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

Abstract.

We calculate the new contributions to the rare decays K$^+ \to \pi^+ \nu \bar \nu$, ${\mathrm K}_{\mathrm L} \to \pi^0 \nu \bar \nu$ and ${\mathrm K}_{\mathrm L} \to \mu^+ \mu^-$ from new Z$^0$ penguin and box diagrams induced by the unit-charged scalars $(\tilde{\pi}^\pm, \tilde{\mathrm H}^\pm, \pi_1^\pm, \pi_8^\pm)$ appearing in the topcolor-assisted technicolor (TC2) models. We find that: (a) the unit-charged top-pion $\tilde{\pi}^\pm$ and b-pion $\tilde{\mathrm H}^\pm$ can provide large contributions to the rare K decays if they are relatively light; (b) the size of the mixing elements ${\mathrm D}_{\mathrm{L,R}}^{ij}$ ($i \neq j$) is strongly constrained by the data of B$^0$ meson mixing: $|a_{\mathrm R}^{\mathrm{ts}}|, |a_{\mathrm R}^{\mathrm{td}}| < 0.01$ for $a_{\mathrm L}^{\mathrm{td}}= a_{\mathrm L}^{\mathrm{ts}}=1/2$ and $m_{\tilde{\mathrm H}^0}\leq 600$ GeV; (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 the long-distance dispersive part of the decay ${\mathrm K}_{\mathrm L} \to \mu^+ \mu^-$, the constraint on the new short-distance part from this decay mode is thus not strong; (e) the typical TC2 model under study is generally consistent with the available rare K-decay data.