Properties of the general NHDM. I. The orbit space

We study the scalar sector of the general N-Higgs-doublet model via geometric constructions in the space of gauge orbits. We give a detailed description of the shape of the orbit space both for general N and, in more detail, for N=3. We also comment on remarkable analogies between NHDM and quantum information theory.Comment: 27 pages, 2 figure

Beyond basis invariants

Physical observables cannot depend on the basis one chooses to describe fields. Therefore, all physically relevant properties of a model are, in principle, expressible in terms of basis-invariant combinations of the parameters. However, in many cases it becomes prohibitively difficult to establish key physical features exclusively in terms of basis invariants. Here, we advocate an alternative route in such cases: the formulation of basis-invariant statements in terms of basis-covariant objects. We give several examples where the basis-covariant path is superior to the traditional approach in terms of basis invariants. In particular, this includes the formulation of necessary and sufficient basis-invariant conditions for various physically distinct forms of CP conservation in two- and three-Higgs-doublet models.Comment: 20 pages, no figure

Custodial SO(4) symmetry and CP violation in N-Higgs-doublet potentials

We study the implementation of global $SO(4)\sim SU(2)_L\otimes SU(2)_R$ symmetry in general potentials with N-Higgs-doublets in order to obtain models with custodial $SO(3)_C$ symmetry. We conclude that any implementation of the custodial SO(4) symmetry is equivalent, by a basis transformation, to a canonical one if $SU(2)_L$ is the gauge factor, $U(1)_Y$ is embedded in $SU(2)_R$ and we require $N$ copies of the doublet representation of $SU(2)_R$. The invariance by SO(4) automatically leads to a CP invariant potential and the basis of the canonical implementation of SO(4) is aligned to a basis where CP-symmetry acts in the standard fashion. We show different but equivalent implementations for the 2HDM, including an implementation not previously considered.Comment: 22pp, REVTeX4. Published versio

On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential

Recently, it has been shown [arXiv:1106.3482] that the two-Higgs-doublet-model potential may exhibit a maximum of 13 distinct accidental symmetries. Such a classification is based on a six-dimensional bilinear scalar field formalism realizing the SO(1,5) symmetry group. This note presents the transformation relations for each of the 13 symmetries in the original scalar field space and their one-to-one correspondence to the space of scalar bilinears, thereby providing firm support for the completeness of the classification.Comment: 11 pages, comments on custodial symmetry added; final version to appear in Physics Letters

Frustrated symmetries in multi-Higgs-doublet models

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.Comment: 7 pages, no figure

Symmetry breaking patterns in 3HDM

An attractive feature of New Physics models with multiple Higgs fields is that they are equipped with discrete symmetry groups in the Higgs and flavour sectors. These symmetry groups are often broken at the global minimum of the Higgs potential, either completely or to a proper subgroup, with certain phenomenological consequences. Here, we systematically explore these symmetry breaking patterns in the scalar sector of the three-Higgs-doublet model (3HDM). We use the full list of discrete symmetry groups allowed in 3HDM, and for each group we find all possible ways it can break by the Higgs vacuum expectation value alignment. We also discuss the interplay between these symmetry groups and various forms of CP-violation in the scalar sector of 3HDM. Not only do our results solve the problem for 3HDM, but they also hint at several general features in multi-scalar sectors.Comment: 24 pages, 5 figures, 2 tables; v2: expanded introduction, matches published versio

CP properties of symmetry-constrained two-Higgs-doublet models

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.Comment: 14 pages, 2 tables, revised version adapted to the journal publicatio

Autophagy activation and enhanced mitophagy characterize the Purkinje cells of pcd mice prior to neuronal death

Purkinje cells are a class of specialized neurons in the cerebellum, and are among the most metabolically active of all neurons, as they receive immense synaptic stimulation, and provide the only efferent output from the cerebellum. Degeneration of Purkinje cells is a common feature of inherited ataxias in humans and mice. To understand Purkinje neuron degeneration, investigators have turned to naturally occurring Purkinje cell degeneration phenotypes in mice to identify key regulatory proteins and cellular pathways. The Purkinje cell degeneration (pcd) mouse is a recessive mutant characterized by complete and dramatic post-natal, cell autonomous Purkinje neuron degeneration and death. As the basis of Purkinje cell death in pcd is unresolved, and contradictory data has emerged for the role of autophagy in Purkinje cell degeneration, we studied the mechanism of Purkinje cell death in pcd mice. BAX null status did not suppress Purkinje neuron death in pcd mice, indicating that classic apoptosis is not responsible for Purkinje cell loss. Interestingly, LC3 Western blot analysis and GFP-LC3 immunostaining of degenerating pcd cerebellum revealed activation of the autophagy pathway. Ultrastructural studies confirmed increased autophagy pathway activity in Purkinje cells, and yielded evidence for mitophagy, in agreement with LC3 immunoblotting of cerebellar fractions. As p62 levels were decreased in pcd cerebellum, our findings suggest that pcd Purkinje cell neurons can execute effective autophagy. However, our results support a role for dysregulated autophagy activation in pcd, and suggest that increased or aberrant mitophagy contributes to the Purkinje cell degeneration in pcd mice