Spin Density Matrix of the $\omega$ in the Reaction $\bar{p} p \, \rightarrow \, \omega \pi^0$

TL;DR

This study measures the spin density matrix of the omega meson produced in antiproton-proton collisions, revealing strong spin alignment and oscillatory behavior across various energies, using two analysis methods for validation.

Contribution

It provides the first detailed measurement of the omega's spin density matrix in this reaction, employing both decay angular distributions and partial wave analysis for consistency.

Findings

Strong spin alignment of the omega observed.

Oscillatory dependence of matrix elements on production angle.

Maximum orbital angular momentum increases from 2 to 5 with energy.

Abstract

The spin density matrix of the $\omega$ has been determined for the reaction $\bar{p} p \, \rightarrow \, \omega \pi^0$ with unpolarized in-flight data measured by the Crystal Barrel LEAR experiment at CERN. The two main decay modes of the $\omega$ into $\pi^0 \gamma $ and $\pi^+ \pi^- \pi^0$ have been separately analyzed for various $\bar{p}$ momenta between 600 and 1940 MeV/c. The results obtained with the usual method by extracting the matrix elements via the $\omega$ decay angular distributions and with the more sophisticated method via a full partial wave analysis are in good agreement. A strong spin alignment of the $\omega$ is clearly visible in this energy regime and all individual spin density matrix elements exhibit an oscillatory dependence on the production angle. In addition, the largest contributing orbital angular momentum of the $\bar{p}p$ system has been identified for the different beam momenta. It increases from $L^{max}_{\bar{p}p}$ = 2 at 600 MeV/c to $L^{max}_{\bar{p}p}$ = 5 at 1940 MeV/c.