Techni-dilaton at Conformal Edge

Understand

Techni-dilaton (TD) was proposed long ago in the technicolor (TC) near criticality/conformality.

• To reveal the critical behavior of TD, we explicitly compute the nonperturbative contributions to the scale anomaly $<\theta^\mu_\mu>$ and to the techni-gluon condensate $<G_{\mu\nu}^2>$, which are generated by the dynamical mass m of the techni-fermions.
• Our computation is based on the (improved) ladder Schwinger-Dyson equation, with the gauge coupling $\alpha$ replaced by the two-loop running one $\alpha(\mu)$ having the Caswell-Banks-Zaks IR fixed point $\alpha_*$: $\alpha(\mu) \simeq \alpha = \alpha_*$ for the IR region $m < \mu < \Lambda_{TC}$, where $\Lambda_{TC}$ is the intrinsic scale (analogue of $\Lambda_{QCD}$ of QCD) relevant to the perturbative scale anomaly.
• We find that $-<\theta^\mu_\mu>/m^4\to const \ne 0$ and $<G_{\mu\nu}^2>/m^4\to (\alpha/\alpha_{cr}-1)^{-3/2}\to\infty$ in the criticality limit $m/\Lambda_{TC}\sim\exp(-\pi/(\alpha/\alpha_{cr}-1)^{1/2})\to 0$ ($\alpha=\alpha_* \to \alpha_{cr}$) (&#34;conformal edge&#34;).