Quadruple Yukawa Unification in the Minimal Supersymmetric Model

Predictions for m_t, tan beta, m_nu_tau are calculated for quadruple third family t-b-tau-nu_tau Yukawa unified models in the MSSM. The renormalisation group equations for the 3 families of the MSSM, including the right handed neutrino, are presented. For right handed tau neutrino Majorana masses that are bigger than 10^11 GeV, the tau neutrino mass is consistent with present cosmological bounds. The m_t, tan beta predictions are approximately equivalent to those in triple third family Yukawa unified models.Comment: 10 pages plain LaTex, uuencoded .epsf files in part 2. Revised version has NO changes to content, merely changed format to .tex fil

String unification, spaghetti diagrams and infra-red fixed points

We consider a scenario in which the minimal supersymmetric standard model (MSSM) is valid up to an energy scale of ∼ 10 16 GeV, but that above this scale the theory is supplemented by extra vector-like representations of the gauge group, plus a gauged U(1)X family symmetry. In our approach the extra heavy matter above the scale ∼ 10 16 GeV is used in two different ways: (1) to allow (two-loop) gauge coupling unification at the string scale; (2) to mix with quarks, leptons and Higgs fields via spaghetti diagrams and so lead to phenomenologically acceptable Yukawa textures. We determine the most economical models in which the extra matter can satisfy both constraints simultaneously. We then give a general discussion of the infra-red fixed points of such models, pointing out the conditions for infra-red stability, then discuss The apparent unification of the gauge couplings at a scale MGUT ∼ 10 16 GeV [1] is an encouraging feature of the MSSM, whose direct experimental verification so far remains out of reach. Nevertheless this conceptual triumph leads naturally to th