Genuine Dilatons in Gauge Theories

Abstract

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 IR through dimensional transmutation. These large scales at α 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 S U ( 3 ) × S U ( 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 IR , and the massless dilaton at α IR corresponds to a light Higgs boson at α ≲ α IR . It is suggested that the W ± 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.