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 $N_C\to \infty$ 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 $M_{\varphi }$ from the trace anomaly as $M_{\varphi }^2{F}_{\varphi }^2=-4⟨{\theta }_{\mu }^{\mu }⟩=-\frac{\beta (\alpha ({\mu }^2))}{\alpha ({\mu }^2)}⟨G_{\lambda \nu }^2({\mu }^2)⟩\simeq N_C{N}_F\frac{16}{{\pi }^4}{m}_F^4$, independently of the renormalization point $\mu$, where $m_F$ is the dynamical mass of the technifermion, and $F_{\varphi }=\mathcal{O}(\sqrt{N_F{N}_C}{m}_F)$ the TD decay constant. It reads $M_{\varphi }^2\simeq (\frac{v_{\mathrm{EW}}}{2}\cdot \frac{5v_{\mathrm{EW}}}{F_{\varphi }}{)}^2\cdot [\frac{8}{N_F}\frac{4}{N_C}]$, ($v_{\mathrm{EW}}=246$ GeV), which implies $F_{\varphi }\simeq 5v_{\mathrm{EW}}$ for $M_{\varphi }\simeq 125\mathrm{GeV}\simeq \frac{1}{2}{v}_{\mathrm{EW}}$ 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 $M_{\varphi }^2/v_{\mathrm{EW}}^2\sim M_{\varphi }^2/F_{\varphi }^2\sim m_F^2/F_{\varphi }^2\sim 1/(N_F{N}_C)\to 0$ 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 ($N_F/N_C\ll 1$).

Comments: revtex4, 36 pages, 7 eps figures, some corrections made, references added; a version to appear in JHEP; typo corrected