Photoproduction of Composite Particles. Asymptotic Behavior in Some Models

The photoproduction amplitude of a spinless composite particle is examined in some models. We study the asymptotic behavior of such an amplitude and the related problem of fixed singularities in the angular momentum plane. By means of the Bethe-Salpeter wave function for the compound vertex and of the Deser-Gilbert-Sudarshan-Ida spectral representation for this wave function, we show how compositeness of the particle produced removes the fixed pole at $J=0\mathrm{}$ in the crossed-channel partial-wave amplitudes.