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

2025/10/31 by Stephan Hagel, Hagel, Stephan, Christian S. Fischer +5 · 1 voice
#hep-ph

paper · pdf · doi:10.48550/arxiv.2510.27423

Abstract

We extend the range of application of the relativistic Dyson-Schwinger/Bethe-Salpeter approach from previously discussed mesons with total angular momentum J ≤ 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^PC=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.

Discussions

• We extended functional calculations of mesons up to J=5. In the channels, for which the employed rainbow-ladder setup is known to work well, we observe Regge trajectories. We find that the "potentials [bsky, 0 points, 0 comments]

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