Constraints on $R$-parity violating couplings from CERN LEP and SLAC SLD hadronic observables

We analyze the one loop corrections to hadronic Z decays in an R-parity violating extension to the minimal supersymmetric standard model. Performing a global fit to all the hadronic observables at the Z peak, we obtain stringent constraints on the R-violating coupling constants ${\lambda }^{\prime }$ and ${\lambda }^{″}.$ The presence of these couplings worsens the agreement with the data relative to the standard model. The strongest constraints come from the b asymmetry parameters $A_b$ and $A_{\mathrm{FB}}\mathrm{}\left(b\right).$ From a classical statistical analysis we find that the couplings ${\lambda }_{i31\mathrm{}}^{\prime },$ ${\lambda }_{i32\mathrm{}}^{\prime },$ and ${\lambda }_{321}^{″}$ are ruled out at the $1\sigma$ level, and that ${\lambda }_{i33\mathrm{}}^{\prime }$ and ${\lambda }_{33i}^{″}$ are ruled out at the $2\sigma$ level. A Bayesian statistical analysis weakens the bounds, but the corresponding ${\chi }^2\mathrm{’}\mathrm{s}$ are uncomfortably large, rendering the relevance of the Bayesian bounds suspect.