Fermi-Yang model of mesons based on a relativistic obe model

Abstract

Nucleon-antinucleon (N N ) bound states are calculated in the framework of relativistic quantum mechanics. The potential is taken from a previous investigation of the nucleon-nucleon (NN) interaction due to the exchange of the π, η, σ, ϵ, ϱ and ω mesons with parameters fitted to the NN phase shifts and to the deutron. The N N interactions is given from that of the NN system by changing the sign of the π and ω exchange contributions as a result of crossing symmetry. This way the ω exchange gives rise to a repulsive core for NN and to short-range attractive forces for N N . In contrast to similar calculations by other authors we obtain N N bound states below 1000 MeV in the partial waves bearing the quantum numbers of the input mesons. In addition, there are bound states, mostly between 1000 MeV and threshold, corresponding to the φ, ϱ′, δ, A 1, A 2, f, f′ and B mesons. The uncoupled L = J partial waves contain at most one bound state. The coupled L = J ± 1 partial waves 3S 1 − 3D 1 and 3P 2 − 3F 2 contain two T = 0 bound states which reflect the mixed singlet-octet mesons ω, φ and f,f′. Most of the calculated bound states are close to the corresponding experimentally observed mesons, but the bound states corresponding to the ϱ and ω and the fictitious σ mesons appear at negative energies. For the ω and σ mesons this is mainly due to the large π exchange contribution. The N N bound state spectrum calculated from pure ω exchange is for a somewhat larger ωN coupling constant than that given from the NN investigation in surprisingly good agreement with the physical (non-strange) meson spectrum if isospin degeneracy is considered.