The optimal polarization formalism and partial waves

Abstract

In contrast to the usual partial-wave analysis ofobservables, in this paper the amplitude analysis of observables is combined with a partial-wave analysis ofamplitudes. Three optimal frames (helicity, transversity and the planar-transverse frame) are explored for the reaction 1/2+1/2→1/2+1/2, first the Lorentz invariance alone, and then, step by step, for the addition of parity conservation, time reversal invariance, and identical particles. The helicity system yields somewhat simpler results than the other two. It is shown that if polarization experiments allow an amplitude analysis, the number of angles (ort-values) at which data need to be collected in order to obtain partial waves up to a given fixed angular momentum is reduced by at least a factor of two. Results are also presented in the special case of the low-energy limit in which the number of amplitudes of significant size decreases. The way this occurs helps in selecting the most informative observables to measure at low energies.