Constituent string model for hybrid mesonic excitations

The model for hybrid excitations of the QCD string with quarks is presented starting from the perturbation theory in the nonperturbative background. The propagation of a system containing $q \bar q$-pair and gluon is considered. The simplified version of the Hamiltonian, including both long-range nonperturbative interaction and Coulomb force, is derived. The masses of the lowest $q \bar q g$ hybrids are evaluated, and numerical results for the spectra are listed.