MSGUT a la Pati-Salam : from Futility to Precision

Abstract

We compute the complete gauge and chiral superheavy mass spectrum and couplings of the Minimal Susy GUT (based on the $ \bf {210- \oot- 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 ($\Delta B\ne 0$) 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.

Version published in Nuclear Physics B with title changed to : "SO(10) MSGUT : spectra, couplings and threshold effects". Additional notes added on consistency checks. Factor of Sqrt 2 in eqns. 78-79 of Journal version corrected

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