String Gauge Unification and Infra - red Fixed Points in MSSM + X Models

In order to achieve gauge unification at the string scale M X ∼ 5 × 10 17 GeV in the minimal supersymmetric standard model (MSSM) it is necessary to add extra gauge non-singlet representations at an intermediate scale M I < M X , leading to a class of models which we refer to as MSSM+X models. We perform a detailed analysis of a large class of MSSM+X models and find that the number of (3,1) representations added must be greater than the total of the number of (3,2) and (1,2) representations. Predictions of M I , M X and α(M X) are obtained for models with up to 5 extra vector representations than the MSSM. Upper bounds on the U(1) string gauge normalisa-tion k 1 and the sum of the squares of the hypercharge assignments of the extra matter are also obtained for the models. We also study the infra-red fixed point behaviour of the top quark Yukawa coupling in a large class of MSSM+X models and find that the low energy MSSM quasi-fixed point prediction of the top quark mass is more likely to be realised in these theories than in the MSSM. In other words the top quark tends to be heavier in MSSM+X models than in the MSSM. The implementation of a U(1) X family symmetry into MSSM+X models to account for the Standard Model fermion masses is discussed and a particular viable model is presented.