FORM FACTORS OF ργ*→π⁰and γγ*→π⁰TRANSITIONS FROM THE FINITE-WIDTH LIGHT-CONE LOCAL QCD SUM RULES

Abstract

Instead of the usual zero-width approximation, the finite-width approximation for the resonance, the ρ-ω mesons, is used to investigate the light-cone local QCD sum rules for the form factors of the transitions, ργ*→π0and γγ*→π0. To be more certain, a product of two weight functions is chosen in the method of the analytic continuation by duality to annihilate the uncertainty in the continuum region and the integrand in the integration range not covered by vector-meson dominance and where the theoretical expression may least be trusted. The resultant form factors in the cases for the zero- and finite-widths are almost the same, both agree well with the experimental measurements, and comparison with the results from the Laplacian transformed light-cone sum rules and etc. is discussed.

The axial anomaly and consistency of the finite-width light-cone local duality sum rule for the form factor of the transition γ* γ* → π0

“…Comparing the theoretical results with the experimental data, useful constraints on the shape of the pion DA in terms of confidential regions for the Gegenbauer coefficients a 2 and a 4 can be obtained. Recently a quite different sum rule, namely the light-cone sum rule based on the analytic continuation by duality (ACD) [5,24,25], has been used to analyze the γ γ * → π 0 transition form factor. It is found that the ACD sum rule provides a reliable way to extract the form factor F γ π from F γ * π (Q 2 , q 2 ), and the rescaled form factor is consistent with the experimental results at least for Q 2 less than 10 GeV 2 [24].…”

“…Recently a quite different sum rule, namely the light-cone sum rule based on the analytic continuation by duality (ACD) [5,24,25], has been used to analyze the γ γ * → π 0 transition form factor. It is found that the ACD sum rule provides a reliable way to extract the form factor F γ π from F γ * π (Q 2 , q 2 ), and the rescaled form factor is consistent with the experimental results at least for Q 2 less than 10 GeV 2 [24]. However, for the special case when both photons are on the mass shell, no satisfactory results of F γ π (0) could be expected by simply extrapolating…”