Technidilaton (TD) was proposed long ago in the technicolor 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 technigluon condensate $⟨\alpha G_{\mu \nu }^2⟩$, which are generated by the dynamical mass $m$ of the technifermions. Our computation is based on the (improved) ladder Schwinger-Dyson equation, with the gauge coupling $\alpha$ replaced by the two-loop running coupling $\alpha (\mu )$ having the Caswell-Banks-Zaks infrared fixed point ${\alpha }_{*}$: $\alpha (\mu )\simeq \alpha ={\alpha }_{*}$ for the infrared region $m<\mu <{\Lambda }_{\mathrm{TC}}$, where ${\Lambda }_{\mathrm{TC}}$ is the intrinsic scale (analogue of ${\Lambda }_{\mathrm{QCD}}$ of QCD) relevant to the perturbative scale anomaly. We find that $-⟨{\theta }_{\mu }^{\mu }⟩/m^4\to \mathrm{const}\ne 0$ and $⟨\alpha G_{\mu \nu }^2⟩/m^4\to (\alpha /{\alpha }_{\mathrm{cr}}-1{)}^{-3/2}\to \infty$ in the criticality limit $m/{\Lambda }_{\mathrm{TC}}\sim \exp (-\pi /(\alpha /{\alpha }_{\mathrm{cr}}-1{)}^{1/2})\to 0$ ($\alpha ={\alpha }_{*}\searrow {\alpha }_{\mathrm{cr}}$, or $N_f\nearrow N_f^{\mathrm{cr}}$) (“conformal edge”). Our result precisely reproduces the formal identity $⟨{\theta }_{\mu }^{\mu }⟩=(\beta (\alpha )/4{\alpha }^2)⟨\alpha G_{\mu \nu }^2⟩$, where $\beta (\alpha )={\Lambda }_{\mathrm{TC}}\frac{\partial \alpha }{\partial {\Lambda }_{\mathrm{TC}}}=-(2{\alpha }_{\mathrm{cr}}/\pi )·(\alpha /{\alpha }_{\mathrm{cr}}-1{)}^{3/2}$ is the nonperturbative beta function corresponding to the above essential singularity scaling of $m/{\Lambda }_{\mathrm{TC}}$. Accordingly, the partially conserved dilatation current implies $(M_{\mathrm{TD}}/m{)}^2(F_{\mathrm{TD}}/m{)}^2=-4⟨{\theta }_{\mu }^{\mu }⟩/m^4\to \mathrm{const}\ne 0$ at criticality limit, where $M_{\mathrm{TD}}$ is the mass of TD and $F_{\mathrm{TD}}$ the decay constant of TD. We thus conclude that at criticality limit the TD could become a “true (massless) Nambu-Goldstone boson” $M_{\mathrm{TD}}/m\to 0$, only when $m/F_{\mathrm{TD}}\to 0$, namely, getting decoupled, as was the case of “holographic technidilaton” of Haba-Matsuzaki-Yamawaki. The decoupled TD can be a candidate of dark matter.

• Received 5 October 2010

DOI:https://doi.org/10.1103/PhysRevD.83.015008