The rare K-decays in the Multiscale Walking Technicolor Model

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, $m_{p8} \geq 249 GeV$ for $F_Q=40GeV$ and $m_{p1}=100 GeV$; (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 $m_{p8}$, $m_{p1} \geq 210 GeV$ if only the contribution from $\pi_1$ is taken into account, and $m_{p8} \geq 580 GeV$ for $m_{p1}=210 GeV$, 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.