Note on tree-level unitarity in the General Two Higgs Doublet Model

Abdesslam Arhrib; Andrew Akeroyd (KEK-Japan); El--Mokhtar Naimi (Univ-Tangier & Rabat)

REVIEW

Note on tree-level unitarity in the General Two Higgs Doublet Model

Andrew Akeroyd (KEK-Japan), Abdesslam Arhrib, El--Mokhtar Naimi (Univ-Tangier & Rabat)

High Energy Physics - Phenomenology · Submitted 3 Jun 2000 · 21 references

Pith's verdict: The λ5 ≠ 0 unitarity analysis is genuinely new and the mechanism is visible in the paper's own equations, but every headline number rests on an undocumented random scan.

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CitationAbdesslam Arhrib, Andrew Akeroyd (KEK-Japan), El--Mokhtar Naimi (Univ-Tangier & Rabat). "Note on tree-level unitarity in the General Two Higgs Doublet Model." arXiv:hep-ph/0006035 (2000). https://pith.science/paper/B6GSGKMB

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Worth your time, with one caveat that matters for how you'd use the numbers. The new content is real: nobody had run tree-level unitarity on the general THDM with the soft-breaking quartic λ5 turned on, and the paper does it. The λ5 = 0 part is a modest improvement on Kanemura–Kubota–Takasugi — they add the eight charged-state channels, which yields exactly one new eigenvalue p1 (Eq. 2.9), and p1 turns out to be what sets the H± ceiling. That's a clean, checkable addition, and they say so plainly rather than overselling it. The eigenvalue algebra in Eqs. 2.5–2.9 is standard and I found no errors in it. The mechanism behind the main claim is analytic and does not depend on any sampling: λ5 enters λ1, λ2, λ3 with opposite-sign tanβ dependence (Eqs. 2.2–2.4), so it can partially cancel the combination that a± bounds. That is the substance of abstract:s2 and it holds up. Where I'd push back is the quantitative envelope. Section 3 says only that masses and mixing angles are varied 'randomly over a very large parameter space' — no ranges, no point count, no convergence check, no maximizing point quoted. Every entry in Table 1 and every curve in Figs. 1–2 is a scan maximum, so an unstated box edge is indistinguishable from a unitarity ceiling. Fig. 1 makes this concrete: the flat Mh ≈ 670 GeV plateau at λ5 = 15 across all tanβ is what you'd expect if the sampled mh range, not the constraint, is doing the terminating. If so, part of 'considerably weakened' is an artifact and the discrimination proposal in Section 3.2 loses its quantitative footing. Related: they assert that imposing |λi| ≤ 8π shifts things only marginally, and never show it — with λ5 = 15 that is not a small assumption. One thing I'd not repeat: the 435 vs 410 GeV gap is not a contradiction. Table 1 is at tanβ ≈ 0.5, KKT's 410 GeV is at tanβ = 1, and the bound strengthens with tanβ, so the ordering is expected. The live issue is the missing scan specification, not that comparison. Audience is THDM phenomenology people and anyone quoting a light-Higgs ceiling as a function of tanβ. Send it out; ask for the scan ranges and a convergence check.

Referee report

Significance

The qualitative observation is worth having. The λ5 dependence is visible analytically in the authors' own eigenvalues: λ3 carries −λ5/4 in Eq. (2.2) and λ1, λ2 carry the tanβ-dependent shifts of Eqs. (2.3)–(2.4), so λ5 enters both the trace and the square-root term of a± in Eq. (2.6). The identification of the additional eigenvalue p1 from the charged 8×8 block is a genuine, checkable increment over KKT, and the point that the Mh ceiling is not a fixed function of tanβ but depends on an extra quartic coupling is a useful one for THDM phenomenology and for interpreting a possible light Higgs signal. The paper is a theoretical note with no data fit and no free parameters introduced ad hoc; its content is a derivation plus a numerical envelope. The derivation is standard and appears sound. The numerical envelope, which is what the abstract actually advertises, is where the assessment has to concentrate, because every number in Table 1 and every curve in Figs. 1–2 is the output of a random scan whose specification is not given.

