Simple Non-Abelian Finite Flavor Groups and Fermion Masses

Abstract

The use of nonabelian discrete groups G as family symmetries is discussed in detail. Out of all such groups up to order g = 31, the most appealing candidates are two subgroups of SU (2)

Stringy origin of non-Abelian discrete flavor symmetries

“…In the case under consideration, the subgroup 2 × 2 , generated by σ 3 and −½, is normal. 2 One can hence write the flavor symmetry as the semi-direct product S 2 ⋉ ( 2 × 2 ). The product of the generators of the two 2 s and the S 2 leads to the following elements of the non-Abelian discrete flavor symmetry group:…”

Large θ 13 in a SUSY SU(5) × T′ model

“…A particularly popular approach has been through the introduction of a family symmetry, with which the number of free parameters in the Yukawa sector can be reduced. The symmetries proposed include the continuous ones, such as SU (2) [15], SU (3) [16] and U (1) [17], and the discrete ones [18], such as A 4 [19], S 4 [20], T [21], A 5 [22]. These discrete symmetries are particularly conducive to the TBM mixing pattern; in particular it has been shown that an additional A 4 symmetry can generate lepton mixing matrix naturally [19].…”

String-derivedD4flavor symmetry and phenomenological implications

“…, the form of A K including the Higgs field is obtained as 4 Moreover, RG effects due to extra U 1 gaugino masses are also significant [29]. Such RG effects are also degenerate between the first and second families in our model, because they have the same U 1 charges.…”

“…Continuous and discrete non-Abelian symmetries, e.g. U 2 , D 4 , S 3 D 3 , A 4 , Q n , 3n 2 , 6n 2 are assumed as flavor symmetries [3][4][5][6][7][8][9][10][11], while Abelian symmetries such as U 1 , Z N are often assumed, too. However, from the viewpoint of 4D field theory their origins are not clear.…”