Axial anomaly and transition form factors.

We investigate the properties of the amplitude induced by the anomaly. In a relatively high energy region those amplitudes are constructed by the vector meson poles and the anomaly terms, in which the anomaly terms can be essentially evaluated by the triangle quark graph. We pay our attention to the anomaly term and make intensive analysis of the existing experimental data, i.e., the electromagnetic π0 and ω transition form factors. Our result shows that it is essential to use the constituent quark mass instead of the current quark mass in evaluating the anomaly term from the triangle graph. Permanent address: Aichi University, Miyoshi Aichi 470-02, Japan Fellow of the Japan Society for the Promotion of Science for Japanese Junior Scientists Much interests have been paid to the non-abelian anomaly because of its fundamental property of quantum gauge theories. These kinds of anomaly are known to be caused by the quantum effects of triangle fermion loops shown in Fig 1. Their amplitudes in the low energy limit is known to be independent either of the higher order corrections or of the internal fermion masses. On the other hand the asymptotic freedom of QCD facilitates us to predict the hadronic amplitudes at extremely high energy region, where again the triangle diagram becomes dominant. Indeed this triangle amplitude correctly reproduces the high energy behavior obtained from the operator product expansion (OPE) technique[1, 2], up to the ambiguity of the coefficient factor. The important observation here is that the amplitudes induced by the anomaly are constrained not only by the low energy theorem[3, 4, 5] but also by the high energy behavior because of the asymptotically freedom, and therefore we may expect that the amplitudes induced by the anomaly are essentially controlled by the triangle quark graph. The most well-known example of the processes induced by the axial anomaly is π → γγ. The triangle quark amplitude reproduces the experimental data for this process excellently. If we want to apply the anomaly induced amplitudes to the relatively higher energy region, the non-anomalous contributions come in the process in addition to the anomaly terms. Then the QCD corrections to this triangle graph becomes important. Especially we have to take account of the following nonperturbative QCD effects: 1) chiral symmetry breaking (generation of constituent quark mass); 2) confinement effects; 3) hadron contributions. Our interest here is investigating the processes induced by the axial anomaly in the high energy region. In the separate paper[6], taking account of the above effects, we have proposed an interpolating formula for the amplitude induced by the axial anomaly. There the amplitudes are constructed by the “vector meson pole terms” and the “anomaly terms”, the latter being essentially evaluated by the quark triangle graph of Fig. 1. In this paper we pay our attention to the anomaly term and make intensive comparison with the existing experimental data. The candidates for investigating the structure of this triangle anomaly amplitudes are the π transition form factors. The result shows that, in addition to the vector meson poles, it is essential to use the constituent quark mass instead of the current quark mass for the internal quark lines of the triangle graph.