Proton decay and flavor violating thresholds in SO(10) models.

Discovery of neutrino mass has put the spotlight on the supersymmetric (SUSY) SO(10) model as a natural candidate for grand unification of forces and matter. However, the suppression of proton decay is a major problem in such SUSY grand unified models. In this Letter we show how to alleviate this problem by simple threshold effects which raise the colored Higgsino masses and the grand unification scale to greater than or similar to 10(17) GeV. There exist only four types of fields arising from different SO(10) representations which can generate this kind of threshold effect. Some of these fields also generate a sizable flavor violation in the quark sector compared to the lepton sector. The b-tau unification can work in these types of models even for intermediate values of tanbeta.

Observable N-N oscillation in high scale seesaw models.

We discuss a realistic high scale (nu(B-L) approximately 10(12) GeV) supersymmetric seesaw model based on the gauge group SU(2)L x SU(2)R x SU(4)c where neutron-antineutron oscillation can be in the observable range. This is contrary to the naive dimensional arguments which say that tau(N-N) is proportional to nu(B-L)5 and should therefore be unobservable for seesaw scale nu(B-L) > or = 10(5) GeV. Two reasons for this enhancement are (i) accidental symmetries which keep some of the diquark Higgs masses at the weak scale and (ii) a new supersymmetric contribution from a lower dimensional operator. The net result is that tau(N-N) is proportional to nu(B-L)2 nu(wk)3 rather than nu(B-L)5. The model also can explain the origin of matter via the leptogenesis mechanism and predicts light diquark states which can be produced at LHC.

Bs-Bs mixing in grand unified models.

We study Bs-Bs mixing in supersymmetry grand unified SO(10), SU(5) models where the mixings among the second and third generation squarks arise due to the existence of flavor violating sources in the Dirac and Majorana couplings which are responsible for neutrino mixings. We find that when the branching ratio of tau-->mugamma decay is enhanced to be around the current experimental bound, Bs-Bs mixing may also contain large contribution from supersymmetry in the SO(10) boundary condition. Consequently, the phase of Bs-Bs mixing is large (especially for small tanbeta and large scalar mass m0) and can be tested by measuring CP asymmetries of Bs decay modes.

Suppressing proton decay in the minimal SO(10) model.

We show that in a class of minimal supersymmetric SO(10) models which have been found to be quite successful in predicting neutrino mixings, all proton decay modes can be suppressed by a particular choice of Yukawa textures. The required texture not only fits all lepton and quark masses as well as Cabibbo-Kobayashi-Maskawa parameters, but it also predicts neutrino mixing parameter U(e3) and Dirac CP phase sin(/delta(MNS)/ to be 0.07-0.09 and 0.3-0.7, respectively.

Unity of elementary particles and forces in higher dimensions.

The idea of unifying all the gauge and Yukawa forces as well as the gauge, Higgs, and fermionic matter particles naturally leads us to a simple gauge symmetry in higher dimensions with supersymmetry. We present a model in which, for the first time, such a unification is achieved in the framework of quantum field theory.