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 qq̅ hadrons with L≥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 qq̅ 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_π(k²)(ω,a₂)→γ π, (ρ,f₂)→ππ, (a₁,a₂)→ρπ, and b₁→ωπ. 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 (ω₀,C₀,m_ud) as employed recently for a successful description of the mass spectra of qq̅ and qqq hadrons, as well as of some pionic amplitudes.