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

Abstract

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 $N_C \cdot α(μ^2)=$ 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 $M_ϕ$ from the trace anomaly as $M_ϕ^2 F_ϕ^2= -4 \langle θ_μ^μ\rangle = - \frac{β(α(μ^2))}{α(μ^2)}\, \langle G_{λν}^2(μ^2)\rangle \simeq N_C N_F\frac{16}{π^4} m_F^4$, independently of the renormalization point $μ$, where $m_F$ is the dynamical mass of the technifermion, and $F_ϕ={\cal O} (\sqrt{N_F N_C}\, m_F)$ the TD decay constant. It reads $M_ϕ^2\simeq (\frac{v_{\rm EW}}{2} \cdot \frac{5 v_{\rm EW}}{F_ϕ})^2 \cdot [\frac{8}{N_F}\frac{4}{N_C}]$, ($v_{\rm EW}=246$ GeV), which implies $F_ϕ\simeq 5 \,v_{\rm EW} $ for $M_ϕ\simeq 125\, {\rm GeV}\simeq \frac{1}{2} v_{\rm EW}$ 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_ϕ^2/v_{\rm EW}^2\sim M_ϕ^2/F_ϕ^2 \sim m_F^2 /F_ϕ^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 $η^\prime$ meson as a pseudo-NG boson of the ordinary QCD with vanishing $U(1)_A$ anomaly in the Veneziano limit ($N_F/N_C \ll 1$).