The ultraviolet landscape of twoHiggs doublet models
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Abstract
We study the predictions of generic ultraviolet completions of twoHiggs doublet models. We assume that at the matching scale between the twoHiggs doublet model and an ultraviolet complete theory – which can be anywhere between the TeV and the Planck scale – arbitrary but perturbative values for the quartic couplings are present. We evaluate the couplings down from the matching scale to the weak scale and study the predictions for the scalar mass spectrum. In particular, we show the importance of radiative corrections which are essential for both an accurate Higgs mass calculation as well as determining the stability of the electroweak vacuum. We study the relation between the mass splitting of the heavy Higgs states and the size of the quartic couplings at the matching scale, finding that only a small class of models exhibit sizeable mass splittings between the heavy scalars at the weak scale. Moreover, we find a clear correlation between the maximal size of the couplings and the considered matching scale.
1 Introduction
Nowadays, there is hardly any doubt that the particle discovered at the LHC in 2012 with a mass of 125 GeV [1, 2] is the Higgs boson necessary for electroweak symmetry breaking (EWSB). Although all measured properties of this particle are in good agreement with the predictions of the Standard Model (SM) [3, 4], it is nevertheless much too early to abandon the possibility that it is only one of several Higgs scalars at the weak scale. It is therefore crucial to study the properties and predictions of models with extended Higgs sectors. TwoHiggs doublet models (THDMs) are the nexttominimal extension of the SM Higgs sector, beyond the minimal extension introducing pure gauge singlet scalars. This additional ingredient can be used to study a wide range of effects: deviations in the couplings of the 125 GeV scalar, the presence of additional neutral Higgs scalars (including the possibility of a state lighter than the SMlike one), new effects mediated by charged Higgs bosons, amongst many other new effects not present in the SM. See for instance Ref. [5] for a detailed overview of these types of models and their phenomenological implications. On the other hand, THDMs address hardly any of the open questions of the SM. For instance both the hierarchy problem and the mechanism responsible for neutrino masses remain unresolved in minimal THDM realizations. THDMs however, are able to accommodate electroweak baryogenesis, providing new sources of CPviolation as well as a modification of the electroweak phase transition to be firstorder [6, 7, 8, 9, 10, 11]. Modifying the electroweak phase transition requires that one or more of the heavy Higgs masses lie near the SM Higgs mass. However, experimental constraints place lower bounds on the charged Higgs masses, hence a split spectrum implying large quartic couplings is required to realise electroweak baryogenesis [12, 13, 14, 15, 16]. Nevertheless, it is likely that – if they indeed turn out to be favoured by experiment at some point – they are only the lowenergy limit of a more fundamental theory, such as supersymmetry (SUSY) or a grand unified theory.
Given the large array of possibilities, it is unclear what the ultraviolet (UV) completion of a given THDM might be and at which scale the additional degrees of freedom become relevant. In such a setting, the measurement of a new scalar resonance can shed light on the nature of the UV completion. This expectation arises as THDMs include new renormalisable operators that are therefore unsuppressed by the new physics scale unlike higher dimensional operators induced via new physics. Conversely the absence of any new resonances beyond the SMlike Higgs constrains the space of possible UV completions. There are many studies exploring this avenue via a bottomup approach, i.e. it is assumed that all properties of a THDM at the weak scale are known and it is checked at which energy scale the theory becomes strongly interacting or suffers from an unstable vacuum [17, 18, 19, 20, 21, 22]. Assuming that the fundamental UV theory is weakly interacting at all energies, this then indicates the highest possible scale at which new physics is required. In contrast, there are also studies which use a topdown approach: a specific UV model, usually the simplest realisation of supersymmetry, is assumed and the matching conditions to the THDM are calculated [23, 24, 25, 26]. These couplings are then evolved down to the low scale where one then checks if what is predicted is in agreement with current measurements. However, the minimal supersymmetric Standard Model (MSSM) as a UV completion for THDMs is peculiar as it predicts that the quartic couplings of the THDM at the matching scale are always small because in the MSSM they are necessarily proportional to the square of the gauge couplings.
Both approaches therefore consider the involved parameters of the theory to be in a very narrow window at the high scale – either they are so large that a perturbative treatment cannot be trusted any more after this point, or they obey special relations, relegating the quartic couplings to comparatively tiny values. A generic UV completion might, however, look very different in the sense that the Lagrangian parameters can take a much larger variety of values. Examples include nonminimal supersymmetric models like the nexttominimal supersymmetric SM or composite Higgs models, see e.g. Refs. [27, 28].
