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 $K^{+}\to {\pi }^{+}\nu \bar{\nu }$, $K_L\to {\pi }^0\nu \bar{\nu }$ and $K_L\to {\mu }^{+}{\mu }^{-}$ from new $Z^0$-penguin and box diagrams induced by the unit-charged scalars $({\tilde{\pi }}^{\pm },{\tilde{H}}^{\pm },{\pi }_1^{\pm },{\pi }_8^{\pm })$ appeared in the Topcolor-assisted technicolor (TC2) models. We find that: (a) the unit-charged top-pion ${\tilde{\pi }}^{\pm }$ 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 $D_{L,R}^{ij}$ ($i\ne j$) 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 $m_{{\tilde{H}}^0}\le 600GeV$; (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 $K_L\to {\mu }^{+}{\mu }^{-}$, 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.

Comments: Latex file, 27 pages and 10 ps and eps figures, to be published in Eur.Phys. J. C