Eur. Phys. J. C (1999) 6: 477-484
https://doi.org/10.1007/s100529800938

Form factors of γ ^* ρ → π and γ ^* γ → π ⁰ transitions and light-cone sum rules

¹ Institut für Theoretische Physik, Universität Würzburg, D-97074, Würzburg, Germany
² On leave from Yerevan Physics Institute, 375036, Yerevan, Armenia

Received: 16 January 1998
Revised: 14 May 1998
Published online: 17 September 2013

Abstract

The method of light-cone QCD sum rules is applied to the calculation of the form factors of γ ^* ρ → π and γ ^* γ → π ⁰ transitions. We consider the dispersion relation for the γ ^*(Q ²)γ ^*(q ²) → π ⁰ amplitude in the variable q². At large virtualities q² and Q², this amplitude is calculated in terms of light-cone wave functions of the pion. As a next step, the light-cone sum rule for the γ ^*(Q ²)ρ → π form factor is derived. This sum rule, together with the quark-hadron duality, provides an estimate of the hadronic spectral density in the dispersion relation. Finally, the γ ^*(Q ²)γ → π ⁰ form factor is obtained taking the q ² = 0 limit in this relation. Our predictions are valid at Q ² ≥ 1 GeV² and have a correct asymptotic behaviour at large Q².