APPLICATION OF JAIN AND MUNCZEK'S BOUND-STATE APPROACH TO γγ-PROCESSES OF π⁰, η_c AND η_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 π 0 , η 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 γγ decay widths of π 0 , η c and η b , and for the π 0 γ ⋆ → γ transition form factor, and compare them with experiment. In the chiral limit, the axial-anomaly result for π 0 → 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 η c and possibly η b , and their γγ-decays. We discuss the reasons for the broad phenomenological success of the bound-state approach of Jain and Munczek.

ηandη′mesons and dimension 2 gluon condensate⟨A2⟩

“…Thus, as shown in Ref. [15], our interaction (15) leads to the deep Euclidean behaviors of quark propagators consistent with the asymptotic freedom of QCD [39]. However, what enables the successful description of pions and kaons in Ref.…”

“…This is unique among the bound state approaches -e.g., see Refs. [38,39] and references therein for discussion. Nevertheless, one keeps the advantage of bound state approaches that from the qq substructure one can calculate many important quantities (such as the pion decay constant f π ) which are just parameters in most of other chiral approaches to the light-quark sector.…”

“…Typically, as in Refs. [21,25,33,39,40,41] for example, it combines the modeled nonperturbative component (which is strong enough to obtain required DχSB) and the known perturbative QCD contribution. Our gluon condensate-induced α eff (Q 2 ) (15) also behaves nonperturbatively at low Q 2 and perturbatively at very high Q 2 , as seen both in its earlier derivation [15] and the alternative derivation in Sec.…”

“…The transition between the neutral pseudoscalar meson P and two photons γ(k) and γ(k ′ ) with momenta k and k ′ can be described by a scalar amplitude we denote T P (k 2 , k ′ 2 ) [39]. The special case of the decay P → γγ into two real, on-shell photons corresponds to the k 2 = k ′ 2 = 0 amplitude…”

“…[15,25,26,39,40,41,42,55], since the incorporation of the quark-photon interactions is the same as adopted there through the scheme of a generalized impulse approximation, where all propagators, bound-state vertices, and quark-photon vertices are dressed. (In the present application, this impulse approximation is illustrated by the qq pseudoscalar-γγ triangle graph in Fig.…”