Abstract
Abstract In light of the observation of a relatively large θ 13, the ever popular Tri-Bimaximal (TBM) neutrino mixing which predicts a vanishing θ 13 needs modifications. In this paper, we shall discuss the possibility of modifying it in a minimal way to fulfil this task. In the first part, a neutrino mass matrix with three independent parameters, which leads to the TM2 mixing, is obtained by analogy with that for the TBM mixing. In the second part, a model that can realize the TM2 mixing is constructed with flavor symmetries A 4 × U(1) × Z 2 × Z 2 × Z 2. It is the variant of a model that gives the TBM mixing, with only one more flavon field included. Furthermore, the imaginary vacuum expectation value (VEV) of this flavon breaks the imposed CP symmetry and results in θ 23 = 45° and the maximal CP violation. Besides, this model building approach can be generalized to the TM1 mixing in a straightforward way.
Highlights
Was in good agreement with experimental results at that time
By analogy with that for the TBM mixing, we find one neutrino mass matrix with only three independent parameters, which is connected with the FriedbergLee symmetry and μ − τ symmetry breaking
As a matter of fact, the mixing pattern given by this mass matrix is the so-called TM2 mixing
Summary
We will modify eq (1.4) minimally to produce a realistic neutrino mixing pattern. [45], a general neutrino mass matrix can be decomposed into two parts, Mee. where the first part obeys the μ − τ symmetry, while the second part breaks it. In order to make physical results manifest, instead of the standard parametrization in eq (1.1), the matrix that diagonalizes eq (2.1) is parameterized in a different way, Uν = R(θ2′ 3)R(θ1′ 2)R(θ1′ 3),. Confronting eq (2.8) with eq (1.1), neutrino mixing angles in the standard parameterization can be extracted as follows, sin θ13. Θ1′ 3 will take the following value which gives sin θ13 = 0.15, sin θ1′ 3 = 0.19 , when c b With this choice, the mixing angles can be calculated directly, sin θ13 = 0.0237, sin θ12 = 0.341, sin θ23 = 0.390. This interesting possibility [48,49,50] is still allowed by experimental results and provides a promising CP-violating effect, with the Jarlskog invariant [51] as large as 0.036
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