In this work, we utilise a topdown approach, but generalise it to a diverse array of UV completions. Hence, we do not make any assumption about the fundamental theory, but allow for arbitrary couplings at the matching scale. The only requirements on the couplings are that they satisfy perturbativity and perturbative unitarity. To obtain reliable predictions for weak scale physics, we perform a stateoftheart analysis using twoloop renormalisation group equations (RGEs) and a twoloop calculation of the scalar masses. Moreover, the stability of the electroweak vacuum is checked at the oneloop level in contrast to the common approach to rely on treelevel conditions [29]. Twoloop RGEs have been applied in earlier works on the highscale behaviour of THDMs [21]. However, they were never previously combined with a matching of the couplings at the looplevel. While one naively expects that the best approach would be to apply oneloop matching when using twoloop RGEs, it has recently been pointed out that this is not the case [30]: when performing Nloop running of the parameters, Nloop matching is required to determine all finite nonlogarithmic contributions correctly. This is particularly important in the presence of large couplings, which one often faces in THDMs. Therefore, we find sizeable deviations in the relations between the low and the highscale compared to previous studies which only applied a treelevel matching in the bottomup approach [17, 18, 19, 20, 21, 22, 31, 32, 33, 34]. This difference is especially pronounced when comparing individual parameter points instead of averaging over the properties of a large set of points.
This paper is organised at follows: in Sect. 2 we fix our conventions for the THDM and define our Ansatz to parametrise the high scale theory. In Sect. 3 we discuss the results, pointing out differences and shortcomings of previous approaches, before we conclude in Sect. 4. In the appendix, we provide details about the calculation of the mass spectrum at loop level.
2 The model and the procedure
2.1 The CPconserving THDM

TypeI Fermions only couple to the second Higgs doublet, i.e. \(Y_1^a = 0~~\forall ~a=d,u,e\) ,

TypeII Downtype fermions couple to \(\Phi _1\), uptype fermions to \(\Phi _2\), i.e. \(Y_1^u = Y_2^d = Y_2^e = 0\) .
2.2 From the matching scale downwards
2.3 Calculating the mass spectrum
 1.
Fix the (\(\overline{\text {MS}}\)) couplings at the matching scale \(\Lambda \).
 2.
Evolve the couplings down to the weak scale. For that, we are using the full twoloop RGEs.
 3.
Calculate the scalar masses and mixing angles including the higher order corrections to the spectrum. In the neutral scalar sector, we compute the full oneloop corrections and add the most important twoloop pieces in the limit of vanishing external momenta. The charged Higgs is calculated at the full oneloop level.
Here, the change in the light Higgs mass is more than 10 GeV, even with this choice of moderately large quartics at the matching scale. For extreme cases where these couplings approach the limit of \(4\pi \), the effects can be much more extreme: points which behave well with twoloop RGEs easily seem to predict tachyonic states at the weak scale if only oneloop RGEs would have been used.
3 Results
3.1 Numerical setup and constraints
3.1.1 Mass spectrum calculation
The running quartics at the one and twoloop level for the input given in (17). The given values for the masses correspond to a twoloop calculation using \(\tan \beta =1.4\) and \(M_{12}=500^2~\text {GeV}^2\)
RGEs  \(\lambda _1(m_t)\)  \(\lambda _2(m_t)\)  \(\lambda _3(m_t)\)  \(\lambda _4(m_t)\)  \(\lambda _5(m_t)\)  \(m_h\)[GeV]  \(m_{H^0}\) [GeV]  \(m_{A^0}\) [GeV]  \(m_{H^+}\) [GeV] 

1loop  0.304  0.202  \(\)0.168  \(\)2.331  2.067  123.6  749.1  660.4  735.8 
2loop  0.370  0.243  \(\)0.084  \(\)1.948  1.695  111.6  749.4  646.0  736.2 
3.1.2 Scanning procedure
If we would start with random values of the quartics as well as \(M_{12}\) at the matching scale and evolve them down, this would correspond to a pure ‘topdown’ approach. However, a parameter scan done in that way would be very inefficient, mainly because the correct Higgs mass of \(m_h \simeq 125 \ \mathrm{GeV}\) would hardly ever be obtained. Therefore, we use the more practical Ansatz and scan for \(\lambda _i(m_t)\) which give the correct Higgs mass at the twoloop level for given values of \(\tan \beta \) and \(M_{12}\). These couplings are then evolved up to higher scales using the full twoloop RGEs of the THDM. Here, we are not only interested in the cutoff scale (i.e. the scale where perturbativity or unitarity breaks down) but also all other intermediate scales \(\Lambda \). This Ansatz is completely equivalent to choosing \(\lambda _i(\Lambda )\) and \(M_{12}(\Lambda )\) randomly at the high scale and keeping only points which have the correct value for \(m_h\) and some desired value for \(M_{12}\) at the low scale – with the virtue that we do not have to run the RGEs on points which are being disregarded in the end.
