Antiproton-Nucleon Annihilation at Rest into Two Mesons andSU(6)Symmetry

We discuss extensively two-meson production processes in antiproton-nucleon annihilation at rest on the $\mathrm{SU}\left(6\right)\mathrm{}$ model. For the orbital angular momenta in the initial and final states we take the $s$ and the $p$ wave, respectively. The effects of the $\mathrm{SU}\left(3\right)\mathrm{}$-invariant interaction and of the first-order $\mathrm{SU}\left(3\right)\mathrm{}$-breaking interaction are taken into account. All the transition amplitudes are expressed in terms of five $\mathrm{SU}\left(6\right)\mathrm{}$-invariant amplitudes [seven in the case when the $\mathrm{SU}\left(3\right)\mathrm{}$-breaking effect is included]. These expressions could give a very convenient tool for a systematic analysis of the experimental results. We derive the relations between transition amplitudes and discuss several useful relations such as $\frac{\sigma (\overline{p}n\to {\pi }^0{\pi }^{-})}{k_{\pi }}=\frac{2\sigma (\overline{p}n\to K^0{K}^{-})}{k_K},$ $\frac{\sigma (\overline{N}N\to \eta \omega )}{k_{\eta \omega }}=\left(\frac{9}{25}\right)\frac{\sigma (\overline{N}N\to \eta \rho )}{k_{\eta \rho }},$ and $\sigma (\overline{N}N\to \pi \varphi )=\sigma (\overline{N}N\to \eta \varphi )=\sigma (\overline{N}N\to \rho \varphi )=\sigma (\overline{N}N\to \omega \varphi )=0\mathrm{}$ (where use is made of the usual $\omega -\varphi$ mixing parameter and $k$ is the relative momentum of the final two mesons).