The rare K-decays in the Multiscale Walking Technicolor Model

Abstract

We calculate the one-loop $Z^0$-penguin contributions to the rare K-decays, $K^{+}\to {\pi }^{+}\nu \bar{\nu }$, $K_L\to {\pi }^0\nu \bar{\nu }$ and $K_L\to {\mu }^{+}{\mu }^{-}$, from the unit-charged technipions ${\pi }_1$ and ${\pi }_8$ in the framework of the Multiscale Walking Technicolor Model. We find that: (a) the ${\pi }_1$ and ${\pi }_8$ can provide one to two orders enhancements to the branching ratios of the rare K-decays; (b) by comparing the experimental data of $Br(K^{+}\to {\pi }^{+}\nu \bar{\nu })$ with the theoretical prediction one finds the lower mass bounds, $m_{p8}\ge 249GeV$ for $F_Q=40GeV$ and $m_{p1}=100GeV$; (c) by comparing the experimental data of $Br(K_L\to {\mu }^{+}{\mu }^{-})$ with the theoretical predictions one finds the lower bounds on $m_{p1}$ and $m_{p8}$, $m_{p1}\ge 210GeV$ if only the contribution from ${\pi }_1$ is taken into account, and $m_{p8}\ge 580GeV$ for $m_{p1}=210GeV$, assuming $F_Q=40GeV$; (d) the assumed ranges of the masses $m_{p1}$ and $m_{p8}$ in the Multiscale Walking Technicolor Model are excluded by the rare K-decay data.

Comments: Latex file, 24 pages with 14 ps and eps figures