Flavor signatures of complex anomalous $tcZ$ couplings

In this work we study the effects of anomalous $tcZ$ couplings. Such couplings would potentially affect several neutral current decays of $K$ and $B$ mesons via $Z$-penguin diagrams. Using constraints from relevant observables in $K$ and $B$ sectors, we find that the 2$\sigma$ upper bound on the branching ratio of ${\cal B}(t \to c Z)$ is $1.47 \times 10^{-5}$ for real coupling and $1.91 \times 10^{-4}$ for complex coupling. The current experimental upper bound from ATLAS and CMS collaborations on the branching ratio of $t \to c Z$ are $2.4 \times 10^{-4}$ and $4.9\times 10^{-4}$ at $95\%$ C.L., respectively. Hence the possibility of observation of $t \to c Z$ decay at the level of $10^{-4}$ would imply the anomalous couplings to be complex. Such complex couplings should also show up its presence in other related decays. We find that an order of magnitude enhancement is possible in the branching ratio of $K_L \to \pi^0 \nu \bar{\nu}$. Further, the complex $tcZ$ coupling can also provide large enhancements in many $CP$ violating angular observables in $B \to K^* \mu^+ \mu^-$ decay.