  A genuine dilaton $\sigma$ allows scales to exist even in the limit of exact
conformal invariance. In gauge theories, these may occur at an infrared fixed
point (IRFP) $\alpha_{\text{IR}}$ through dimensional transmutation. These
large scales at $\alpha_{\text{IR}}$ can be separated from small scales
produced by $\theta^\mu_\mu$, the trace of the energy-momentum tensor. For
quantum chromodynamics (QCD), the conformal limit can be combined with chiral
$SU(3) \times SU(3)$ symmetry to produce chiral-scale perturbation theory
$\chi$PT$_\sigma$, with $f_0(500)$ as the dilaton. The technicolor (TC)
analogue of this is crawling TC: at low energies, the gauge coupling $\alpha$
goes directly to (but does not walk past) $\alpha_{\text{IR}}$, and the
massless dilaton at $\alpha_{\text{IR}}$ corresponds to a light Higgs boson at
$\alpha \lesssim \alpha_{\text{IR}}$. It is suggested that the $W^\pm$ and
$Z^0$ bosons set the scale of the Higgs boson mass. Unlike crawling TC, in
walking TC, $\theta^\mu_\mu$ produces $all$ scales, large and small, so it is
hard to argue that its ``dilatonic'' candidate for the Higgs boson is not
heavy.
