\Gamma(\ppp \to \gamma + \chi_{c0})$ is expected to be highly suppressed if $\ppp$ is a pure D-wave state, but could be enhanced by mixing [@Zhu; @KR; @YNY; @KL; @B88].

The “missing decay modes” of the $\pp$ [@psip], such as $\rho \pi$ and $K^* \bar K + {\rm~c.c.}$, are a long-standing puzzle [@rhopi; @Suz; @fsi; @GW; @FK]. Recently Suzuki [@Suz01] showed that if a $\pp$ decay amplitude due to coupling to virtual (but nearly on-shell) charmed particle pairs interferes destructively with the standard three-gluon amplitude, the suppression of these (and other) modes in $\pp$ final states can be understood. We pursue this suggestion further in Section III using the $\pp$–$\ppp$ mixing model described earlier. We propose that as a result of coupled-channel effects the expected decay width $\Gamma(\pp \to \rho \pi) \simeq 0.5$ keV and other “missing” modes could show up as corresponding partial widths in $\ppp$ decays, possibly enhanced by a considerable factor depending on the mixing angle. Since the latter state has a total width nearly 100 times that of the $\pp$, each of these partial widths still corresponds to a small branching ratio.

If coupling to charmed particle pairs is responsible for mixing the $\pp$ and the $\ppp$, 