Intermediate Scales in SUSY SO(10), b-\tau unification and Hot Dark Matter Neutrinos

Considerations of massive neutrinos, baryogenesis as well as fermion mass textures in the grand unified theory framework provide strong motivations for supersymmetric(SUSY) SO(10) as the theory beyond the standard model. If one wants to simultaneously solve the strong CP problem via the Peccei-Quinn mechanism, the most natural way to implement it within the framework of the SUSY SO(10) model is to have an intermediate scale ($v_{BL}$) (corresponding to B-L symmetry breaking) around the invisible axion scale of about 10$^{11}$ - 10$^{12}$ GeV. Such a scale is also desirable if $\nu_{\tau}$ is to constitute the hot dark matter (HDM) of the universe. In this paper, we discuss examples of superstring inspired SUSY SO(10) models with intermediate scales that are consistent with the low energy precision measurements of the standard model gauge couplings. The hypothesis of $b-\tau$ unification which is a successful prediction of many grand unified theories is then required of these models and the resulting prediction of $b$-quark mass is used as a measure of viability of these schemes. Detailed analysis of a model with a $v_{BL}\simeq 10^{11}$ GeV, which satisfies both the requirements of invisible axion and $\nu_{\tau}$ as HDM is presented and shown to lead to $m_b\simeq 4.9$ GeV in the one-loop approximation.Comment: Latex file; 20 pages; Four figures available on reques

Effects of 126 dimensional Higgs scalar on Bottom-Tau unification and quasi-infrared fixed point

In the presence of ${\bf 126 + \bar{126}}$ Higgs multiplets in a SO(10) theory, the fermion masses get contributions from an induced vacuum expectation value (VEV) of a $SU(2)_L$ doublet residing in ${\bf 126}$ which differentiates between quarks and leptons by a relative sign leading to a significant correction to the prediction of the mass ratio of the bottom quark and the tau lepton for ranges of the mass of this extra doublet. We perform a two-loop renormalization group analysis of the minimal version of the one-step supersymmetric SO(10) model to display this and re-calculate the corrections to the top quark mass in the presence of such an induced VEV. We show that these effects make the infra-red fixed point scenario consistent with experimental results.Comment: revised version with same conclusions. To appear in Phys. Rev.