Parametrizations of the spin density matrix

E. Di Salvo (1) , Z.J. Ajaltouni (1)

1 LPC - Laboratoire de Physique de Clermont

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

Mots clés: strong interaction; parametrization; selection rule; 23.20.En; 23.20.Js; 23.40.Bw; 24.10.-i; Spin density matrix; New physics; spin: density matrix; angular momentum: conservation law; parity: conservation law; decay: weak interaction

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]

E. Di Salvo, Z.J. Ajaltouni. Parametrizations of the spin density matrix. Annals Phys., 2021, 428, pp.168448. ⟨10.1016/j.aop.2021.168448⟩. ⟨hal-03107960⟩