Strongly-correlated-resonances model: Existence theorem and solution

The problem of the existence of solutions to the equations for the differential cross section and polarization in the strongly-correlated-resonances model with simple assumptions about the background amplitudes (ideal scrm) is examined. It is found that, besides the fulfillment of qualitative predictions, an equation of constraint at each angle must be satisfied by the six quantities which characterize the data between two consecutive junctions (two amplitudes, two initial phases, and two heights) in order for a solution to exist. As an application, the equation of constraint is tested with π+p elastic data in the backward hemisphere between 0.82 and 2.08 GeV/c (where the predictions of the ideal model are fulfilled to a good degree of approximation). It is found to be consistent with the data. This quantitative test supplements previous qualitative ones, and could be also applied to the pure-isospin processes π-p → ΛK0, π+p → Σ+K+, π-p → etan, and K-p → Λπ0. Expressions for the background and resonance amplitudes in terms of the relevant experimental quantities in the ideal scrm are also given. These could be used as a first approximation to a more exact solution to the data