Major objections (4)

[§3, Table 1, Figs. 1–2] The entire quantitative content of the paper rests on an unspecified random scan. Section 3 states only that 'we vary all the Higgs masses and mixing angles randomly over a very large parameter space'. No scan ranges are given for MH±, MA, Mh, MH, α or tanβ; no number of sampled points is stated; no convergence or stability check is reported; and no maximizing parameter point is exhibited for any entry of Table 1 or any point of the curves in Figs. 1–2. Because every quoted bound is a scan maximum, an unstated box edge is numerically indistinguishable from a unitarity ceiling. This matters directly for abstract:s2: the claim that λ5 'weakens the mass bounds considerably' is a statement about maxima, and the reader cannot tell how much of the weakening is the eigenvalue constraint and how much is where the sampling stopped. The authors should state the scan ranges and point count, show that the maxima are stable under enlargement of the ranges, and, for at least the endpoints of each curve in Fig. 1, report the parameter point that saturates the bound together with the eigenvalue that is saturated.
[Table 1 and §3.1] The comparison in Table 1 is not apples-to-apples and the accompanying text overstates what the table shows. The text says that imposing only |a+| ≤ 8π reproduces KKT's Mh ≤ 410 GeV, and that 'when all eigenvalue bounds are applied simultaneously we find improved bounds'. A superset of constraints cannot produce a weaker bound, yet Table 1 lists Mh = 435 GeV for this work against 410 GeV for KKT. The caption attributes the table to tanβ ≈ 0.5 while the introduction attributes KKT's 410 GeV to tanβ = 1, and since the bound strengthens with tanβ the ordering 435 > 410 is the expected one. That resolution needs to be stated in the table itself, with the tanβ value used for each column, and the word 'improved' should be replaced by an explicit statement of what is being compared at what tanβ. As written, the table appears to contradict the text that introduces it.
[Fig. 1 and §3.2] For λ5 = 15 the authors report 'a horizontal line at Mh ≈ 670 GeV' across the whole plotted tanβ range. A bound that is exactly flat in tanβ over the entire range is precisely what one expects when the sampled mh interval, rather than the eigenvalue constraint, terminates the scan. The authors should demonstrate that this plateau is a unitarity ceiling and not a scan artefact, for example by exhibiting the saturating parameter point at two well-separated values of tanβ and showing that the same eigenvalue sits at 8π in both cases, and by showing that the plateau is unchanged when the upper end of the sampled mh range is raised. If the plateau does move with the scan box, the statement that λ5 = 15 raises the ceiling 'for all values of tanβ' needs to be withdrawn or requantified.
[§3.2 and Conclusions] The discrimination proposal is stated more strongly than the paper's own perturbativity discussion supports. Figures 1 and 2 are produced without imposing |λi| ≤ 8π, and the text notes that imposing it 'strongly disfavours' tanβ ≥ 30 and lowers the MA and MH± bounds by 10–20 GeV. But the illustrative example used to make the discrimination case is 'λ5 = 1 comfortably permits values of tanβ = 60', which lies in the region the perturbativity cut removes. The abstract's suggestion that a measurement of Mh and tanβ may discriminate between the two potentials should therefore be qualified: the discriminating region is bounded above in tanβ by perturbativity, and the size of the surviving region should be shown, for example as a shaded allowed band in the (Mh, tanβ) plane for λ5 = 0 and for representative λ5 ≠ 0 with |λi| ≤ 8π imposed. The phrase 'only leads to minor changes' in §3.2 should also be reconciled with the quoted 10–20 GeV shifts.

Minor objections (8)

