Technidilaton at the conformal edge

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) similar or equal to alpha = alpha(*) for the infrared 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) -> const not equal 0 and <alpha G(mu nu)(2)>/m(4) -> (alpha/alpha(cr) - 1)(-3/2) -> infinity in the criticality limit m/Lambda(TC) similar to exp(-pi/(alpha/alpha(cr) - 1)(1/2)) -> 0 (alpha = alpha(*) SE arrow alpha(cr), or N-f NE arrow N-f(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(TC) partial derivative alpha/partial derivative Lambda(TC) = -(2 alpha(cr)/pi) center dot (alpha/alpha(cr) - 1)(3/2) is the nonperturbative beta function corresponding to the above essential singularity scaling of m/Lambda(TC). Accordingly, the partially conserved dilatation current implies (M-TD/m)(2)(F-TD/m)(2) = -4 <theta(mu)(mu)>/m(4) -> const not equal 0 at criticality limit, where M-TD is the mass of TD and F-TD the decay constant of TD. We thus conclude that at criticality limit the TD could become a "true (massless) Nambu-Goldstone boson" M-TD/m -> 0, only when m/F-TD -> 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.