# Minimal SUSY SO(10) Model and Neutrino Oscillations

##### 抄録

Many neutrino experiments in the last few years have reported their large statistic data which all converge to the conclusion that the three known neutrinos have masses and mix among themselves. The mixing angles in the quark sector are known to be
very small, whereas that for neutrinos are large. Understanding this difference between quarks and leptons is a major challenge of theoretical particle physics. This is especially acute in the
framework of Grand Unified Theories (GUT) which unifies quarks and leptons. In this thesis, we show that a very simple supersymmetric
SO(10) model predicts a large atmospheric mixing angle, as well as a large solar angle as
required to fit observations and a small but non-vanishing U_{e3} without any extra assumption. The
small neutrino masses are provided by the seesaw mechanism which is also one of the key ingredients of the model. This is the first extensive analysis that shows this model can have the correct
predictions for the two mixing angles as well as the mass differences required to explain the oscillation data. The prediction of the third angle U_{e3} can be tested in ongoing and planned experiments.
This model has a number of other predictions; in particular, we have deduced the predictions of the model for proton decay. We find the upper bounds on the partial lifetime of neutron decay modes. These results can also be used to test the model.
The specific form of the seesaw mechanism that we need to make our prediction imply constraints on the physics at the GUT scale. We find that (i) SO(10) must break to SU(5) before breaking to the standard model; (ii) B-L symmetry must break at the time of
SO(10) breaking and (iii) constraints of unification seem to require that the minimal model must have a 54 dimensional Higgs field together with the minimal set of {210,10,126,126-bar}.

University of Maryland, College Park, MD 20742-7011 (301)314-1328.

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