Old Wine in a New Bottle: Technidilaton as the 125 GeV Higgs -- Dedicated to the late Professor Yoichiro Nambu

We show that the Standard Model (SM) Higgs Lagrangian is identical to the nonlinear realization of both the scale and chiral symmetries ("scale-invariant nonlinear sigma model"), and is further gauge equivalent to the "scale-invariant Hidden Local Symmetry (HLS) model" having possible new vector bosons as the HLS gauge bosons with scale-invariant mass: SM Higgs is nothing but a (pseudo) dilaton. The effective theory of the walking technicolor has precisely the same type of the scale-invariant nonlinear sigma model, thus further having the scale-invariant HLS gauge bosons (technirho's, etc.). The technidilaton mass M_\phi comes from the trace anomaly, which yields M_\phi^2 F_\phi^2 \simeq (2.5)^2 [(8/N_F)(4/N_C)] v^4 via PCDC, in the underlying walking SU(N_C) gauge theory with N_F massless flavors, where F_\phi is the decay constant and v=246 GeV. This implies F_\phi \simeq 5 v for M_\phi \simeq 125 GeV \simeq v/2 in the one-family walking technicolor model (N_F=8, N_C=4), in good agreement with the current LHC Higgs data. In the anti-Veneziano limit, N_C \rightarrow \infty, with N_C \alpha= fixed and N_F/N_C= fixed (\gg 1), we have a result: M_\phi^2/v^2\sim M_\phi^2/F_\phi^2 \sim 1/(N_F N_C) \rightarrow 0. Then the technidilaton is a naturally light composite Higgs out of the strongly coupled conformal dynamics, with its couplings even weaker than the SM Higgs.