Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach

TL;DR

This paper extends the Bethe-Salpeter formalism to calculate light meson spectra with total angular momentum J=3, enabling the study of Regge trajectories and comparing theoretical predictions with experimental data.

Contribution

It introduces calculations for J=3 states in the Bethe-Salpeter approach, expanding the analysis of Regge trajectories for light mesons beyond previous J≤2 studies.

Findings

Linear Regge trajectories for ρ- and φ-mesons within numerical accuracy

Discrepancies in other channels suggest the need for more sophisticated models

Highlights limitations of the rainbow-ladder approximation

Abstract

We extend the calculation of relativistic bound-states of a fermion anti-fermion pair in the Bethe-Salpeter formalism to the case of total angular momentum $J=3$. Together with results for $J \le 2$ this allows for the investigation of Regge trajectories in this approach. We exemplify such a study for ground and excited states of light unflavored mesons as well as strange mesons within the rainbow-ladder approximation. For the $\rho$- and $\phi$-meson we find a linear Regge trajectory within numerical accuracy. Discrepancies with experiment in other channels highlight the need to go beyond rainbow-ladder and to consider effects such as state mixing and more sophisticated quark-antiquark interaction kernels.