https://doi.org/10.1140/epja/s10050-026-01880-x
Regular Article - Theoretical Physics
Spectra of light and heavy mesons with 
in a relativistic Bethe–Salpeter approach
1
Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 16, 35392, Giessen, Germany
2
Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, Campus Gießen, 35392, Giessen, Germany
a
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Received:
7
November
2025
Accepted:
9
May
2026
Published online:
1
July
2026
Abstract
We extend the range of application of the relativistic Dyson–Schwinger/Bethe–Salpeter approach from previously discussed mesons with total angular momentum 
to the ones with 
. 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 
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.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Communicated by David Blaschke.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