[§2, Eqs. (2.5)–(2.9)] The eigenvalues of the 8×8 charged block are stated without derivation, and the reader is asked to accept that the block yields exactly f−, e2, f1, c±, b± and p1. Since the new eigenvalue p1 is the paper's principal technical addition, it would help to give the 8×8 matrix, or at least its non-zero structure, in an appendix so that the counting can be checked independently.
[§2, third submatrix] The sentence 'The 2×2 matrix possesses the eigenvalues d± and c±, with d± = c±' is circular as written: if d± = c± then the third submatrix introduces no new constraint, and the notation d± is redundant. Either state the eigenvalues of that block explicitly or drop d± from Eq. (3.1).
[§1 and §2] The discrete symmetry is written as 'Φi → −Φi', which is ambiguous as to which doublet is flipped; the standard convention is Φ2 → −Φ2. The same remark applies where the symmetry is invoked in §2 to argue that λ5 = 0 restores it.
[Table 1 caption] The caption should state the tanβ value used for each column and the scan ranges employed, so that the table can be read without cross-referencing §3.1.
[Figs. 1–2] The figures would be easier to use if the curves were labelled directly with their λ5 values rather than only in the caption, and if the vertical axis of Fig. 2 identified which scalar saturates the bound at each λ5.
[References] Reference [14] misspells 'Gasalbuoni' as 'Gasalbuni'. Reference [20] is a conference contribution (hep-ph/9911541) and should be labelled as such. Reference [18] cites two unpublished theses as the source of the quartic-vertex expressions; if a published source exists for those expressions it should be added.
[§3.2] The sentence 'Imposing this condition only leads to minor changes in the numerical results which will be commented on when necessary' is vague; the comment that follows gives 10–20 GeV shifts, which should be stated at the point where the condition is introduced.
[Throughout] There are several typographical errors: 'focussed' for 'focused', 'which will covered' for 'which will be covered', and inconsistent rendering of the λ5 ≠ 0 condition in the section headings.

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The paper

The paper claims

Adding the discrete-symmetry-breaking quartic coupling lambda5 to the Two Higgs Doublet Model relaxes tree-level unitarity upper bounds on Higgs masses and removes the tight correlation between the lightest CP-even Higgs mass and tan(beta).

The reading

In the Standard Model the Higgs boson mass is not predicted, but it cannot be arbitrarily large: if the Higgs is too heavy, the probability amplitudes for Higgs-Higgs scattering grow past the limit allowed by unitarity, and the theory stops making sense at high energy. The same logic applies to extended Higgs sectors. This paper works in the Two Higgs Doublet Model, which has five physical Higgs bosons (two neutral CP-even, one neutral CP-odd, and a charged pair), and asks how heavy they can be before tree-level scattering amplitudes violate unitarity. The technical tool is the matrix of quartic scalar couplings, whose eigenvalues must all stay below 8 pi. The authors compute that matrix in the unphysical field basis, where the entries are simple, and then rotate to physical fields. For the case where the potential respects a discrete symmetry (lambda5 = 0), they recover the eigenvalues of Kanemura, Kubota and Takasugi, add one more from charged-scalar channels those authors omitted, and impose all constraints at once. The resulting mass ceilings are tighter for the heavy CP-even, CP-odd and charged Higgs, though the lightest CP-even ceiling comes out slightly higher than the earlier number. The main new content is the case lambda5 not equal to zero, where the discrete symmetry is only softly broken. Because lambda5 enters the largest eigenvalues with large coefficients, it can partially cancel the other quartic couplings, so heavier Higgs bosons remain consistent with unitarity. The tight link between the lightest CP-even mass and tan(beta) that holds at lambda5 = 0 dissolves, and large tan(beta) becomes allowed. The authors suggest that measuring both the lightest Higgs mass and tan(beta) could therefore tell us whether the discrete symmetry is exact or softly broken.

Extended reading notes

Core claim

The paper's central assertion is that 'the inclusion of the discrete symmetry breaking term weakens the mass bounds considerably' (abstract, sentence 2), and specifically that with lambda5 not equal to zero the strong correlation between the lightest CP-even Higgs mass and tan(beta) found at lambda5 = 0 is relaxed, so that 'lambda5 = 1 comfortably permits values of tan(beta) = 60' whereas at lambda5 = 0 'values of tan(beta) >= 20 are strongly disfavoured'. If correct, the tree-level unitarity ceiling on the lightest CP-even Higgs is not a fixed function of tan(beta) but depends on an additional quartic coupling, and a measurement of the pair could discriminate between an exact and a softly broken discrete symmetry.

