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

TL;DR

This paper analyzes how extended Higgs sectors affect radiative corrections to Z boson decays into bottom quarks, providing formulas and constraints that help refine models beyond the Standard Model.

Contribution

It derives general one-loop correction formulas for extended Higgs sectors and applies them to set bounds on charged and neutral Higgs boson masses.

Findings

Charged Higgs bosons worsen agreement with experimental data.

R_b measurements set lower bounds on charged Higgs masses.

Neutral Higgs contributions also impose constraints.

Abstract

We explore the radiative corrections to the process $Z \to b \bar b$ in models with extended Higgs sectors. The observables $R_b = \Gamma(Z \to b \bar b)/\Gamma(Z \to \rm{hadrons})$ and the $Z b \bar b$ 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.