Natural suppression of proton decay in supersymmetric type III seesaw models

Supersymmetric Standard Model (MSSM) has two sources of rapid proton decay: (i) R-parity breaking terms and (ii) higher dimensional Planck induced B-violating terms; its extensions to include neutrino masses via the type I seesaw mechanism need not have the first of these problems due to the existence of B−L as a gauge symmetry but for sure always have the second one. If instead, neutrino masses are explained in a type III seesaw extension of standard model, an anomaly free gauge symmetry different from B−L is known to exist. In this note, it is shown that a realistic supersymmetric versions of this model can be constructed (MSSM as well as SUSY left-right with type III seesaw) which eliminate R-parity violating couplings and suppress Planck scale contributions to proton decay. The degree of suppression of the latter depends on the weak gauge group. For the left-right case, the suppression to the desired level is easily achieved.