Associated quarkonia production in a single boson $e^{+}e^{−}$~annihilation

We present the preliminary results on the study of the cross sections for charmonium pair and bottomonium pair production in a single boson $e^+e^-$~annihilation. Processes have been studied in a wide range of energies, which are to be achieved at future $e^+e^-$~colliders, such as ILC and FCC. The contribution of color singlets states to production of vector and pseudoscalar states have been taken into account. Both QCD and EW production mechanisms have been considered including their interference and one-loop QCD correction. Cases of both intermediate bosons have been investigated: $\gamma$ and $Z$. All the calculations were performed in terms of perturbative technique and NRQCD-factorization.