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 ${\ensuremath{\lambda}}^{\ensuremath{'}}$ and ${\ensuremath{\lambda}}^{\ensuremath{''}}.$ 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 ${A}_{\mathrm{FB}}(b).$ From a classical statistical analysis we find that the couplings ${\ensuremath{\lambda}}_{i31}^{\ensuremath{'}},$ ${\ensuremath{\lambda}}_{i32}^{\ensuremath{'}},$ and ${\ensuremath{\lambda}}_{321}^{\ensuremath{''}}$ are ruled out at the $1\ensuremath{\sigma}$ level, and that ${\ensuremath{\lambda}}_{i33}^{\ensuremath{'}}$ and ${\ensuremath{\lambda}}_{33i}^{\ensuremath{''}}$ are ruled out at the $2\ensuremath{\sigma}$ level. A Bayesian statistical analysis weakens the bounds, but the corresponding ${\ensuremath{\chi}}^{2}\mathrm{'}\mathrm{s}$ are uncomfortably large, rendering the relevance of the Bayesian bounds suspect.