The incompleteness of complete pseudoscalar-meson photoproduction

Abstract

[Background] A complete set is a minimum set of observables which allows one to determine the underlying reaction amplitudes unambiguously. Pseudoscalar-meson photoproduction from the nucleon is characterized by four such amplitudes and complete sets involve single- and double-polarization observables. [Purpose] Identify complete sets of observables, and study how measurements with finite error bars impact their potential to determine the reaction amplitudes unambiguously. [Method] The authors provide arguments to employ the transversity representation in order to determine the amplitudes in pseudoscalar-meson photoproduction. It is studied whether the amplitudes in the transversity basis for the $\gamma p\to K^{+}\Lambda$ reaction can be estimated without ambiguity. To this end, data from the GRAAL collaboration and mock data from a realistic model are analyzed. [Results] It is illustrated that the moduli of normalized transversity amplitudes can be determined from precise single-polarization data. Starting from mock data with achievable experimental resolution, it is quite likely to obtain imaginary solutions for the relative phases of the amplitudes. Also the real solutions face a discrete phase ambiguity which makes it impossible to obtain a statistically significant solution for the relative phases at realistic experimental conditions. [Conclusions] Single polarization observables are effective in determining the moduli of the amplitudes in a transversity basis. Determining the relative phases of the amplitudes from double-polarization observables is far less evident. The availability of a complete set of observables does not allow one to unambiguously determine the reaction amplitudes with statistical significance.

15 pages, 6 figures, 8 tables

References in corpus (4)

• Measurement of beam-recoil observables Ox, Oz and target asymmetry for the reaction gamma p -> K Lambda
• A Bayesian analysis of kaon photoproduction with the Regge-plus-resonance model
• Measurements of polarized photo-pion production on longitudinally polarized HD and Implications for Convergence of the GDH Integral
• Information Content of Polarization Measurements

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• The complete experiment problem of pseudoscalar meson photoproduction in a truncated partial wave analysis
• Amplitude- and truncated partial-wave analyses combined: A novel, almost theory-independent single-channel method for extracting photoproduction multipoles directly from measured data
• On the spin-observables in pseudoscalar meson photoproduction
• Complete sets of observables in 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
• Incompleteness of complete kaon photoproduction