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

Abstract

The predictions for transition form factors ${\gamma }^{\ast }\to \gamma f_2(1270)$ and ${\gamma }^{\ast }\to \gamma a_2(1320)$ and corresponding $e^{+}{e}^{-}\to {\gamma }^{\ast }\to f_2\gamma$ and $e^{+}{e}^{-}\to {\gamma }^{\ast }\to a_2\gamma$ 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 $e^{+}{e}^{-}\to {\gamma }^{\ast }\to f_2\gamma$ and $e^{+}{e}^{-}\to {\gamma }^{\ast }\to a_2\gamma$ 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 $\sigma (e^{+}{e}^{-}\to {\gamma }^{\ast }\to f_2\gamma )/\sigma (e^{+}{e}^{-}\to {\gamma }^{\ast }\to a_2\gamma )\approx 25/9$, obtained with the help of the $q\bar{q}$ model of $a_2$ and $f_2$ and QCD, is used to determine the $\sigma (e^{+}{e}^{-}\to {\gamma }^{\ast }\to a_2\gamma )$ at high energies. Recent BABAR measurement of the $e^{+}{e}^{-}\to f_2\gamma \to {\pi }^{+}{\pi }^{-}\gamma$ cross section at $10.58$ GeV gives hope for detailed investigation of the ${\gamma }^{\ast }(s)\to f_2\gamma$ and ${\gamma }^{\ast }(s)\to a_2\gamma$ transition form factors at high energy region.

Comments: 10 pages, 2 figures, many changes, title changed