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

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.