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In the present work the $Z^\prime tc$ coupling is bounded by using thecurrent experimental data on the $D^{0}-\bar{D^{0}}$ meson-mixing system. It isfound that the strength associated to this coupling is less than $5.75\times10^{-2}$. The single top production through the $e^+e^-\to Z^\prime\to tc$process at the $Z^\prime$ boson resonance is studied and we found that around$10^7$ $tc$ events will be expected at the International Linear Collider. Forthe $Z^\prime\to tc$ decay, we predict a branching ratio of $10^{-2}$.

Bounding the $Z^\prime tc$ coupling from $D^{0}-\bar{D^{0}}$ mixing and single top production at the ILC