Dependence of Form Factors of γγ~*→π~0 Transition to the Finiteness of the Resonance Widths

In the framework of the local quantum chromodynamics sum rules,instead of the usual zero-width approximation,the finite-width approximation for the resonances,the ρ-ω mesons,is used to investigate the form factor of the transition γγ*→π0.According to the method of the analytic continuation by duality,the weight function,the polynomial of a low order N,is added to the dispersion integral to annihilate the integrand in the region where both resonance saturation and the QCD asymptotic expression are least reliable.The resultant form factor in the cases for the zero-and finitewidths are almost the same,and agree well with the experimental measurements,it thus shows a weak dependence of the form factor on the finiteness of the widths of the resonances,and justifies the correctness of the asymptotic form of the pion light-cone wave function.