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Register a new userGlobal Dyson-Schwinger-Bethe-Salpeter Approach to Mesons with Open Flavour
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Exploiting an interplay of the Bethe-Salpeter equation enabling us to regard mesons as bound states of quark and antiquark and the Dyson-Schwinger equation controlling the dressed quark propagator, we amend existing studies of quarkonia by a comprehensive description of open-flavour mesons composed of all conceivable combinations of quark flavour. Employing throughout a fixed set of model parameters, we predict some basic characteristics of these mesons, i.e., their masses, leptonic decay constants and corresponding in-hadron condensates entering in a generalized formulation of the Gell-Mann-Oakes-Renner relation.
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Recently, we completed a comprehensive investigation of a huge part of the entire meson spectrum by considering both quarkonia and open-flavour mesons by means of a single common framework which unites the homogeneous Bethe-Salpeter equation that describes mesons as quark-antiquark bound states and the Dyson-Schwinger equation that governs the full quark propagator: Adopting two (as a matter of fact, not extremely diverse) models that attempt to grasp all principal aspects of the effective strong interactions entering identically in both these equations, we derived within this unique setup, for all mesons analysed, their masses and leptonic decay constants as well as, for the pseudoscalar ones among these mesons, their in-hadron condensates. Here, as a kind of promotion or teaser, we give but a few examples of the resulting collections of data, laying the main emphasis on the dependence of our insights on the effective-interaction model underlying all such outcomes.
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.
We investigate the electromagnetic form factors of the Delta and the Omega baryons within the Poincare-covariant framework of Dyson-Schwinger and Bethe-Salpeter equations. The three-quark core contributions of the form factors are evaluated by employing a quark-diquark approximation. We use a consistent setup for the quark-gluon dressing, the quark-quark bound-state kernel and the quark-photon interaction. Our predictions for the multipole form factors are compatible with available experimental data and quark-model estimates. The current-quark mass evolution of the static electromagnetic properties agrees with results provided by lattice calculations.
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.
In theoretical hadron physics mesons are a center of attention. Constructed in a simpler way than baryons in the quark model, they still present a considerable challenge if one aims at an understanding of all their aspects in terms of quarks and gluons in the context of Quantum Chromodynamics, the quantum field theory of the strong interaction. Complementary to (constituent-) quark models, reductions of the Bethe-Salpeter equation, lattice QCD, and effective field theories, the Dyson-Schwinger-equation approach has emerged as a well-suited formalism for the covariant study of hadron properties. In particular, radially excited mesons exhibit a sensitivity to long-range strong-interaction physics. This sensitivity has recently been studied with the help of the Bethe-Salpeter equation. Here these studies are reviewed and continued together with an account of possible future developments.
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