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+ --> pi(+)<nu(nu)ov er bar>, K-L --> pi(0)<nu(nu)over bar> and K-L --> mu(+)mu(-) new Z(0) peng uin and box diagrams induced by the unit-charged scalers (<(pi)over bar (+/ -)>, <(H)over tilde (+/-)>, pi(1)(+/-), pi(8)(+/-)) appearing in the topcol or-assisted technicolor (TC2) models. We find that: (a) the unit-charged to p-pion <(pi)over tilde (+/-)> and b-pion <(H)over tilde (+/-)> can provide large contributions to the rare K decays if they are relatively light; (b) the size of the mixing elements D-L,R(ij) (i not equal j) is strongly const rained 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<((H0))over bar> less than or equal to 600 GeV ; (c) the enhancements to the branching ratios of rare K decays from new sc alars can be as large as one order of magnitude; (d) there is a strong canc ellation between the short- and the long-distance dispersive part of the de cay K-L --> mu(+)mu(-), the constraint on the new short-distance part from this decay mode is thus not strong; (e) the typical TC2 model under study i s generally consistent with the available rare K-decay data.