$A^b_{FB}$ and $R_b$ at LEP and New Right-Handed Gauge Bosons

We explore models with additional right-handed gauge bosons that couple predominantly to the third generation in the context of $b\bar{b}$ production at LEP. In particular we investigate potential new contributions to $\delta g_{Rb}$ that are needed if the measured $A^b_{FB}$ at the $Z$ peak is interpreted as a signal of new physics. We identify two sources of large $\delta g_{Rb}$ corrections: $Z-Z^\prime$ mixing at tree-level, and one-loop effects from a new $SU_R(2)$ triplet of gauge bosons. We find that the latter can contribute to $\delta g_{Rb}$ at the 1%-level. We place bounds on the mass of the additional $Z^\prime$ gauge boson that occurs in these models using the $R_b$ measurements from LEP-II. We find that even in cases where the $Z^\prime$ couples almost exclusively to the $b$ and $t$-quarks, masses lighter than about 500 GeV are already excluded.