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

Abstract

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.