Masses of Light Flavor Mesons using Bethe-Salpeter Approach

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.