Unification, Multiplets and Proton Decay

Abstract

We make a detailed analysis of gauge coupling unification in supersymmetry. When the Standard Model gauge group is embedded in a Grand Unified Theory, new particles often appear below the GUT scale in order to predict the right phenomenology at low energy. While these new particles are beyond the reach of accelerator experiments, they change the prediction of \alpha_s. Here we classify all the (SU(3)_C,SU(2)_L,U(1)_Y) representations which improve or worsen the prediction. Running experimentally determined values of the coupling constants at two loops we calculate the allowed range of masses of fields in these representations. We explore the implication of these results in SU(5) and SU(3)^3 (trinification) models. We discover that minimal trinification predicts light triplet Higgs particles which lead to proton decay with a lifetime in the vicinity of the current experimental bound.Comment: figures replaced, new calculations and references added. A quantitative description of dependence of unification on varying input parameters as well as varying the sparticle spectrum is added. This version to appear in PR