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 π±p differential cross sections and polarizations and the π⁻p→π⁰n 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.