R_b and New Physics: A Comprehensive Analysis

We survey the implications for new physics of the discrepancy between the LEP measurement of $R_b$ and its Standard Model prediction. Two broad classes of models are considered: ($i$) those in which new $Z\bbar b$ couplings arise at tree level, through $Z$ or $b$-quark mixing with new particles, and ($ii$) those in which new scalars and fermions alter the $Z \bbar b$ vertex at one loop. We keep our analysis as general as possible in order to systematically determine what kinds of features can produce corrections to $R_b$ of the right sign and magnitude. We are able to identify several successful mechanisms, which include most of those which have been recently been proposed in the literature, as well as some earlier proposals (\eg\ supersymmetric models). By seeing how such models appear as special cases of our general treatment we are able to shed light on the reason for, and the robustness of, their ability to explain $R_b$.