Maximal neutrino mixing from a minimal flavor symmetry

Abstract

We study a number of models, based on a non-Abelian discrete group, that successfully reproduce the simple and predictive Yukawa textures usually associated with U͑2͒ theories of flavor. These models allow for solutions to the solar and atmospheric neutrino problems that do not require altering successful predictions for the charged fermions or introducing sterile neutrinos. Although Yukawa matrices are hierarchical in the models we consider, the mixing between second-and third-generation neutrinos is naturally large. We first present a quantitative analysis of a minimal model proposed in earlier work, consisting of a global fit to fermion masses and mixing angles, including the most important renormalization group effects. We then propose two new variant models: The first reproduces all important features of the SU(5)ϫU(2) unified theory with neither SU͑5͒ nor U͑2͒. The second demonstrates that discrete subgroups of SU͑2͒ can be used in constructing viable supersymmetric theories of flavor without scalar universality even though SU͑2͒ by itself cannot.

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

“…A lot of effort has been put in reproducing the TB pattern by the use of non-Abelian discrete symmetries: the best known groups implemented in the construction of flavour models are A 4 , S 4 [81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97], T ′ [98][99][100][101][102][103][104][105][106][107] and ∆ (27) [108][109][110]. A common feature among many of these realizations is to get a spontaneous breaking scheme responsible for the TB mixing by the use of a convenient assignment of the quantum numbers to the SM particles and the introduction of a suitable set of scalar fields, the "flavons", which, getting non-zero vacuum expectation values (VEVs), are responsible for the symmetry breaking of G f .…”

Models of flavour with discrete symmetries

“…Carone and R.F. Lebed [47,48,49] showed that the physics of vacuum alignement simplifies if the continuous family symmetry SU (2) f is replaced by the discrete non-Abelian family symmetry T ′ ⊗ Z 3 in the SUSYGUT model of flavour SU (5) ⊗ SU (2) f proposed by Romanino, Barbieri and Hall [50,51,52]. The group T ′ is the group of proper rotations that leave a regular tetrahedron invariant in the SU (2) double covering of SO (3).…”

“…The discrete symmetry will therefore be a subgroup of SO(3) f or SU (3) f . Models in which the discrete non-Abelian flavour symmetry is only broken at low energies became very popular in the last few years [29,30,31,32,33,34,35,36,37,38] . The search for an adequate discrete group has concentrated on the smallest subgroups of SO (3) or SU (3) that have at least one singlet and one doublet irreducible representations to accomodate the fermions in each family [39].…”

Heterotic discrete flavor model

“…For recent reviews, see [8] and [9]. One model where many of the masses and mixings are calculable is the T ′ model [10] which has been explored in detail in [11][12][13][14][15][16][17][18][19], where T ′ is the binary tetrahedral group which is economical in the sense that it has only 24 elements yet still has sufficient irreps (1 1 , 1 2 , 1 3 , 2 1 , 2 2 , 2 3 , and 3) to arrange masses and mixings in agreement with the experimental data. The top quark is naturally split off from the light quarks by the choice of embedding in T ′ , the Cabibbo angle is directly calculable, etc.…”