Meson Production in Antiproton-Nucleon Annihilation

The antiproton-nucleon system at rest and its annihilation are discussed. Final states of two mesons, of many mesons with all but one in a vector resonance, and of two vector resonances are the main concern, although the decay to lepton pairs and other properties of the $\overline{p}$-nucleon system are also considered. The basic assumptions are that annihilations proceed mainly through an intermediate vector meson (${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ decay) or pseudoscalar meson (${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ decay) and also that $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry is valid for obtaining unknown coupling constants. The unknown parameters in the $\mathrm{SU}\left(3\right)\mathrm{}$ couplings are determined by fitting to experiment, with the following interesting results: $g_{\rho \mathrm{NN}}>~g_{\omega \mathrm{NN}}$ and $g_{{\eta }^{*}\mathrm{NN}}\approx -2\mathrm{}{g}_{\pi \mathrm{NN}}$, where ${\eta }^{*}$ refers to the 960-MeV $\eta \pi \pi$ resonance, and the above coupling constants for the $\rho$ and $\omega$ are the sum of the ${\gamma }_{\mu }$ and ${\sigma }_{\mu \nu }{q}_{\nu }$ coefficients. $g_{\rho \mathrm{NN}}\ge g_{\omega \mathrm{NN}}$ at $q^2=-4\mathrm{}{m}_{N^2}$ is shown to be consistent with nuclear-force calculations around $q^2=0\mathrm{}$, and the above value for $g_{{\eta }^{*}\mathrm{NN}}$ helps explain the rapid increase with energy of the proton Compton-scattering cross section. The $\mathrm{SU}\left(3\right)\mathrm{} \overline{B}\mathrm{BV}$ interaction is determined from the rates for ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ annihilations of $\overline{p}p$ to ${\pi }^{+}{\pi }^{-}{\pi }^0$, ${\pi }^{+}{\pi }^{-}$, $K^{+}{K}^{-}$, and $K_1{K}_2$, the $\mathrm{VVP}$ coupling from $\omega \to 3\pi$ and $\phi \to 3\pi$, and the $\overline{B}\mathrm{BP}$ interaction from the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ decays of $\overline{p}p$ to $K^{*}{\overline{K}}^{*}$, ${\rho }^0{\rho }^0$, and ${\rho }^0{\omega }^0$. We discuss briefly the relation of the $\mathrm{SU}\left(3\right)\mathrm{}$ couplings determined here and the results of broken $\mathrm{SU}\left(6\right)\mathrm{}$ and $U\left(12\right)\mathrm{}$. In particular, we show that $\frac{d}{f}=2\mathrm{}$ for $\overline{B}\mathrm{BV}$ at $q^2=-4\mathrm{}{m}_{N^2}$, in contradiction to the value $\frac{3}{2}$ given by $\mathrm{SU}\left(6\right)\mathrm{}$ and $U\left(12\right)\mathrm{}$; we also conclude that the $\frac{d}{f}$ ratio is not constant for the $\overline{B}\mathrm{BV}$ coupling. A table of relative rates and graphs of expected mass spectra are given for final states consisting of a vector resonance plus pseudoscalar meson, and a comparison with the available experimental evidence is made. The approximate agreement expected is observed. The discussion of the vector-vector final states leads to the prediction that $\Gamma (\overline{p}p\to {\rho }^0{\rho }^0)\approx \Gamma (\overline{p}p\to {\omega }^0{\omega }^0)$, and we also determine that $\frac{(\overline{p}p\to e^{+}{e}^{-})}{(\overline{p}p\to {\pi }^{+}{\pi }^{-})}\approx 2\times {10}^{-5\mathrm{}}$. Finally we conclude that the assumptions made are thus far consistent with experiment.