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On the number of solutions to a crossing symmetric neutral π-π model

Research paper by O. Brander

Indexed on: 01 Jun '75Published on: 01 Jun '75Published in: Communications in Mathematical Physics



Abstract

The crossing symmetry of the π-π system has invited many authors to try different versions of the bootstrap hypothesis on it. In the last few years, there has been some hope that the positivity conditions of Martin, Balachandran and Nuyts, Roskies, and, most recently, the Roy physical region constraints, might be sufficient to fix the low π-π partial waves with very little additional information, like the position and width of the ϱ resonance. This hope was recently proved too optimistic by Basdevant, Froggatt and Petersen. A similar result was obtained by the present author in an approximately crossing symmetric, solvable model. In this paper we strengthen this latter result by determining the multiplicity of the exact solution to a crossing symmetric neutral π-π model. We consider only theS wave, but the multiplicity would increase by the addition of other coupled channels. The analysis is not confined to weak coupling only, and includes all solutions, in particular also a class of logarithmically decreasing ones, which are left out by most other authors.