eta and eta' in a coupled Schwinger-Dyson and Bethe-Salpeter approach

Abstract

Extending our earlier treatments of pi0, eta_c and eta_b, we study the eta-eta' system and its gamma-gamma decays using a model which is a leading version of the consistently coupled Schwinger-Dyson (SD) and Bethe-Salpeter (BS) approach. The electromagnetic interactions are incorporated through a (generalized) impulse approximation consistent with this bound-state approach, so that the Ward-Takahashi identities of QED are preserved when quarks are dynamically dressed. To overcome some of the limitations due to the ladder approximation, we introduce a minimal extension to the bound--state approach employed, so that the U_A(1) problem is avoided. Pointing out which of our predictions hold in the coupled SD-BS approach in general, and which are the consequences of the specific, chosen model, we present the results for the axial-current decay constants of eta_8, eta_0, and of their physical combinations eta and eta', the results for the gamma-gamma decay constants of eta_0 and eta_8, for the two-photon decay widths of eta and eta', and for the mixing-independent R-ratio constructed from them.