Complexity of hadronic amplitudes via quark loops

Abstract

The structure of hadronic transition amplitudes h→h'+h" via quark triangle loops is investigated in terms of hadron quark vertex functions Γ(q^{^}), using for illustration the case of the ρ→ππ transition. A Bethe-Salpeter model based on the Covariant-Instantaneity-Ansatz (CIA) for its kernel which provides an exact interconnection between the 3D and 4D forms the BS wave function, determines the structure Γ(q^{^})~D(q^{^})⊗φ(q^{^}). The nonlocality feature inherent in the vertex function causes the imaginary part of g_ρππ calculated from the loop integral to be generally different from its dispersion relation value which would be obtained from analyticity of g_{ρπ π} in the ρ-mass. Pending a proper understanding of this nonlocality (associated with confining interactions) only the real part of g_ρππ is found unambiguous while the imaginary part is model-dependent.