Revisiting the U_A(1) problems

Abstract

We survey various U_A(1) problems and attempt to resolve the two puzzles related to the eta mesons that have experimental verification. Specifically, we first explore the Goldstone structure of the eta and eta' mesons in the context of eta-eta' mixing using ideas based on QCD. Then we study the eta decays eta->3pi0, eta'->3pi0 and eta'->eta pi pi. Finally we arrive at essentially the same picture in the dynamical scheme based on consistently coupled Schwinger-Dyson and Bethe-Salpeter integral equations. This chirally well-behaved bound-state approach clarifies the distinction between the usual axial-current decay constants and the gamma gamma decay constants in the eta-eta' complex. Allowing for the effects of the SU(3) flavor symmetry breaking in the quark-antiquark annihilation, leads to the improved eta-eta' mass matrix.