Balázs' Low-Energy Approximation

Abstract

Using an approach due originally to Balázs and reformulated to some extent in this paper, we study the problem of simulating short-range forces with a pole approximation in the framework of a partial-wave dispersion relation. The two-particle meson-baryon channels $S=-3\mathrm{}$, $T=0\mathrm{}$ and $S=0\mathrm{}$, $T=\frac{3}{2}$ are treated in detail, with particular emphasis placed upon determining the dependence of the solutions upon various parameters occurring in the calculation. Further, a multichannel formulation for the approximation scheme is given. The matching procedure, by which residues of the poles which represent short-range forces are determined, is found to affect the results strongly, whereas the exact location of these poles is relatively unimportant. We conclude that the method cannot be applied unambiguously, but that inclusion of shortrange effects leads to relatively good agreement with experiment in examples treated so far by the author when a technique similar to a cutoff is used.