The $\xi (2220)$ Revistited

Abstract

We calculated the decay widths of the $1^3{F}_2$ and $1^3{F}_4$ $s\bar{s}$ 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 ${}^3{F}_2$ state $s\bar{s}$ meson is much larger than previously believed making this explanation unlikely. On the other hand the predicted width of the ${}^3{F}_4$ state, although broader than the observed width, is consistent within the uncertainties of the model. This interpretation predicts large partial widths to $K{K}^{\ast }(892)$ and $K^{\ast }(892)K^{\ast }(892)$ 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 ${}^3{F}_4$ $s\bar{s}$ 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.

Revised version to be published in Phys. Rev. D. Minor changes. Latex file uses revtex version 3 and epsfig, 3 postcript figures are attached. The full postcript version with embedded figures is available at ftp://ftp.physics.carleton.ca/pub/theory/godfrey/ocipc9511.ps.Z

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