Limits on Pion-Nucleon Charge-Exchange Polarization

Triangle inequalities implied by isosymmetry yield upper and lower bounds for the pion-nucleon charge-exchange polarization in terms of the elastic ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ differential cross sections and polarizations and the ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ differential cross section. We have evaluated these bounds at a number of energies and observe an intriguing regularity: The upper and lower bounds approach each other closely, "pinching" the polarization value, at certain values of the center-of-mass scattering angle which are essentially independent of the energy.