Symmetry constraints in optimal polarization formalisms with an application to p− p scattering

Abstract

The paper contains results (a) for the general optimal polarization formalism with constraints from time reversal invariance, identical particles, and parity conservation, (b) for the specific reaction involving four spin- 1 2 particles, (c) for the application of the formalism to elastic p− p scattering at 6 GeV/c and at 800 MeV. The choice of the orientation axes under various symmetry constraints is discussed for the general optimal formalism, showing the narrowing of the choices which nevertheless retains an infinite continuum of possibilities. The transformation properties of amplitudes among these various optimal frames are specified. The transformation of observables among these frames is also discussed for the reaction with four spin- 1 2 particles. Then the relationship between the observables and the bilinear combination of amplitudes is given for the reaction with four spin- 1 2 particles, for the constraints of identical particles, identical particles and time reversal invariance, and identical particles and time reversal invariance and parity conservation. The results are applied to the analysis of the Argonne data at 6 GeV/c, t = −0.6 GeV 2/c 2, for elastic p− p scattering. The amplitudes are easily determined when the proper optimal frame is used, and the display of the amplitudes in other optimal frames suggest some features that may be significant in searching for dynamics. Another application is presented to 800 MeV elastic p− p scattering at several angles, showing that in the proper optimal frame very accurate results can be obtained about a subset of amplitude parameters on the basis of an incomplete set of data. Such an analysis is shown to be helpful in the design of future experiments.