APPLICATION OF JAIN AND MUNCZEK'S BOUND-STATE APPROACH TO γγ-PROCESSES OF π0, ηc AND ηb

Abstract

We point out the problems affecting most quark–antiquark bound-state approaches when they are faced with the electromagnetic processes dominated by Abelian axial anomaly. However, these problems are resolved in the consistently coupled Schwinger–Dyson and Bethe–Salpeter approach. Using one of the most successful variants of this approach, we find the dynamically dressed propagators of the light u and d quarks, as well as the heavy c and b quarks, and find the Bethe–Salpeter amplitudes for their bound states π0, ηc and ηb. Thanks to incorporating the dynamical chiral symmetry breaking, the pion simultaneously appears as the (pseudo)Goldstone boson. We give the theoretical predictions for the γγ decay widths of π0, ηc and ηb, and for the π0γ⋆→γ transition form factor, and compare them with experiment. In the chiral limit, the axial-anomaly result for π0→γγ is reproduced analytically in the consistently coupled Schwinger–Dyson and Bethe–Salpeter approach, provided that the quark–photon vertex is dressed consistently with the quark propagator, so that the vector Ward–Takahashi identity of QED is obeyed. On the other hand, the present approach is also capable of quantitatively describing systems of heavy quarks, concretely ηc and possibly ηb, and their γγ-decays. We discuss the reasons for the broad phenomenological success of the bound-state approach of Jain and Munczek.