As it is well-known for a long time now, the observables in a single-channel scattering problem remain invariant once the amplitude is multiplied by an overall phase. This phase is generally allowed to depend on a full set of independent kinematic variables for the considered process. For a 2-body reaction, this means that the phase can depend on energy and angle.
For partial wave analysis problems, ambiguities that originate from a phase rotation are generally referred to as continuum ambiguities. However, once partial waves are extracted by fitting a polynomial amplitude in a truncated partial wave analysis (TPWA), so-called discrete ambiguities are also known to occur. The names of both types of ambiguities refer to the regions in amplitude space where the observables are unchanged. Such can be either continuously connected regions, or sets of discrete points.
This talk will elaborate the effect that general full continuum ambiguities, i.e. arbitrary phase rotations, have on the level of partial waves. Then, also discrete ambiguities in TPWA problems are illustrated and formalized. Finally, the connections between both types of ambiguities are worked out. All illustrations proceed on simple toy-model examples for spinless 2 → 2 scattering.