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Geometric minimization of highly symmetric potentials Degée, Audrey ; Ivanov, Igor ; Keus, Venus in Journal of High Energy Physics [=JHEP] (2013), 2013 In non-minimal Higgs mechanisms, one often needs to minimize highly symmetric Higgs potentials. Here we propose a geometric way of doing it, which, surprisingly, is often much more efficient than the ... [more ▼] In non-minimal Higgs mechanisms, one often needs to minimize highly symmetric Higgs potentials. Here we propose a geometric way of doing it, which, surprisingly, is often much more efficient than the usual method. By construction, it gives the global minimum for any set of free parameters of the potential, thus offering an intuitive understanding of how they affect the vacuum expectation values. For illustration, we apply this method to the S_4 and A_4-symmetric three-Higgs-doublet models. We find that at least three recent phenomenological analyses of the A_4-symmetric model used a local, not the global minimum. We discuss coexistence of minima of different types, and comment on the mathematical origin of geometrical CP-violation and on a new symmetry linking different minima. [less ▲] Detailed reference viewed: 37 (4 ULg)Symmetries of the scalar sector of multi-Higgs-doublet models Keus, Venus Doctoral thesis (2012) In pursuit of the origin of the masses of particles in the Standard Model, the Brout- Englert-Higgs Mechanism predicts the existence of a scalar boson, whose discovery has been the main goal of the Large ... [more ▼] In pursuit of the origin of the masses of particles in the Standard Model, the Brout- Englert-Higgs Mechanism predicts the existence of a scalar boson, whose discovery has been the main goal of the Large Hadron Collider. However, introducing this scalar boson does not provide the answer to all inadequacies of the Standard Model. Many different Beyond Standard Model theories have been proposed in order to explain these anomalies. Multi-Higgs-doublet models are among these models. We restrict ourselves to the scalar sector of multi-Higgs-doublet-models. The huge number of free parameters in the scalar potential in these models, makes it impossible to study the most general case for any N. In order to reduce the number of free parameters, one could impose symmetries on the scalar potential. Therefore, it is important to explore which symmetries can be implemented in the scalar sector, how these symmetries are broken, how they could be encoded in the Yukawa sector and what the resulting properties of the fermions are. Classifying these symmetries in the scalar sector is the main focus of this thesis. We have found certain symmetries that are always broken in models with more than two doublets, which we name ”frustrated symmetries”. Examples of such symmetries are presented in 3HDM, and one particular symmetry, the octahedral symmetry, is studied further. This symmetry seems to be the largest realizable discrete symmetry that can be imposed on the scalar sector in 3HDM, and interestingly results in a 2HDM-like mass spectrum. In the attempt towards the classification of possible symmetries in the scalar sector of the NHDM, we find that these symmetry groups are either subgroups of the maximal torus, or certain finite Abelian groups which are not subgroups of maximal tori. For the subgroups of the maximal torus, we present an algorithmic strategy that gives the full list of possible realizable Abelian symmetries for any given N . We extend this strategy to include Abelian antiunitary symmetries (with generalized CP transformations) in NHDM. We also show that multi-Higgs-doublet models can naturally accommodate scalar dark matter candidates protected by the group Zp , since these groups are realizable in NHDM. These models do not require any significant fine-tuning and can lead to a variety of forms of microscopic dynamics among the dark matter candidates. [less ▲] Detailed reference viewed: 74 (15 ULg)Z_p scalar dark matter from multi-Higgs-doublet models Ivanov, Igor ; Keus, Venus in Physical Review. D : Particles and Fields (2012), 86(1), 0160047 In many models, stability of dark matter particles is protected by a conserved Z_2 quantum number. However dark matter can be stabilized by other discrete symmetry groups, and examples of such models with ... [more ▼] In many models, stability of dark matter particles is protected by a conserved Z_2 quantum number. However dark matter can be stabilized by other discrete symmetry groups, and examples of such models with custom-tailored field content have been proposed. Here we show that electroweak symmetry breaking models with N Higgs doublets can readily accommodate scalar dark matter candidates stabilized by groups Z_p with any $p \le 2^{N-1}$, leading to a variety of kinds of microscopic dynamics in the dark sector. We give examples in which semi-annihilation or multiple semi-annihilation processes are allowed or forbidden, which can be especially interesting in the case of asymmetric dark matter. [less ▲] Detailed reference viewed: 20 (3 ULg)Z_p scalar dark matter from multi-Higgs-doublet models Keus, Venus Speech/Talk (2012) Detailed reference viewed: 10 (1 ULg)Abelian symmetries in NHDM Keus, Venus Scientific conference (2012, March 06) Detailed reference viewed: 7 (1 ULg)Abelian symmetryies in NHDM Keus, Venus ; Ivanov, Igor ; Diverse speeche and writing (2012) Detailed reference viewed: 20 (3 ULg)Abelian symmetries in multi-Higgs-doublet models Ivanov, Igor ; Keus, Venus ; in Journal of Mathematical Physics (2012) 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 ... [more ▼] 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 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. [less ▲] Detailed reference viewed: 16 (1 ULg)Abelian symmetries in NHDM Keus, Venus Scientific conference (2011, August 27) Detailed reference viewed: 5 (1 ULg)Frustrated symmetries in multi-Higgs-doublet models Ivanov, Igor ; Keus, Venus in Physics Letters B (2011), 695(5), 459-462 Within multi-Higgs-doublet models, one can impose symmetries on the Higgs potential, either discrete or continuous, that mix several doublets. In two-Higgs-doublet model any such symmetry can be conserved ... [more ▼] Within multi-Higgs-doublet models, one can impose symmetries on the Higgs potential, either discrete or continuous, that mix several doublets. In two-Higgs-doublet model any such symmetry can be conserved or spontaneously violated after the electroweak symmetry breaking (EWSB), depending on the coefficients of the potential. With more than two doublets, there exist symmetries which are always spontaneously violated after EWSB. We discuss the origin of this phenomenon and show its similarity to frustration in condensed matter physics. [less ▲] Detailed reference viewed: 42 (16 ULg) |
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