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In this paper, we analyze the possible anomalous $tcZ$ coupling effects inthe $b \to s $ mediated decays $\bar B \to \bar K^* \mu^+ \mu^-$ and $B_s \to\mu^+ \mu^-$. After exploiting the available experimental data, the combinedconstraints on the anomalous coupling $X_{ct}^L$ are derived. It is found that,the bound on the magnitude $|X_{ct}^L|$ is dominated by the branching ratios ofthese two decays. Furthermore, one sign-flipped solution is excluded by thelongitudinal fraction of $\bar B \to \bar K^* \mu^+ \mu^-$ at the low dileptonmass region. After considering the combined constraints, for general complexcoupling $X_{ct}^L$, the predicted upper bound on $\mathcal B (t \to cZ)$ arecompatible with that from the recent CMS direct search. In particular, for thecase of real coupling $X_{ct}^L$, the upper bound reads $\mathcal B (t \tocZ)<1.0\times 10^{-4}$, which is much lower than the current CMS bound butstill accessible at the LHC. With improved measurements at the LHC, the colsercorrelations between the $t \to cZ$ and $b \to s$ mediated (semi-) leptonicdecays are expected in the near future.

Constraints on anomalous $tcZ$ coupling from $\bar B \to \bar K^* \mu^+ \mu^-$ and $B_s \to \mu^+ \mu^-$ decays