Load-bearing premise

Every quantitative bound in Table 1 and Figures 1 and 2 is the maximum found by a random scan over Higgs masses and mixing angles, and the paper never states the scan ranges, the number of sampled points, or any convergence check (Section 3: 'we vary all the Higgs masses and mixing angles randomly over a very large parameter space'). The implicit premise is that this sampling is dense enough that the observed maxima are the true maxima. The paper's own numbers undercut that premise: the lightest CP-even bound of 435 GeV in Table 1 exceeds the 410 GeV the authors say they reproduce from the single constraint |a+| <= 8 pi, which is impossible for a superset of constraints unless the scan misses the extremal region.

Original abstract

Tree-level unitarity constraints on the masses of the Higgs bosons in the general Two Higgs Doublet Model (THDM) are studied. We first consider the case where the Higgs potential is invariant under a discrete symmetry transformation, and derive strong constraints on the mass of the lightest CP-even Higgs boson ($M_h$) as a function of $\tan\beta$. We then show that the inclusion of the discrete symmetry breaking term weakens the mass bounds considerably. It is suggested that a measurement of $M_h$ and $\tan\beta$ may enable discrimination between the two Higgs potentials.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,620 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.24 · randomized assignment 0.01 · states quantitative result 0.22 · compares with prior results 0.41 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Tree-level unitarity constraints on the masses of the Higgs bosons in the general Two Higgs Doublet Model (THDM) are studied. We first consider the case where the Higgs potential is invariant under a discrete symmetry transformation, and derive strong constraints on the mass of the lightest CP-even Higgs boson ($M_h$) as a function of $\tan\beta$. We then show that the inclusion of the discrete symmetry breaking term weakens the mass bounds considerably. It is suggested that a measurement of $M_h$ and $\tan\beta$ may enable discrimination between the two Higgs potentials.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Tree-level unitarity constraints on the masses of the Higgs bosons in the general Two Higgs Doublet Model (THDM) are studied.	contribution 0.88	0.73	0.07	asserted 0.75
s1	We first consider the case where the Higgs potential is invariant under a discrete symmetry transformation, and derive strong constraints on the mass of the lightest CP-even Higgs boson ($M_h$) as a function of $\tan\beta$.	contribution 0.62	0.94	0.13	asserted 1.00
s2	We then show that the inclusion of the discrete symmetry breaking term weakens the mass bounds considerably.	result 0.99	0.90	0.31	asserted 1.00
s3	It is suggested that a measurement of $M_h$ and $\tan\beta$ may enable discrimination between the two Higgs potentials.	interpretation 0.89	0.27	0.42	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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.** Maximum Mh in GeV as a function of tan β for various values of λ5. the λi also restrict the allowed values of tan β in the THDM. Using the condition in [19] which requires |λi | ≤ 8π, we found that tan β ≥ 30 is strongly disfavoured. In Fig.2 we plot the maximum mass values (MS) of all the Higgs bosons as a function of λ5. Again all the Higgs masses and mixing angles have been varied randomly. We see that λ5 = 0 corresponds to the values in

**Figure 2.** Maximum mass value of the Higgs scalars (

Figures reproduced from arXiv:hep-ph/0006035 by the authors.

References

Works cited (21)

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A. Arhrib, Th´ ese d’Etat, University Cadi Ayyad (Marakesh, M orocco) Unpublished; A. Kraft, PhD Thesis , University of Karlsruhe (Germany) Unpublish ed

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Combining LHC Higgs limits with XENON and relic-density constraints rules out a 160-600 GeV Higgs in the Inert Doublet Model, and a four-lepton plus missing-energy channel at 14 TeV could reveal the surviving scenarios.
The Inert Doublet Model of Dark Matter and the LUX-ZEPLIN High-Recoil Event
hep-ph 2026-09 conditional novelty 4.0 of 10

The Inert Doublet Model can consistently explain the LZ 248 keV nuclear recoil event through endothermic inelastic scattering, with a favored dark matter mass of 1080 GeV and a mass splitting of 369 keV.
Exploring Potential Higgs Resonances at 650 GeV and 95 GeV in the 2HDM Type III
hep-ph 2025-05 conditional novelty 4.0 of 10

