Transition form factors ${\gamma }^{\ast }\to \gamma f_2(1270)$ and ${\gamma }^{\ast }\to \gamma a_2(1320)$ in the $e^{+}{e}^{-}$ collisions

The predictions for transition form factors ${\gamma }^{\ast }\to \gamma f_2(1270)$ and ${\gamma }^{\ast }\to \gamma a_2(1320)$ and corresponding $e^+e^-\to \gamma^\to f_2\gamma$and$e^+e^-\to \gamma^\to a_2\gamma$ cross sections are obtained for the energy region up to $2$ GeV. These predictions are coordinated with the recent Belle data on the ${\gamma }^{\ast }(Q^2)\gamma \to f_2$ transition. It is shown that the QCD asymptotics of the amplitudes of the reactions $e^+e^-\to \gamma^\to f_2\gamma$and$e^+e^-\to \gamma^\to a_2\gamma$ can be reached only by taking into account a compensation of contributions of $\rho (770)$, $\omega (782)$ with contributions of their radial excitations. The relation $\sigma(e^+e^-\to \gamma^\to f_2\gamma)/\sigma(e^+e^-\to \gamma^\to a_2\gamma)\approx 25/9$,obtainedwiththehelpofthe$q\bar q$modelof$a_2$and$f_2$andQCD,isusedtodeterminethe$\sigma(e^+e^-\to \gamma^\to a_2\gamma)$athighenergies\mathrm{.}RecentBABARmeasurementofthe$e^+e^-\to f_2\gamma\to\pi^+\pi^-\gamma$crosssectionat$10.58$ GeV gives hope for detailed investigation of the ${\gamma }^{\ast }(s)\to f_2\gamma$ and $\gamma^(s)\to a_2\gamma$ transition form factors at high energy region.