Form Factors of $γ^{*}ρ\toπ$ and $γ^{*}γ\toπ^0$ Transitions and Light-Cone Sum Rules

Details Form Factors of $γ^{*}ρ\toπ$ and $γ^{*}γ\toπ^0$ Transitions and Light-Cone Sum Rules Form Factors of $γ^{*}ρ\toπ$ and $γ^{*}γ\toπ^0$ Transitions and Light-Cone Sum Rules

1997-12-19

arxiv.org/abs/hep-ph/9712451v2

Eur.Phys.J.C6:477-484,1999

Physics

High Energy Physics

High Energy Physics - Phenomenology

18 pages, 5 figures, Latex, epsfig; added more details on uncertainties and fits of the numerical results, version to appear i

Scientific paper

10.1007/s100520050357

The method of light-cone QCD sum rules is applied to the calculation of the form factors of $\gamma^*\rho \to \pi$ and $\gamma^*\gamma \to \pi^0$ transitions. We consider the dispersion relation for the $\gamma^*(Q^2)\gamma^*(q^2) \to \pi^0$ 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 $\gamma^*(Q^2) \rho \to \pi $ 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 $\gamma^*(Q^2)\gamma \to \pi^0$ 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 $Q^2$.

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