3.1.3 Theoretical constraints
We place several conditions on the resulting parameter points. First, as mentioned earlier, we apply the unitarity conditions [38, 39]. For this we use the quartic couplings entering the twoloop mass spectrum calculation. Therefore the resulting unitarity constraints, when translated to the physical masses, differ w.r.t. the typical treelevel considerations. Note that this approach is the \(\overline{\text {MS}}\) analogue of using the shifted couplings in an onshell scheme as proposed in Ref. [54]. We enforce convergence of the perturbative series by demanding that the twoloop correction to all scalar masses has to be smaller than the oneloop corrections, \( (m_\phi ^{2})^{\mathrm{2L}}  (m_\phi ^{2})^{ \mathrm 1L} < (m_{\phi }^{2})^{\mathrm{Tree}}  (m_\phi ^{2})^{\mathrm{1L}} \), with \(\phi =h,H,A\) [51, 54]. We also apply the conditions for a stable vacuum: Since loop effects in the Higgs sector are crucial it is not reliable to use the common treelevel checks as has been demonstrated in Ref. [55]. Instead, we numerically check the vacuum stability using the tool Vevacious [56]. This determines the stability of the oneloop effective potential at the low scale. Vevacious makes use of the homotopy continuation method provided with HOM4PS2 [57] to find all treelevel extrema of the scalar potential. It then includes the oneloop corrections according to Coleman and Weinberg [58] and searches numerically for all minima in the vicinity of the treelevel extrema. We only take parameter points into consideration which feature a stable electroweak vacuum, i.e. we disregard regions of parameter space where the electroweak minimum is the false vacuum. The reason is that the tunnelling to minima with VEV values up to a few TeV is very efficient and always leads to a shortlived electroweak vacuum on cosmological time scales.^{5}
3.1.4 Experimental constraints
3.2 Numerical results
We now turn to the discussion of the numerical results. We start with summarising the overall results, i.e. what are the preferred values of the quartic couplings at the matching scale, and how does the physics at the weak scale depend on the couplings and the matching scale. Afterwards, we go into detail and analyse the impact of the included higher order corrections.
3.2.1 The couplings at the matching scale
Since \(\lambda _1\) and \(\lambda _2\) are the most important quartic couplings, i.e. they determine the magnitude of the SMlike Higgs mass as well as (treelevel) vacuum stability, it is natural to investigate their possible ranges. Recall in the MSSM \(\lambda _1=\lambda _2 >0\) while treelevel vacuum stability of THDMs restricts both \(\lambda _1\) and \(\lambda _2\) to positive values at the electroweak scale. In Fig. 3, we present the values of \(\lambda _1\) and \(\lambda _2\) at the matching scale, divided into three ranges of matching scales: \(10^{3}\)–\(10^{6}\hbox { GeV}\) (left), \(10^{6}\)–\(10^{9}\hbox { GeV}\) (middle) and \(10^{9}\)–\(10^{19}\hbox { GeV}\) (right). The maximal (positive) values which we find for these two couplings are constrained by perturbative unitarity checks which restrict \(\lambda _{1(2)} < 8\pi /6\) if at the same time all other quartic couplings are zero.
3.2.2 The spectrum of THDMs
We turn to the discussion of the scalar mass spectrum. The largest difference between general THDMs and THDMs arising from a UV completion, like the MSSM, is that the mass splitting between the heavy scalars can be very large. In contrast, the THDM matched to the MSSM always predicts that the heavy CPeven and odd Higgs states are nearly degenerate, and the charged Higgs mass only differs by the W boson mass.
The most unexpected feature is the largest mass splittings do not appear for the largest values of quartic couplings at the matching scale, but for moderately large couplings of \({\mathcal {O}}(26)\) and large values of \(M_{12}\) of \({\mathcal {O}}(1\hbox { TeV})\). The reason is that for those values of \(M_{12}\) larger quartic couplings are forbidden as the corrections to \(m_h\) become too large.
Note that while Fig. 4 displays the case of typeI Yukawas, the picture is very similar for typeII, and hence the conclusions are the same. The only difference is that the upper left plot featuring \(M_{12}<200\,\)GeV is not populated in the THDMII because of the tighter constraints on the charged Higgs mass from B observables.
Interestingly, when looking at the average mass splittings between the heavy scalars, we obtain a different picture, as is shown in Fig. 5. In this figure we show the perbin averaged \(\Delta M\) instead of the maximal value per bin as before. We find that, while mass splittings of \(\sim 150\hbox { GeV}\) typically occur for low \(M_{12}\), max\((\lambda _i) > rsim 2\) and matching scales below \(10^{10}\hbox { GeV}\), this is not any more the case for larger values of \(M_{12}\) where smaller mass splittings of 50–100 \(\hbox { GeV}\) are preferred.
3.2.3 Impact of scalar loop corrections on the light Higgs
We show the results for the THDM of both typeI (upper row) and typeII (lower row) in Fig. 6 in the twodimensional plane matching scale vs \(M_{12}(\Lambda )\) to represent the minimal, maximal and average Higgs mass correction in the respective bin. We see that while the minimal correction is smaller than \(100\hbox { GeV}\) almost throughout the entire plane, the maximal correction can be as large as \(300\hbox { GeV}\) for small matching scales. The reason for this behaviour is clear: large loop corrections are driven by large couplings at the electroweak scale – which are more likely to be obtained with low matching scales as can be seen in the previous figures. Even the averaged radiative corrections to the Higgs mass are \({\mathcal {O}}(100\hbox { GeV})\). This shows that a calculation beyond leading order is absolutely crucial for obtaining sensible predictions. Of course, one might feel uncomfortable by these huge loop corrections and wonder about the validity of the perturbative series. As we have stated above, we applied the condition that the twoloop corrections must always be smaller than the oneloop corrections to filter out the most pathological points. In principle, one can apply even stronger constraints on the size of these loop corrections. This would correspond to disfavouring certain classes of UV completions with very large quartic couplings and might be a conservative approach. We always included these extreme parameter regions in order to stress the necessity to include radiative corrections to the scalar masses in 2HDMs which hasn’t been done in literature before.
