mutual coupling to charmed particle pairs is precisely the mixing discussed in the previous section. Let us assume that this mixing and the couplings of $\pp$ and $\ppp$ to $\rho \pi$ and $K \overline{K}^*(892) + {\rm c.c.}$ are such as to cancel the $\pp$ hadronic widths to these final states \[which are related to one another by flavor SU(3)\]. In this case we have $$\mat{\rho \pi}{\pp} =
\mat{\rho \pi}{2^3S_1} \cos \phi - \mat{\rho \pi}{1^3D_1} \sin \phi = 0~~,$$ = + = /   , so that [*the missing $\rho \pi$ (and related) decay modes of $\pp$ show up instead as decay modes of $\ppp$, enhanced by the factor of $1/\sin^2 \phi$*]{}. The possible effects of this enhancement are shown in Table IV for the two solutions for $\phi$. One expects ${\cal B}(\ppp \to \rho \pi) \simeq 10^{-4}$ for $\phi \simeq -27^\circ$ and $\simeq 4 \times 10^{-4}$ for the favored value $\phi \simeq 12^\circ$. Either branching ratio is compatible with the current upper bound ${\cal B}(\ppp \to \rho \pi) < 1.3 \times
10^{-3} \times[5~{\rm nb}/\sigma(\ppp)]$ [@Zhu].

  ----------------------------------------- --------------- ---------------
              $\phi$ ($^\circ$)              $- 27 \pm 2$     $12 \pm 2$
               $1/\sin^2 \phi$               $4.8 \pm 0.6$    $22 \pm 6$
      $\Gamma(\ppp \to \rho \pi)$ (keV)      $2.1 