Compatible abelian symmetries in N-Higgs-Doublet Models

Journal of Physics A: Mathematical and Theoretical, 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 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 .

We investigate finite abelian groups which can represent symmetries of the N -Higgsdoublet models with quarks. We build a general formalism based on the powerful method of the Smith normal form and obtain an analytic upper bound on the order of abelian symmetry groups for any N . We investigate in detail the case N = 2 and rederive known results in a more compact and intuitive fashion. We also study the NHDM with the maximal finite abelian symmetry for all small N cases up to N = 5, and show that in each case all Yukawa textures compatible with such symmetry originate from a unique basic structure. This work opens the way to a systematic exploration of phenomenology of the NHDM with a desired symmetry, and illustrates the power of the Smith normal form technique.

2012

Classifying the symmetries of the scalar sector in multi-Higgs-doublet models 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". In the attempt towards the classification of possible symmetries in the scalar sector of the NHDM, we find that these symmetry groups

Physical review, 2009

We consider the impact of imposing generalized CP symmetries on the Higgs sector of the two-Higgs-doublet model, and identify three classes of symmetries. Two of these classes constrain the scalar potential parameters to an exceptional region of parameter space which respects either a Z2 discrete flavor symmetry or a U (1) symmetry. We exhibit a basis-invariant quantity that distinguishes between these two possible symmetries. We also show that the consequences of imposing these two classes of CP symmetry can be achieved by combining Higgs Family symmetries, and that this is not possible for the usual CP symmetry. We comment on the vacuum structure and on renormalization in the presence of these symmetries. Finally, we demonstrate that the standard CP symmetry can be used to build all the models we identify, including those based on Higgs Family symmetries.

Journal of High Energy Physics, 2014

We catalogue and study three-Higgs-doublet models in terms of all possible allowed symmetries (continuous and discrete, Abelian and non-Abelian), where such symmetries may be identified as flavour symmetries of quarks and leptons. We analyse the potential in each case, and derive the conditions under which the vacuum alignments (0, 0, v), (0, v, v) and (v, v, v) are minima of the potential. For the alignment (0, 0, v), relevant for dark matter models, we calculate the corresponding physical Higgs boson mass spectrum. Motivated by supersymmetry, we extend the analysis to the case of three up-type Higgs doublets and three down-type Higgs doublets (six doublets in total). Many of the results are also applicable to flavon models where the three Higgs doublets are replaced by three electroweak singlets.

Symmetry

Imposing a family symmetry on the Standard Model in order to reduce the number of its free parameters, due to the Schur’s Lemma, requires an explicit breaking of this symmetry. To avoid the need for this symmetry to break, additional Higgs doublets can be introduced. In such an extension of the Standard Model, we investigate family symmetries of the Yukawa Lagrangian. We find that adding a second Higgs doublet (2HDM) does not help, at least for finite subgroups of the U ( 3 ) group up to the order of 1025.

Physical Review D, 2009

We consider the impact of imposing generalized CP symmetries on the Higgs sector of the two-Higgs-doublet model, and identify three classes of symmetries. Two of these classes constrain the scalar potential parameters to an exceptional region of parameter space which respects either a Z2 discrete flavor symmetry or a U (1) symmetry. We exhibit a basis-invariant quantity that distinguishes between these two possible symmetries. We also show that the consequences of imposing these two classes of CP symmetry can be achieved by combining Higgs Family symmetries, and that this is not possible for the usual CP symmetry. We comment on the vacuum structure and on renormalization in the presence of these symmetries. Finally, we demonstrate that the standard CP symmetry can be used to build all the models we identify, including those based on Higgs Family symmetries.

Physics Letters B, 2010

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 geometric frustration in condensed-matter physics.

Journal of High Energy Physics, 2011

We investigate possible symmetry properties of the scalar sector of Multi-Higgs-Doublet Models, and, to some extent, the generalization of such models to gauge groups other than SU (2) L × U (1) Y . In models where the C (charge conjugation) violating operator C is not present, the scalar potential is invariant under a group larger than the gauge group, O(4) when the Higgs fields are doublets. If the Higgs fields develop aligned vacuum expectation values, this symmetry will break to an O(3) subgroup, which in general is further broken by loop corrections involving the gauge bosons. Assuming such corrections are small, the physical properties of the Higgs sector will approximately organize into representations of SO(3). If the vacuum expectation values of the Higgs fields are aligned in the direction of the C even fields, the mass spectra of the charged and C odd sectors will be degenerate. Moreover, if the Higgs fields develop a pair of non-aligned vacuum expectations values, so that the charge conjugation symmetry is spontaneously broken (but not the U (1) electromagnetic gauge invariance), a pair of light charged Higgs bosons should appear.

Nuclear Physics B, 2011

We characterize models where electroweak symmetry breaking is driven by two light Higgs doublets arising as pseudo-Nambu-Goldstone bosons of new dynamics above the weak scale. They represent the simplest natural two Higgs doublet alternative to supersymmetry. We construct their low-energy effective Lagrangian making only few specific assumptions about the strong sector. These concern their global symmetries, their patterns of spontaneous breaking and the sources of explicit breaking. In particular we assume that all the explicit breaking is associated with the couplings of the strong sector to the Standard Model fields, that is gauge and (proto)-Yukawa interactions. Under those assumptions the scalar potential is determined at lowest order by very few free parameters associated to the top sector. Another crucial property of our scenarios is the presence of a discrete symmetry, in addition to custodial SO(4), that controls the T -parameter. That can either be simple CP or a Z 2 that distinguishes the two Higgs doublets. Among various possibilities we study in detail models based on SO(6)/SO(4)× SO(2), focussing on their predictions for the structure of the scalar spectrum and the deviations of their couplings from those of a generic renormalizable two Higgs doublet model.