Parametrizations of the Spin Density Matrix

TL;DR

This paper introduces two new parametrizations of the spin density matrix that inherently satisfy non-negativity constraints, facilitating more accurate data fits and analysis in various particle decay processes, with potential applications beyond the standard model.

Contribution

It presents two novel parametrizations of the spin density matrix that automatically fulfill non-negativity, along with methods to improve data fitting when the matrix rank is reduced, and discusses inferring matrix elements from decay widths.

Findings

Proposed parametrizations satisfy non-negativity without parameter bounds.

Developed methods for improved data fitting with low-rank density matrices.

Illustrated applications in strong and weak decays, relevant for beyond standard model physics.

Abstract

We propose for the spin density matrix two parametrizations which automatically fulfil 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.