The main difference between the cases of typeI and typeII Yukawas stem from the more stringent constraints on the latter type [63], leading to a lower bound on \(m_{H^\pm _{\mathrm{typeII}}}\) of \({\mathcal {O}}(600\hbox { GeV})\). Since \(M_{12}\) sets the overall scale of the heavy Higgs states, this cut constrains a combination of \(\lambda _i\) and \(M_{12}\) and therefore leads to larger minimal \(M_{12}\) values for typeII models.
Finally we want to illustrate the ranges of treelevel input parameters that we have to use in order to achieve a 125 GeV lightest Higgs. As explained in Sec. III A 1, it is necessary to often use negative \(m_h^{2,\mathrm{tree}}\) in order to achieve the correct Higgs mass at the twoloop order. In Fig. 7, we present the range which we used for our study. We contrast this against the electroweakscale \(M_{12}\) and show the perbin average of the \(\lambda _i\) in this plane. We observe that valid spectra are only compatible with positive \(m_h^{2,\mathrm{tree}}\) if the quartics are moderate, \(\lesssim 4\). Couplings beyond this value cause the loop corrections to be so large that negative squared input masses are needed – and the larger the quartic couplings, the more extreme ranges of \(m_h^{2,\mathrm{tree}}\) are needed. One can see from these large loop corrections that a treelevel study of the Higgs sector is very unreliable. This also underlines the need to test for vacuum stability at the loop level.
3.2.4 The sensitivity of the cutoff scale on higherorder corrections
The size of the loop corrections discussed in the previous subsection can be translated into the shift in cutoff scale, see Ref. [30] for further details. We define this scale as the largest scale up to which a perturbative treatment of the THDM is still justifiable, i.e. as the point at which either one of the quartic couplings becomes larger than \(4\pi \) or where the perturbative unitarity conditions are not satisfied any more due to the RGE evolution of the \(\lambda \)’s.
We show the number of points affected by these considerations in Fig. 8. More specifically we show the cutoff scale when using twoloop Higgs mass corrections at the top mass scale (i.e. a twoloop matching of the THDM to the SM) and twoloop RGE running (denoted (2, 2)) against the cutoff when doing treelevel matching at the weak scale and oneloop running, (T, 1). For the latter, we use Eqs. (3)–(7) in order to obtain the treelevel – or onshell – couplings from the mass spectrum for each point.
3.2.5 Vacuum stability
Finally we comment on the conditions for electroweak vacuum stability. As discussed earlier, we use the oneloop effective potential in order to find all extrema in the vicinity of the treelevel extrema checking whether there exists a deeper global minimum. We only keep points which feature a stable desired electroweak vacuum configuration. The resulting constraints are in general different from the usual treelevel vacuum stability conditions, see Ref. [55] for more details. In Fig. 9, we show the fraction of parameter points in each bin which passed the oneloop constraints which would also have passed the treelevel vacuum stability conditions. For calculating the treelevel constraints, we again use the treelevel couplings obtained by Eqs. (3)–(7) and calculate the treelevel potential.
In accordance with Ref. [55], we find that large regions of parameter space which feature a perfectly fine EWSB global minimum at the oneloop order would have been regarded unstable by the treelevel checks – meaning that these regions are resurrected by the radiative corrections. While for small \(M_{12}\), the treelevel conditions would have allowed almost all of the parameter points, it is clearly seen that for larger values of \({\mathcal {O}}(400\hbox { GeV})\) and higher, far less than half of the points would have been considered allowed when applying the conventional checks. Interestingly, \(M_{12}\) is the most decisive factor in the change of treelevel forbidden to looplevel allowed. The size of the quartic couplings instead plays an important though inferior role. In particular, for \(M_{12} > rsim 600\hbox { GeV}\) and max\((\lambda _i)_{\mathrm{EWSB}} > rsim 5\) (which is of course exactly the region where the scalar loop corrections are large and therefore also the corrections to the potential), virtually all the parameter space would be ruled out by the treelevel checks – but not so once the radiative corrections are taken into account. The reason for this behaviour can be found in the size of the scalar loop corrections in this region: as discussed earlier, \(M_{12}\) drives the (positive) loop corrections to the lightest Higgs mass. As a result, in an \(\overline{\text {MS}}\) scheme, we often need large negative \(\lambda _{1,2}\) in order to obtain the correct Higgs mass at twoloop order. The area in the figure where almost none of the allowed points would have been allowed at the tree level corresponds to exactly this situation. As a matter of fact, although the threshold corrections drive \(\lambda _{1,2}\) to quite large negative numbers, their treelevel – or onshell – equivalents are usually also negative. However, since negative \(\lambda _{1,2}\) lead to field directions which are unbounded from below at treelevel [65], the treelevel calculation would result in the statement that these points are excluded. At the loop level, however, the situation is different as the large loop corrections can lift the potential in these unboundedfrombelow directions and therefore stabilize the vacuum [55]. Lastly note that the lack of parameter points on the righthand side (displaying the THDMII case) for both low \(M_{12}\) and \(\lambda _i\) is again due to the stronger cuts on \(m_{H^\pm }\) which require either of both to be large in order to produce the large masses needed.
