Single and double seesaw for quark-lepton and neutrino masses

A left-right model of quarks and leptons based on the gauge group $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ is studied. Here the scalar sector consists of only two doublets namely (1,2,1,1) and (1,1,2,1) but familiar bidoublet (1,2,2,0) is removed. Quarks and charged leptons get mass from a single see-saw mechanism but neutrinos get mass from a double see-saw mechanism. In this type of models the heaviest right handed neutrino can be of order $10^{13}$ GeVs or less in a natural way, depending on the size of related Yukawa couplings.