Masses of Light Flavor Mesons using Bethe-Salpeter Approach

TL;DR

This paper uses the Bethe-Salpeter and Dyson-Schwinger equations with specific truncations to calculate the spectrum of light mesons, ensuring chiral symmetry is preserved and employing the Padé approximation for mass extraction.

Contribution

It introduces a consistent truncation scheme for light meson spectrum calculation using Bethe-Salpeter and Dyson-Schwinger equations with the Maris-Tandy model and vertex choices, maintaining gauge symmetry.

Findings

Consistent truncations yield reliable meson mass predictions.

The Padé approximation effectively locates meson poles.

Vertex choices impact the spectrum results.

Abstract

This work employs the approach based on the Bethe-Salpeter and Dyson-Schwinger equations to study the light meson spectrum. The Dyson-Schwinger equation of the quark propagator is truncated using the Maris-Tandy model for the dressed gluon propagator, which incorporates both the infrared enhancement and the perturbatively correct ultraviolet behavior. Additionally, for the dressed quark-gluon vertex, we apply its bare form and the Ball-Chiu model, which minimally satisfies the constraint imposed by the gauge symmetry through its Ward-Green-Takahashi identity. Consistent truncation of both Bethe-Salpeter and Dyson-Schwinger equations requires that axial-vector Ward-Takahashi identity, arising from chiral symmetry of the Lagrangian of quantum chromodynamics, must not be violated. We utilize this identity as an additional constraint to truncate the Bethe-Salpeter equation and examine the impact of two choices of quark-gluon vertex, along with the application of the Maris-Tandy model on the light meson spectrum. To extract the masses of flavored and unflavored light mesons, we solve the inhomogeneous Bethe-Salpeter equation using the Pad$\acute{e}$ approximation, which enables us to locate the poles of the Bethe-Salpeter amplitude without requiring a numerical solution in the timelike region of momentum space. We find that truncations of the Bethe-Salpeter equation based on bare and Ball-Chiu vertices, coupled with the Maris-Tandy model, yield consistent results.