Relativistic effects in the production of pseudoscalar and vector doubly heavy mesons from e^+e^- annihilation

On the basis of the perturbative QCD and the relativistic quark model we investigate the relativistic and bound state effects in the production processes of a pair of $S$-wave doubly heavy mesons with opposite charge conjugation consisting of $b$ and $c$ quarks. All possible relativistic corrections in the production amplitude including the terms connected with the transformation law of the bound state wave function to the reference frame of the moving pseudoscalar $\mathcal{P}-$ and vector $\mathcal{V}-$ mesons are taken into account. We obtain a growth of the cross section for the reaction $e^{+}+e^{-}\to J\mathrm{/}\mathrm{\Psi }+{\eta }_c$ due to considered effects by a factor $2÷2.5$ in the range of the center-of-mass energy $\sqrt{s}=6÷12$ GeV.