Top-quark flavor-changing $tqZ$ couplings and rare $\Delta F=1$ processes

We model-independently study the impacts of anomalous $tqZ$ couplings ($q=u,c$), which lead to the $t\to q Z$ decays, on low energy flavor physics. It is found that the $tuZ$-coupling effect can significantly affect the rare $K$ and $B$ decays, whereas the $tcZ$-coupling effect is small. Using the ATLAS's branching ratio (BR) upper bound of $BR(t\to uZ) < 1.7\times 10^{-4}$, the influence of the anomalous $tuZ$-coupling on the rare decays can be found as follows: (a) The contribution to the Kaon direct CP violation can be up to $Re(\epsilon'/\epsilon) \lesssim 0.8 \times 10^{-3}$; (b) $BR(K^+\to \pi^+ \nu \bar \nu) \lesssim 12 \times 10^{-11}$ and $BR(K_L \to \pi^0 \nu\bar \nu)\lesssim 7.9 \times 10^{-11}$; (c) the BR for $K_S \to \mu^+ \mu^-$ including the long-distance effect can be enhanced by $11\%$ with respect to the standard model result, and (d) $BR(B_d \to \mu^+ \mu^-) \lesssim 1.97 \times 10^{-10}$. In addition, although $Re(\epsilon'/\epsilon)$ cannot be synchronously enhanced with $BR(K_L\to \pi^0 \nu \bar\nu)$ and $BR(K_S\to \mu^+ \mu^-)$ in the same region of the CP-violating phase, the values of $Re(\epsilon'/\epsilon)$, $BR(K^+ \to \pi^+ \nu \bar\nu)$, and $BR(B_d \to \mu^+ \mu^-)$ can be simultaneously increased.