$S$ Parameter in the Holographic Walking/Conformal Technicolor

Kazumoto Haba; Shinya Matsuzaki; Koichi Yamawaki

doi:10.1143/PTP.120.691

paper

$S$ Parameter in the Holographic Walking/Conformal Technicolor

arXiv:0804.3668 · doi:10.1143/PTP.120.691

Abstract

We explicitly calculate the $S$ parameter in entire parameter space of the holographic walking/conformal technicolor (W/C TC), based on the deformation of the holographic QCD by varying the anomalous dimension from $γ_{m} ≃ 0$ through $γ_{m} ≃ 1$ continuously. The $S$ parameter is given as a positive monotonic function of $ξ$ which is fairly insensitive to $γ_{m}$ and continuously vanishes as $S \sim ξ^{2} \to 0$ when $ξ \to 0$ , where $ξ$ is the vacuum expectation value of the bulk scalar field at the infrared boundary of the 5th dimension $z = z_{m}$ and is related to the mass of (techni-) $ρ$ meson ( $M_{ρ}$ ) and the decay constant ( $f_{π}$ ) as $ξ \sim f_{π} z_{m} \sim f_{π} / M_{ρ}$ for $ξ ≪ 1$ . However, although $ξ$ is related to the techni-fermion condensate $\condense$, we find no particular suppression of $ξ$ and hence of $S$ due to large $γ_{m}$ , based on the correct identification of the renormalization-point dependence of $\condense$ in contrast to the literature. Then we argue possible behaviors of $f_{π} / M_{ρ}$ as $\condense \to 0$ near the conformal window characterized by the Banks-Zaks infrared fixed point in more explicit dynamics with $γ_{m} ≃ 1$ . It is a curious coincidence that the result from ladder Schwinger-Dyson and Bethe-Salpeter equations well fits in the parameter space obtained in this paper. When $f_{π} / M_{ρ} \to 0$ is realized, the holography suggests a novel possibility that $f_{π}$ vanishes much faster than the dynamical mass $m$ does.

typo, a version to be published in Progress of Theoretical Physics

S Parameter in the Holographic Walking/Conformal Technicolor

Abstract

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$S$ Parameter in the Holographic Walking/Conformal Technicolor