Using a well-established effective interaction in a rainbow-ladder truncation model of QCD, we fix the remaining model parameter to the bottomonium ground-state spectrum in a covariant Bethe-Salpeter equation approach and find surprisingly good agreement with the available experimental data including the 2^{--} Upsilon(1D) state. Furthermore, we investigate the consequences of such a fit for charmonium and light-quark ground states.Comment: 6 pages, 4 figures, 2 table

We investigate tensor mesons as quark-antiquark bound states in a fully covariant Bethe-Salpeter equation. As a first concrete step we report results for masses of J P C = 2 ++ mesons from the chiral limit up to bottomonium and sketch a comparison to experimental data. All covariant structures of the fermion-antifermion system are taken into account and their roles and importance discussed in two different bases. We also present the general construction principle for covariant Bethe-Salpeter amplitudes of mesons with any spin and find eight covariant structures for any J > 0.

We study hadronic decays of mesons and baryons in the context of the Dyson-Schwinger equations of QCD. Starting from a well-established effective interaction in rainbow-ladder truncation, we consistently calculate all ingredients of the appropriate decay diagrams. The resulting strong couplings are presented as functions of the quark mass from the chiral limit up to the respective decay thresholds. In particular, we investigate the \rho \pi \pi and for the first time the \Delta N \pi transitions. Both meson and baryon results compare well to available lattice QCD results as well as experimental data and present the first step towards a comprehensive covariant study of hadron resonances in the Dyson-Schwinger approach

The Bethe-Salpeter equation in QCD connects the gauge-dependent gluon and quark degrees of freedom with the gauge-invariant properties of mesons. We study the ρ meson mass and decay constant for various versions of the gauge-dependent input functions discussed in the literature, which start to differ generically below the hadronic scale, and show qualitative different infrared behavior. We find that, once the gauge-dependent quark-gluon vertex is permitted to vary as well, the ρ mass and decay constant is reproduced equally well for all forms investigated. A possible conclusion from this is that these ρ-meson properties are only sensitive to changes in the input at scales above a few hundred MeV.

In the functional approach to quantum chromodynamics, the properties of hadronic bound states are accessible via covariant integral equations, e.g. the Bethe–Salpeter equation for mesons. In particular, one has to deal with linear, homogeneous integral equations which, in sophisticated model setups, use numerical representations of the solutions of other integral equations as part of their input. Analogously, inhomogeneous equations can be constructed to obtain off-shell information in addition to bound-state masses and other properties obtained from the covariant analogue to a wave function of the bound state. These can be solved very efficiently using well-known matrix algorithms for eigenvalues (in the homogeneous case) and the solution of linear systems (in the inhomogeneous case). We demonstrate this by solving the homogeneous and inhomogeneous Bethe–Salpeter equations and find, e.g. that for the calculation of the mass spectrum it is as efficient or even advantageous to use the inhomogeneous equation as compared to the homogeneous. This is valuable insight, in particular for the study of baryons in a three-quark setup and more involved systems.

We discuss how to extract observables from an inhomogeneous vertex Bethe-Salpeter equation without resorting to the corresponding homogeneous equation. As an example we present a prediction for the $e^+e^-$ decay width of the $\rho(1450)$ or $\rho'$ meson. We also attempt to identify the momentum range contributing to a vector meson's decay constant.Comment: 3 pages, 3 figures, talk presented at the conference "Quark Confinement and the Hadron Spectrum IX", Madrid, Spain, 30th of August-3rd of September 2010; submitted to the proceeding

We analyze the chiral phase transition with the help of the QCD gap equation. Various models for the effective interaction in rainbow truncation are contrasted with regard to the resulting chiral transition temperatures. In particular, we investigate possible systematic relations of the details of the effective interaction and the value of Tc. In addition, we quantify changes to the transition temperature beyond the rainbow truncation.