Degenerate Neutrinos in Left Right Symmetric Theory

Abstract

Various hints on the neutrino masses namely, ({\em i}) the solar neutrino deficit ({\em ii}) the atmospheric neutrino deficit ({\em iii}) the need for the dark matter and/or ({\em iv}) the non-zero neutrinoless double beta decay collectively imply that all the three neutrinos must be nearlty degenerate. This feature can be understood in the left right symmetric theory. We present a model based on the group $SU(2)_{L}\times SU(2)_R\times U(1)_{B-L}\times SU(2)_H$ which can explain the required departures from degeneracy in neutrino masses and large mixing among them without assuming any of the mixing in the quark or charged lepton sector to be large as would be expected in a typical $SO(10)$ model.