Interpolating Axial Anomaly Induced Amplitudes

Abstract

We propose an interpolating formula for the amplitude induced by the axial anomaly, concentrating on the $\pi^0\gamma^{\ast}\gamma^{\ast}$ transition form factor. The QCD corrections to this amplitude are generally described by two major contributions coming from the $q\bar{q}$ bound state and the background continuous spectrum, respectively. For the first contribution, we include the lowest vector bound state using the realization of the dynamical gauge boson of hidden local symmetry. The second contribution is included as the triangle quark loop in which a constituent mass is adopted as a internal quark mass and the amplitudes are smeared out around the threshold. Using the resulting form factor, we fit the experimental data for the $\pi^0\gamma$ and the $\omega\pi^0$ transition form factors and show that our result describes the experimental data well.