Radiative Corrections to the $Zb\bar{b}$ Vertex and Constraints on Extended Higgs Sectors

Abstract

We explore the radiative corrections to the process $Z\to b\bar{b}$ in models with extended Higgs sectors. The observables $R_b=\Gamma (Z\to b\bar{b})/\Gamma (Z\to \mathrm{hadrons})$ and the $Zb\bar{b}$ coupling asymmetry, $A_b=(g_L^2-g_R^2)/(g_L^2+g_R^2)$, are sensitive to these corrections. We present general formulae 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 $SU(2{)}_c$ 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 masses. Constraints on models due to the one-loop contributions of neutral Higgs bosons are also examined.

54 pages, 11 figures

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