4 Summary and conclusions
In this paper, we have studied generic predictions from UV completions of THDMs. We have not specified the particular UVcomplete model but rather investigated the lowenergy consequences of general boundary conditions at a particular matching scale, i.e. leaving the THDM parameters arbitrary at this scale. By the use of the twoloop renormalisation group equations, those parameters were then evolved down to the electroweak scale where we also applied the twoloop threshold corrections for the Higgs mass. All obtained spectra have then been confronted with the current experimental constraints as well as the vacuum stability considerations. We further demanded perturbativity and perturbative unitarity of the theory everywhere between the TeV and the matching scale. We have seen correlations between the matching scale and the mass splitting \(\Delta M\) in the heavy Higgs sector at the electroweak scale. As a generic feature, we find that large matching scales near the Planck scale would predict very small \(\Delta M\) independent of the size of the quartic couplings at the scale. If, in turn, this splitting should be of the order of several hundreds of GeV, this would point to very large couplings at a matching scale not much larger than the TeV scale probed so far at experiments, placing serve constraints on the possibility of realising electroweak baryogenesis in THDMs.
We have highlighted the importance of the loop corrections to the Higgs mass which need to be taken into account for reliable predictions. Likewise, we have shown that an examination of the stability of the electroweak vacuum needs to be done beyond tree level – or else we would wrongly consider many perfectlyallowed regions of parameter space as ruled out.
Footnotes
 1.
We assume that the UV completion also respects the \(Z_2\) symmetry at least at treelevel, i.e. the additional couplings \(\lambda _6 H_1^2 (H_1^\dagger H_2)\) and \(\lambda _7 H_2^2 (H_1^\dagger H_2)\) are at most loop induced like in the MSSM and will be neglected in this study.
 2.
It has recently been pointed out that for a reliable check of perturbative unitarity in THDMs, the contributions from finite scattering energies s should also be included which were widely ignored before [35].
 3.
These loop corrections necessarily spoil the relations Eqs. (3)–(7) which are only valid at treelevel or in an onshell renormalisation scheme. In order to get a connection to the highscale when working in an onshell scheme, one needs to calculate the counterterms \(\delta \lambda \) in order to extract the \(\overline{\text {MS}}\) couplings including higher order corrections. These corrected parameters then need to be used in the RGEs when running up in scale [30].
 4.
In some specific supersymmetric models, the only way to obtain a phenomenologically viable spectrum is actually to start with a tachyonic treelevel spectrum which turns into a consistent spectrum at the bottom of a (potentially global) electroweak minimum appearing only at the loop level. See for instance Refs. [52, 53].
 5.
We only consider minima which are ‘close’ to the electroweak one. In this regime, the fixedorder calculation at the oneloop level gives reliable results. For minima involving much larger VEVs, one must consider the RGEimproved potential, also including potentially large effects from gravity. In addition one would need to carefully estimate the tunnelling rate at finite temperature including also the impact of inflation and reheating which was so far done only for the SM [59]. This is beyond the scope of this paper. Instead, we assume that the vacuum at very high energies can be stabilised by Planck suppressed operators which otherwise do not have any impact on the phenomenological results [60].
 6.
We stick to the fixed estimate because it’s not even clear in well established models like the NMSSM how a robust and pointdependent uncertainty estimate should be performed.
Notes
Acknowledgements
We thank Johannes Braathen and Mark D. Goodsell for useful discussions and the LPTHE in Paris for hospitality. MEK is supported by the DFG Research Unit 2239 “New Physics at the LHC”. TO has received funding from the German Research Foundation (DFG) under Grant Nos. EXC1098, FOR 2239 and GRK 1581, and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 637506, “\(\nu \)Directions”). TO would also like to thank the CERN Theoretical Physics Department for hospitality and support. FS is supported by the ERC Recognition Award ERCRA0008 of the Helmholtz Association.
