On the analyticity properties of five-particle amplitudes in quantum field theory

In a five-particle process a+b to 1+2+3, where the invariant mass of 2 and 3 is such that this pair can scatter only elastically in the final state, the conventional production amplitude T is related easily to a new amplitude T/sub 23-/ which has simpler analyticity properties than T in relativistic quantum field theory. Concerning the physical interpretation of T/sub 23-/, its (l, m) partial wave can be consistently regarded as the inelastic scattering amplitude for a+b to 1+(one composite particle with angular momentum (l, m)). It is shown that T/sub 23-/ and its absorptive part have analyticity properties in three angular variables which generalize those of the four-particle amplitudes inside the Lehmann ellipses. The problem of deriving dispersion relations for T/sub 23-/ is also investigated. (21 refs).