\pm 0.4$   $9.8 \pm 3.0$
   ${\cal B}(\ppp \to \rho \pi)~(10^{-4})$   $0.9 \pm 0.2$   $4.1 \pm 1.4$
  ----------------------------------------- --------------- ---------------

  : Predicted $\ppp \to \rho \pi$ partial widths and branching ratios for two solutions of mixing angle $\phi$.

An alternative mechanism discussed by Suzuki [@Suz01] for introducing an additional non-perturbative $\pp$ decay amplitude is mixing with a vector glueball state (first discussed in the context of $J/\psi$ decays [@glu]). In this case the $\ppp$ is permitted, but not required, to mix with the vector glueball, so there is no particular reason for the missing partial widths for $\pp$ decays to show up as corresponding $\ppp$ partial decay rates.

Gérard and Weyers [@GW] have proposed that the three-gluon decay of the $\pp$ is absent or suppressed, and that the $\pp$ decays to hadrons instead mainly via a two-step process involving an intermediate $c \bar c(^1P_1)$ state. Feldmann and Kroll [@FK] have proposed that the $J/\psi \to \rho \pi$ decay is [*enhanced*]{} (rather than $\pp \to
\rho \pi$ being suppressed) by mixing of the $J/\psi$ with light-quark states, notably $\omega$ and $\phi$. Both mechanisms do not imply any special role for $\ppp$ charmless decays. Arguments against them raised in the last of Refs.[@rhopi] 