Baryonium with a phenomenological Skyrmion-type potential

In this paper, we investigate the nucleon-antinucleon static energies in the Skyrme model with the product Anzatz. The calculation shows that, in the ungroomed $S\overline{S}$ (Skyrmion and anti-Skyrmion) channel which leads to rapid annihilation, there exists a quasistable bound state which may give a natural explanation for the near-threshold enhancement in the proton-antiproton $(p\overline{p})$ mass spectrum reported by the BES Collaboration and the Belle Collaboration. Similar to the phenomenological well potential of the deuteron, we construct a phenomenological Skyrmion-type potential to study this narrow $p\overline{p}$-resonance in $J/\psi \to \gamma p\overline{p}$. By this potential model, a $p\overline{p}$ baryonium with small binding energies is suggested and the decay width of this state is calculated by WKB approximation. In this picture the decay is attributed to quantum tunneling and $p\overline{p}$ annihilation. Prediction on the decay mode from the baryonium annihilation at rest is also pointed out.

Figure 1

The static energy of the Skyrmion–anti-Skyrmion system, where $m_p^c$ is the classical single Skyrmion mass without quantum correction.

Figure 2

The Skyrmion-type potential of the $p\overline{p}$-system.