Constraining Grand Unification using first and second generation sfermions

TL;DR

This paper explores how measurements of first and second generation sfermion spectra can constrain grand unification models like SU(5), SO(10), and E6, providing analytic relations and sum rules to distinguish between these theories.

Contribution

It introduces an analytic framework and sum rules to connect low-energy sfermion masses with high-scale GUT parameters, aiding in model discrimination.

Findings

Derived expressions for high-scale parameters from low-scale sfermion masses.

Proposed a sum rule for SO(10) mass predictions.

Compared analytic results with numerical two-loop calculations.

Abstract

We investigate the spectrum of supersymmetric grand unification models based on the gauge groups SU(5), SO(10) and E6, paying particular attention to the first and second generation. We demonstrate how the measurement of the first or second generation sfermion spectrum may be used to constrain the underlying grand unification structure. The smallness of first and second generation Yukawa interactions allows us to perform an analytic analysis, deriving expressions for the high scale parameters in terms of the low scale sfermion masses. We also describe a sum rule that provides an SO(10) mass prediction, distinct from SU(5), and discuss E6 models, both with and without extra exotic matter at low energies. The derived relations are compared with numerical results including two-loop running and the full Yukawa dependence.