MSGUT a la Pati-Salam : from Futility to Precision

TL;DR

This paper performs detailed calculations of the mass spectrum and couplings in the Minimal Susy GUT based on SO(10), demonstrating that high-precision unification predictions are feasible and sensitive to model parameters.

Contribution

It provides the complete superheavy mass spectrum, couplings, and threshold corrections in MSGUT, enabling precise phenomenological analysis and challenging previous assumptions about the futility of such calculations.

Findings

Threshold corrections are within 10% of one-loop values for generic parameters.

Explicit couplings and mass formulas for matter fermions are derived.

The results enable detailed RG-based phenomenological studies of MSGUT.

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 ($\Delta B\neq 0$) 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.