Masses of q²q̅² states in a Bethe-Salpeter model

Abstract

Ground-state masses of q²q̅² states ("true" and "mock" baryonium) are investigated in the framework of a Bethe-Salpeter formalism motivated from QCD. The four-particle system is described by pairwise interactions between qq or qq̅ pairs with a spectator approximation for the non-interacting pair. The quark-quark interactions are Coulomb plus harmonic interactions; the harmonic terms have been modified to produce linear confinement for heavier quarks, in agreement with experimental spectra. The confining interaction is proportional to the strong coupling constant α_s. Apart from the quark masses, the confining interaction is characterized by three basic parameters: (i) a universal spring constant ω₀; (ii) a constant C₀/ω²₀, which defines the vacuum structure; (iii) a constant A₀, which provides a smooth transition from quadratic to linear confinement as one goes from light to heavy quark systems. These three constants [ω₀ = 0.158 GeV;C₀ = 0.296;A₀ = 0.0283] have been shown to produce excellent fits to all quarkonia states [qq̅, qQ̅,QQ̅] as well as baryon spectra (qqq); thus our predictions for q²q̅² states contain no free parameters. In this model, the L = 0 ground states occur in the range 1.8–2 GeV, 2.15–2.3 GeV and 6.72–6.75 GeV for u²u̅²,s ²s̅² and c²c̅² states, respectively. We discuss the prospects for these states to be seen experimentally. In the case of the s²s̅² state, this is likely to have a rather narrow width, and may correspond to the X(2.22 GeV) meson observed in radiative decays of the J/ψmeson. The c²c̅² state might also be visible as a ψψ resonance with an appreciable width.