Form Factors of ${\gamma }^{\ast }\rho \to \pi$ and ${\gamma }^{\ast }\gamma \to {\pi }^0$ 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 ${\gamma }^{\ast }\rho \to \pi$ and ${\gamma }^{\ast }\gamma \to {\pi }^0$ transitions. We consider the dispersion relation for the ${\gamma }^{\ast }(Q^2){\gamma }^{\ast }(q^2)\to {\pi }^0$ 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 ${\gamma }^{\ast }(Q^2)\rho \to \pi$ 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 ${\gamma }^{\ast }(Q^2)\gamma \to {\pi }^0$ form factor is obtained taking the $q^2=0$ limit in this relation. Our predictions are valid at $Q^2\ge 1{GeV}^2$ and have a correct asymptotic behaviour at large $Q^2$.

18 pages, 5 figures, Latex, epsfig; added more details on uncertainties and fits of the numerical results, version to appear in Eur. Phys. J. C

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