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 → ∞ with N C · α(μ 2) = fixed and N F /N C = fixed (≫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 \( {M}_{\phi}^2{F}_{\phi}^2=-4\left\langle {\theta}_{\mu}^{\mu}\right\rangle =-\frac{\beta \left(\alpha \left({\mu}^2\right)\right)}{\alpha \left({\mu}^2\right)}\left\langle {G}_{\lambda \nu}^2\left({\mu}^2\right)\right\rangle \simeq {N}_C{N}_F\frac{16}{\pi^4}{m}_F^4 \), independently of the renormalization point μ, where m F is the dynamical mass of the technifermion, and \( {F}_{\phi }=\mathcal{O}\left(\sqrt{N_F{N}_C}{m}_F\right) \) the TD decay constant. It reads \( {M}_{\phi}^2\simeq {\left(\frac{\upsilon_{\mathrm{EW}}}{2}\cdot \frac{5{\upsilon}_{\mathrm{EW}}}{F_{\phi }}\right)}^2\cdot \left[\frac{8}{N_F}\frac{4}{N_C}\right],\left({\upsilon}_{\mathrm{EW}}=246\;\mathrm{GeV}\right) \), 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 2 ϕ /υ 2EW ∼ M 2 ϕ /F 2 ϕ ∼ m 2 F /F 2 ϕ ∼ 1/(N F N C ) → 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).
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ArXiv ePrint: 1508.07688
Dedicated to the late Professor Yoichiro Nambu
An erratum to this article is available at https://doi.org/10.1007/JHEP11(2016)158.
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Matsuzaki, S., Yamawaki, K. Walking on the ladder: 125 GeV technidilaton, or Conformal Higgs. J. High Energ. Phys. 2015, 1–57 (2015). https://doi.org/10.1007/JHEP12(2015)053
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DOI: https://doi.org/10.1007/JHEP12(2015)053