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

Zhenjun Xiao; Chongsheng Li; Kuangta Chao

doi:doi:10.1007/s100529900048

2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 10, 51-62
DOI 10.1007/s100529900048

The rare K decays and Z⁰ penguin contributions in the topcolor-assisted technicolor models

Zhenjun Xiao^1,2,3 - Chongsheng Li^1,2 - Kuangta Chao^1,2

¹ CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, P.R. China
² Department of Physics, Peking University, Beijing 100871, P.R. China
³ Department of Physics, Henan Normal University, Xinxiang 453002, P.R. China

Received: 24 November 1998 / Revised version: 16 February 1999 / Published online: 15 July 1999

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 Z⁰ 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 B⁰ meson mixing: $\vert a_{\mathrm R}^{\mathrm {ts}}\vert, \vert a_{\mathrm R}^{\mathrm {td}}\vert < 0.01$ 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.