Constraining the vacuum expectation values in naturally R-parity conserving supersymmetric models

We obtain a relation between right-handed gauge boson mass and soft squark mass in naturally R-parity conserving general supersymmetric left-right models. This relation implies that either WR is lighter than twice the soft squark mass, or a ratio of vacuum expectation values (VEVs) in the model, denoted by tanα, is close to its value of unity in the limit of vanishing D-terms. Generally, we find that for heavy WR tanα is larger than one, and that the right-handed sneutrino VEV, responsible for spontaneous R-parity breaking, is at most of the order MSUSY /h∆R, where MSUSY is supersymmetry breaking scale and h∆R is the Yukawa coupling in Majorana mass term for right-handed neutrinos. These constraints follow from SU(3)c and U(1)em gauge invariance of the ground state of the theory. PACS numbers: 12.60.Jv, 11.30.Fs, 14.70.Fm, 11.30.Qc