Fixed-tDispersion Relations and Polarization in Pion-Nucleon Charge-Exchange Scattering

We evaluate the real parts of the pion-nucleon charge-exchange amplitudes using fixed-$t$ dispersion relations with the imaginary parts of the amplitudes found at low energy from partial-wave analysis and at high energy from a simple $s$-channel absorptive model. We find that the calculated polarization, though quantitatively somewhat small, has all the correct qualitative features.