A. Krassnigg

Nucleon Mass from a Covariant Three-Quark Faddeev Equation

We report the first study of the nucleon where the full Poincaré-covariant structure of the three-quark amplitude is implemented in the Faddeev equation. We employ an interaction kernel which is consistent with contemporary studies of meson properties and aspects of chiral symmetry and its dynamical breaking, thus yielding a comprehensive approach to hadron physics. The resulting current-mass evolution of the nucleon mass compares well with lattice data and deviates only by ∼5% from the quark-diquark result obtained in previous studies.

Toward unifying the description of meson and baryon properties

We present a Poincare covariant Faddeev equation, which enables the simultaneous prediction of meson and baryon observables using the leading order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The solution describes a nucleons dressed-quark core. The evolution of the nucleon mass with current-quark mass is discussed. A nucleon-photon current, which can produce nucleon form factors with realistic Q{sup 2} evolution, is described. Axial-vector diquark correlations lead to a neutron Dirac form factor that is negative, with r{sub 1}{sup nu} > r{sub 1}{sup nd}. The proton electric-magnetic form factor ratio falls with increasing Q{sup 2}.

Perspective on rainbow-ladder truncation

Prima facie the systematic implementation of corrections to the rainbow-ladder truncation of QCDs Dyson-Schwinger equations will uniformly reduce in magnitude those calculated mass-dimensioned results for pseudoscalar and vector meson properties that are not tightly constrained by symmetries. The aim and interpretation of studies employing rainbow-ladder truncation are reconsidered in this light.

Spectra of heavy quarkonia in a Bethe-Salpeter-equation approach

In a covariant Bethe-Salpeter-equation approach and with a rainbow-ladder truncated model of QCD, we investigate the use of an effective interaction with the goal of reproducing QCD phenomenology. We extend previous studies and present results for ground and excited meson states in the bottomonium and charmonium systems, where the results are surprisingly good for most states. In addition, we formulate a critical outlook on states with exotic quantum numbers as well as the light-quark domain.

Rho-meson, Bethe-Salpeter equation, and the far infrared

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 themeson 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, themass and decay constant is reproduced equally well for all forms investigated. A possible conclusion from this is that these �-meson properties are only sensitive to changes in the input at scales above a few hundred MeV.

A covariant view on the nucleons' quark core

Abstract Established results for the quark propagator in Landau gauge QCD, together with a detailed comparison to lattice data, are used to formulate a Poincare-covariant Faddeev approach to the nucleon. The resultant three-quark amplitudes describe the quark core of the nucleon. The nucleon’s mass and its electromagnetic form factors are calculated as functions of the current quark mass. The corresponding results together with charge radii and magnetic moments are discussed in connection with the contributions from various ingredients in a consistent calculation of nucleon properties, as well as the role of the pion cloud in such an approach.

Schwinger functions and light-quark bound states

Abstract.We examine the applicability and viability of methods to obtain knowledge about bound states from information provided solely in Euclidean space. Rudimentary methods can be adequate if one only requires information about the ground and first excited state and assumptions made about analytic properties are valid. However, to obtain information from Schwinger functions about higher mass states, something more sophisticated is necessary. A method based on the correlator matrix can be dependable when operators are carefully tuned and errors are small. This method is nevertheless not competitive when an unambiguous analytic continuation of even a single Schwinger function to complex momenta is available.

ON THE COMPLEXION OF PSEUDOSCALAR MESONS

A strongly momentum-dependent dressed-quark mass function is basic to QCD. It is central to the appearance of a constituent-quark mass-scale and an existential prerequisite for Goldstone modes. Dyson-Schwinger equation (DSEs) studies have long emphasised this importance, and have proved that QCDs Goldstone modes are the only pseudoscalar mesons to possess a nonzero leptonic decay constant in the chiral limit when chiral symmetry is dynamically broken, while the decay constants of their radial excitations vanish. Such features are readily illustrated using a rainbow-ladder truncation of the DSEs. In this connection we find (in GeV): fηc(1S)=0.233, mηc(2S)=3.42; and support for interpreting η(1295), η(1470) as the first radial excitations of η(548), η′(958), respectively, and K(1460) as the first radial excitation of the kaon. Moreover, such radial excitations have electromagnetic diameters greater than 2 fm. This exceeds the spatial length of lattices used typically in contemporary lattice-QCD.

QCD chiral transition temperature in a Dyson-Schwinger-equation context

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 T{sub c}. In addition, we quantify changes to the transition temperature beyond the rainbow truncation.

First Look at Heavy–Light Mesons with a Dressed Quark–Gluon Vertex

Following up on earlier work, we investigate possible effects of a dressed quark–gluon vertex in heavy–light mesons. In particular, we study corrections to the popular rainbow-ladder truncation of the Dyson–Schwinger–Bethe–Salpeter equation system. We adopt a simple interaction kernel which reduces the resulting set of coupled integral equations to a set of coupled algebraic equations, which are solved numerically. In this way, we extend previous studies to quark–antiquark systems with unequal current-quark masses, at first for the pseudoscalar case, and investigate the resulting set of problems and solutions. We attempt to find patterns in—as well as to quantify corrections to—the rainbow-ladder truncation. In addition, we open this approach to phenomenological predictions of the heavy quark symmetry.