Rotating QCD string and the meson spectrum

Abstract

The spectra of light-light and heavy-light mesons are described by spinless Salpeter equation and Dirac equation respectively, which predict linear dependence of the meson mass squared M^2 on angular momentum J and number of radial nodes n. Both spectra are computed by the WKB method and shown to agree with exact numerical data within few percent even for the lowest levels. The drawback of Salpeter and Dirac equation is that (inverse) Regge slopes do not coincide with the string ones, 2\pi\sigma and \pi\sigma respectively, because the string dynamics is not taken into account properly. The lacking string rotation is introduced via effective Hamiltonian derived from QCD which generates linear Regge trajectories for light mesons with the correct string slope.