Constraints onπNPhase-Shift Analysis f from Angular Distributions of Production Reactions

A model-independent angular-momentum decomposition of the $\pi N\to \pi \pi N$ reaction amplitudes is exploited to relate angular distributions of each final-state particle with the absorption parameters ${{\eta }_{l_{\pm }}}^I$ used in $\pi N$-scattering phase-shift analyses. This relation provides constraints in the form of lower bounds on ($1-{{\eta }_{l_{\pm }}}^2$) for specific sets of angular momentum and parity scattering states. Available data on production reactions from threshold to 600 MeV are examined and the consistency of various phase-shift solutions with these constraints is discussed. The Cence solution does not appear to agree with the energy dependence of the inelastic cross section, as deduced from available data on total, elastic, and charge-exchange $\pi N$ cross sections. None of the existing phase-shift solutions at 290 MeV provides for absorption in partial waves with $J>\mathrm{}\frac{3}{2}$, while our analysis shows that production data require such absorption.