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

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.

9 pages, 3 figures; Based on materials of the contribution "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT*, October 19-23, 2009

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• Infrared and Ultraviolet QCD dynamics with quark mass for J=0,1 mesons

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• Effects of a dressed quark-gluon vertex in pseudoscalar heavy-light mesons
• Aspects of open-flavour mesons in a comprehensive DSBSE study
• Accounting for the analytical properties of the quark propagator from Dyson-Schwinger equation
• Mass spectrum of pseudo-scalar glueballs from a Bethe-Salpeter approach with the rainbow-ladder truncation
• Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach
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• Poincare covariant pseudoscalar and scalar meson spectroscopy in Wigner-Weyl phase
• Charming quasi-exotic open-flavor mesons
• Quasi-exotic open-flavor mesons
• Extending the truncated Dyson-Schwinger equation to finite temperatures
• Pseudo-scalar {\boldm $q\bar{q}$} bound states at finite temperatures within a Dyson-Schwinger--Bethe-Salpeter approach
• S- and D-wave vector charmonia