A Simple Method to detect spontaneous CP Violation in multi-Higgs models

For models with several Higgs doublets we present an alternative method to the one proposed by Branco, Gerard and Grimus, in 1984, to check whether or not CP is spontaneously violated in the Higgs potential. The previous method is powerful and rigorous. It requires the identification of a matrix $U$ corresponding to a symmetry of the Lagrangian and verifying a simple relation involving the vacuum expectation values. The nonexistence of such a matrix signals spontaneous CP violation. However, as the number of Higgs doublets increases, finding such a matrix $U$ may not be straightforward and it may turn out to be easier to analyse the potential by going to the so-called Higgs basis. The transformation to the Higgs basis is straightforward once the vacuum expectation values are known. The method proposed in this work is also powerful and rigorous and can be particularly useful to analyse models with more than two Higgs doublets and with continuous symmetries.Comment: 9 pages, no figures. v2: minor changes, matching JHEP versio

Implications of symmetries in the scalar sector

Symmetries play a very important r\^ole in Particle Physics. In extended scalar sectors, the existence of symmetries may permit the models to comply with the experimental constraints in a natural way, and at the same time reduce the number of free parameters. There is a strong interplay among internal symmetries of the scalar potential, its CP properties and mass degeneracies of the physical scalars. Some of these aspects were discussed in this talk.Comment: 8 pages, to be published in the Proceedings of DISCRETE2018: 6th Symposium on Prospects in the Physics of Discrete Symmetries, 26-30 Nov 2018. Vienna, Austri

Spontaneous symmetry breaking in the S3S_3-symmetric scalar sector

We present a detailed study of the vacua of the $S_3$-symmetric three-Higgs-doublet potential, specifying the region of parameters where these minimisation solutions occur. We work with a CP conserving scalar potential and analyse the possible real and complex vacua with emphasis on the cases in which the CP symmetry can be spontaneously broken. Results are presented both in the reducible-representation framework of Derman, and in the irreducible-representation framework. Mappings between these are given. Some of these implementations can in principle accommodate dark matter and for that purpose it is important to identify the residual symmetries of the potential after spontaneous symmetry breakdown. We are also concerned with constraints from vacuum stability.Comment: 37 pages. v2: Minor changes in the references, matches published version. v3: Table 6 corrected: two additional cases conserve CP. Related discussion adapted. Version consistent with JHEP Erratu

Symmetries and Mass Degeneracies in the Scalar Sector

We explore some aspects of models with two and three SU(2) scalar doublets that lead to mass degeneracies among some of the physical scalars. In Higgs sectors with two scalar doublets, the exact degeneracy of scalar masses, without an artificial fine-tuning of the scalar potential parameters, is possible only in the case of the inert doublet model (IDM), where the scalar potential respects a global U(1) symmetry that is not broken by the vacuum. In the case of three doublets, we introduce and analyze the replicated inert doublet model, which possesses two inert doublets of scalars. We then generalize this model to obtain a scalar potential, first proposed by Ivanov and Silva, with a CP4 symmetry that guarantees the existence of pairwise degenerate scalar states among two pairs of neutral scalars and two pairs of charged scalars. Here, CP4 is a generalized CP symmetry with the property that $({\rm CP}4)^n$ is the identity operator only for integer $n$ values that are multiples of 4. The form of the CP4-symmetric scalar potential is simplest when expressed in the Higgs basis, where the neutral scalar field vacuum expectation value resides entirely in one of the scalar doublet fields. The symmetries of the model permit a term in the scalar potential with a complex coefficient that cannot be removed by any redefinition of the scalar fields within the class of Higgs bases (in which case, we say that no real Higgs basis exists). A striking feature of the CP4-symmetric model is that it preserves CP even in the absence of a real Higgs basis, as illustrated by the cancellation of the contributions to the CP violating form factors of the effective ZZZ and ZWW vertices.Comment: 52 pages, 2 figures, second revised version with new material, as published by JHE

Spontaneous symmetry breaking in three-Higgs-doublet S3S_3-symmetric models

The talk summarises work done by the authors consisting of a detailed study of the possible vacua in models with three Higgs doublets with $S_3$ symmetry and without explicit CP violation. Different vacua require special regions of the parameter space which were analysed in our work. We establish the possibility of spontaneous CP violation in this framework and we also show which complex vacua conserve CP. In our work we discussed constraints from vacuum stability. The results presented here are relevant for model building.Comment: 11 pages, no figures. Prepared for the proceedings of DISCRETE2016: the Fifth Symposium on Prospects in the Physics of Discrete Symmetries, 28 November-3 December 2016, University of Warsaw, Poland, to appear in the Journal of Physics: Conference Series (JPCS

Limb-girdle muscular dystrophy in a Portuguese patient caused by a mutation in the telethonin gene

Limb-girdle muscular dystrophy 2G is caused by mutations in the telethonin (TCAP) gene in chromosome 17q11-12. This rare form of hereditary muscle disease was originally described in Brazilian patients and was recently identified in Chinese and Moldavian patients. We present the first Portuguese patient with a limb-girdle muscular dystrophy caused by a mutation in the TCAP gene. A Caucasian male, 50 years old, presented in his early twenties, slowly progressive weakness in upper and lower limbs. Neurologic examination revealed severe atrophy and weakness in the muscles of the arms, thighs and legs' anterior compartment. Muscle MRI of the thighs and legs revealed severe atrophy of all the muscles of the thighs and legs' anterolateral compartment, in a symmetrical way. Molecular studies identified the homozygous c.157C > T (p.Gln53X) mutation in exon 2 of the TCAP gene, already described in Brazilian patients

Comportamento dinâmico de pontes pedonais de madeira

Na Parte 2 do Eurocódigo 5 é proposto, para tipologias correntes, um processo simplificado de verificação do estado-limite de vibração para pontes de madeira sujeitas à acção de grupos de peões, o qual utiliza estimativas do valor máximo da aceleração no tabuleiro. Neste trabalho procede-se à comparação entre os valores determinados por esse método e os obtidos por análise dinâmica de modelos numéricos de Elementos Finitos, sob a acção de grupos de peões de dimensão e frequência de passada variáveis. Descrevem-se ainda os modelos probabilísticos utilizados na geração do carregamento dinâmico correspondente a estes grupos

Reverse logistics for recycling: the customer service determinants

Customer service is a central concern in the logistics practice and a study topic in the forward logistics research. This article investigates the elements of customer service and their importance in reverse logistics for recycling. Since consumer is the first intervenient in any reverse system that aims to recycle household residues, the provision of an adequate customer service gains an increased importance. Applying multivariate statistical methods (exploratory factor analysis, confirmatory factor analysis and discriminant analysis) to the data from a sample of 267 Portuguese citizens, this study identifies the levels of customer service in this reverse logistics chain and evaluates their relative importance in achieving consumers' participation. The study finds that, as in forward logistics, the customer service in reverse channels for recycling also has a hard and a soft level, being the former more important than the later. The results of this research suggest important guidelines to improve such a complex logistics service