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We study Two-Higgs-Doublet Models (2HDM) where Abelian symmetries have been introduced, leading to a drastic reduction in the number of free parameters in the 2HDM. Our analysis is inspired in BGL models, where, as the result of a symmetry of the Lagrangian, there are tree-level scalar mediated Flavour-Changing-Neutral-Currents, with the flavour structure depending only on the CKM matrix. A systematic analysis is done on the various possible schemes, which are classified in different classes, depending on the way the extra symmetries constrain the matrices of couplings defining the flavour structure of the scalar mediated neutral currents. All the resulting flavour textures of the Yukawa couplings are stable under renormalisation since they result from symmetries imposed at the Lagrangian level. We also present a brief phenomenological analysis of the most salient features of each class of symmetry constrained 2HDM.
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The two-Higgs-doublet model can be constrained by imposing Higgs-family symmetries and/or generalized CP symmetries. It is known that there are only six independent classes of such symmetry-constrained models. We study the CP properties of all cases in the bilinear formalism. An exact symmetry implies CP conservation. We show that soft breaking of the symmetry can lead to spontaneous CP violation (CPV) in three of the classes.
In extensions of the Standard Model with two Higgs doublets, flavour changing Yukawa couplings of the neutral scalars may be present at tree level. In this work we consider the most general scenario in which those flavour changing couplings are absent. We re-analyse the conditions that the Yukawa coupling matrices must obey for such emph{general flavour conservation} (gFC), and study the one loop renormalisation group evolution of such conditions in both the quark and lepton sectors. We show that gFC in the leptonic sector is one loop stable under the Renormalization Group Evolution (RGE) and in the quark sector we present some new Cabibbo like solution also one loop RGE stable. At a phenomenological level, we obtain the regions for the different gFC parameters that are allowed by the existing experimental constraints related to the 125 GeV Higgs.
We propose a class of Two Higgs Doublet Models where there are Flavour Changing Neutral Currents (FCNC) at tree level, but under control due to the introduction of a discrete symmetry in the full Lagrangian. It is shown that in this class of models, one can have simultaneously FCNC in the up and down sectors, in contrast to the situation encountered in BGL models. The intensity of FCNC is analysed and it is shown that in this class of models one can respect all the strong constraints from experiment without unnatural fine-tuning. It is pointed out that the additional sources of flavour and CP violation are such that they can enhance significantly the generation of the Baryon Asymmetry of the Universe, with respect to the Standard Model.
We propose a two Higgs doublet Type III seesaw model with $mu$-$tau$ flavor symmetry. We add an additional SU(2) Higgs doublet and three SU(2) fermion triplets in our model. The presence of two Higgs doublets allows for natural explanation of small neutrino masses with triplet fermions in the 100 GeV mass range, without fine tuning of the Yukawa couplings to extremely small values. The triplet fermions couple to the gauge bosons and can be thus produced at the LHC. We study in detail the effective cross-sections for the production and subsequent decays of these heavy exotic fermions. We show for the first time that the $mu$-$tau$ flavor symmetry in the low energy neutrino mass matrix results in mixing matrices for the neutral and charged heavy fermions that are not unity and which carry the flavor symmetry pattern. This flavor structure can be observed in the decays of the heavy fermions at LHC. The large Yukawa couplings in our model result in the decay of the heavy fermions into lighter leptons and Higgs with a decay rate which is about $10^{11}$ times larger than what is expected for the one Higgs Type III seesaw model with 100 GeV triplet fermions. The smallness of neutrino masses constrains the neutral Higgs mixing angle $sinalpha$ in our model in such a way that the heavy fermions decay into the lighter neutral CP even Higgs $h^0$, CP odd Higgs $A^0$ and the charged Higgs $H^pm$, but almost never to the heavier neutral CP even Higgs $H^0$. The small value for $sinalpha$ also results in a very long lifetime for $h^0$. This displaced decay vertex should be visible at LHC. We provide an exhaustive list of collider signature channels for our model and identify those that have very large effective cross-sections at LHC and almost no standard model background.
The Two Higgs Doublet Model (2HDM) with spontaneously broken $Z_2$ symmetry predicts a production of domain walls at the electroweak scale. We derive cosmological constraints on model parameters for both Type-I and Type-II 2HDMs from the requirement that domain walls do not dominate the Universe by the present day. For Type-I 2HDMs, we deduce the lower bound on the key parameter $tanbeta > 10^5$ for a wide range of Higgs-boson masses $sim$ 100 GeV or greater close to the Standard Model alignment limit. In addition, we perform numerical simulations of the 2HDM with an approximate as well as an exact $Z_2$ symmetry but biased initial conditions. In both cases, we find that domain wall networks are unstable and, hence, do not survive at late times. The domain walls experience an exponential suppression of scaling in these models which can help ameliorate the stringent constraints found in the case of an exact discrete symmetry. For a 2HDM with softly-broken $Z_2$ symmetry, we relate the size of this exponential suppression to the soft-breaking bilinear parameter $m_{12}$ allowing limits to be placed on this parameter of order $mu$eV, such that domain wall domination can be avoided. In particular, for Type-II 2HDMs, we obtain a corresponding lower limit on the CP-odd phase $theta$ generated by QCD instantons, $theta stackrel{>}{{}_sim} 10^{-11}/(sinbeta cosbeta)$, which is in some tension with the upper limit of $theta stackrel{<}{{}_sim} 10^{-11}$--$10^{-10}$, as derived from the non-observation of a non-zero neutron electric dipole moment. For a $Z_2$-symmetric 2HDM with biased initial conditions, we are able to relate the size of the exponential suppression to a biasing parameter $varepsilon$ so as to avoid domain wall domination.
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