Ambiguities in model-independent partial-wave analysis

Partial-wave analysis is an important tool for analyzing large data sets in hadronic decays of light and heavy mesons. It commonly relies on the isobar model, which assumes multihadron final states originate from successive two-body decays of well-known undisturbed intermediate states. Recently, analyses of heavy-meson decays and diffractively produced states have attempted to overcome the strong model dependences of the isobar model. These analyses have overlooked that model-independent, or freed-isobar, partial-wave analysis can introduce mathematical ambiguities in results. We show how these ambiguities arise and present general techniques for identifying their presence and for correcting for them. We demonstrate these techniques with specific examples in both heavy-meson decay and pion-proton scattering.