Wednesday, March 13, 2013

1303.2936 (Tom Vrancx et al.)

The incompleteness of complete pseudoscalar-meson photoproduction    [PDF]

Tom Vrancx, Jan Ryckebusch, Tom Van Cuyck, Pieter Vancraeyveld
[Background] A complete set is a minimum set of observables which allows 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. In all realistic situations measuring a complete set of observables does not allow one to determine the reaction amplitudes with statistical significance.
View original: http://arxiv.org/abs/1303.2936

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