Upper Bound on theWRMass in AutomaticallyR-Conserving Supersymmetric Models

We show that in automatically $R$-conserving minimal supersymmetric (SUSY) left-right symmetric models there is a theoretical upper limit on the mass of the right-handed $W_R$ boson given by $M_{W_R}\le \frac{g{M}_{\mathrm{SUSY}}}{f}$, where $M_{\mathrm{SUSY}}$ is the scale of SUSY breaking, $g$ the weak gauge coupling, and $f$ the Yukawa coupling responsible for generating the right-handed neutrino masses. If $M_{W_R}$ violates the above bound, the ground state of the theory breaks electromagnetism. The only way to avoid this bound while keeping the theory automatically $R$ conserving is to expand the theory to include very specific kinds of additional multiplets.