Twin Higgs mechanism and a composite Higgs boson

We combine the twin Higgs mechanism with the paradigm of composite Higgs models. In this class of models the Higgs is a pseudo-Nambu-Goldstone boson from a strongly coupled sector near the TeV scale, and it is additionally protected by a discrete symmetry due to the twin mechanism. We discuss the model-building issues associated with this setup and quantify the tuning needed to achieve the correct electroweak vacuum and the Higgs mass. In contrast to standard composite Higgs models, the lightest resonance associated with the top sector is the uncolored mirror top, while the colored top partners can be made parameterically heavier without extra tuning. In some cases, the vector resonances are predicted to lie in the multi-TeV range. We present models where the resonances—both fermions and vectors—being heavier alleviates the pressure on naturalness coming from direct searches demonstrating that theories with low tuning may survive constraints from the Large Hadron Collider.

Figure 1

Pictorial representation of the dynamics of a composite Higgs model protected by the twin Higgs mechanism. In the model under consideration, $G/H=\mathrm{SO}(8)/\mathrm{SO}(7)$. This global symmetry is explicitly broken by the interactions with the two external copies of the SM (exchangeable under a $Z_2$ symmetry).

Figure 2

Comparison between the spectra of minimally tuned composite Higgs and composite twin Higgs models.

Figure 3

Model A: $Z_2$ breaking in the gauge sector, with $f=800\mathrm{GeV}$ and $\kappa =1$. Left: Tuning versus $g_{\rho }$. The growth in the tuning with respect to the minimal value $f^2/v^2$ around $g_{\rho }\sim 5$ is due to the fact that one has to invoke a cancellation between the $g^2-{g^{\prime }}^2$, which is taken into account in the numerical analysis. The red line is the scaling with $g_{\rho }^2$ as predicted by Eq. (57). Right: Tuning versus $m_{\mathrm{\Psi }}/f$. We scan over a range $[0.5,10]\mathrm{TeV}$ for composite masses and [2, 10] for $g_{\rho }$, where the top mass is fixed at $m_t(\sim \mathrm{TeV})=150\mathrm{GeV}$. We defined $m_{\mathrm{\Psi }}$ as the geometric average of the composite masses. The gray points correspond to values of $g_{\rho }$ that LHC14 will probe (left panel).

Figure 4

Summary of the mass of composite resonances for composite twin Higgs for various $Z_2$-breaking mechanisms and minimal tuning. The first case reflects Fig. 3 and the second [26] is obtained by a simple rescaling. They both have an unconstrained fermionic scale with a “predicted” range for the masses of composite vector resonances. The last two models have an unconstrained mass for the vector resonances and a predicted range for the fermionic scale [see Eq. (62)].