Resonant Solutions of the Low Equation from Fixed-Point Theorems

Abstract

Fixed-point theorems are used to prove the existence of a class of solutions to the one-meson Low equation of the static-baryon model. The main result is that there exist solutions involving an arbitrary choice of narrow resonances. This is true for any crossing matrix with a finite number of channels, and for any cutoff function of a large class. For sufficiently small coupling constants, the solutions can be constructed by a convergent iteration procedure. The stable particles and the arbitrarily chosen resonances are associated with Castillejo-Dalitz-Dyson poles of an appropriate denominator function. The methods used do not suffice to show that solutions of the bootstrap type exist. Our earlier work is improved in that resonances are allowed and a bigger range of coupling constants and a weaker cutoff are permitted. The analysis is based on a crossing-symmetric $\frac{N}{D}$ formulation of the Low equation.