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Genuine Dilatons in Gauge Theories

A genuine dilaton $σ$ allows scales to exist even in the limit of exact conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP) $α_{\text{IR}}$ through dimensional transmutation. These large scales at $α_{\text{IR}}$ can be separated from small scales produced by $θ^μ_μ$, 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 $χ$PT$_σ$, with $f_0(500)$ as the dilaton. The technicolor (TC) analogue of this is crawling TC: at low energies, the gauge coupling $α$ goes directly to (but does not walk past) $α_{\text{IR}}$, and the massless dilaton at $α_{\text{IR}}$ corresponds to a light Higgs boson at $α\lesssim α_{\text{IR}}$. 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, $θ^μ_μ$ produces $all$ scales, large and small, so it is hard to argue that its ``dilatonic'' candidate for the Higgs boson is not heavy.