Application of the quark-confining string to theψspectroscopy

We report the results of the nonrelativistic application of the quark-confining string model to the study of $\psi$ spectroscopy. This string model is defined by a relativistic-invariant, gauge-invariant, and reparametrization-invariant action describing quarks interacting with color SU(3) gauge fields. The model has no gluonic degrees of freedom, but has instead string degrees of freedom. Quark masses and the quark-gluon coupling constant are the only parameters of the model. In the Schrödinger limit and in the absence of light quarks, the longitudinal modes of the quark-antiquark pair and the rotational modes of the string for a meson reduce to the charmonium model with a linear potential. String vibrations, which are absent in the charmonium model, provide additional levels. They start coming in at around 4.0 GeV; the density of states increases as an exponential function of the mass. The two lowest vibrational levels in the $e^{+}{e}^{-}$ channel have energies at 4.0 GeV and 4.4 GeV. Relativistic corrections are estimated to be small for the low-lying states so that the Schrödinger approximation is justified. We consider this application to $\psi$ spectroscopy as a test of the model.