A Circular Electron-Positron Collider with center-of-mass energy of $\sqrt{s}=240$ GeV has been proposed as a future High Energy Physics project. With such energy, it will be possible to study in detail Higgs physics, but apparently it will not be possible to study top quark physics, when one relies on the top quark pair production mechanism. However, one still has the possibility to produce a single top quark in association with a charm quark, using Flavor-Changing Neutral Current interactions, which arises in several scenarios of new physics. We explore here a model that can produce this signal at detectable levels, namely the Left-Right Mirror Model, which is a Left-Right model that includes mirror fermions, motivated as a possible solution to the Strong CP problem. We find that for particular scenarios of the model parameters, which are in agreement with the most up-to-date experimental constraints, the signal coming from $e^+e^-\to V\to tc$ process ($V=Z,\,Z^{\prime}$) could give evidence for Flavor-Changing Neutral Current interactions, even for masses of a new neutral gauge boson as high as $m_{Z'}=7$ TeV.

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