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

## TL;DR

This paper investigates the quark-antiquark interaction in light mesons using a relativistic string Hamiltonian, demonstrating how confining potential flattening and corrections influence Regge trajectories and support their universality.

## Contribution

It introduces a model incorporating flattened confining potential, self-energy, and string corrections to explain the linearity and universality of Regge trajectories in light mesons.

## Key findings

- Both radial and orbital Regge slopes decrease by ~30% due to flattening.
- Self-energy correction maintains linearity of Regge trajectories at high excitations.
- Universal gluon-exchanged potential yields similar slopes for radial and orbital 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, $\beta_n$ of the radial and $\beta_l$ of the orbital RT, decrease by $\sim 30\%$ with the value of $\beta_n=1.30(5)$~GeV$^2$ being larger than $ \beta_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 $\beta_0=0.51(1)~ $GeV$^2$ is equal to the squared centroid mass of $\rho(1S)$. 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, $\beta_n=1.15(8)$~GeV$^2$, and its value coincides with the slope of the orbital RT, $\beta_l=1.08(8)$~GeV$^2$ within theoretical errors, producing the universal RT.