Bethe-Salpeter-Motivated Modelling of Pseudo-Goldstone Pseudoscalar Mesons

TL;DR

This paper models light pseudoscalar mesons as fermion-antifermion bound states using an approximation to the Bethe-Salpeter formalism that incorporates relativistic effects and effective interactions, aligning well with observed meson properties.

Contribution

It introduces a Bethe-Salpeter-inspired approach that accounts for relativistic effects and pseudo-Goldstone nature in modeling light pseudoscalar mesons, providing accurate predictions of their properties.

Findings

Predicted meson masses and decay constants match experimental data.

Effective interactions successfully incorporate pseudo-Goldstone characteristics.

Light-quark-mass values are consistent with expectations.

Abstract

We apply a description of bound states of fermion and antifermion by means of our approximation to the Bethe-Salpeter formalism that retains part of the information on relativistic effects provided by the full fermion propagator to the lightest pseudoscalar mesons. Therein, the pseudo-Goldstone nature of the latter quark-antiquark bound states is taken into account by appropriately formulated effective interactions. Scrutinizing the predictions of this bound-state approach for meson masses, decay constants and in-meson condensates by relying on a generalized Gell-Mann-Oakes-Renner relation shows that the light-quark-mass values required for agreement are all in the right ballpark.