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.

revtex, one eps figure, 25 pages, discussion on two mixing angles scheme included, references added, version to appear in J. Phys. G

References in corpus (3)

• Dynamical generation of the gauged SU(2) linear sigma model
• Anomalous gamma -> 3 pi amplitude in a bound-state approach
• Meson PVV Interactions are determined by Quark Loops

Cited by in corpus (19)

• Infrared Properties of QCD from Dyson-Schwinger equations
• Flavour symmetry breaking and meson masses
• Relativistic Many-Body Hamiltonian Approach to Mesons
• Ground-State Scalar $\bar{q}q$ Nonet: SU(3) Mass Splittings and Strong, Electromagnetic, and Weak Decay Rates
• Constituent Quark Masses and the Electroweak Standard Model
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach at finite temperature
• eta and eta' mesons and dimension 2 gluon condensate <A^2>
• η' Multiplicity and the Witten-Veneziano relation at finite temperature
• ${\eta }^{\prime }$ and $\eta$ mesons at high T when the U_A(1) and chiral symmetry breaking are tied
• Dynamical SU(3) linear sigma model and the mixing of eta'-eta and sigma-f_0 mesons
• eta and eta' in a coupled Schwinger-Dyson and Bethe-Salpeter approach. II. The gamma^* gamma transition form factors
• A $U_A(1)$ symmetry restoration scenario supported by the generalized Witten-Veneziano relation and its analytic solution
• Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the $U_A(1)$ Symmetry
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach using a generalization of the Witten-Veneziano relation
• A Dyson-Schwinger model beyond isospin limit prepared for investigating U_A(1)-breaking temperature dependence
• The u-d quark mass difference and nuclear charge symmetry breaking
• Aspects of model dependence of eta'-eta complex treated by going beyond the isospin limit
• SU(3) Mass Splittings for $\bar{q}q$ Mesons and $qqq$ Baryons
• Bypassing the axial anomalies