Masses of Light Flavor Mesons using Bethe-Salpeter Approach
Iqra Liaqat, Faisal Akram
TL;DR
The paper addresses nonperturbative light-flavor meson spectroscopy in QCD using a continuum framework based on Dyson-Schwinger equations for the quark propagator and Bethe-Salpeter equations for meson bound states. It employs the Maris-Tandy model for the dressed-gluon interaction and compares truncations with a bare quark–gluon vertex (rainbow-ladder) and a Ball-Chiu vertex that preserves the axial-vector Ward-Takahashi identity, enabling a symmetry-consistent study of both pseudoscalar and vector channels. The authors use the inhomogeneous BSE together with a Padé approximation to locate poles, extracting ground-state masses such as $m_ \approx 0.139$ GeV, $m_K \approx 0.47$ GeV, and $m_\rho \approx 0.80$ GeV, and they verify consistency between the RL and BC truncations under the MT kernel. The work demonstrates that symmetry-preserving truncations within the DSE/BSE framework can yield reliable light-meson spectra and sets a foundation for extending the kernel beyond RL to study scalar and vector channels with improved accuracy.
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.