Light Kaluza-Klein States in Randall-Sundrum Models with Custodial SU(2)

TL;DR

This work analyzes Randall–Sundrum scenarios with custodial SU(2)_L × SU(2)_R and LR parity, focusing on how tree-level and 1-loop corrections to electroweak observables constrain the spectrum. While custodial protection drives T small at tree level, 1-loop contributions from bidoublet embeddings tend to push T negative, requiring careful regional tuning of fermion localization to remain EW-allowed with KK masses around 3 TeV. The study also examines gauge–Higgs unification, where Higgs arises from higher-dimensional gauge fields, finding similarly constrained viable regions with light KK modes and distinctive vector-like fermions mixing with the top. Across both frameworks, a consistent prediction is a set of light KK gauge bosons and top-mixing vector-like quarks within reach of the LHC, alongside measurable shifts in top and bottom couplings. This positions these RS constructions as testable beyond-Standard-Model scenarios with clear experimental targets at current and future colliders.

Abstract

We consider Randall-Sundrum scenarios based on SU(2)_L x SU(2)_R and a discrete parity exchanging L with R. The custodial and parity symmetries can be used to make the tree level contribution to the T parameter and the anomalous couplings of the bottom quark to the Z very small. We show that the resulting quantum numbers typically induce a negative T parameter at one loop that, together with the positive value of the S parameter, restrict considerably these models. There are nevertheless regions of parameter space that successfully reproduce the fit to electroweak precision observables with light Kaluza-Klein excitations accessible at colliders. We consider models of gauge-Higgs unification that implement the custodial and parity symmetries and find that the EW data singles out a very well defined region in parameter space. In this region one typically finds light gauge boson Kaluza-Klein excitations as well as light SU(2)_L singlet, and sometimes also doublet, fermionic states, that mix with the top quark, and may yield interesting signatures at future colliders.

Figures (7)

• Figure 1: Contribution to $\delta g_{b\,L}/g_{b\,L}$ from Eq. (\ref{['epsilonb:dobletes']}), labeled by "gauge", the contribution due mixing with the lightest modes of $b'_{R}$, and the sum of the two, for models based on $SU(2)_{R}$ doublets and for $\tilde{k} = k e^{-kL} = 1.5$ TeV. The solid line gives $\delta g_{b\,L}/g_{b\,L}$ from Eq. (\ref{['epsilonb']}) for models based on bidoublets of $SU(2)_{L} \times SU(2)_{R}$. It is assumed that the Higgs is localized on the IR brane. The band is the current $2\sigma$ bound.
• Figure 2: Contribution to the $T$ parameter involving the KK modes of Eq. (\ref{['Bidoubletsinglet']}), which couple to the Higgs through the top Yukawa coupling. We use $\tilde{k} = 1.5~{\rm TeV}$ and $m_{\rm top} = 167~{\rm GeV}$. The dots indicate the point beyond which the theory is strongly coupled at the scale of the first KK mode. It is assumed that the Higgs field is exactly localized on the IR brane.
• Figure 3: Contribution to the $T$ parameter involving the KK modes of Eq. (\ref{['Bidoubletsinglet']}), which couple to the Higgs through the top Yukawa coupling. We use $\tilde{k} = 1.5~{\rm TeV}$ and $m_{\rm top} = 167~{\rm GeV}$. It is assumed that the Higgs field has the profile of gauge-Higgs unification models, Eq. (\ref{['higgs:norm']}).
• Figure 4: Diagrams that give the dominant contribution to the $T$ parameter when only vector-like bidoublets are present. When the $SU(2)_{L}$ singlet top quark is also an $SU(2)_{R}$ singlet as in Eq. (\ref{['Bidoubletsinglet']}), there are no diagrams contributing to $\Pi_{11}$. We show explicitly the relative minus sign between the isospin charges of $q^{t}$ and $\chi^{d}$. The top mass insertions in the zero-mode propagator are resummed to all orders. Each cross represents an insertion of the EW breaking mass mixing the singlet $t$ with $q^{t}_{n}$ or $\chi^{d}_{n}$.
• Figure 5: Contribution to the $T$ parameter involving the KK modes of the bidoublets and triplets which couple to the Higgs through the top Yukawa coupling, for the parity and quantum number assignments given in Eq. (\ref{['Bidoublettriplet']}), We use $\tilde{k} = 1.5~{\rm TeV}$ and $m_{\rm top} = 167~{\rm GeV}$. It is assumed that the Higgs has the profile of gauge-Higgs unification models, Eq. (\ref{['higgs:norm']}).