Walking on the Ladder: 125 GeV Technidilaton, or Conformal Higgs -Dedicated to the late Professor Yoichiro Nambu-

The walking technicolor based on the ladder Schwinger-Dyson gap equation is studied, with the scale-invariant coupling being an idealization of the Caswell-Banks-Zaks infrared fixed point in the anti-Veneziano limit, such that $N_C rightarrow infty$ with $N_C cdot alpha(mu^2)=$ fixed and $N_F/N_C=$ fixed ($gg 1$), of the $SU(N_C)$ gauge theory with massless $N_F$ flavors near criticality. We show that the 125 GeV Higgs can be naturally identified with the technidilaton (TD) predicted in the walking technicolor, a pseudo Nambu-Goldstone (NG) boson of the spontaneous symmetry breaking of the approximate scale symmetry. Ladder calculations yield the TD mass $M_phi$ from the trace anomaly as $M_phi^2 F_phi^2= -4 langle theta_mu^mu rangle = - frac{beta(alpha (mu^2))}{alpha(mu^2)}, langle G_{lambda u}^2(mu^2)rangle simeq N_C N_Ffrac{16}{pi^4} m_F^4$, independently of the renormalization point $mu$, where $m_F$ is the dynamical mass of the technifermion, and $F_phi={cal O} (sqrt{N_F N_C}, m_F)$ the TD decay constant. It reads $M_phi^2simeq (frac{v_{rm EW}}{2} cdot frac{5 v_{rm EW}}{F_phi})^2 cdot [frac{8}{N_F}frac{4}{N_C}]$, ($v_{rm EW}=246$ GeV), which implies $F_phisimeq 5 ,v_{rm EW} $ for $M_phi simeq 125, {rm GeV}simeq frac{1}{2} v_{rm EW}$ in the one-family model ($N_C=4, N_F=8$), in good agreement with the current LHC Higgs data. The result reflects a generic scaling $ M_phi^2/v_{rm EW}^2sim M_phi^2/F_phi^2 sim m_F^2 /F_phi^2 sim 1/(N_F N_C) rightarrow 0 $ as a vanishing trace anomaly, namely the TD has a mass vanishing in the anti-Veneziano limit, similarly to $eta^prime$ meson as a pseudo-NG boson of the ordinary QCD with vanishing $U(1)_A$ anomaly in the Veneziano limit ($N_F/N_C ll 1$).