**Abstract**

A genuine dilaton $\sigma $ allows scales to exist even in the limit of ${\alpha}_{\mathrm{IR}}$ through dimensional transmutation. These large scales at ${\alpha}_{\mathrm{IR}}$ can be separated from
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*exact*conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP)
A genuine dilaton $\sigma $ allows scales to exist even in the limit of ${\alpha}_{\mathrm{IR}}$ through dimensional transmutation. These large scales at ${\alpha}_{\mathrm{IR}}$ 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 $SU\left(3\right)\times SU\left(3\right)$ symmetry to produce chiral-scale perturbation theory $\chi $ PT ${}_{\sigma}$ , with ${f}_{0}\left(500\right)$ 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) ${\alpha}_{\mathrm{IR}}$ , and the massless dilaton at ${\alpha}_{\mathrm{IR}}$ corresponds to a light Higgs boson at $\alpha \lesssim {\alpha}_{\mathrm{IR}}$ . 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

*exact*conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP)*all*scales, large and small, so it is hard to argue that its “dilatonic” candidate for the Higgs boson is not heavy. Full article
(This article belongs to the Special Issue Spontaneous Breaking of Conformal Symmetry)

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