Dynamical generation of flavour

Abstract

We propose the generation of Standard Model fermion hierarchy by the extension of renormalizable SO(10) GUT with O(N g ) family gauge symmetry. In this scenario, Higgs representations of SO(10) also carry family indices and are called Yukawons. Vacuum expectation values of these Yukawon fields break GUT and family symmetry and generate MSSM Yukawa couplings dynamically. We have demonstrated this idea using ${\mathbf {10}}\oplus {\mathbf {210}} \oplus {\mathbf {126}} \oplus {\overline {\mathbf {126}}}$ Higgs irrep, ignoring the contribution of 1 2 0-plet which is, however, required for complete fitting of fermion mass-mixing data. The effective MSSM matter fermion couplings to the light Higgs pair are determined by the null eigenvectors of the MSSM-type Higgs doublet superfield mass matrix $\mathcal {H}$ . A consistency condition on the doublet ([1,2,±1]) mass matrix ( $\text {Det}(\mathcal {H})=$ 0) is required to keep one pair of Higgs doublets light in the effective MSSM. We show that the Yukawa structure generated by null eigenvectors of $\mathcal {H}$ are of generic kind required by the MSSM. A hidden sector with a pair of (S a b ; ϕ a b ) fields breaks supersymmetry and facilitates $D_{O(N_{g})}\hspace *{-1pt}=$ 0. SUSY breaking is communicated via supergravity. In this scenario, matter fermion Yukawa couplings are reduced from 15 to just 3 parameters in MSGUT with three generations.