Transition form factors $γ^*\to γf_2(1270)$ and $γ^*\to γa_2(1320)$ in the $e^+e^-$ collisions

Abstract

The predictions for transition form factors $γ^*\to γf_2(1270)$ and $γ^*\to γa_2(1320)$ and corresponding $e^+e^-\to γ^*\to f_2γ$ and $e^+e^-\to γ^*\to a_2γ$ cross sections are obtained for the energy region up to $2$ GeV. These predictions are coordinated with the recent Belle data on the $γ^*(Q^2)γ\to f_2$ transition. It is shown that the QCD asymptotics of the amplitudes of the reactions $e^+e^-\to γ^*\to f_2γ$ and $e^+e^-\to γ^*\to a_2γ$ can be reached only by taking into account a compensation of contributions of $ρ(770)$, $ω(782)$ with contributions of their radial excitations. The relation $σ(e^+e^-\to γ^*\to f_2γ)/σ(e^+e^-\to γ^*\to a_2γ)\approx 25/9$, obtained with the help of the $q\bar q$ model of $a_2$ and $f_2$ and QCD, is used to determine the $σ(e^+e^-\to γ^*\to a_2γ)$ at high energies. Recent BABAR measurement of the $e^+e^-\to f_2γ\toπ^+π^-γ$ cross section at $10.58$ GeV gives hope for detailed investigation of the $γ^*(s)\to f_2γ$ and $γ^*(s)\to a_2γ$ transition form factors at high energy region.