On the effect of resonances in composite Higgs phenomenology

TL;DR

This work extends the phenomenology of SO(5)/SO(4) composite Higgs models beyond the leading $O(p^2)$ chiral Lagrangian by constructing an $O(p^4)$ basis and introducing a minimal, controllable PUVC-inspired framework for light resonances. It shows how resonances with quantum numbers $ ho^L=(3,1)$, $ ho^R=(1,3)$, $ ho^{L/R}$, $ ilde{ m u}=(1,1)$, and $ ext{Δ}=(3,3)$ couple to Nambu–Goldstone bosons and alter high-energy scattering amplitudes ${ m A}(s,t,u)$ and ${ m B}(s,t,u)$, including contributions to the Peskin–Takeuchi $S$ parameter. The analysis finds that vector resonances are relatively narrow and primarily modify $s$-channel processes, while scalar resonances can dominantly enhance several $WW$ scattering channels, with potential observability in $hh$ production for light scalars with sizable couplings. The results provide a practical, parameter-reduced way to connect composite Higgs theories to LHC signatures, guiding search strategies for light resonances in VBF processes. Overall, PUVC offers a robust framework to capture the qualitative and quantitative impact of low-lying resonances on high-energy vector boson scattering in this class of models.

Abstract

We consider a generic composite Higgs model based on the coset SO(5)/SO(4) and study its phenomenology beyond the leading low-energy effective lagrangian approximation. Our basic goal is to introduce in a controllable and simple way the lowest-lying, possibly narrow, resonances that may exist is such models. We do so by proposing a criterion that we call partial UV completion. We characterize the simplest cases, corresponding respectively to a scalar in either singlet or tensor representation of SO(4) and to vectors in the adjoint of SO(4). We study the impact of these resonances on the signals associated to high-energy vector boson scattering, pointing out for each resonance the characteristic patterns of depletion and enhancement with respect to the leading-order chiral lagrangian. En route we derive the O(p^4) general chiral lagrangian and discuss its peculiar accidental and approximate symmetries.

Figures (13)

• Figure 1: The NG bosons of $SO(5)/SO(4)$ live on the four-sphere $S^4$. A generic vacuum points in a direction forming an angle $\theta$ with that fixed by the 'gauged' $SO(4)^\prime$. The electroweak symmetry breaking can be seen as due to the misalignment $\theta$. Even assuming no misalignment at the tree level, a non-vanishing $\theta = \langle \pi \rangle/f$ is generated at the loop level after the NG 4-vector acquires a vev $\langle \pi \rangle \not =0$ (black curve).
• Figure 2: Contribution of $\rho^L$ to the $W_L^+W_L^- \to W_L^+ W_L^-$ (upper left), $W_L^+W_L^- \to hh$ (upper right) and $W_L^+ W_L^- \to Z_L h$ (lower panel) cross sections for $\xi = 0.5$, $m_{\rho_L} = 1.5\,$TeV and $a_{\rho_L} = 2/\sqrt{3}$, which implies $\Gamma_{\rho_L} = 123\,$GeV. The dotted red and dashed black curves respectively show the $O(p^2)$ and $O(p^4)$ predictions, as obtained by using eq.(\ref{['eq:ABfromrhoatOp4']}) with $\alpha_1=0$. The solid black curve shows the full effect of the $\rho^L$ exchange, as computed by means of eq.(\ref{['eq:ABfromrhofull']}).
• Figure 3: Contribution of $\eta$ to the $W_L^+W_L^+ \to W_L^+ W_L^+$ (left) and $W_L^+W_L^- \to hh$ (right) cross sections for $\xi = 0.5$, $m_{\eta} = 1.5\,$TeV and $a_{\eta} = 1$, which implies $\Gamma_\eta = 1.1\,$TeV. The dotted red and dashed black curves respectively show the $O(p^2)$ and $O(p^4)$ predictions, as obtained from eq.(\ref{['eq:ABfrometaatOp4']}). The solid black curve shows the full effect of the $\eta$ exchange, as computed by means of eq.(\ref{['eq:ABfrometafull']}).
• Figure 4: Contribution of $\eta$ to the $W_L^+W_L^- \to hh$ cross section for $a_\eta = 0.5$ (black solid curve), $a_\eta=1$ (red dotted curve) and $a_\eta =2$ (blue dashed curve). The other input parameters are fixed as in Fig. \ref{['fig:etapart']}.
• Figure 5: Contribution of $\Delta$ to the $W_L^+W_L^- \to W_L^+ W_L^-$ (upper left), $W_L^+W_L^- \to hh$ (upper right), $W_L^+W_L^+ \to W_L^+ W_L^+$ (lower left) and $W_L^+Z_L \to W_L^+ Z_L$ (lower right) cross sections for $\xi = 0.5$, $m_{\Delta} = 1.5\,$TeV and $a_{\Delta} = 1$, which implies $\Gamma_\Delta = 277\,$GeV. The dotted red and dashed black curves respectively show the $O(p^2)$ and $O(p^4)$ predictions, as obtained from eq.(\ref{['eq:ABfromDeltaatOp4']}). The solid black curve shows the full effect of the $\Delta$ exchange, as computed by means of eq.(\ref{['eq:ABfromDeltafull']}).