Spectra of light and heavy mesons with $J \le 5$ in a relativistic Bethe-Salpeter approach

TL;DR

This paper extends the relativistic Bethe-Salpeter approach to mesons with higher angular momentum ($J=4,5$), providing new tensor representations, exploratory spectra, and insights into Regge trajectories, while discussing model limitations.

Contribution

It introduces the first general Dirac tensor representations for $J=4,5$ mesons and applies a rainbow-ladder truncation to explore their spectra and Regge trajectories.

Findings

Predicted masses for ground state mesons with $J^{P,C}=3^{--}, 4^{++}, 5^{--}$.

Identified Regge trajectories in certain channels.

Highlighted the limitations of the rainbow-ladder truncation.

Abstract

We extend the range of application of the relativistic Dyson-Schwinger/Bethe-Salpeter approach from previously discussed mesons with total angular momentum $J \le 3$ to the ones with $J=4,5$. On a technical level, the new element is the general Dirac tensor representations for the latter which, to our knowledge, are presented here for the first time. As a first application, we provide an exploratory spectrum for these mesons in a rainbow-ladder truncation of Dyson-Schwinger and Bethe-Salpeter equations. We discuss the merits and limitations of this truncation and explore the shape of the heavy-quark potential corresponding to the underlying effective running coupling. With our predictions for the masses of ground state mesons with quantum numbers $J^{P,C}=3^{--}, 4^{++}, 5^{--}$ we identify Regge trajectories in channels where the interaction model can be trusted on a semi-quantitative level. In other channels, discrepancies with experiments confirm the well-known need to go beyond rainbow-ladder in the Dyson-Schwinger/Bethe-Salpeter approach by using more sophisticated interactions.