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

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

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