Masses ofq
2
\bar q
2 states in a Bethe-Salpeter model |
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Authors: | J T Londergan A N Mitra |
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Institution: | (1) Department of Physics and Nuclear Theory Center, Indiana University, 47405 Bloomington, IN, USA;(2) Department of Physics, Indiana University, 47405 Bloomington, IN, USA;(3) Present address: Department of Physics, University of Delhi, 110007 Delhi, India |
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Abstract: | Ground-state masses ofq
2
–2 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 betweenqq orq
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
s. Apart from the quark masses, the confining interaction is characterized by three basic parameters: (i) a universal spring constant
0; (ii) a constantC
0/
0
2
, which defines the vacuum structure; (iii) a constantA
0, which provides a smooth transition from quadratic to linear confinement as one goes from light to heavy quark systems. These three constants
0 = 0.158 GeV;C
0=0.296;A
0=0.0283] have been shown to produce excellent fits to all quarkonia states q
,q
,Q
] as well as baryon spectra (qqq); thus our predictions forq
2
2 states contain no free parameters. In this model, theL=0 ground states occur in the range 1.8–2 GeV, 2.15–2.3 GeV and 6.72–6.75 GeV foru
2
2,s
2
2 andc
2
2 states, respectively. We discuss the prospects for these states to be seen experimentally. In the case of thes
2
2 state, this is likely to have a rather narrow width, and may correspond to theX(2.22 GeV) meson observed in radiative decays of theJ/ meson. Thec
2
2 state might also be visible as a ![psgr](/content/r04326j875064528/xxlarge968.gif) resonance with an appreciable width.Research supported in part by the National Science Foundation under grant NSF-PHY 86-06364Research supported in part by the U.S. Department of Energy |
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Keywords: | |
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