Masses of q22 states in a Bethe-Salpeter model

Londergan, J. T. ; Mitra, A. N. (1987) Masses of q22 states in a Bethe-Salpeter model Few-Body Systems, 2 (2). pp. 55-70. ISSN 0177-7963

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Ground-state masses of q22 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 αs. Apart from the quark masses, the confining interaction is characterized by three basic parameters: (i) a universal spring constant ω0; (ii) a constant C020, 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 q22 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 u22,s 22 and c22 states, respectively. We discuss the prospects for these states to be seen experimentally. In the case of the s22 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 c22 state might also be visible as a ψψ resonance with an appreciable width.

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