COMPLETENESS RULES FOR SPIN OBSERVABLES IN PSEUDOSCALAR MESON PHOTOPRODUCTION

The number and type of measurements needed to ascertain the amplitudes for pseudoscalar meson photoproduction are analyzed in this paper. It is found that eight carefully selected measurements can determine the four transversity amplitudes without discrete ambiguities. That numbe r of measurements is one less than previously believed. We approach th is problem in two distinct ways: (1) solving for the amplitude magnitu des and phases directly, and (2) using a bilinear helicity product for mulation to map an algebra of measurements over to the well-known alge bra of the 4x4 gamma matrices. It is shown that the latter method lead s to an alternate proof that right carefully chosen experiments suffic e for determining the transversity amplitudes completely. In addition, Fierz transformations of the gamma matrices are used to develop usefu l linear and nonlinear relationships between the spin observables. The se relationships not only help in finding complete sets of experiments , but also yield important constraints between the 16 observables for this reaction.