SO(10)SUSY GUT for fermion masses: Lepton flavor andCPviolation

Abstract

We discuss the results of a global ${\ensuremath{\chi}}^{2}$ analysis of a simple $SO(10)$ supersymmetric grand unified theory (SUSY GUT) with ${D}_{3}$ family symmetry and low energy $R$ parity. The model describes fermion mass matrices with 14 parameters and gives excellent fits to 20 observable masses and mixing angles in both quark and lepton sectors, giving six predictions. Bi-large neutrino mixing is obtained with hierarchical quark and lepton Yukawa matrices, thus avoiding the possibility of large lepton flavor violation. The model naturally predicts small 1--3 neutrino mixing, with $\mathrm{sin}{\ensuremath{\theta}}_{13}\ensuremath{\simeq}0.05--0.06$. In this paper we evaluate the predictions for the lepton flavor violating processes, $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$, $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and also the electric dipole moment of the electron (${d}_{e}$), the muon, and the tau, assuming universal squark and slepton masses (${m}_{16}$) and a universal soft SUSY breaking $A$ parameter (${A}_{0}$) at the GUT scale. We find $\mathrm{Br}(\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma})$ is naturally below present bounds, but may be observable by MEG. Similarly, ${d}_{e}$ is below present bounds, but it is within the range of future experiments. We also give predictions for the light Higgs mass (using FeynHiggs). We find an upper bound given by ${m}_{h}\ensuremath{\le}127\text{ }\text{ }\mathrm{GeV}$, with an estimated $\ifmmode\pm\else\textpm\fi{}3\text{ }\text{ }\mathrm{GeV}$ theoretical uncertainty. Finally we present predictions for SUSY particle masses in the favored region of parameter space.