Dynamics of the quark-antiquark interaction and the universality of Regge trajectories

The dynamical picture of a quark-antiquark interaction in light mesons, which provides linearity of radial and orbital Regge trajectories (RT), is studied with the use of the relativistic string Hamiltonian with flattened confining potential (CP) and taking into account three negative corrections: the gluon-exchange, the self-energy, and the string corrections. Due to the flattening effect the radial slope βn and the orbital slope βl of the Regge trajectories decrease by ∼30% as compared to those in linear CP, while the string correction decreases only the orbital slope by the value ∼10%. The self-energy correction is very important and has large magnitude, ∼-300 MeV for high excitations. It also provides the linearity of the RT, built for the centroid squared masses, and gives a small value of the intercept, β0=0.50(1) GeV2, equal to the squared centroid mass of ρ(1S). If the universal gluon-exchange potential without fitting parameters and screening function, as in heavy quarkonia, is taken, then the radial slope, βn=1.15(9) GeV2 (l≠0), and the orbital slope, βl=1.03(9) GeV2, have close values and the RT can be considered as approximately universal.