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The predictions for transition form factors $\gamma^*\to \gamma f_2(1270)$and $\gamma^*\to \gamma a_2(1320)$ and corresponding $e^+e^-\to \gamma^*\tof_2\gamma$ and $e^+e^-\to \gamma^*\to a_2\gamma$ cross sections are obtainedfor the energy region up to $2$ GeV. These predictions are coordinated with therecent Belle data on the $\gamma^*(Q^2)\gamma\to f_2$ transition. It is shownthat 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 reachedonly by taking into account a compensation of contributions of $\rho(770)$,$\omega(782)$ with contributions of their radial excitations. The relation$\sigma(e^+e^-\to \gamma^*\to f_2\gamma)/\sigma(e^+e^-\to \gamma^*\toa_2\gamma)\approx 25/9$, obtained with the help of the $q\bar q$ model of $a_2$and $f_2$ and QCD, is used to determine the $\sigma(e^+e^-\to \gamma^*\toa_2\gamma)$ at high energies. Recent BABAR measurement of the $e^+e^-\tof_2\gamma\to\pi^+\pi^-\gamma$ cross section at $10.58$ GeV gives hope fordetailed investigation of the $\gamma^*(s)\to f_2\gamma$ and $\gamma^*(s)\toa_2\gamma$ transition form factors at high energy region.

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

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