The $\xi(2220)$ Revistited

Abstract

We calculated the decay widths of the $1^3F_2$ and $1^3F_4$ $s\bar{s}$ mesons and compared them to the measured properties of the $\xi(2220)$ (now known as the $f_4(2220)$). Including previously neglected decay modes we found that the width of the $^3F_2$ state $s\bar{s}$ meson is much larger than previously believed making this explanation unlikely. On the other hand the predicted width of the $^3F_4$ state, although broader than the observed width, is consistent within the uncertainties of the model. This interpretation predicts large partial widths to $K K^*(892)$ and $K^*(892) K^*(892)$ final states which should be looked for. A second possibility that would account for the different properties of the $\xi(2220)$ seen in different experiments is that two hadronic states exist at this mass. The first would be a broader $^3F_4$ $s\bar{s}$ state which is seen in hadron beam experiments while the second would be a narrow state with high glue content seen in the gluon rich $J/\psi$ radiative decay. Further experimental results are needed to sort this out.