Supersymmetry and Unification: Heavy Top Was the Key

I review the unification of gauge couplings of strong, weak and electro-magnetic interactions. I start by recalling the history of the most important prediction of low-energy supersymmetry: the correct value of the weak mixing angle tied to a large top quark mass. I then turn to the discussion of the present day situation of the minimal supersymmetric Grand Unified Theories based on SU(5) and SO(10) groups, and I show why the minimal SU(5) is in accord with experiment. For the sake of completeness I also summarize the problems and possible solutions of the minimal ordinary SU(5). One version, based on the minimal Georgi-Glashow model, augmented by the adjoint fermion, predicts a light fermion triplet to lie below TeV or so. Its (lepton number violating) decays offer a hope of probing neutrino (Majorana) masses and mixings at the LHC.Comment: To be published in the proceedings of the Scientific and Human Legacy of Julius Wess, Memorial Workshop held in Donji Milanovac, Serbia, August 201

Proton decay and grand unification

I review the theoretical and experimental status of proton decay theory and experiment. Regarding theory, I focus mostly, but not only, on grand unification. I discuss only the minimal, well established SU(5) and SO(10) models, both ordinary and supersymmetric. I show how the minimal realistic extensions of the original Georgi - Glashow model can lead to interesting LHC physics, and I demonstrate that the minimal supersymmetric SU(5) theory is in perfect accord with experiment. Since no universally accepted model has of yet emerged, I discuss the effective operator analysis of proton decay and some related predictions from a high scale underlying theory. A strong case is made for the improvement of experimental limits, or better the search of, two body neutron decay modes into charged kaons and charged leptons. Their discovery would necessarily imply a low energy physics since they practically vanish in any theory with a desert in energies between M_W and M_GUT.Comment: Based on the plenary talks at the SUSY09 and PASCOS09 conference

See-saw and grand unification

I review the profound connection between the see-saw mechanism for neutrino masses and grand unification. This connection points naturally towards SO(10) grand unified theory. The emphasis here is on the supersymmetric theory, but I also discuss salient features of its split supersymmetry version and ordinary non-supersymmetric SO(10). Particular attention is paid to the crucial issue of the minimal such theory, i.e. the question of the Higgs sector needed to break SO(10) down to the Minimal Supersymmetric Standard Model or the Standard Model. Some essential features of the see-saw mechanism are clarified, in particular its precise origin at the high scale.Comment: Talk given at SEESAW25: International Conference on the Seesaw Mechanism and the Neutrino Mass, Paris, France, 10-11 Jun 200

A Truly Minimal Left-Right Symmetric Extension of the Standard Model

By invoking the existence of a general custodial O(2) symmetry, a minimal Left-Right symmetric model based on the gauge group G=SU(2)L SU(2)R U(1)BL is shown to require the existence of only two physical Higgs bosons. The lighter Higgs is predicted to have a small mass which could be evaluated by standard perturbation theory. The fermionic mass matrices are recovered by insertion of ad hoc fermion-Higgs interactions. The model is shown to be undistinguishable from the standard model at the currently reachable energies.Comment: 1 figure in a separate ps fil

Proton decay, supersymmetry breaking and its mediation

We study the breaking of supersymmetry and its transmission to the light states in the context of the minimal SU(5) grand unified theory, with no additional singlets. This simple theory can be taken as a prototype for a program of breaking simultaneously grand unified symmetry and supersymmetry. The main predictions are: (i) d=6 proton decay is completely negligible and d=5 is in accord with experiment, (ii) supersymmetry breaking is mainly mediated by gravity.Comment: 18 page