Anomalous $tqZ$ coupling effects in rare B- and K-meson decays

As a top-factory, the LHC is performing a direct study of top-quark anomalous FCNC couplings, which are, however, correlated closely with the rare B- and K-meson decays. In this paper, we study the effects of anomalous $tqZ$ (with $q=u,c$) couplings in the rare decays $B_{s,d}\to {\mu }^{+}{\mu }^{-}$, $B\to X_s \nu \bar\nu$,$B\to K^{(*)}\nu \bar\nu$,$K^+\to \pi^+ \nu \bar\nu$,and$K_L\to \pi^0 \nu \bar\nu$. With the up-to-date experimental bounds on the branching ratios of these channels, constraints on the left-handed anomalous couplings $X_{ct}^L$ and $X_{ut}^L$ are derived, respectively. With these low-energy constraints taken into account, we find that, for real couplings $X_{ct}^L$ and $X_{ut}^L$, the indirect upper bounds on $\mathcal{B}(t\to qZ)$ are much lower than that from the D0 collaboration, but are still compatible with the $5\sigma$ discovery potential of ATLAS with an integrated luminosity of $10 {\rm fb}^{-1}$. With refined measurements to be available at the LHCb, the future super-B factories, the NA62 at CERN, and the KOTO at J-PARC, closer correlations between the $t\to qZ$ and the rare B- and K-meson decays are expected in the near future, which will be helpful for the searches of the top-quark FCNC decays at the LHC.