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The rare K-decays and $Z^0$-penguin contributions in the Topcolor-assisted technicolor models

We calculate the new contributions to the rare decays $K^+ \to π^+ ν\bar ν$, $K_L \to π^0 ν\bar ν$ and $K_L \to μ^+ μ^-$ from new $Z^0$-penguin and box diagrams induced by the unit-charged scalars $(\tildeπ^\pm, \tilde{H}^\pm, π_1^\pm, π_8^\pm)$ appeared in the Topcolor-assisted technicolor (TC2) models. We find that: (a) the unit-charged top-pion $\tildeπ^\pm$ and b-pion $\tilde{H}^\pm$ can provide large contributions to the rare K-decays if they are relatively light; (b) the size of mixing elements $D_{L,R}^{ij}$ ($i \neq j$) is strongly constrained by the data of $B^0$ meson mixing: $|a_R^{ts}|, |a_R^{td}| < 0.01$ for $a_L^{td}=a_L^{ts}=1/2$ and $m_{\tilde{H}^0}\leq 600GeV$; (c) the enhancements to the branching ratios of rare K-decays from new scalars can be as large as one order of magnitude; (d) there is a strong cancellation between the short- and long-distance dispersive part of the decay $K_L \to μ^+ μ^-$, the constraint on the new short-distance part from this decay mode is thus not strong; (e) the typical TC2 model under study is generally consistent with the available rare K-decay data.