Possible ambiguities in πN phase-shift analysis

Possible ambiguities in the reconstruction of πN scattering amplitudes from experimental data and the elastic unitarity condition below the threshold of inelastic processes are discussed. Discussion is restricted to partial waves with l = 0 and 1 and it is shown that certain twofold ambiguities can occur if only two experimental quantities are measured (the cross section plus polarization or one of the polarization parameters). It is also shown that these ambiguities can be removed by a further measurement, unless the polarization happens to be zero or the experiment is performed at an unfortunately chosen angle, for which both sets of amplitudes predict the same value for the corresponding experimental quantity