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

TL;DR

This work derives general one-loop radiative corrections to the $Z\rightarrow b\bar{b}$ vertex in extended Higgs sectors and uses $R_b$ and $A_b$ to constrain such models. The authors express corrections to the left- and right-handed $Zb\bar{b}$ couplings in terms of charged- and neutral-Higgs couplings and masses, then apply the results to Type I/II two-Higgs-doublet models and more general multi-doublet/singlet scenarios. They find that charged-Higgs loops in models with only doublets/singlets tend to worsen agreement with data, enabling $R_b$ to set lower bounds on charged-Higgs masses, while neutral-Higgs contributions become relevant only when $\lambda_b$ is enhanced (e.g., large $\tan\beta$ in Type II). Neutral-Higgs effects are negligible in Type I but nontrivial in Type II under certain vev configurations; overall, $R_b$ provides strong constraints on the Higgs-sector parameter space while $A_b$ remains less restrictive.

Abstract

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

Figures (6)

• Figure 1: The constraints from $R_b$ and $A_b$ on the right-- and left--handed $Z b \bar{b}$ couplings. Plotted are the allowed deviations $\delta g^{R,L}_{\rm new}$ of the couplings from their SM values. The 1$\sigma$ errors are shown as solid lines and the 2$\sigma$ errors as dashed lines. The central value, at $\delta g^L_{\rm new} = 0.0037$ and $\delta g^R_{\rm new} = 0.0219$, is marked by the cross.
• Figure 2: Feynman diagrams of the leading $m_t^2$ contributions to the electroweak corrections to $Z\rightarrow b \bar{b}$ in the SM.
• Figure 3: Feynman diagrams of the electroweak corrections to $Z\rightarrow b \bar{b}$ in a model with an extended Higgs sector.
• Figure 4: Feynman diagrams for the corrections to $Z \rightarrow b \bar{b}$ involving neutral Higgs bosons in the loop.
• Figure 5: Constraints from $R_b$ on the charged Higgs mass and $\tan\beta$ in the Type II 2HDM. The area below the solid line is excluded at 95% confidence level. Also shown are the 99% and 99.9% confidence levels (dashed lines). We also show the 95% confidence level lower bound on $M_{H^+}$ from the $b \rightarrow s \gamma$ branching ratio CLEO99Borzumati98 (dot-dashed). The vertical dotted line is the direct search bound on the charged Higgs mass, $M_{H^+} > 77.3$ GeV lephiggs.