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

Abstract

The pion transition form factor at the photon mass-shell of q21 = q22 = 0 is fixed by the axial anomaly, which may serve as a criterion in checking the consistency of the underlying quantum chromodynamics (QCD). We choose to work in the symmetric kinematical region where two photons have the same virtualities and hope to reproduce the experimental value of from light-cone QCD sum rules instead of direct extrapolation of the QCD expression to such a low-energy scale. The form factor of the transition γ*γ* → π0 is investigated in the framework of the zero- and finite-width light-cone local duality QCD sum rules. The expression of the pion transition form factor at large t is independent of the twist-two and twist-three pion distribution amplitudes; therefore a more accurate conclusion may be reached. The influence of the light quark mass and the ωρπ coupling constant to our sum rules is also considered. The consistency between the axial anomaly, the intermediate hadronic structure and the QCD perturbative dynamics is tested to be true within a reasonable region of input parameters.