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

Abstract

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 and taking into account the self-energy and string corrections. Due to the flattening effect both slopes, $β_n$ of the radial and $β_l$ of the orbital RT, decrease by $\sim 30\%$ with the value of $β_n=1.30(5)$~GeV$^2$ being larger than $ β_l=0.95(5)$~GeV. The self-energy correction provides the linearity of RT and remains important up to very high excitations; the string correction decreases the slope of the orbital RT, while the intercept $β_0=0.51(1)~ $GeV$^2$ is equal to the squared centroid mass of $ρ(1S)$. If the universal gluon-exchanged potential without fitting parameters and screening function, as in heavy quarkonia, is taken, then the slope of the radial RT decreases, $β_n=1.15(8)$~GeV$^2$, and its value coincides with the slope of the orbital RT, $β_l=1.08(8)$~GeV$^2$ within theoretical errors, producing the universal RT.