Variety ofSO(10)GUTs with natural doublet-triplet splitting via the missing partner mechanism

Abstract

We present a new class of unified $SO(10)$ models where the grand unified theory symmetry breaking down to the standard model gauge group involves just one scale, in contrast to the conventional $SO(10)$ models which require two scales. Further, the models we discuss possess a natural doublet-triplet splitting via the missing partner mechanism without fine-tuning. Such models involve $560+\overline{560}$ pair of heavy Higgs fields along with a set of light fields. The $560+\overline{560}$ are the simplest representations of $SO(10)$ besides the $126+\overline{126}$ which contain an excess of color triplets over $SU(2{)}_{L}$ doublets. We discuss several possibilities for realizing the missing partner mechanism within these schemes. With the $126+\overline{126}$ multiplets, three viable models are found with additional fields belonging to ${210+2\ifmmode\times\else\texttimes\fi{}10+120}$, ${45+10+120}$, or ${210+16+\overline{16}+10+120}$. With the $560+\overline{560}$, a unique possibility arises for the missing partner mechanism, with additional ${2\ifmmode\times\else\texttimes\fi{}10+320}$ fields. These models are developed in some detail. It is shown that fully realistic fermion masses can arise in some cases, while others can be made realistic by addition of vectorlike representations. Naturally large neutrino mixing angles, including sizable ${\ensuremath{\theta}}_{13}$, can emerge in these models. The couplings of the ${H}_{u}({H}_{d})$ Higgs doublets of the minimal supersymmetric standard model which give masses to the up quarks (down quarks and leptons) are not necessarily equal at the grand unification scale and would lead to a new phenomenology at the low-energy scales.