Radiative corrections to theZbb¯vertex and constraints on extended Higgs sectors

We explore the radiative corrections to the process $\overrightarrow{Z}b\overline{b}$ in models with extended Higgs sectors. The observables $R_b\equiv \Gamma \left(\overrightarrow{Z}b\overline{b}\right)/\Gamma \left(\overrightarrow{Z}\mathrm{hadrons}\right)$ and the $\mathrm{Zb}\overline{b}$ coupling asymmetry, $A_b\equiv {(g}_L^2-g_R^2{)/(g}_L^2{+g}_R^2),$ are sensitive to these corrections. We present general formulas for the one-loop corrections to $R_b$ and $A_b$ in an arbitrary extended Higgs sector, and derive explicit results for a number of specific models. We find that in models containing only doublets, singlets, or larger multiplets constrained by a custodial $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_c$ symmetry, so that $M_W{=M}_Z\cos {\theta }_W$ at tree level, the one-loop corrections due to virtual charged Higgs bosons always worsen agreement with experiment. The $R_b$ measurement can be used to set lower bounds on the charged Higgs boson masses. Constraints on models due to the one-loop contributions of neutral Higgs bosons are also examined.