A4 Group and Tri-bimaximal Neutrino Mixing – A Renormalizable Model

Abstract

The tetrahedron A4 group has been widely used in studying neutrino mixing matrix. It provides a natural framework of model building for the tri-bimaximal mixing matrix. In this class of models, it is necessary to have two Higgs fields, χ and χ ′ , transforming under A4 as 3 with one of them having vacuum expectation values for the three components to be equal and another having only one of the components to be non-zero. These specific vev structures require separating χ and χ ′ from communicating with each other. The clash of the different vev structures for χ and χ ′ is the so called sequestering problem. In this work, I show that it is possible to construct renormalizable supersymmetric models producing the tri-bimaximal neutrino mixing with no sequestering problem.The current data from neutrino oscillation experiments[1] can be described by three neutrino mixing. The mixing matrix V can be well fitted by the tri-bimaximal mixing of the form[2]Here P = Diag(e iα1 , e iα2 , e iα3 ) is a Majorana phase matrix. Since an overall phase does not play a role in any physical process, only two of the α 1,2,3 are physically independent. The tri-bimaximal form for neutrino mixing was first proposed by Harrison, Perkins and Scott[2], and further studied by Xing [2]. Also independently proposed by He and Zee [2]. Many theoretical efforts have been made to produce such a mixing pattern. Among them theories based on A 4 symmetry provide some interesting examples [3,4,5]. Most of the attempts made in the literature assumed certain vacuum expectation value (vev) structures for Higgs fields without specific renormalizable models to realize them. Attempts to build renormalizable models have been made in Refs. [4,5]. Here I construct a realistic renormalizable model with supersymmetry (SUSY) which produces the tri-bimaximal mixing.In addition to the standard

Tri/Bi-maximal lepton mixing and leptogenesis

“…2. The second pattern [17,20,22] is similar to the previous one and it still originates in an A 4 context. The mass matrices are the following:…”

“…2. The second pattern has been presented in [40] and it is similar to that of [17,20,22], discussed in the previous case, exchanging the structure of the Dirac and the Majorana mass matrices:…”

The interplay between GUT and flavour symmetries in a Pati-Salam × S4 model

“…Using the following unitary matrix to move from the basis in [158] to our basis, 55) JHEP08 (2010)001 we find (up to irrelevant phases) the following flavon VEV alignment. 6 We will comment in a while about the presence of equivalent solutions.…”

Type II seesaw supersymmetric neutrino model forθ13≠0

“…and therefore between the charged and chargeless lepton subsectors of the supersymmetric A 4 × A 3 model. It happens that this constraint coincides precisely with the so-called sequestering problem [23,24,43]. The A 3 subsymmetry is therefore a requirement of the sequestering problem.…”

“…Using the method of Ref. [24], we can approach the solution of the minimum conditions V for the A 4 triplet χ through the relations they read explicitly as 0 = 36λ 2 υ χ 1 υ χ 2 υ 2…”