The rare K-decays in the Multiscale Walking Technicolor Model

We calculate the one-loop $Z^0$-penguin contributions to the rare K-decays, $K^+ \to π^+ ν\bar ν$, $K_L \to π^0 ν\bar ν$ and $K_L \to μ^+ μ^-$, from the unit-charged technipions $π_1$ and $π_8$ in the framework of the Multiscale Walking Technicolor Model. We find that: (a) the $π_1$ and $π_8$ can provide one to two orders enhancements to the branching ratios of the rare K-decays; (b) by comparing the experimental data of $Br(K^+ \to π^+ ν\bar ν)$ 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 $Br(K_L \to μ^+ μ^-)$ 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 $π_1$ 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.

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