Compositeness and elementarity in theories with crossing

Abstract

It is shown that in anS-matrix with crossing, criteria of compositeness based on the vanishing of renormalization constants can be applied in a consistent way, allowing us to study the crucial dependence of the left-hand singularities on the degree of elementarity of the exchanged particles. Then, using both field theory andS-matrix approaches, we solve a paradox about an «impossibility», stated several times in the literature, of distinguishing between elementarity and compositeness of two baryons in two crossed channels: on the contrary, we exhibit different physical interpretations for distinct domains of the parameters values, at the boundary of which the amplitude undergoes critical change. We discriminate the various cases where each particle is either elementary or composite; when only one of these two baryons is («chain» or «ladder») composite, its mass is always the heaviest one. Next, we discuss and compare in our explicit model theZ=0, strong coupling limit and reciprocal bootstrap approaches, together with a discussion of approximations currently used in theN/D calculations. The vanishing of bothZ, while keeping finite the coupling constants, implies a characteristic symmetry in the theory.