$S$ 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 ${\gamma }_m\simeq 0$ through ${\gamma }_m\simeq 1$ continuously. The $S$ parameter is given as a positive monotonic function of $\xi$ which is fairly insensitive to ${\gamma }_m$ and continuously vanishes as $S\sim {\xi }^2\to 0$ when $\xi \to 0$, where $\xi$ 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-) $\rho$ meson ($M_{\rho }$) and the decay constant ($f_{\pi }$) as $\xi \sim f_{\pi }{z}_m\sim f_{\pi }/M_{\rho }$ for $\xi \ll 1$. However, although $\xi$ is related to the techni-fermion condensate $\condense$, we find no particular suppression of $\xi$ and hence of $S$ due to large ${\gamma }_m$, based on the correct identification of the renormalization-point dependence of $\condense$ in contrast to the literature. Then we argue possible behaviors of $f_{\pi }/M_{\rho }$ as $\condense \to 0$ near the conformal window characterized by the Banks-Zaks infrared fixed point in more explicit dynamics with ${\gamma }_m\simeq 1$. 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 $f_{\pi }/M_{\rho }\to 0$ is realized, the holography suggests a novel possibility that $f_{\pi }$ vanishes much faster than the dynamical mass $m$ does.

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

Cited by in corpus (2)

• Holographic technicolor models and their S-parameter
• QCD condensates in ADS/QCD