R-parity violation and non-abelian discrete family symmetry

Abstract

We investigate the implications of R-parity violating operators in a model with family symmetry. The family symmetry can determine the form of R-parity violating operators as well as the Yukawa matrices responsible for fermion masses and mixings. In this paper we consider a concrete model with non-abelian discrete symmetry Q 6 which contains only three R-parity violating operators. We find that ratios of decay rates of the lepton flavor violating processes are fixed thanks to the family symmetry, predicting BR(τ → 3e)/BR(τ → 3µ) ∼ 4m 2 µ /m 2 τ .

Bilinear R-parity violation with flavor symmetry

“…In its "generic" formulation the model can not address issues associated to fermion mass hierarchies and mixings, such as those of neutrinos. Both Abelian [12][13][14][15][16][17] and non-Abelian [18][19][20][21][22] flavor symmetries have been used in the literature to constrain the R-parity violating terms. In this letter we propose a flavored version of bilinear R-parity violation.…”

$$Q_{6}$$ Q 6 as the flavor symmetry in a non-minimal SUSY $$SU(5)$$ S U ( 5 ) model

“…This is a drawback in the present model, and it is the price we have to pay for going beyond the minimal [53,54]. In addition, there is flavon, Y B , which has already been used in supersymmetric models [13][14][15][16][17] in order to have a flavor invariant Majorana mass matrix. Regarding the fermion sector, N i denotes the RHN, which is a singlet under the SU (5) gauge group; F i and T j stand for the 5-plets and the antisymmetric 10-plet, respectively.…”

“…(16),C u =B u , according to Eq. (15). In the neutrino sector, the degeneracy, h 0u 2 = h 0u 1 ≡ h 0u , in the effective mass matrix given in Eq.…”

“…In particular, the flavor symmetry group Q 6 [12] has been proposed as responsible of these kind of textures in the quarks as well as in the leptonic sector [13][14][15][16][17]. The rich phenomenology that Q 6 provides in the SUSY scenario is remarkable; one of these features is to prohibit the dangerous terms that mediate fast proton decay, rather than invoking the R-parity symmetry [14,15]. The immediate question that arises is, how does the Q 6 symmetry work within a GUT framework?…”

“…By itself, the SUSY SU (5) matter content provides the tools to accommodate masses and mixings via the extension of the Higgs scalar sector, although gauge coupling unification may be compromised. This philosophy has been worked out with success in non-supersymmetric [48][49][50] and supersymmetric [13][14][15][16][17] scenarios, where the concept of flavor has been extended to the Higgs sector.…”