References
 1.ATLAS Collaboration, G. Aad et al., Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B 716 1–29 (2012). arXiv:1207.7214
 2.C.M.S. Collaboration, S. Chatrchyan, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B 716, 30–61 (2012). arXiv:1207.7235 ADSCrossRefGoogle Scholar
 3.LHC Higgs Cross Section Working Group Collaboration, D. de Florian et al., Handbook of LHC Higgs Cross sections: 4. Deciphering the nature of the Higgs Sector. arXiv:1610.07922
 4.ATLAS, CMS Collaboration, G. Aad et al., Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s}=7 \) and 8 TeV. JHEP 8, 045 (2016). arXiv:1606.02266
 5.G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher, J.P. Silva, Theory and phenomenology of twoHiggsdoublet models. Phys. Rept. 516, 1–102 (2012). arXiv:1106.0034 ADSCrossRefGoogle Scholar
 6.L.D. McLerran, M.E. Shaposhnikov, N. Turok, M.B. Voloshin, Why the baryon asymmetry of the universe is approximately 10**10. Phys. Lett. B 256, 451–456 (1991)ADSCrossRefGoogle Scholar
 7.N. Turok, J. Zadrozny, Electroweak baryogenesis in the two doublet model. Nucl. Phys. B 358, 471–493 (1991)ADSCrossRefGoogle Scholar
 8.A.G. Cohen, D.B. Kaplan, A.E. Nelson, Spontaneous baryogenesis at the weak phase transition. Phys. Lett. B 263, 86–92 (1991)ADSCrossRefGoogle Scholar
 9.V. Zarikas, The Phase transition of the two Higgs extension of the standard model. Phys. Lett. B 384, 180–184 (1996). arXiv:hepph/9509338 ADSMathSciNetCrossRefGoogle Scholar
 10.J.M. Cline, P.A. Lemieux, Electroweak phase transition in two Higgs doublet models. Phys. Rev. D 55, 3873–3881 (1997). arXiv:hepph/9609240 ADSCrossRefGoogle Scholar
 11.L. Fromme, S.J. Huber, M. Seniuch, Baryogenesis in the twoHiggs doublet model. JHEP 11, 038 (2006). arXiv:hepph/0605242 ADSCrossRefGoogle Scholar
 12.G.C. Dorsch, S.J. Huber, K. Mimasu, J.M. No, The Higgs vacuum uplifted: revisiting the electroweak phase transition with a second Higgs doublet. JHEP 12, 086 (2017). arXiv:1705.09186 ADSCrossRefGoogle Scholar
 13.P. Basler, M. Krause, M. Muhlleitner, J. Wittbrodt, A. Wlotzka, Strong first order electroweak phase transition in the CPconserving 2HDM revisited. JHEP 02, 121 (2017). arXiv:1612.04086 ADSCrossRefGoogle Scholar
 14.G .C. Dorsch, S .J. Huber, K. Mimasu, J .M. No, Hierarchical versus degenerate 2HDM: The LHC run 1 legacy at the onset of run 2. Phys. Rev. D93(11), 115033 (2016). arXiv:1601.04545 ADSGoogle Scholar
 15.G .C. Dorsch, S .J. Huber, K. Mimasu, J .M. No, Echoes of the electroweak phase transition: discovering a second Higgs doublet through \(A_0 \rightarrow ZH_0\). Phys. Rev. Lett. 113(21), 211802 (2014). arXiv:1405.5537 ADSCrossRefGoogle Scholar
 16.G.C. Dorsch, S.J. Huber, J.M. No, A strong electroweak phase transition in the 2HDM after LHC8. JHEP 10, 029 (2013). arXiv:1305.6610 ADSCrossRefGoogle Scholar
 17.N. Chakrabarty, U.K. Dey, B. Mukhopadhyaya, Highscale validity of a twoHiggs doublet scenario: a study including LHC data. JHEP 12, 166 (2014). arXiv:1407.2145 ADSCrossRefGoogle Scholar
 18.N. Chakrabarty, B. Mukhopadhyaya, Highscale validity of a two Higgs doublet scenario: metastability included. Eur. Phys. J. C77(3), 153 (2017). arXiv:1603.05883 ADSCrossRefGoogle Scholar
 19.P. Ferreira, H.E. Haber, E. Santos, Preserving the validity of the TwoHiggs Doublet Model up to the Planck scale. Phys. Rev. D 92, 033003 (2015). arXiv:1505.04001. [Erratum: Phys. Rev. D94, no.5,059903(2016)]ADSCrossRefGoogle Scholar
 20.N. Chakrabarty, B. Mukhopadhyaya, Highscale validity of a two Higgs doublet scenario: predicting collider signals. Phys. Rev D96(3), 035028 (2017). arXiv:1702.08268 ADSGoogle Scholar
 21.D. Chowdhury, O. Eberhardt, Global fits of the twoloop renormalized TwoHiggsDoublet model with soft Z\(_{2}\) breaking. JHEP 11, 052 (2015). arXiv:1503.08216 ADSCrossRefGoogle Scholar
 22.P. Basler, P.M. Ferreira, M. Mühlleitner, R. Santos, High scale impact in alignment and decoupling in twoHiggs doublet models. Phys. Rev. D97(9), 095024 (2018). arXiv:1710.10410 ADSGoogle Scholar
