Completeness rules for spin observables in pseudoscalar meson photoproduction

Abstract

The number and type of measurements needed to ascertain the amplitudes for pseudoscalar meson photoproduction are analyzed in this paper.It is found that 8 carefully selected measurements can determine the four transversity amplitudes without discrete ambiguities. That number of measurements is one less than previously believed. We approach this problem in two distinct ways: (1) solving for the amplitude magnitudes and phases directly; and (2) using a bilinear helicity product formulation to map an algebra of measurements over to the well-known algebra of the 4 × 4 Gamma matrices. It is shown that the latter method leads to an alternate proof that 8 carefully chosen experiments suffice for determining the transversity amplitudes completely. In addition, Fierz transformations of the Gamma matrices are used to develop useful linear and nonlinear relationships between the spin observables. These relationships not only help in finding complete sets of experiments, but also yield important constraints between the 16 observables for this reaction. Typeset using REVT E XRecently, Keaton and Workman (KW) [2] argued that selecting a complete set of observables is more complicated than the above BDS rule. However, KW were not able to provide sufficient conditions for resolving all ambiguities. Their work inspired us to investigate the problem of determining which experiments can provide a "complete set," e.g. those

Production of η and η′ mesons on nucleons and nuclei

“…Cross section data alone, even with improved precision, can certainly not solve this problem since a unique description of photoproduction of a single pseudoscalar meson off nucleons requires the measurement of at least eight carefully selected observables [87].…”

Single-energy amplitudes for pion photoproduction in the first resonance region

“…An amplitude reconstruction requires more observables [5], and is the most model-independent method, but results in transversity amplitudes, for each energy-angle pair, only up to an unknown phase. If multipoles are the goal, an angular integral is required, and this cannot be performed without determining the phase.…”

“…As these do not constitute a complete experiment, in the strict sense of Ref. [5], some assumptions are required. The fits were performed between 280 MeV and 420 MeV, using a truncated multipole expansion, including E 0+ , M 1− , E 1+ , and M 1+ , the remaining terms assumed to be real and given by the electric Born terms.…”

Measurement of the double polarization observable E in the reactionγp→pη′

“…The former two resonances are not listed in the Particle Data Tables and could contribute to the missing resonances, if they exist. In order to ascertain an unambiguous solution for a partial wave analysis, the measurement of at least 8 single and double polarization observables is required [6]. One of the observables describing the helicity asymmetry is E and can be obtained using a circularly polarized photon beam in combination with a longitudinally polarized target.…”