Constraining Grand Unification using first and second generation sfermions

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.