Nearly Conformal Composite Higgs Model

We analyze a composite Higgs model based on the confining $SU(3)$ gauge theory with $N_f=8$ Dirac fermions in the fundamental representation. This gauge theory has been studied on the lattice and shown to be well described by a dilaton effective field theory (EFT). Here we modify the EFT by assigning standard-model quantum numbers such that four of the composite pseudo-Nambu-Goldstone boson (pNGB) fields form the standard-model Higgs doublet, by coupling it to the top quark and by adding to the potential a term that triggers electroweak symmetry breaking. The model contains a pNGB Higgs boson, a set of heavier pNGBs, and an approximate dilaton in the same mass range. We study the phenomenology of the model and discuss the amount of tuning required to ensure consistency with current direct and indirect bounds on new physics, highlighting the role of the dilaton field.

Figure 1

The ratio $m_h^2/v^2$, as a function of $w$, for $y=2.06\pm 0.05$ and $F_{\pi }^2/F_d^2=0.086\pm 0.015$ [22], for the LSD measurements taken at the second fermion mass ($m_{f2}$) in the range [5]. The horizontal black dashed line represents the experimental value $m_h^2/v^2\simeq 0.26$. The yellow shaded region is the uncertainty, which is dominated by the substantial uncertainty in the measurement of the mass $M_d$ of the scalar, and in the quantity $F_{\pi }^2/F_d^2$. For the best case scenario of $w=4.7$, the resulting uncertainty in $m_h^2/v^2$ is approximately an order of magnitude larger than the central value. Still, as the error in the measurement of $M_d$ is reduced, the range of acceptable $w$ values required to maintain $m_h^2/v^2\approx 0.26$ will diminish and potentially shift slightly.