In a 2HDM Type III, a 650 GeV CP-odd Higgs decaying via H(125)Z with H->γγ and Z->bb, plus a 95 GeV light Higgs, can accommodate both the CMS 650 GeV and the 95 GeV diphoton excesses at about 2.5 sigma.
A new insight into the phase transition in the early Universe with two Higgs doublets
hep-ph 2017-12 conditional novelty 4.0 of 10

A strong first-order electroweak phase transition is achievable in the Type I and Type II two-Higgs-doublet models, and the critical-temperature field value correlates with the zero-temperature one-loop potential depth.
Simplified dark matter models with two Higgs doublets: I. Pseudoscalar mediators
hep-ph 2017-01 conditional novelty 4.0 of 10

In a two-Higgs-doublet model with a pseudoscalar mediator, projected 13 TeV LHC mono-Z and mono-Higgs searches constrain the dark matter coupling more strongly than mono-jet searches over much of the parameter space.
Inert Doublet Model in light of LHC Run I and astrophysical data
hep-ph 2015-08 conditional novelty 4.0 of 10

Combining LHC Run I, Planck relic-density, and LUX direct-detection limits on the Inert Doublet Model leaves dark scalars above about 45 GeV, nearly degenerate above 200 GeV, ordered MH± >= MA > MH, and yields benchma...
Extending two-Higgs-doublet models by a singlet scalar field - the Case for Dark Matter
hep-ph 2014-08 conditional novelty 4.0 of 10

A singlet-scalar dark matter particle added to Type I and Type II two-Higgs-doublet models survives LUX and SuperCDMS direct-detection limits only for masses above roughly 55 GeV, except for a few Type II points near ...
h\to \gamma \gamma In Inert Higgs Doublet Model
hep-ph 2012-01 conditional novelty 4.0 of 10

In the Inert Higgs Doublet Model the charged Higgs loop can raise or lower the Higgs-to-diphoton rate relative to the Standard Model, and an open invisible decay h to SS suppresses it.
New renormalization scheme in extended Higgs sectors for Higgs precision measurements
hep-ph 2024-11 conditional novelty 3.0 of 10

A new 2HDM renormalization scheme fixes the mixing-angle counterterms so that h to ZZ* and h to tau tau NLO rates equal the tree-level scaled SM rates, giving unambiguous NLO predictions for other Higgs decays.
Theory and phenomenology of two-Higgs-doublet models
hep-ph 2011-05 accept novelty 3.0 of 10

The review organizes the theory and phenomenology of two-Higgs-doublet models, including flavour-safe variants, charged-scalar searches, vacuum stability, and minimal spontaneous CP-violation constructions.
Higgs Physics: It ain't over till it's over
hep-ph 2018-08 accept novelty 2.0 of 10

The review consolidates the theory and LHC measurements of the 125 GeV Higgs boson, argues the Standard Model scalar sector is structurally complete, and organizes the search for new physics in the symmetry-breaking s...
Scalar sector of Two-Higgs-Doublet models: A mini-review
hep-ph 2015-07 conditional novelty 2.0 of 10

After the 125 GeV Higgs, 2HDM scalar parameter space is squeezed by stability, unitarity, and T-parameter constraints, with softly broken U(1) symmetry allowing heavier individual nonstandard scalars than exact Z2.
Building and testing models with extended Higgs sectors
hep-ph 2017-02 accept novelty 1.0 of 10

A pedagogical survey of how extended Higgs sectors are built and tested, covering 2HDM, NHDM, singlet and triplet extensions, and their collider and astroparticle signatures.

How later papers used it

159 later papers cite it

Evidence: some. 137 of the citing papers share no author with it, and 18 of those carry a confident label from Pith's citation classifier.

Pith read 6 of the 193 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 20 papers with this label

Employed the most restrictive set of conditions proposed in this paper and discussed their impact relative to the simplified approach first used in its own preliminary study.

Single Higgs-boson production at a photon-photon collider: general 2HDM versus MSSM (2011) · 0.80 · paraphrased: the licence does not allow quoting

How the literature uses it

148 arXiv papers cite this in 181 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 144 sentences without a confident label

Builds on it 1 paper

This method can be extended to the scenario where extra scalar fields are present [ref] .

