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 γp → K + reaction can be estimated without ambiguity. To this end, data from the GRAAL collaboration and simulations 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 simulations 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.

Hunting the Resonances in \(p(\gamma ,K^{ + })\Lambda \): (Over) Complete Measurements and Partial-Wave Analyses

“…[1,8] The extraction of the δ i is more challenging as it requires data for at least four double-polarization observables [9]. We have shown in Refs.…”

“…We have shown in Refs. [1,8] that a mathematically complete set does not allow one to unambiguously extract the phases of the NTA. Indeed, for data with finite error bars, continuous and discrete ambiguities hamper the extraction of the phases.…”

“…[1]. In an amplitude analysis, one extracts the transversity amplitudes from a given set of observables in a modelindependent way.…”

“…The observables are related to the complex reaction amplitudes by bilinear relations [1]. Since the expressions for the asymmetries are invariant under the scaling operation Λ data (UD) in the bin 1.86 ≤ W ≤ 1.88 GeV.…”

“…The direction of the x-axis is such that the x-component of the meson momentum is positive. It has been pointed out [1] that with the eye on amplitude extraction the so-called transversity basis offers great advantages over all other common choices for the quantization axes. It is defined as…”