Regge-like quark-antiquark excitations in the effective-action formalism

Radial excitations of the quark-antiquark string sweeping the Wilson-loop area are considered in the framework of the effective-action formalism. Identifying these excitations with the daughter Regge trajectories, we find corrections which they produce to the constituent quark mass. The energy of the quark-antiquark pair turns out to be mostly saturated by the constituent quark masses, rather than by the elongation of the quark-antiquark string. Specifically, while the constituent quark mass turns out to increase as the square root of the radial-excitation quantum number, the energy of the string increases only as the fourth root of that number.