Rates for the reactions antiproton-proton --> pi phi and gamma phi

We study antiproton-proton annihilation at rest into $\pi\phi$ and $\gamma\phi$. Rescattering by $\overline{K^*}K+K^*\overline{K}$ and $\rho^{+}\rho^{-}$ for $\overline{p}p\rightarrow\pi\phi$ states is sizable, of order $(0.90\, {\rm to}\,2.6)\times 10^{-4}$ in the branching ratio, but smaller than experiment. For $\overline{p}p\rightarrow\gamma\phi$ the rescattering contributions are negligible, but the $\gamma\phi$ channel is well explained by a $\rho\phi$ intermediate state combined with vector meson dominance.