Hyperfine meson splittings: chiral symmetry versus transverse gluon exchange

Abstract

Meson spin splittings are examined within an effective Coulomb gauge QCD Hamiltonian incorporating chiral symmetry and a transverse hyperfine interaction necessary for heavy quarks. For light and heavy quarkonium systems the pseudoscalar-vector meson spectrum is generated by approximate Bardeen-Cooper- Schrieffer, random-phase approximation diagonalizations. This relativistic formulation includes both S and D waves for the vector mesons which generates a set of coupled integral equations. A smooth transition from the heavy to the light quark regime is found with chiral symmetry dominating the p-r mass difference. A reasonable description of the observed meson spin splittings and chiral quantities, such as the quark condensate and the p mass, is obtained. Similar comparisons with Tamm-Dancoff diagonalizations, which violate chiral symmetry, are deficient for light pseudoscalar mesons, indicating the need to simultaneously include both chiral symmetry and a hyperfine interaction. The hb mass is predicted to be around 9400 MeV, consistent with other theoretical expectations and above the unconfirmed 9300 MeV candidate. Finally, for comparison with lattice results, the J reliability parameter is also evaluated.