S Parameter in the Holographic Walking/Conformal Technicolor

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 γm ≃ 0 through γm ≃ 1 continuously. The S parameter is given as a positive monotonic function of ξ which is fairly insensitive to γm and continuously vanishes as S ∼ ξ2 → 0 when ξ → 0, where ξ is the vacuum expectation value of the bulk scalar field at the infrared boundary of the 5th dimension z = zm and is related to the mass of (techni-) ρ meson (Mρ) and the decay constant (ƒπ) as ξ ∼ ƒπ zm ∼ ƒπ / Mρ for ξ ≪ 1. However, although ξ is related to the techni-fermion condensate 〈TT〉, we find no particular suppression of ξ and hence of S due to large γm, based on the correct identification of the renormalization-point dependence of 〈TT〉 in contrast to the literature. Then we argue possible behaviors of ƒπ/Mρ as 〈TT〉 → 0 near the conformal window characterized by the Banks-Zaks infrared fixed point in more explicit dynamics with γm ≃ 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 ƒπ/Mρ → 0 is realized, the holography suggests a novel possibility that ƒπ vanishes much faster than the dynamical mass m does.