Electroweak constraints on warped models with custodial symmetry

TL;DR

The authors investigate warped extra-dimensional models with custodial symmetry to protect the $T$ parameter and the $Z b_L\bar b_L$ coupling. They show that loop corrections to these observables are calculable and correlated, and perform a global electroweak fit to derive bounds on the KK spectrum. The analysis finds that gauge KK modes are typically above ~2 TeV (with strong dependence on fermion localization), while light KK fermions can lie in the few-hundred-GeV range, offering rich Tevatron/LHC phenomenology, including enhanced Higgs production channels. The work provides a framework for testing gauge-Higgs unification and related custodial models against precision data and collider searches.

Abstract

It has been recently argued that realistic models with warped extra dimensions can have Kaluza-Klein particles accessible at the Large Hadron Collider if a custodial symmetry, SU(2)_V \times P_{LR}, is used to protect the T parameter and the coupling of the left-handed bottom quark to the Z gauge boson. In this article we emphasize that such a symmetry implies that the loop corrections to both the T parameter and the Z b_L \bar{b}_L coupling are calculable. In general, these corrections are correlated, can be sizable, and should be considered to determine the allowed parameter space region in models with warped extra dimensions and custodial symmetry, including Randall-Sundrum models with a fundamental Higgs, models of gauge-Higgs unification and Higgsless models. As an example, we derive the constraints that arise on a representative model of gauge-Higgs unification from a global fit to the precision electroweak observables. A scan over the parameter space typically leads to a lower bound on the Kaluza-Klein excitations of the gauge bosons of about 2-3 TeV, depending on the configuration. In the fermionic sector one can have Kaluza-Klein excitations with masses of a few hundred GeV. We present the constraints on these light fermions from recent Tevatron searches, and explore interesting discovery channels at the LHC.

Figures (6)

• Figure 1: Correlation between the one-loop contributions to the $T$ parameter, denoted by $\Delta T$, and the one-loop contributions to $\delta g_{b_{L}}/g_{b_{L}}$ in the model of Eq. (\ref{['multiplets']}). We show representative curves for a few values of the left-handed top quark localization parameter, $c_{1}$, and the bottom quark localization parameter, $c_{3}$, as the right-handed top localization parameter, $c_{2}$, is varied. We take the mass of the first KK excitation of the $SU(2)_L$ gauge bosons $m_1^\mathrm{gauge} = 3.75~{\rm TeV}$. The band corresponds to the 2-$\sigma$ bound on $\delta g_{bL}/g_{bL}$, assuming no large corrections to the $Z b_R \bar{b}_R$ coupling.
• Figure 2: Lower bound on $\tilde{k} = k\,e^{-kL}$ as a function of $c_3$ and $c_\mathrm{light}$ for fixed $c_1=0.2$ and $c_{\rm RH} = -0.6$ (left panel). The different contours, from dark to light, correspond to $\tilde{k}=1030, 1100, 1300, 1500, 1700$ and $2000$ GeV, respectively. The minimum is $\tilde{k}_\mathrm{min}=1$ TeV, corresponding to $c_3 \approx -0.55$ and $c_\mathrm{light} \approx 0.48$. In the right panel we show the lower bound on $\tilde{k}$ as a function of $c_\mathrm{light}$ for fixed $c_{RH} = c_3=-0.6$ and three values of $c_1$. We also show the lower bound on $\tilde{k}$ for $c_{1} = 0.2$ and $c_{3} = -0.6$, assuming $c_{\rm RH} = -c_{\rm light}$. The mass of the first gauge KK modes is $m^{\rm gauge}_{1} \approx 2.5~\tilde{k}$.
• Figure 3: Lower bound on $\tilde{k} = k\,e^{-kL}$ as a function of $c_\mathrm{light}$ allowing different contributions to the $S$ parameter in the model of Section \ref{['Fit:section']}. The three lines correspond to the one-loop contribution from the spectrum in the model, Eq. (\ref{['S:eq']}) (solid line), twice that amount (dashed line) and a value of $\Delta S_f$ that minimizes the $\chi^2$ for each value of the parameters (dotted line). In all cases, $c_{1} = 0.2$ and $c_{\rm RH} = c_{3} = -0.6$.
• Figure 4: Lower bound on $\tilde{k} = k\,e^{-kL}$ as a function of $c_\mathrm{light} = - c_{\rm RH}$ when the light generations arise from doublets of $SU(2)_{L}$ or $SU(2)_{R}$, including all effects (solid line), setting the one-loop contributions to $\Delta S_{f}$ to zero (dashed line), and choosing values of $\Delta S_f$ that minimize the $\chi^2$ for each value of the parameters (dash-dotted line). We also show the lower bound on $\tilde{k}$ when the right-handed light fermions are localized at $c_{\rm RH} = -0.6$ (near the UV brane), as a function of the localization parameter for left-handed light fermions, $c_\mathrm{light}$ (dotted line). In all cases we have fixed $c_1=0.2$ and $c_3=-0.6$.
• Figure 5: Mass of the first level quarks of the third generation for the model of Section \ref{['Fit:section']} and a $\tilde{k}$ that saturates the bound, assuming $c_{\rm RH} = - c_{\rm light}$ (dotted curve in the right panel of Fig. \ref{['ktilde:fig']}). In the left panel we show the masses of the three degenerate quarks with charges $5/3$, $2/3$ and $-1/3$ as a function of $c_3$ and $c_\mathrm{light}$, for fixed $c_1=0.2$. The different contours, from dark to light, correspond to $m_1=500, 600, 750, 1000, 1250$ and $1500$ GeV, respectively. In the right panel we show the mass of the three lightest quark KK modes with charge 2/3 as a function of $c_\mathrm{light}$ for fixed $c_1=0.2$ and $c_3=-0.6$.