 23.H.E. Haber, R. Hempfling, The Renormalization group improved Higgs sector of the minimal supersymmetric model. Phys. Rev. D 48, 4280–4309 (1993). arXiv:hepph/9307201 ADSCrossRefGoogle Scholar
 24.M. Gorbahn, S. Jager, U. Nierste, S. Trine, The supersymmetric Higgs sector and \(B\bar{B}\) mixing for large tan \(\beta \). Phys. Rev. D 84, 034030 (2011). arXiv:0901.2065 ADSCrossRefGoogle Scholar
 25.G. Lee, C .E .M. Wagner, Higgs bosons in heavy supersymmetry with an intermediate m\(_A\). Phys. Rev. D92(7), 075032 (2015). arXiv:1508.00576 ADSGoogle Scholar
 26.H. Bahl, W. Hollik, Precise prediction of the MSSM Higgs boson masses for low MA. arXiv:1805.00867
 27.J. Mrazek, A. Pomarol, R. Rattazzi, M. Redi, J. Serra, A. Wulzer, The other natural two Higgs doublet model. Nucl. Phys. B 853, 1–48 (2011). arXiv:1105.5403 ADSCrossRefGoogle Scholar
 28.L. Zarate, The Higgs mass and the scale of SUSY breaking in the NMSSM. JHEP 07, 102 (2016). arXiv:1601.05946 ADSCrossRefGoogle Scholar
 29.A. Barroso, P.M. Ferreira, I.P. Ivanov, R. Santos, Metastability bounds on the two Higgs doublet model. JHEP 06, 045 (2013). arXiv:1303.5098 ADSCrossRefGoogle Scholar
 30.J. Braathen, M.D. Goodsell, M.E. Krauss, T. Opferkuch, F. Staub, Nloop running should be combined with Nloop matching. Phys. Rev. D97(1), 015011 (2018). arXiv:1711.08460 ADSGoogle Scholar
 31.H.S. Cheon, S.K. Kang, Constraining parameter space in typeII twoHiggs doublet model in light of a 126 GeV Higgs boson. JHEP 09, 085 (2013). arXiv:1207.1083 ADSCrossRefGoogle Scholar
 32.S. Gori, H.E. Haber, E. Santos, High scale flavor alignment in twoHiggs doublet models and its phenomenology. JHEP 06, 110 (2017). arXiv:1703.05873 ADSCrossRefGoogle Scholar
 33.P.S. BhupalDev, A. Pilaftsis, Maximally symmetric two Higgs doublet model with natural standard model alignment. JHEP 12, 24 (2014). arXiv:1408.3405. [Erratum: JHEP11,147(2015)]ADSCrossRefGoogle Scholar
 34.D. Das, I. Saha, Search for a stable alignment limit in twoHiggsdoublet models. Phys. Rev. D 91(9), 095024 (2015). arXiv:1503.02135 ADSCrossRefGoogle Scholar
 35.M.D. Goodsell, F. Staub, Improved unitarity constraints in TwoHiggsDoubletModels. Phys. Lett. B 788, 206–212 (2019). https://doi.org/10.1016/j.physletb.2018.11.030 ADSCrossRefGoogle Scholar
 36.H.E. Haber, G.L. Kane, The search for supersymmetry: probing physics beyond the standard model. Phys. Rept. 117, 75–263 (1985)ADSCrossRefGoogle Scholar
 37.M. Gabelmann, M. Mühlleitner,, F. Staub, Automatised matching between two scalar sectors at the oneloop level (2018). arXiv:1810.12326
 38.S. Kanemura, T. Kubota, E. Takasugi, LeeQuiggThacker bounds for Higgs boson masses in a two doublet model. Phys. Lett. B 313, 155–160 (1993). arXiv:hepph/9303263 ADSCrossRefGoogle Scholar
 39.A.G. Akeroyd, A. Arhrib, E.M. Naimi, Note on tree level unitarity in the general two Higgs doublet model. Phys. Lett. B 490, 119–124 (2000). arXiv:hepph/0006035 ADSCrossRefGoogle Scholar
 40.F. Staub, SARAH. arXiv:0806.0538
 41.F. Staub, From superpotential to model files for FeynArts and CalcHep/CompHep. Comput. Phys. Commun. 181, 1077–1086 (2010). arXiv:0909.2863 ADSCrossRefGoogle Scholar
 42.F. Staub, Automatic calculation of supersymmetric renormalization group equations and self energies. Comput. Phys. Commun. 182, 808–833 (2011). arXiv:1002.0840 ADSCrossRefGoogle Scholar
 43.F. Staub, SARAH 3.2: Dirac Gauginos, UFO output, and more. Comput. Phys. Commun. 184, 1792–1809 (2013). https://doi.org/10.1016/j.cpc.2013.02.019 ADSCrossRefGoogle Scholar
 44.F. Staub, SARAH 4: A tool for (not only SUSY) model builders. Comput. Phys. Commun. 185, 1773–1790 (2014). arXiv:1309.7223 ADSCrossRefGoogle Scholar
 45.F. Staub, Exploring new models in all detail with SARAH. Adv. High Energy Phys. 2015, 840780 (2015). arXiv:1503.04200 MathSciNetzbMATHGoogle Scholar
