Δ(27) family symmetry and neutrino mixing

Varzielas, Ivo de Medeiros

doi:10.1007/jhep08(2015)157

Cited by 33 publications

(17 citation statements)

References 101 publications

(176 reference statements)

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“…A well known example is TM1 mixing [32,33,34,35], when V 1 , V 2 ⊥ (2, −1, −1) T . S 4 can be used to achieve TM1 [36], as can other groups [37]. Most of the models we consider here are examples of this type, as are the CSD2 models with 2 RHN neutrinos [7,9].…”

Section: Lepton Mixing In the Csd Frameworkmentioning

confidence: 99%

Effective alignments and the landscape of S4 flavor models

2019

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We explore the concept of effective alignments: contractions of multiple flavour symmetry breaking flavon fields. These contractions give rise to directions that are hard or impossible to obtain directly by breaking the flavour symmetry. Within this context, and using S 4 as the flavour symmetry to exemplify, we perform a phenomenological check of lepton flavour models built from pairing any two effective alignments up to order 2 (in flavon contractions). The check is performed for each pair of effective alignments in a framework with models of constrained sequential dominance type, in a basis where the charged leptons are diagonal. We thus obtain an indication of which effective alignments are interesting for model building, within this so-called S 4 landscape. We find three types of viable topologies and provide examples of models realizing this strategy for each topology.The formulation of the Standard Model (SM) was one of the biggest successes of particle physics, accounting for most interactions of matter known to date. Notwithstanding its success, it is still a theory that leaves unsanswered some questions. Why are there three copies of fermions? Why are their masses hierarchical? What gives rise to the specific mixing patterns observed? These questions (among others) are part of what is known as the flavour problem [1].The inclusion of a flavour symmetry to the SM became a prolific way to attempt to meaningfully answer some of the questions posed by the flavour problem. These flavour symmetries affect not the gauge structure of the model, rather they restrict the way the different particles are able to interact with each other in the Yukawa sector. As such, this strategy has been widely used to predict the leptonic mixing structure, for which the flavour symmetries favoured are typically non-Abelian discrete symmetries. In these flavour models, we can take the SM to be a low-energy version of a more complete model which includes a flavour symmetry that has been broken by either scalar fields that are singlets with respect to the SM gauge structure (these are called flavons and it is this paradigm we will be discussing), or by enlarging the Higgs sector. Then, the vacuum expectation values (VEV) of the scalars dictate the Yukawa structures. In leptonic flavour models, the type-I seesaw mechanism is employed and Sequential Dominance (SD) [2, 3, 4, 5] is a useful paradigm for model building, with Constrained Sequential Dominance (CSD) [6] remaining a viable strategy to produce predictive models [7,8,9,10,11,12].Since in the indirect approach models the mixing structure is defined by the flavon VEVs, the problem trickles down to choosing appropriate VEVs to match the observed mixing pattern. Nevertheless, this is still a question that must be in accordance to the scalar potential of the chosen flavour model (both the flavour symmetry chosen and the number of flavons will influence the outcome). Moreover, cross-terms in the scalar potential that arise from the interaction of the different flavons will, in gene...

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Section: Lepton Mixing In the Csd Frameworkmentioning

confidence: 99%

Effective alignments and the landscape of S4 flavor models

2019

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“…This is a partially constant mixing, where the first column is independent of neutrino masses. A common example is TM1 mixing [46,47,48,49], which arises when V 1 , V 2 ⊥ (2, −1, −1) T and can be obtained adequately with S 4 [50] or other groups [35]. Another example is the CSD2 model with two RHNs.…”

Section: Lepton Mixing In the Csd Frameworkmentioning

confidence: 99%

“…As an example of the possible effects of these perturbations on phenomenology, we reconsider the EAs in Eq. (35) , which we then use to generate simplified models (with 2 RH neutrinos). These simplified models are not viable for the unperturbed EAs.…”

Section: Effects Of Cross Couplingsmentioning

confidence: 99%

“…In addition, we extend the discussion from previous CSD models by not specifying the hierarchy between M 1 , M 2 and M 3 . Although the idea of EAs is not new [35], it remains unexplored as implementation at the non-renormalizable level leads to difficulties where typically a desired EA cannot be separated from other undesired EAs which at best reduce the predictivity and at worst spoil the fermion masses and mixing. Here we demonstrate specific UV completions that forbid most contractions of the VEVs that are in principle allowed at the effective level (and which would lead to undesirable contributions).…”

Section: Introductionmentioning

confidence: 99%

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Effective alignments as building blocks of flavor models

2018

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Flavour models typically rely on flavons -scalars that break the family symmetry by acquiring vacuum expectation values in specific directions. We develop the idea of effective alignments, i.e. cases where the contractions of multiple flavons give rise to directions that are hard or impossible to obtain directly by breaking the family symmetry. Focusing on the example where the symmetry is S 4 , we list the effective alignments that can be obtained from flavons vacuum expectation values that arise naturally from S 4 . Using those effective alignments as building blocks, it is possible to construct flavour models, for example by using the effective alignments in constrained sequential dominance models. We illustrate how to obtain several of the mixing schemes in the literature, and explicitly construct renormalizable models for three viable cases, two of which lead to trimaximal mixing scenarios.

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“…The groups employed are quite diverse, mostly discrete subgroups of SU (3) with triplet representations. Of note are the groups T 7 [34][35][36][37][38][39][40][41][42] and ∆ (27) [43][44][45][46][47][48][49][50][51][52][53][54] as the smallest with distinct triplet and anti-triplet representations. A 4 , the smallest group with a triplet representation [55][56][57][58][59][60] was one of the first groups explored and remains very popular after the measurement of θ 13 [61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], as does the group S 4 , which also has triplet representations [77][78][79][80]…”

Section: Introductionmentioning

confidence: 99%

Novel Randall-Sundrum model withS3flavor symmetry

2016

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We propose a simple and predictive model of fermion masses and mixing in a warped extra dimension, with the smallest discrete non-Abelian group S3 and the discrete symmetries Z2 ⊗ Z4. Standard Model fields propagate in the bulk and the mass hierarchies and mixing angles are accounted for the fermion zero modes localization profiles, similarly to the the Randall-Sundrum (RS) model. To the best of our knowledge, this model is the first implementation of an S3 flavor symmetry in this type of warped extra dimension framework. Our model successfully describes the fermion masses and mixing pattern and is consistent with the current low energy fermion flavor data. The discrete flavor symmetry in our model leads to predictive mixing inspired textures, where the Cabbibo mixing arises from the down type quark sector whereas up type quark sector contributes to the remaining mixing angles.

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Δ(27) family symmetry and neutrino mixing

Cited by 33 publications

References 101 publications

Effective alignments and the landscape of S4 flavor models

Effective alignments and the landscape of S4 flavor models

Effective alignments as building blocks of flavor models

Novel Randall-Sundrum model withS3flavor symmetry

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