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

Shinya Matsuzaki; Koichi Yamawaki

doi:10.1007/JHEP12(2015)053

paper

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

arXiv:1508.07688 · doi:10.1007/JHEP12(2015)053

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 $N_{C} \cdot α (μ^{2}) =$ fixed and $N_{F} / N_{C} =$ fixed ( $≫ 1$ ), of the $S U (N_{C})$ 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 $M_{ϕ}^{2} F_{ϕ}^{2} = - 4 ⟨ θ_{μ}^{μ} ⟩ = - \frac{β ( α ( μ ^{2} ))}{α ( μ ^{2} )} ⟨ G_{λ ν}^{2} (μ^{2})⟩ ≃ N_{C} N_{F} \frac{16}{π ^{4}} m_{F}^{4}$ , independently of the renormalization point $μ$ , where $m_{F}$ is the dynamical mass of the technifermion, and $F_{ϕ} = O (N_{F} N_{C} m_{F})$ the TD decay constant. It reads $M_{ϕ}^{2} ≃ (\frac{v _{EW}}{2} \cdot \frac{5 v _{EW}}{F _{ϕ}})^{2} \cdot [\frac{8}{N _{F}} \frac{4}{N _{C}}]$ , ( $v_{EW} = 246$ GeV), which implies $F_{ϕ} ≃ 5 v_{EW}$ for $M_{ϕ} ≃ 125 GeV ≃ \frac{1}{2} v_{EW}$ 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 $M_{ϕ}^{2} / v_{EW}^{2} \sim M_{ϕ}^{2} / F_{ϕ}^{2} \sim m_{F}^{2} / F_{ϕ}^{2} \sim 1/ (N_{F} N_{C}) \to 0$ as a vanishing trace anomaly, namely the TD has a mass vanishing in the anti-Veneziano limit, similarly to $η^{'}$ meson as a pseudo-NG boson of the ordinary QCD with vanishing $U (1)_{A}$ anomaly in the Veneziano limit ( $N_{F} / N_{C} ≪ 1$ ).

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

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

Abstract

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