Dynamical regimes of the QCD string with quarks

Abstract

The effective action of the quark-antiquark system at large distances is derived from QCD, implementing the minimal area law of the Wilson loop. The system is quantized by the path integral method and the quantum Hamiltonian is obtained. Two dynamical regimes are found: at large orbital excitations ( l⪢1) the system behaves as a string leading to linear Regge trajectories with a slope 1 2 πσ , while at small l one obtains a potential-like relativistic or nonrelativistic regime. The resulting spectra for these two regimes merge very smoothly and form a simple pattern of nearly straight-line Regge trajectories with a slope very close to (2 πσ) −1.