A natural MSSM from a novel SO(10), Yukawa unification, light sparticles, and SUSY implications at LHC

The SO(10) model with a heavy Higgs spectrum consisting of 560 + 560<overline> and a light Higgs spectrum consisting of 2 10 + 320 plet representations of SO(10) is unique among SO(10) models. It has the remarkable property that VEVs of 560 and 560<overline> can simultaneously reduce the rank of the gauge group and further reduce the remaining symmetry down to the Standard Model gauge group. Additionally, on mixing with the light fields all the Higgs fields become heavy except for one pair of light Higgs doublets just as in MSSM. This model has not been fully explored thus far because of the technical difficulty of computing the couplings of the heavy and the light Higgs sectors, specifically the interaction (560 560) 320 involving the coupling of tensor-spinors with a third rank mixed tensor 320. An explicit analysis of such couplings is given in this paper. Spontaneous symmetry breaking of the SO(10) symmetry is carried out by reducing the gauge group to SU(3)(c) x SU(2)(L) x U(1)(Y) with just one pair of light Higgs. Thus a natural deduction of MSSM arises from the SO(10) model with no fine tuning needed. Further, it is shown that the light Higgs doublet of the model is a linear combination of the Higgs doublet fields of the 2x10 and the 320 Higgs fields. It is shown that in this class of SO(10) models b - t - tau unification can be achieved with tan beta as low as 5-10. An analysis of the sparticle spectrum within renormalization group evolution is given which leads to a bi-modal sparticle spectrum consisting of a compressed low mass spectrum for sleptons and weakinos and a high mass spectrum of gluino, squarks, and heavy Higgs. While the LSP is the light neutralino, the NLSP is found to be the light stau lying close to the LSP, while the remaining leptons, and the weakinos are also in close proximity to the LSP with masses in the few hundred GeV range. The cross section for slepton production and weakino production are estimated and appear promising for SUSY at the LHC. However, a more dedicated analysis is needed to predict the size of the supersymmetric signatures at the LHC.