QCD string in light-light and heavy-light mesons

Abstract

The spectra of light-light and heavy-light mesons are calculated within the framework of the QCD string model, which is derived from QCD in the Wilson loop approach. Special attention is paid to the proper string dynamics that allows us to reproduce the straight-line Regge trajectories with the inverse slope being $2\ensuremath{\pi}\ensuremath{\sigma}$ for light-light and twice as small for heavy-light mesons. We use the model of the rotating QCD string with quarks at the ends to calculate the masses of several light-light mesons lying on the lowest Regge trajectories and compare them with the experimental data as well as with the predictions of other models. The masses of several low-lying orbitally and radially excited heavy-light states in the D, ${D}_{s},$ B, and ${B}_{s}$ mesons spectra are calculated in the einbein (auxiliary) field approach, which has proven to be rather accurate in various calculations for relativistic systems. The results for the spectra are compared with the experimental and recent lattice data. It is demonstrated that an account of the proper string dynamics encoded in the so-called string correction to the interquark interaction leads to an extra negative contribution to the masses of orbitally excited states that resolves the problem of the identification of the $D(2637)$ state recently claimed by the DELPHI Collaboration. For heavy-light system we extract the constants $\overline{\ensuremath{\Lambda}},$ ${\ensuremath{\lambda}}_{1},$ and ${\ensuremath{\lambda}}_{2}$ used in heavy quark effective theory and find good agreement with the results of other approaches.