Phenomenological implications of a minimal F-theory GUT with discrete symmetry

Abstract

Abstract:We discuss the origin of both non-Abelian discrete family symmetry and Abelian continuous family symmetry, as well as matter parity, from F-theory SUSY GUTs. We propose a minimal model based on the smallest GUT group SU(5), together with the non-Abelian family symmetry D 4 plus an Abelian family symmetry, where fluxes are responsible for doublet-triplet splitting, leading to a realistic low energy spectrum with phenomenologically acceptable quark and lepton masses and mixing. We show how a Z 2 matter parity emerging from F-theory can suppress proton decay while allowing neutronantineutron oscillations, providing a distinctive signature of the set-up.

R-parity violation in F-theory

“…By contrast, only for a subset of possible flavour index assignments for baryon number violating (but lepton number conserving) u c d c d c couplings are within the bounds in Table 5. The constraint on the first family up quark coupling λ 1jk for the u c 1 d c j d c k interaction is so stringent, that this operator must only be permitted for the cases u c mixing is allowed, then such operators could lead to an effective u c 1 d c j d c k operator suppressed by small mixing angles, in which case it could induce n −n oscillations [16].…”

“…Recently, some of us have analysed various phenomenological aspects of F-theory effective models using the spectral cover description [15,16,17]. While, in F-constructions, R-parity conservation (RPC) can emerge either as a remnant symmetry of extra U (1) factors, or it can be imposed by appealing to some geometric property of the internal manifold and the flux [18], there is no compelling reason to assume this.…”

MSSM from F-theory SU(5) with Klein monodromy

“…This monodromy action is the Weyl group S 4 , however a subgroup is equally admissible as the action. Transitive subgroups are subject to the theorems of Galois theory, which will allow us to determine what properties the coefficients of the quartic factor of Equation (3.4) must have in order to have roots with a particular symmetry [36]- [39]. In this paper we shall focus on the Klein group,…”

MSSM-like from SU 5 × D 4 models

“…In this paper, we develop another manner to deal with monodromy of F-GUT that is different from the one proposed first in [18], and further explored in [27,30,31], where matter curves of the same orbit of monodromy are identified. In our approach, we use the non abelian flux conjecture of [15,16] to think of monodromy group of F-theory SU 5 models as a non abelian flavor symmetry Γ. Non trivial irreducible representations of the non abelian discrete group Γ are used to host the three generations of fundamental matter; a feature that opens a window to build semi-realistic models with matter curves distinguished from each other in accord with mass hierarchy and mixing neutrino physics [32,33,34].…”

“…but as approached in [14,15] in dealing with local models. For simplicity, we use a short way to introduce this parity by requiring, up to an overall phase, invariance of C 5 = 0, C 10 = 0, C 20 = 0 under the following transformations along the spectral fiber; see [14,15,16] for explicit details,…”