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We propose for the spin density matrix two parametrizations whichautomatically fulfil the non-negativity conditions, without setting any boundon the parameters. The first one relies on a theorem, that we prove, and it israther simple and easily adaptable to some specific reactions, where, forexample, parity is conserved or angular momentum conservation entails selectionrules. Moreover, in the case when the rank is less than the order of thedensity matrix, we show how to improve the fits to the data, either byimplementing previous suggestions, or by elaborating an alternative method, forwhich we prove a second theorem. Our second parametrization is a variant ofprevious treatments, it appears suitable for some particular processes.Moreover, we discuss about the possibility of inferring the elements of thedensity matrix from the differential decay width. Last, we illustrate variousexamples of current interest, both in strong and weak decays; some of them maybe helpful in the investigation of physics beyond the standard model.

Parametrizations of the Spin Density Matrix