Evaluation of an incompletely measured spin density matrix
Shai Dagan, Yossef Dothan · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1982
A method for the determination of the density matrix of a resonant state using incomplete measurements pertaining to its decay is developed. In order to define the bounds on the density-matrix elements, the positivity and rank conditions are used. The method proceeds in two steps. First one obtains a particular density matrix which satisfies the positivity and rank conditions and reproduces the experimental data. This matrix is calculated by maximizing the information entropy. Then using this matrix as a starting point and the tolerance of the data presented by the experimental errors, the actual bounds on the density-matrix elements are found by means of a parametrization which assures both positivity and the rank condition. The method was successfully tested on data for $f$ production in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}f+n$ at 12 GeV/c and the subsequent decay $f\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}$.