Grand Yukawonification : SO(10) grand unified theories with dynamical Yukawa couplings

Abstract: Renormalizable SO(10) grand unified theories (GUTs), extended by $O(N_g)_F$ family gauge symmetry, generate minimal supersymmetric Standard Model flavour structure dynamically via vacuum expectation values of "Yukawon" Higgs multiplets. For concrete illustration and calculability, we work with the fully realistic minimal supersymmetric GUTs based on the $\bf{210 \oplus {\overline{126}}\oplus 126} $ GUT Higgs system - which were already parameter counting minimal relative to other realistic models. $SO(10)$ fermion Higgs channels $\bf{{\overline{126}},10}$($\mathbf{120}$) extend to symmetric(antisymmetric) representations of $O(N_g)_F$, while $\mathbf{210,126}$ are symmetric. $N_g=3$ dynamical Yukawa generation reduces the matter fermion Yukawas from 15 to 3 (21 to 5) without (with) the $\bf{120}$ Higgs. Yukawon GUTs are thus ultraminimal in parameter counting terms. Consistent symmetry breaking is ensured by a hidden sector Bajc-Melfo(BM) superpotential with a pair of symmetric $O(N_g)$ multiplets $\phi,S $, of which the latter's singlet part $S_s$ breaks supersymmetry and the traceless part $\hat S $ furnishes flat directions to cancel the $O(N_g)$ D-term contributions of the visible sector. Novel dark matter candidates linked to flavour symmetry arise from both the BM sector and GUT sector minimal supersymmetric Standard Model singlet pseudo-Goldstones. These relics may be viable light($< 50 $ GeV) cold dark matter as reported by DAMA/LIBRA. In contrast to the new minimal supersymmetric SO(10) grand unified theory (NMSGUT) even sterile neutrinos can appear in certain branches of the flavour symmetry breaking without the tuning of couplings.