Grand Unification in particle physics is appealing for merging three of the four elementary forces into one at very high energies. Besides the corresponding unification of gauge couplings, Grand Unified Theories predict unified Yukawa couplings of quarks and leptons to a Higgs boson. Yukawa unification has been tested by measuring the fermion masses at today's particle colliders and found to hold for heavy, but to fail for light fermions. This work is a study of corrections to Yukawa unification from higher-dimensional operators in a supersymmetric model with SO(10) gauge symmetry. Due to the unification of down quarks and leptons the large flavour mixing measured in neutrino oscillations induces large flavour-changing neutral currents among down-type quarks. The resulting effects in kaon physics observables strongly constrain the flavour structure of Yukawa corrections.

ABSTRACT: Simple SUSY GUT models based on the gauge group SO(10) require t - b - τ Yukawa coupling unification, in addition to gauge coupling and matter unification. The Yukawa coupling unification places a severe constraint on the expected spectrum of superpartners, with scalar masses ~ 10 TeV while gaugino masses are quite light. For Yukawa-unified models with μ> 0, the spectrum is characterized by three mass scales: i). first and second generation scalars in the multi-TeV range, ii). third generation scalars, μ and mA in the few-TeV range and iii). gluinos in the ~ 350-500 GeV range with chargino masses around 100-160 GeV. In such a scenario, gluino pair production should occur at large rates at the CERN LHC, followed by gluino three-body decays into neutralinos or charginos.

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We construct a supersymmetric SO(10) \times U(1)_F model of the Yukawa interactions at the grand unification scale from knowledge of a phenomenological set of mass matrices obtained by a previous bottom-up approach. The U(1)_F family symmetry determines the textures for the Majorana and generic Dirac mass matrices, while the SO(10) symmetry relates each particular element of the up, down, neutrino and charged lepton Dirac matrices. The dominant second and third family contributions in the Dirac sector are renormalizable, while the remaining contributions to the Dirac mass matrices are of higher order, restricted by the U(1)_F family symmetry to a small set of tree diagrams, and mainly complex-symmetric. The tree diagrams for the Majorana mass matrix are all non-renormalizable and of progressively higher-order, leading to a nearly geometrical structure. Pairs of {\bf 1, 45, 10} and {\bf 126} Higgs representations enter with those having large vacuum expectation values breaking the symmetry down to SU(3)_c \times SU(2)_L \times U(1)_Y near the grand unification scale. In terms of 12 parameters expressed as the Yukawa couplings times vacuum expectation values for the Higgs representations employed, a realistic set of 15 quark and lepton masses (including those for the 3 heavy righthanded Majorana neutrinos) and 8 mixing parameters emerges for the neutrino scenario involving the non-adiabatic conversion of solar neutrinos and the depletion of atmospheric muon-neutrinos through oscillations into tau-neutrinos.

The recent high precision results from the LEP supercollider at CERN appear favorable for supergravity unification of the electroweak and the strong forces. The proceedings of the SUSY 93 Workshop focus on further precise predictions of unification which may be observed in the laboratory. In addition, the proceedings cover a wide range of other topics in supersymmetry, supergravity, particle physics, string theory and cosmology and their interconnections. They include both theoretical and experimental papers, hence presenting a complete and comprehensive picture of this important subject.

This volume collects the edited tutorial lectures given at The Second International Summer School in High Energy Physics in Mugla, Turkey, in September 2006 - an annual event with international participation and a special focus on work done in the regions of central Asia. With emphasis on the standard model and beyond, lectures were devoted to presenting an introduction and update to many relevant topics.