Form Factors of $γ^{*}ρ\toπ$ and $γ^{*}γ\toπ^0$ 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 $γ^*ρ\to π$ and $γ^*γ\to π^0$ transitions. We consider the dispersion relation for the $γ^*(Q^2)γ^*(q^2) \to π^0$ amplitude in the variable $q^2$. At large virtualities $q^2$ and $Q^2$, 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 $γ^*(Q^2) ρ\to π$ 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 $γ^*(Q^2)γ\to π^0$ form factor is obtained taking the $q^2=0$ limit in this relation. Our predictions are valid at $Q^2 \geq 1 {GeV}^2$ and have a correct asymptotic behaviour at large $Q^2$.