General Composite Higgs Models

TL;DR

The paper develops a general framework for four-dimensional pseudo-Goldstone Higgs models based on the $SO(5)/SO(4)$ coset, introducing the Minimal Higgs Potential (MHP) hypothesis to render the one-loop Higgs potential calculable through generalized Weinberg sum rules. It shows that a 125 GeV Higgs mass generally requires light fermion resonances, and that electroweak precision tests can be satisfied with either light or heavy vector resonances, with a heavy Higgs around 320 GeV also compatible in some regions. The construction encompasses moose/deconstructed models as special limits and provides parametric relations between the Higgs and resonance spectra across several representative setups. The framework thus yields a broader, calculable class of composite Higgs scenarios that can be tested via searches for heavy fermions and vector resonances at the LHC.

Abstract

We construct a general class of pseudo-Goldstone composite Higgs models, within the minimal SO(5)/SO(4) coset structure, that are not necessarily of moose-type. We characterize the main properties these models should have in order to give rise to a Higgs mass around 125 GeV. We assume the existence of relatively light and weakly coupled spin 1 and 1/2 resonances. In absence of a symmetry principle, we introduce the Minimal Higgs Potential (MHP) hypothesis: the Higgs potential is assumed to be one-loop dominated by the SM fields and the above resonances, with a contribution that is made calculable by imposing suitable generalizations of the first and second Weinberg sum rules. We show that a 125 GeV Higgs requires light, often sub-TeV, fermion resonances. Their presence can also be important for the models to successfully pass the electroweak precision tests. Interestingly enough, the latter can also be passed by models with a heavy Higgs around 320 GeV. The composite Higgs models of the moose-type considered in the literature can be seen as particular limits of our class of models.

Figures (12)

• Figure 1: Values of $\gamma_f/(-\gamma_g)$ versus $\gamma_f/(2\beta_f)$, that is the value of $\xi$ one would get by neglecting the gauge contribution to the Higgs potential. The points are obtained by a numerical scan, requiring $m_H \in [100,150]$ GeV. (a) The range of the parameters is taken as follows: $m_{iQ},m_{iS} \in [0,8f]$, $\theta_{qQ},\theta_{tQ},\theta_{qS},\theta_{tS} \in�[0, 2\pi]$, $a_\rho \in [1/\sqrt{2}, 2]$. $\epsilon_t$, as defined in eq.(\ref{['eq:WeinSolNs2Nq2']}), has been obtained by fixing $m_{top}$ while $m_\rho$ by fixing $\xi$. The green line represents $\xi=0.1$. In most of the points $\gamma_g\simeq -\gamma_f$ and it is never possible to go in the region where $\gamma_f \gg - \gamma_g$. (b) The range of the parameters is taken, in the notation of Panico:2011pw, as follows: $g_*, \tilde{g}_* \in [0,8]$, $M_Q, M_S, m, \Delta \in [0,8f]$, $y_R/(\sqrt{2}y_L) \in [0.3, 0.6]$ and $y_L$ has been obtained fixing $m_{top}$, cutting for $\xi \in [0.05, 0.15]$. The green band represents the actual values of $\xi\in [0.05, 0.15]$. In most of the points still $\gamma_g\simeq -\gamma_f$, but now there is a region where the gauge contribution is negligible.
• Figure 2: Mass of the LFR (in GeV), before EWSB, as a function of the Higgs mass (in GeV). The green circles represent the singlet while the purple triangles represent the exotic doublet with $Y=7/6$. The masses $m_Q, m_{\rho_1}$ and $m_{\rho_2}$ are taken in the range $[0, 8 f]$, $a_{\rho_1}, a_{\rho_2} \in [1/2,2]$ and $a_\text{mix} \in [0,5]$; $\epsilon$ and $m_S$ have been obtained by fixing $m_{top}$ and $\xi$. EWPT and the bound (\ref{['DSbound']}) have not been imposed.
• Figure 3: $S$ and $T$ parameters for the points of the numerical scan with a light Higgs: $m_H \in [ 100, 150]$ GeV. The ellipses are the 99% and 90% C.L., for a mean value of $m_H = 125$ GeV. The green circles are the points which pass both EWPT and the bound (\ref{['DSbound']}), the blue triangles pass EWPT but are ruled out by the bound (\ref{['DSbound']}) and the red squares don't pass EWPT. The range of the input parameters is as indicated in fig.\ref{['fig:mLNr2Na1Ns1Nq1']}.
• Figure 4: $S$ and $T$ parameters for the points of the numerical scan for a heavy Higgs ($m_H \in [300, 350]$ GeV) and $\xi = 0.15$. The ellipses are the 99% and 90% C.L., for a mean value of $m_H = 325$ GeV. The green circles are the points which pass the EWPT (and the bound (\ref{['DSbound']})) while the red squares are the points which don't pass EWPT. The ranges of the input parameters is as indicated in fig.\ref{['fig:mLNr2Na1Ns1Nq1']}.
• Figure 5: Mass of the LFR (in GeV), before EWSB, as a function of the Higgs mass (in GeV). The green circles represent the singlet while the purple triangles represent the exotic doublet with $Y=7/6$. All the fermion masses are taken in the range $[0, 6 f]$, the angles $\theta_q, \theta_t \in [0,2 \pi]$ and $a_{\rho} \in [1/\sqrt{2},2]$. The mixing $\epsilon_t$ and the mass $m_\rho$ have been obtained by fixing $m_{top}$ and $\xi$ respectively. EWPT and the bound (\ref{['DSbound']}) have not been imposed.