γ* → γf ₂(1270) and γ* → γa ₂(1320) Transition Form Factors in e ⁺ e ⁻ Collisions

The γ* → γf₂(1270) and γ* → γa₂(1320) transition form factors are considered up to high energies, along with the cross sections for the respective processes e⁺e⁻ → γ* → f₂γ and e⁺e⁻ → γ* → a₂γ. It is shown that QCD asymptotic behavior of the amplitudes for the reactions e⁺e⁻ → γ* → f₂γ and e⁺e⁻ → γ* → a₂γ can be reached after the compensation of the contributions of the ρ(770) and ω(782) mesons with the contributions of their radial excitations. The ratio σ(e⁺e⁻ → γ* → f₂γ)/σ(e⁺e⁻ → γ* → a₂γ) ≈ 25/9, obtained on the basis of the two-quark model of a₂ and f₂ and within QCD, is used to determine σ(e⁺e⁻ → γ* → a₂γ) at high energies. Recent data from the Belle detector on the γ*(Q²)γ → f₂ transition over the region extending up to Q² = 30 GeV² are taken into account. A substantial improvement of experimental accuracies is required for a detailed comparison of our predictions with experimental data at high energies. A recent measurement of the e⁺e⁻ → f₂γ → π⁺π⁻γ cross section at 10.58 GeV with the BaBar detector gives grounds to hope for this.