 46.W. Porod, SPheno, a program for calculating supersymmetric spectra, SUSY particle decays and SUSY particle production at e+ e colliders. Comput. Phys. Commun. 153, 275–315 (2003). arXiv:hepph/0301101 ADSCrossRefGoogle Scholar
 47.W. Porod, F. Staub, SPheno 3.1: Extensions including flavour, CPphases and models beyond the MSSM. Comput. Phys. Commun. 183, 2458–2469 (2012). https://doi.org/10.1016/j.cpc.2012.05.021
 48.F. Staub, W. Porod, Improved predictions for intermediate and heavy supersymmetry in the MSSM and beyond. Eur. Phys. J. C77(5), 338 (2017). arXiv:1703.03267 ADSCrossRefGoogle Scholar
 49.M.D. Goodsell, K. Nickel, F. Staub, TwoLoop Higgs mass calculations in supersymmetric models beyond the MSSM with SARAH and SPheno. Eur. Phys. J. C 75(1), 32 (2015). arXiv:1411.0675 ADSCrossRefGoogle Scholar
 50.M. Goodsell, K. Nickel, F. Staub, Generic twoloop Higgs mass calculation from a diagrammatic approach. Eur. Phys. J. C 75(6), 290 (2015). arXiv:1503.03098 ADSCrossRefGoogle Scholar
 51.J. Braathen, M.D. Goodsell, F. Staub, Supersymmetric and nonsupersymmetric models without catastrophic Goldstone bosons. Eur. Phys. J. C 77(11), 757 (2017). arXiv:1706.05372 ADSCrossRefGoogle Scholar
 52.K.S. Babu, R.N. Mohapatra, Minimal supersymmetric leftright model. Phys. Lett. B 668, 404–409 (2008). arXiv:0807.0481 ADSCrossRefGoogle Scholar
 53.L. Basso, B. Fuks, M.E. Krauss, W. Porod, Doublycharged Higgs and vacuum stability in leftright supersymmetry. JHEP 07, 147 (2015). arXiv:1503.08211 ADSCrossRefGoogle Scholar
 54.M.E. Krauss, F. Staub, Perturbativity constraints in BSM models. Eur. Phys. J. C 78(3), 185 (2018). arXiv:1709.03501 ADSCrossRefGoogle Scholar
 55.F. Staub, Reopen parameter regions in TwoHiggs Doublet models. Phys. Lett. B 776, 407–411 (2018). arXiv:1705.03677 ADSCrossRefGoogle Scholar
 56.J.E. CamargoMolina, B. O’Leary, W. Porod, F. Staub, Vevacious: a tool for finding the global minima of oneloop effective potentials with many scalars. Eur. Phys. J. C 73(10), 2588 (2013). arXiv:1307.1477 ADSCrossRefGoogle Scholar
 57.T. Lee, T. Li, C. Tsai, Hom4ps2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method. Computing 83(2), 109–133 (2008)MathSciNetCrossRefGoogle Scholar
 58.S.R. Coleman, E.J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking. Phys. Rev. D 7, 1888–1910 (1973)ADSCrossRefGoogle Scholar
 59.J.R. Espinosa, G.F. Giudice, E. Morgante, A. Riotto, L. Senatore, A. Strumia, N. Tetradis, The cosmological Higgstory of the vacuum instability. JHEP 09, 174 (2015). arXiv:1505.04825 ADSCrossRefGoogle Scholar
 60.A. Hook, J. Kearney, B. Shakya, K.M. Zurek, Probable or improbable universe? Correlating electroweak vacuum instability with the scale of inflation. JHEP 01, 061 (2015). arXiv:1404.5953 ADSCrossRefGoogle Scholar
 61.P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, K.E. Williams, HiggsBounds: confronting arbitrary Higgs sectors with exclusion bounds from LEP and the tevatron. Comput. Phys. Commun. 181, 138–167 (2010). arXiv:0811.4169 ADSCrossRefGoogle Scholar
 62.P. Bechtle, O. Brein, S. Heinemeyer, O. Stål, T. Stefaniak, G. Weiglein, K.E. Williams, HiggsBounds—4: improved tests of extended Higgs Sectors against exclusion bounds from LEP, the tevatron and the LHC. Eur. Phys. J. C 74(3), 2693 (2014). arXiv:1311.0055 ADSCrossRefGoogle Scholar
 63.M. Misiak, M. Steinhauser, Weak radiative decays of the B meson and bounds on \(M_{H^\pm }\) in the TwoHiggsDoublet Model. Eur. Phys. J. C 77(3), 201 (2017). arXiv:1702.04571 ADSCrossRefGoogle Scholar
 64.W. Porod, F. Staub, A. Vicente, A Flavor Kit for BSM models. Eur. Phys. J. C 74(8), 2992 (2014). arXiv:1405.1434 ADSCrossRefGoogle Scholar
 65.N.G. Deshpande, E. Ma, Pattern of symmetry breaking with two Higgs doublets. Phys. Rev. D 18, 2574 (1978)ADSCrossRefGoogle Scholar
 66.J. Braathen, M.D. Goodsell, Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops. JHEP 12, 056 (2016). arXiv:1609.06977 ADSMathSciNetCrossRefGoogle Scholar
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