Genuine Dilatons in Gauge Theories

Abstract

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.

arXiv comment19 pages, 5 figures, version accepted by "Universe" (open access), special issue "Spontaneous Breaking of Conformal Symmetry". Expanded (3 more pages) and revised: abstract, text (especially Secs. 3 and 6), a new figure (Fig. 4), extra footnotes and references

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