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

TL;DR

This paper predicts transition form factors and cross sections for specific meson-photon processes in electron-positron collisions up to 2 GeV, aligning with recent experimental data and QCD asymptotics.

Contribution

It provides new theoretical predictions for transition form factors and cross sections, incorporating contributions from meson resonances and their excitations, and relates these to recent experimental measurements.

Findings

QCD asymptotics require resonance contribution compensation.

Predicted cross section ratio for $f_2$ and $a_2$ channels is approximately 25/9.

Recent BABAR data supports potential high-energy transition form factor studies.

Abstract

The predictions for transition form factors $\gamma^*\to \gamma f_2(1270)$ and $\gamma^*\to \gamma a_2(1320)$ and corresponding $e^+e^-\to \gamma^*\to f_2\gamma$ 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 $\gamma^*(Q^2)\gamma\to f_2$ 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 $\sigma(e^+e^-\to \gamma^*\to f_2\gamma)/\sigma(e^+e^-\to \gamma^*\to a_2\gamma)\approx 25/9$, obtained with the help of the $q\bar q$ model of $a_2$ and $f_2$ and QCD, is used to determine the $\sigma(e^+e^-\to \gamma^*\to a_2\gamma)$ 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 $\gamma^*(s)\to f_2\gamma$ and $\gamma^*(s)\to a_2\gamma$ transition form factors at high energy region.