Heavy pseudoscalar mesons in a Schwinger-Dyson--Bethe-Salpeter approach

TL;DR

This paper uses the Bethe-Salpeter formalism with momentum-dependent quark masses derived from Schwinger-Dyson equations to accurately compute the mass spectrum of heavy pseudoscalar mesons, including excited states.

Contribution

It introduces a numerical scheme that effectively describes ground and excited states of heavy pseudoscalar mesons within the Bethe-Salpeter approach with momentum-dependent quark masses.

Findings

Accurately describes $ ext{π}$, $K$, $D$, $D_s$, and $ ext{η}_c$ ground states.

Provides insights into excited pseudoscalar meson states.

Relates results to future experiments at FAIR.

Abstract

The mass spectrum of heavy pseudoscalar mesons, described as quark-antiquark bound systems, is considered within the Bethe-Salpeter formalism with momentum-dependent masses of the constituents. This dependence is found by solving the Schwinger-Dyson equation for quark propagators in rainbow-ladder approximation. Such an approximation is known to provide both a fast convergence of numerical methods and accurate results for lightest mesons. However, as the meson mass increases, the method becomes less stable and special attention must be devoted to details of numerical means of solving the corresponding equations. We focus on the pseudoscalar sector and show that our numerical scheme describes fairly accurately the $\pi$, $K$, $D$, $D_s$ and $\eta_c$ ground states. Excited states are considered as well. Our calculations are directly related to the future physics programme at FAIR.