case of U(1), Int. J. Mod. Phys. A14 (1999) 3313 [hep-ph/9607278]

1999 arXiv
[19]

Sartore, M

L. Sartore, M. Maniatis, I. Schienbein and B. Herrmann,The general Two-Higgs Doublet Model in a gauge-invariant form, JHEP 12 (2022) 051 [2208.13719]

2022 arXiv
[20]

Ma and M

E. Ma and M. Maniatis,Symbiotic Symmetries of the Two-Higgs-Doublet Model, Phys. Lett. B683 (2010) 33 [0909.2855]

2010 arXiv
[21]

Q.-H. Cao, K. Cheng and C. Xu,Global Symmetries and Effective Potential of 2HDM in Orbit Space, 2305.12764

arXiv
[22]

Xiao and L

Z.-j. Xiao and L. Guo,B0 anti-B0 mixing and B —> X(s) gamma decay in the third type 2HDM: Effects of NLO QCD contributions, Phys. Rev. D69 (2004) 014002 [hep-ph/0309103]

2004 arXiv
[23]

Krawczyk and D

M. Krawczyk and D. Temes,2HDM(II) radiative corrections in leptonic tau decays, Eur. Phys. J. C 44 (2005) 435 [hep-ph/0410248]

2005 arXiv
[24]

Lopez-Val and J

D. Lopez-Val and J. Sola,Neutral Higgs-pair production at Linear Colliders within the general 2HDM: Quantum effects and triple Higgs boson self-interactions, Phys. Rev. D81 (2010) 033003 [0908.2898]

2010 arXiv
[25]

Lopez-Val, J

D. Lopez-Val, J. Sola and N. Bernal,Quantum effects on Higgs-strahlung events at Linear Colliders within the general 2HDM, Phys. Rev. D81 (2010) 113005 [1003.4312]

2010 arXiv
[26]

Diaz-Cruz, C.G

J.L. Diaz-Cruz, C.G. Honorato, J.A. Orduz-Ducuara and M.A. Perez,One-loop decays A0→ZZ,Zγ,γγ within the 2HDM and its search at the LHC, Phys. Rev. D90 (2014) 095019 [1403.7541]

2014 arXiv
[27]

Jenniches, C

L. Jenniches, C. Sturm and S. Uccirati,Electroweak corrections in the 2HDM for neutral scalar Higgs-boson production through gluon fusion, JHEP 09 (2018) 017 [1805.05869]

2018 arXiv
[28]

Su,Probing loop effects in wrong-sign Yukawa coupling region of Type-II 2HDM, Eur

W. Su,Probing loop effects in wrong-sign Yukawa coupling region of Type-II 2HDM, Eur. Phys. J. C 81 (2021) 404 [1910.06269]

2021 arXiv
[29]

Grimus, L

W. Grimus, L. Lavoura, O.M. Ogreid and P. Osland,A Precision constraint on multi-Higgs-doublet models, J. Phys. G 35 (2008) 075001 [0711.4022]

2008 arXiv
[30]

Brodsky and P

S.J. Brodsky and P. Hoyer,The ¯h Expansion in Quantum Field Theory, Phys. Rev. D83 (2011) 045026 [1009.2313]. – 50 –

2011 arXiv
[31]

Gunion, H.E

J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson,The Higgs Hunter’s Guide, Front. Phys. 80 (2000) 1

2000
[32]

Gunion, H.E

J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson,Errata for the Higgs hunter’s guide, hep-ph/9302272

arXiv
[33]

Coleman and E.J

S.R. Coleman and E.J. Weinberg,Radiative Corrections as the Origin of Spontaneous Symmetry Breaking, Phys. Rev. D7 (1973) 1888

1973

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [34]

Denner,Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch

A. Denner,Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41 (1993) 307 [0709.1075]. – 51 –

arXiv 1993

[2] [5]

Branco, P.M

G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva,Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [1106.0034]

arXiv 2012

[3] [1]

Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01

2022

[4] [2]

Lee,A Theory of Spontaneous T Violation, Phys

T.D. Lee,A Theory of Spontaneous T Violation, Phys. Rev. D8 (1973) 1226

work page 1973

[5] [3]

Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh

A.D. Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz.5 (1967) 32

1967

[6] [4]

Martin,A Supersymmetry primer, Adv

S.P. Martin,A Supersymmetry primer, Adv. Ser. Direct. High Energy Phys.18 (1998) 1 [hep-ph/9709356]

arXiv 1998

[7] [6]

Nagel,New aspects of gauge-boson couplings and the Higgs sector, Ph.D

F. Nagel,New aspects of gauge-boson couplings and the Higgs sector, Ph.D. thesis, Heidelberg U., 2004

work page 2004

[8] [7]

Maniatis, A

M. Maniatis, A. von Manteuffel, O. Nachtmann and F. Nagel,Stability and symmetry breaking in the general two-Higgs-doublet model, Eur. Phys. J.C48 (2006) 805 [hep-ph/0605184]

arXiv 2006