Light mesons in the symmetric-vertex approximation

TL;DR

This paper calculates light meson spectra using a symmetry-preserving approach that includes fully-dressed quark-gluon vertices, resulting in predictions that align well with experimental data and improve upon previous models.

Contribution

The authors develop a symmetry-preserving method incorporating fully-dressed quark-gluon vertices in the Bethe-Salpeter framework for light mesons, extending previous approximations.

Findings

Meson masses agree well with experimental values.

Method improves upon rainbow-ladder approximation.

Extension to different quark masses maintains Ward-Takahashi identities.

Abstract

We compute the spectrum of light mesons, composed by up, down, and strange quarks, using a symmetry-preserving approximation that permits the inclusion of fully-dressed quark-gluon vertices in the key dynamical equations. This method is characterized by the use of the standard symmetric kinematic configuration as a seed in the corresponding Schwinger-Dyson equation, yielding finally the full kinematic dependence of all eight form factors composing the transversely-projected quark-gluon vertex. The extension of this approach to the case of distinct nonvanishing current quark masses is discussed, and the compatibility with the fundamental Ward-Takahashi identities demonstrated. The corresponding Bethe-Salpeter kernel is composed by three different diagrammatic structures, which may be deduced from the attendant quark gap equation by applying the standard "cutting" rules. The masses of the light mesons are computed by first determining the eigenvalue of the Bethe-Salpeter equation as a function of Euclidean momenta, and then using the Schlessinger extrapolation method to determine the Minkowski momentum for which this eigenvalue becomes unity. The resulting meson masses are in good agreement with experimental values, and substantially improve upon predictions from the rainbow-ladder approximation.