Using a perturbative model, we study the asymptotic behavior of weak amplitudes, looking in particular for the existence of fixed poles. The weakly interacting particles are considered as either elementary or composite. Our conclusions can be summarized as follows: The existence of fixed poles is model-dependent. In particular: (1) If both interacting particles are elementary, we find the usual fixed poles at $J={\sigma }_1+{\sigma }_2-n$, $n\ge 1$, where ${\sigma }_1$ and ${\sigma }_2$ are the spins of the particles. (2) If the weakly interacting particles are composite, the amplitude is superconvergent (even being nonunitary) and there are no fixed poles, at least for $J\ge 0$. (3) In the case of photoproduction of a spinless composite particle, i.e., an amplitude with only one elementary particle with spin one, there is no fixed pole at $J=0\mathrm{}$. If we consider that the elementary particle has spin $\sigma$, we argue that the pole at $J=\sigma -1\mathrm{}$ disappears, while the ones at $J=\sigma -n$ with $n>\mathrm{}1\mathrm{}$ may or may not exist, depending on the wave function of the produced hadron. We conclude by discussing the implications of our results, and in particular the limitations on the hypothesis of partially conserved axial-vector current.

• Received 21 August 1967

DOI:https://doi.org/10.1103/PhysRev.167.1441