Quarkonium fine-hyperfine splittings and the Lorentz structure of the confining potential with vacuum-polarization corrections

Within the framework of the Poggio-Schnitzer flavor-independent static-potential model with long-distance vacuum-polarization correction, we analyze the Lorentz-Dirac structure of the confinement potential with reference to the charmonium hyperfine splittings. In view of the questionable existence and/or doubtful identity of the X(2830) and chi(3455) states, we give preference to the Lorentz-Dirac character of the confinement potential in the form of an approximately equal admixture of scalar and vector components with no anomalous moment. This in turn predicts the 1S0 partners of psi and psi' to be near the 3.0- and 3.6-GeV mass regions, respectively. This also suggests the 1P1 state of charmonium is to be found above the 3P0 state near the mass region of 3.48 GeV