No light dilaton in gauge theories

We study the dynamical breakdown of approximate scale invariance in gauge theories with slowly varying couplings and without ultraviolet cutoff. We isolate the high energy contribution to the dilaton mass and obtain an expression for it in terms of the fermion self-energy Σ(k). Σ(k) is determined via an analytical treatment of the linearized, ladder Schwinger-Dyson equation. We find that this contribution to the dilaton mass is large and is surprisingly insensitive to the β-function when the β-function is small. The result is that for a technicolor theory with a slowly varying coupling there is no light dilaton. At most there is a massive scalar, the analog of the standard Higgs scalar, with a mass tied to the technifermion mass scale.