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

Abstract

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 ${W_R}$ is lighter than twice the soft squark mass, or a ratio of vacuum expectation values (VEVs) in the model, denoted by $\tan\alpha$, is close to its value of unity in the limit of vanishing D-terms. Generally, we find that for heavy $W_R$ $\tan\alpha$ is larger than one, and that the right-handed sneutrino VEV, responsible for spontaneous R-parity breaking, is at most of the order $M_{SUSY}/h_{\Delta_R}$, where $M_{SUSY}$ is supersymmetry breaking scale and $h_{\Delta_R}$ 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.