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Register a new userSymmetries and renormalisation in two-Higgs-doublet models
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We discuss the classification of symmetries and the corresponding symmetry groups in the two-Higgs-doublet model (THDM). We give an easily useable method how to determine the symmetry class and corresponding symmetry group of a given THDM Higgs potential. One of the symmetry classes corresponds to a Higgs potential with several simultaneous generalised CP symmetries. Extending the CP symmetry of this class to the Yukawa sector in a straightforward way, the so-called maximally-CP-symmetric model (MCPM) is obtained. We study the evolution of the quartic Higgs-potential parameters under a change of renormalisation point. Finally we compute the so called oblique parameters S, T, and U, in the MCPM and we identify large regions of viable parameter space with respect to electroweak precision measurements. We present the corresponding allowed regions for the masses of the physical Higgs bosons. Reasonable ranges for these masses, up to several hundred GeV, are obtained which should make the (extra) Higgs bosons detectable in LHC experiments.
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N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.
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 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.
We show that a topological Nambu monopole exists as a regular solution for a large range of parameters in two Higgs doublet models, contrary to the standard model admitting only non-topological Nambu monopoles. We analyze a Higgs potential with a global $U(1)$ symmetry and a discrete symmetry $mathbb{Z}_2$. The monopole is attached by two topological $Z$ strings ($Z$ flux tubes) from both sides. Despite of a trivial second homotopy group, the discrete symmetry $mathbb{Z}_2$ together with a non-trivial first homotopy group for $Z$ strings topologically ensures the topological stability. After analytically constructing an asymptotic form of such a configuration, we explicitly construct a solution of the equation of motion based on a 3D numerical simulation, in which magnetic fluxes spherically emanating from the monopole at large distances are deformed in the vicinity of the monopole. Since the monopoles are expected to be abundant in the present universe, they might be observed in the current monopole searches.
We demonstrate how residual flavour symmetries, infrared signatures of symmetry breaking in complete models of flavour, can naturally forbid (or limit in a flavour specific way) flavour-changing neutral currents (FCNC) in multi-Higgs-doublet models (MHDM) without using mass hierarchies. We first review how this model-independent mechanism can control the fermionic mixing patterns of the Standard Model, and then implement the symmetries in the Yukawa sector of MHDM, which allows us to intimately connect the predictivity of a given flavour model with its ability to sequester FCNC. Finally, after discussing various subtleties of the approach, we sketch an $A_4$ toy model that realises an explicit example of these simplified constructions.
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