Hadronic transition amplitudes under null-plane Bethe-Salpeter dynamics

Abstract

A two-tier form of the Bethe-Salpeter (BS) framework is employed for the evaluation of a few typical transition amplitudes involving strong and electromagnetic decays of qq\ifmmode\bar\else\textasciimacron\fi{} hadrons with L\ensuremath{\ge}0. The two-tier BS framework, whose rationale has been described in some recent publications, is characterized by (i) a three-dimensional reduction of the BS equation under the null-plane ansatz to make a first contact with mass spectral data and (ii) a reconstructed four-dimensional BS wave function to restore the virtual qq\ifmmode\bar\else\textasciimacron\fi{} effects (higher Fock states) for the evaluation of hadronic transition amplitudes through the lowest-order Feynman (quark-triangle) diagrams. The processes explicitly considered are the pion form factor ${F}_{\ensuremath{\pi}}$(${k}^{2}$), (\ensuremath{\omega},${a}_{2}$)\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}, (\ensuremath{\rho},${f}_{2}$)->\ensuremath{\pi}\ensuremath{\pi}, (${a}_{1}$,${a}_{2}$)\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}, and ${b}_{1}$\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}. These illustrate the different types of coupling structures that are generally encountered in such a composite-hadron model. The agreement with the data on almost all these amplitudes is excellent, using the same basic constants (${\ensuremath{\omega}}_{0}$,${C}_{0}$,${m}_{\mathrm{ud}}$) as employed recently for a successful description of the mass spectra of qq\ifmmode\bar\else\textasciimacron\fi{} and qqq hadrons, as well as of some pionic amplitudes.