Spin Density Matrix For Spin-3/2 Particles

TL;DR

This paper introduces a Cartesian parametrization of the spin density matrix for spin-3/2 particles, facilitating calculations of hadron polarizations in high energy reactions.

Contribution

It provides a new Cartesian form of the spin density matrix for spin-3/2 particles and derives equations linking spin polarizations, aiding in polarization calculations.

Findings

Derived four equations relating spin polarizations.

Presented probabilistic interpretations of spin polarizations.

Applied the framework to electron-positron annihilation.

Abstract

The description of particles with spin can be attained by using a spin density matrix in high energy reaction. In this paper we present a parametrization of the spin density matrix for spin -3/2 particles in the Cartesian form. Comparing the standard form which is given by the spherical tensor operator with the Cartesian form yields four equations for the spin polarizations. These four equations can be used to eliminate the dependent spin polarizations. We also present the probabilistic interpretations of these spin polarizations by defining the spin operator in the spherical coordinate frame. These results can be used in the cross section to calculate the hadron polarizations. To illustrate this, we calculate the inclusive electron-positron annihilation process in terms of spin polarizations.