Implications of Unitarity and Charge Breaking Minima in Left-Right Symmetric Model · Unitarity Constraints · 0.81

Uses its method or tool 17 papers

We perform a random scan over the 2HDM parameter space using the public code [ref] , we then require that each parameter point complies with the following theoretical and experimental constraints: * Theoretical constraints: Unitarity [ref] , Perturbativity [ref] , and Vacuum stability [ref] . * Collider constraints: Agreement with electroweak precision observables (EWPOs) [ref] through the oblique parameters ($S$, $T$, $U$) [ref] , agreement with current collider measurements of the Higgs signal strength as well as limits obtained from various searches of additional Higgs bosons at the LEP, Tevatron and LHC, in which we make use of [ref] and [ref] . and finally agreement with the current limits from B physics observables by using the public code [ref] .

Identifying light charged Higgs boson in the $\mu\nu$ channel in 2HDM Type-III · Results and discussion · 1.00
With the prepared random parameter points, we cumulatively impose the following steps for the theoretical and experimental constraints: Step-(i) Theory+FCNC: We require a parameter point to satisfy the theoretical stabilities and the FCNC results, by using the public code 2HDMC-v1.8.0 [ref] . * Higgs potential being bounded from below [ref] ; * Perturbative unitarity of the amplitudes of scalar-scalar, scalar-vector, and vector-vector scatterings at high energies [ref] ; * Perturbativity of the quartic couplings [ref] ; * Vacuum stability [ref] . * FCNC observables: In type-I and type-X, the viable space of $(,)$ is determined practically by $b→s$ [ref] .

Status of the two-Higgs-doublet model in light of the CDF $m_W$ measurement · Scanning strategies · 0.99
The program [ref] was used for calculating the cross sections ($σ$'s) and BRs as well as testing the following theoretical and experimental constraints. * Vacuum stability [ref] : the scalar potential should be bounded by $λ_1 >0$, $λ_2>0$, $λ_3>-√(λ_1λ_2)$, $λ_3+λ_4-λ_5>-√(λ_1λ_2)$. * Perturbativity constraints [ref] , which imply the condition $|λ_i|8π(i=,...5)$. * Tree-level perturbative unitarity [ref] : requiring unitary when $2→2$ scattering processes involving Higgs and gauge bosons at high energy. * Oblique EW parameters ($S$, $T$ and $U$) [ref] , which control the mass splitting between the Higgs states, with the following measured values [ref] :

Analysis of the $gg\to H\to hh\to4\tau$ process in the 2HDM lepton specific model at the LHC · Bounds and constraints in the parameter space scans · 0.96

Compares with it 2 papers

Our bounds following from conditions ([ref]) read [ M_H 697,; 707,; M_A 706,; M_h 446.; ] They are in good agreement with the most precise analytical results of Ref. [ref] .[Small discrepancies are due to the uncertainty of the numerical method applied in our analysis.] Larger differences appear between our results and results of Ref. [ref] (see also comparison in [ref] ), which are probably due to uncertainties of the numerical method used in [ref] .

Yukawa independent constraints for Two Higgs Doublet Models with a 125 GeV Higgs boson · Constraints on masses of the scalars · 1.00
The above perturbative constraints are slightly less constraining than the full set of unitarity constraints [ref] established using the high energy approximation as well as the equivalence theorem.

Neutral Higgs boson pair production in photon-photon annihilation in the Two Higgs Doublet Model · Theoretical and experimental constraints · 0.82

Cites it as background 16 papers

It is convenient to split the constraints into three categories: (i) Theoretical consistency constraints: positivity of the potential [ref] and perturbative unitarity [ref] , (ii) Experimental constraints on the charged-Higgs sector.

Constraining the Two-Higgs-Doublet-Model parameter space · Introduction and notation · 0.88
already exist in the literature [ref] .

New limits on $\mathbf{\tan\beta}$ for 2HDMs with $\mathbf{Z_2}$ symmetry · Introduction · 0.84
From the theoretical point of view, these models are usually confronted with two conditions: (i) the electroweak vacuum must be stable or at least sufficiently long-lived [ref] , (ii) unitarity should not be violated [ref] .

Improved unitarity constraints in Two-Higgs-Doublet-Models · Introduction · 0.96

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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