Dynamical regimes of the QCD string with light and heavy quarks

Abstract

The generalization of the effective action [1] of the quark--antiquark system in the confining vacuum is performed for the case of arbitrary quark masses. The interaction of quarks is described by the averaged Wilson loop for which we use the minimal area law asymptotics. The system is quantized by the path integral method and the quantum Hamiltonian is obtained. It contains not only quark degrees of freedom but also the string energy density. As well as in the equal masses case [1] two dynamical regimes are found [2]: for large orbital excitations ($l \gg 1$) the system is represented as rotating string, which leads to asymptotically linear Regge trajectories, while at small $l$ one obtains a potential-like relativistic or nonrelativistic regime. In the limiting cases of light-light and heavy-light mesons a unified description is developed [2]. For the Regge trajectories one obtains nearly straight-line patterns with the slope very close to $1/2 \pi \sigma$ and $1/ \pi\sigma$ correspondingly. The upper bound on the light quark(s) masses which doesn't change considerably this property of the trajectories is also found.