Reconciling the LEP and Slac Measurements of Sin^2(\Theta_W)

We consider whether a discrepancy between the SLAC and LEP measurements of $\text{Sw}$ can be explained by new physics. We find that only the contribution of a new neutral gauge boson, $Z^{\mathrm{\prime }}$, nearly degenerate with the Z can affect the SLAC measurement while leaving the LEP observables almost unaffected. We briefly discuss possible signals for this new gauge boson, including changes in the $Z$ lineshape when measured with polarised electrons, small changes in $R_b$, $A_{FB}^e$, and larger changes in two jet and $t\bar{t}$ production at hadron colliders.