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.

arXiv comment35 pages, 12 figures; Version 2 has been accepted for publication in Phys. Rev. C

References in corpus (41)

• Extended Partial-Wave Analysis of piN Scattering Data
• Baryon spectroscopy
• Updated analysis of $\pi$N elastic scattering data to 2.1~GeV: The Baryon Spectrum
• Completeness Rules for Spin Observables in Pseudoscalar Meson Photoproduction
• Polarization Observables for Two-Pion Production off the Nucleon
• Well-established nucleon resonances revisited by double-polarization measurements
• Measurement of the beam asymmetry $\Sigma$ for ${\pi }^0$ and $\eta$ photoproduction on the proton at $E_{\gamma }=9$ GeV
• Study of $\eta$ and ${\eta }^{\prime }$ photoproduction at MAMI
• First measurement of the helicity asymmetry for $\gamma p\to p{\pi }^0$ in the resonance region
• Photoproduction Reactions and Non-Strange Baryon Spectroscopy
• Partial-Wave Analysis of Nucleon-Nucleon Elastic Scattering Data
• Beam asymmetry for pi+ and pi0 photoproduction on the proton for photon energies from 1.102 to 1.862 GeV
• Measurement of pi^0 photoproduction on the proton at MAMI C
• Accurate Test of Chiral Dynamics in the \boldmath$\vec{\gamma }p\to {\pi }^{0}p$ Reaction
• Polarization observables in vector meson photoproduction
• Photon beam asymmetry $\Sigma$ for $\eta$ and ${\eta }^{\prime }$ photoproduction from the proton
• Radiative pi0 photoproduction on protons in the Delta+(1232) region
• First measurement of the helicity asymmetry $E$ in $\eta$ photoproduction on the proton
• First Measurement of the Polarization Observable E in the $\vec{p}(\vec{\gamma },{\pi }^{+})n$ Reaction up to 2.25 GeV
• The N(1520) 3/2- helicity amplitudes from an energy-independent multipole analysis based on new polarization data on photoproduction of neutral pions
• Measurement of the Beam Asymmetry $\Sigma$ in the Forward Direction for pi0 Photoproduction
• Information Content of Polarization Measurements
• Amplitude ambiguities in pseudoscalar meson photoproduction
• Cross Section for $\gamma n\to {\pi }^{0}n$ measured at Mainz/A2
• Measurement of the ${}^{1}H$($\vec{\gamma }$, $\vec{p}$)${\pi }^0$ reaction using a novel nucleon spin polarimeter
• Differential Cross Section Measurements for $\gamma n\to {\pi }^{-}p$ Above the First Nucleon Resonance Region
• Ambiguities in the partial-wave analysis of pseudoscalar-meson photoproduction
• Beam Asymmetry $\mathbf{\Sigma }$ for the Photoproduction of $\eta$ and ${\eta }^{\prime }$ Mesons at ${\mathbf{E}}_{\gamma }=8.8$GeV
• First measurement of the polarization observable $E$ and helicity-dependent cross sections in single ${\pi }^0$ photoproduction from quasi-free nucleons
• Amplitude reconstruction from complete electroproduction experiments and truncated partial-wave expansions
• Exclusive photoproduction of ${\pi }^0$ up to large values of Mandelstam variables $s,t$ and $u$ with CLAS
• The incompleteness of complete pseudoscalar-meson photoproduction
• Exclusive ${\mathbf{\pi }}^0\mathbf{p}$ electroproduction off protons in the resonance region at photon virtualities 0.4~GeV${}^2$ $\le {\mathbf{Q}}^2\le 1$~GeV${}^2$
• Amplitude extraction in pseudoscalar-meson photoproduction: towards a situation of complete information
• Study of ambiguities in ${\pi }^{-}p\to \Lambda K^0$ scattering amplitudes
• Differential cross section and photon beam asymmetry for the gamma p -> pi+ n reaction at forward pi+ angles at Egamma=1.5-2.95 GeV
• Complete experiments in pseudoscalar meson photoproduction revisited
• Photon asymmetry measurements of $\overrightarrow{\gamma }\mathrm{p}\to {\pi }^0\mathrm{p}$ for E${}_{\gamma }$=320$-$650 MeV
• Complete set of observables for photoproduction of two pseudoscalars on a nucleon
• The complete experiment problem of pseudoscalar meson photoproduction in a truncated partial wave analysis
• Complete sets of observables in pseudoscalar-meson photoproduction

Cited by in corpus (5)

• Light Baryon Spectroscopy
• Light baryon resonances from a coupled-channel study including $\mathbf{K\Sigma }$ photoproduction
• Coupled-channel analysis of pion- and eta-electroproduction with the Jülich-Bonn-Washington model
• Minimal complete sets for two pseudoscalar meson photoproduction
• New graphical criterion for the selection of complete sets of polarization observables and its application to single-meson photoproduction as well as electroproduction