Spin and Parity of theωMeson

The spin and parity of the $\omega$ meson have been determined to be $1^{-}$ by a quantitative comparison of the density of points on the Dalitz plot with the predicted density of points. The simplest matrix element for the $J=1^{-}$ meson (which predicts maximum density of points at the center of the Dalitz plot and zero density on the boundary) fits the data remarkably well. On the other hand, the simplest matrix elements for $1^{+}$ and $0^{-}$ mesons (both of which predict zero density at the center of the plot) do not fit at all. A quantitative treatment for higher $J$ values has not been attempted. However, the simplest matrix elements for $J=2^{+} \mathrm{and} 2^{-}$ also vanish at the center of the Dalitz plot, and are again inconsistent with the data.