Partially composite Goldstone Higgs boson

We consider a model of dynamical electroweak symmetry breaking with a partially composite Goldstone Higgs boson. The model is based on a strongly interacting fermionic sector coupled to a fundamental scalar sector via Yukawa interactions. The $\mathrm{SU}(4)\times \mathrm{SU}(4)$ global symmetry of these two sectors is broken to a single SU(4) via Yukawa interactions. Electroweak symmetry breaking is dynamically induced by condensation due to the strong interactions in the new fermionic sector which further breaks the global symmetry $\mathrm{SU}(4)\to \mathrm{Sp}(4)$. The Higgs boson arises as a partially composite state which is an exact Goldstone boson in the limit where SM interactions are turned off. Terms breaking the SU(4) global symmetry explicitly generate a mass for the Goldstone Higgs boson. The model realizes in different limits both (partially) composite Higgs and (bosonic) technicolor models, thereby providing a convenient unified framework for phenomenological studies of composite dynamics. It is also a dynamical extension of the recent elementary Goldstone Higgs model.

Figure 1

Contours of the absolute value of the mass parameter $\sqrt{|m_{\mathrm{\Phi }}^2|}$ ($\sqrt{\delta m^2}$) are depicted in the upper (lower) panel for fixed values of $s_{\theta }=0.1$ and $C_g=1$. The mass of the lightest scalar eigenstate is fixed to 125 GeV. On the gray shaded region on the left, no solution for the Higgs mass condition is found. In the upper panel, below the solid cyan curve, $m_{\mathrm{\Phi }}^2>0$. In the lower panel, $\delta m^2$ is always positive. Dashed lines indicate the value of the composite-pion decay constant, $f$, in GeV.

Figure 2

Contours of the absolute value of the mass parameter $\sqrt{|m_{\mathrm{\Phi }}^2|}$ ($\sqrt{\delta m^2}$) are depicted in the upper (lower) panel for fixed values of $s_{\theta }=0.3$ and $C_g=1$. The mass of the lightest scalar eigenstate $h_1$ is fixed to 125 GeV. On the gray shaded region on the left, no solution for the Higgs mass condition is found. In the upper panel, below the solid cyan curve, $m_{\mathrm{\Phi }}^2>0$. In the lower panel, $\delta m^2$ is always positive. Dashed lines indicate the value of the composite-pion decay constant, $f$, in GeV.

Figure 3

The (absolute) value of the coeffcient $|{\kappa }_t|$ is depicted for fixed values of $s_{\theta }=0.1$ and $C_g=1$. The mass of the lightest scalar eigenstate is fixed to 125 GeV. On the gray shaded region on the left, no solution for the Higgs mass condition is found.

Figure 4

Values of the SU(4)-invariant quartic coupling, ${\lambda }_{\mathrm{\Phi }}$ (upper panel), and the SU(4)-breaking one, $\delta \lambda$ (lower panel), for a fixed value $C_g=1$. The mass of the lightest scalar eigenstate, $h_1$, is fixed to 125 GeV. On the gray shaded regions, one of the couplings becomes large ($\gtrsim 1$).