Moravcsik's theorem on complete sets of polarization observables reexamined

Abstract

We revisit Moravcsik's theorem on the unique extraction of amplitudes from polarization observables, which has been originally published in 1985. The proof is (re-) written in a more formal and detailed way and the theorem is corrected for the special case of an odd number of amplitudes (this case was treated incorrectly in the original publication). Moravcsik's theorem, in the modified form, can be applied in principle to the extraction of an arbitrary number of $N$ helicity amplitudes. The uniqueness theorem is then applied to hadronic reactions involving particles with spin. The most basic example is Pion-Nucleon scattering ($N=2$), the first non-trivial example is pseudoscalar meson photoproduction ($N=4$) and the most technically involved case treated here is given by pseudoscalar meson electroproduction ($N=6$). The application of Moravcsik's theorem to electroproduction yields new results, which for the first time provide insights into the structure and content of complete sets for this particular process. The uniqueness-statements for the various reactions are compared and an attempt is made to recognize general patterns, which emerge under the application of the theorem.