Constraints on $R$-parity violating couplings from lepton universality

We analyze the one loop corrections to leptonic W and Z decays in an R-parity violating extension to the minimal supersymmetric standard model. We find that lepton universality violation in the Z line-shape variables alone would strengthen the bounds on the magnitudes of the ${\lambda }^{\prime }$ couplings, but a global fit on all data leaves the bounds virtually unchanged at $|{\lambda }_{33k}^{\prime }|<~0.42$ and $|{\lambda }_{23k}^{\prime }|<~0.50$ at the $2\sigma$ level. Bounds from W decays are less stringent: $|{\lambda }_{33k}^{\prime }|<~2.4$ at $2\sigma ,$ as a consequence of the weaker Fermilab experimental bounds on lepton universality violation in W decays. We also point out the potential of constraining R-parity violating couplings from the measurement of the ${\rm Y}$ invisible width.