We compute the complete gauge and chiral superheavy mass spectrum and couplings of the Minimal Susy GUT (based on the 210 − 126 − 126 − 10 irreps as the Higgs system) by decomposing SO(10) labels in terms of Pati Salam subgroup labels. The spectra are sensitive functions of the single complex parameter that controls MSGUT symmetry breaking. We scan for the dependence of the threshold corrections to the Weinberg angle and Unification scale as functions of this parameter. We find that for generic values of the GUT scale parameters the modifications are within 10% of the one loop values and can be much smaller for significant regions of the parameter space. This shows that contrary to longstanding conjectures, high precision calculations are not futile but rather necessary and feasible in the MSGUT. The couplings of the matter supermultiplets are made explicit and used to identify the channels for exotic (∆B = 0) processes and to write down the associated bare d = 5 operators (some of both are novel). The mass formulae for all matter fermions are derived. This sets the stage for a comprehensive RG based phenomenological analysis of the MSGUT.

We present rules for rewriting SO(10) tensor and spinor invariants in terms of invariants of its "Pati-Salam" maximal subgroup (SU(4)×SU(2) L × SU(2) R ) supplemented by the discrete symmetry called D parity. Explicit decompositions of quadratic and cubic invariants relevant to GUT model building are presented and the role of D parity in organizing the terms explained. Our rules provide a complete and explicit method for obtaining the "Clebsch-Gordon" Coefficients for SO(10) ↔ G P S in a notation appropriate for field theory models. We illustrate the usefulness our methods by calculating previously unavailable mass matrices and couplings of the SU (2) L doublets and SU (3) c triplets in the minimal Susy SO(10) GUT which are essential to specify the phenomenology of this model. We also present the bare effective potential for Baryon number violation in this model and show that it recives novel contributions from exchange of triplet Higgsinos contained the in "neutrino mass" Higgs submultiplets Σ 126 (10, 1, 3). This further tightens the emerging connection between neutrino mass and proton decay.

The magnetic moments of J P = 3 2 + decuplet baryons have been calculated in the chiral constituent quark model (χCQM) with explicit results for the contribution coming from the valence quark polarizations, sea quark polarizations, and their orbital angular momentum. Since the+ decuplet baryons have short lifetimes, the experimental information about them is limited. The χCQM has important implications for chiral symmetry breaking as well as SU (3) symmetry breaking since it works in the region between the QCD confinement scale and the chiral symmetry breaking scale. The predictions in the model not only give a satisfactory fit when compared with the experimental data but also show improvement over the other models. The effect of the confinement on quark masses has also been discussed in detail and the results of χCQM are found to improve further with the inclusion of effective quark masses.

We predict a clean signal at the Large Hadron Collider ( √ s=14TeV) for a scenario where there is a top-like, charge + 2 3 vectorlike isosinglet fermion. Such a quark, via mixing with the standard model top, can undergo decays via both flavour-changing Z-boson coupling and flavour-changing Yukawa interactions. We concentrate on the latter channel, and study the situation where, following its pair-production, the heavy quark pair gives rise to two tops and two Higgs boson. We show that the case where each Higgs decays in the bb channel, there can be a rather distinct and background-free signal that can unveil the existence of the vectorlike isosinglet quark of this kind.