Neutrino Oscillations and Other Key Issues in Supersymmetric SU(4)_c \times SU(2)_L \times$ SU(2)_R

Abstract

We try to gain an understanding of the recent Superkamiokande data on neutrino oscillations and several other important phenomenological issues within the framework of supersymmetric $SU(4{)}_c\times SU(2{)}_L\times SU(2{)}_R$ ($\equiv G_{422}$). By supplementing $G_{422}$ with a U(1)-$\mathcal{R}$ symmetry, we can provide an explanation of the magnitude $M_G$ ($\sim 10^{16}$ GeV) of the $G_{422}$- symmetry breaking scale, resolve the MSSM $\mu$ problem, and understand why proton decay has not been seen (${\tau }_p\gg 10^{34}$ yr). The family dependent $\mathcal{R}$ - symmetry also helps provide an explanation of the charged fermion mass hierarchies as well as the magnitudes of the CKM matrix elements. Several additional heavy states in the mass range $10^4-10^7$ GeV are predicted, and the MSSM parameter $\tan \beta$ turns out to be of order unity. The atmospheric neutrino problem is explained through ${\nu }_{\mu }-{\nu }_{\tau }$ mixing with ${\sin }^{2}2{\theta }_{\mu \tau }\simeq 1$. The resolution of the solar neutrino puzzle is via the small angle MSW oscillations and necessarily requires a sterile neutrino ${\nu }_s$ which, thanks to the $\mathcal{R}$ - symmetry, has a tiny mass.

Comments: 14 pages, LATEX. The new version emphasizes the small angle \nu_e-\nu_s MSW oscillations instead of the large angle \nu_e-\nu_s vacuum oscillations