Supersymmetric $SU(2{)}_L\times SU(2{)}_R\times SU(4{)}_c$ and observable neutron-antineutron oscillation

We show that in a large class of supersymmetric $SU(2)_L\times SU(2)_R\times SU(4)_c$ models with the see-saw mechanism for neutrino masses and an R-parity conserving vacuum, there are diquark Higgs bosons with masses ($M_{qq}$) near the weak scale even though the scale of $SU(2{)}_R\times SU(4{)}_c$ symmetry breaking is around ${10}^{10}$ GeV. This happens because these masses ($M_{qq}$) arise out of higher dimensional operators needed to stabilize the charge conserving vacuum in the model. This feature has the interesting implication that the $\mathrm{\Delta }B=2$ processes such as neutron-anti-neutron oscillation can have observable rates while at the same time yielding neutrino masses in the range of current interest.