Application of Jain and Munczek's bound-state approach to gamma gamma-processes of pi0, eta_c and eta_b

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 pi0, eta_c and η_b. Thanks to incorporating the dynamical chiral symmetry breaking, the pion simultaneously appears as the (pseudo)Goldstone boson. We give the theoretical predictions for the gamma-gamma decay widths of pi0, eta_c and eta_b, and for the pi0 gamma* -> gamma transition form factor, and compare them with experiment. In the chiral limit, the axial-anomaly result for pi0->gamma-gamma 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 eta_c and possibly eta_b, and their gamma-gamma decays. We discuss the reasons for the broad phenomenological success of the bound-state approach of Jain and Munczek.

RevTeX, 37 pages, 7 eps figures, submitted to Int. J. Mod. Phys. A

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• Pion mass and decay constant
• Hadron Physics from the Global Color Model of QCD
• Semileptonic decays of heavy mesons
• eta and eta' in a coupled Schwinger-Dyson and Bethe-Salpeter approach
• Nonperturbative QCD with Modern Tools
• The analytic structure of heavy quark propagators
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• Two Photon Transition Form Factor of $\bar{c}c$ Quarkonia
• Revisiting the U_A(1) problems
• gamma^* gamma -> pi^0 transition and asymptotics of gamma^* gamma and gamma^* gamma^* transitions of other unflavored pseudoscalar mesons
• eta and eta' mesons and dimension 2 gluon condensate <A^2>
• Anomalous gamma -> 3 pi amplitude in a bound-state approach
• Pseudoscalar Meson Nonet at Zero and Finite Temperature
• eta and eta' in a coupled Schwinger-Dyson and Bethe-Salpeter approach. II. The gamma^* gamma transition form factors
• Pseudoscalar qqbar mesons and effective QCD coupling enhanced by <A^2> condensate
• 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
• Axial anomaly and the interplay of quark loops with pseudoscalar and vector mesons in the gamma* --> pi+ pi0 pi- process
• Pion observables calculated in Minkowski and Euclidean spaces with Ansätze for quark propagators