Constraining the SU(2)ᵣ breaking scale in naturally R-parity conserving supersymmetric models

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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 α, is close to its value of unity in the limit of vanishing D-terms. Generally, we find that for heavy Wᵣ α is larger than one, and that the right-handed sneutrino VEV, responsible for spontaneous R-parity breaking, is at most of the order MSUSY/hΔᵣ, where MSUSY is supersymmetry breaking scale and hΔᵣ 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.