Meson Properties in a Dyson-Schwinger Approach

Dyson-Schwinger equations (DSEs) are a nonperturbative continuum approach to quantum chromodynamics (QCD). Hadrons are studied in this framework of infinitely many coupled integral equations with the help of a coherent truncation scheme. In particular, the solution of the quark Dyson-Schwinger equation and the Bethe- Salpeter equation for a quark-antiquark system are used to describe mesons in a Poincaré-covariant way. Chiral symmetry and its dynamical breaking are incorporated model-independently via the axial-vector Ward-Takahashi identity. This leads to exact results like a massless pion in the chiral limit. While realistic models in rainbow-ladder truncation have been used successfully to study pseudoscalar and vector meson ground- and recently radially excited states, axial-vector mesons are not described satisfactorily in this truncation. Simple exploratory studies beyond rainbow-ladder approximation indicate that such steps involving realistic models will lead to improved descriptions of axial-vector mesons and reliable predictions about the so-called "exotic`` mesons. These, in contrast to a quantum mechanical framework, arise naturally as quark-antiquark bound states in a DSE approach. Furthermore, recent studies of pseudoscalar meson radial excitations have shown that investigations of the spectra and properties of these states can restrict models of the quark-(anti)quark interaction at large distances and thereby provide insight into the confinement mechanism. The aim of this project is to study these possibilities in detail, both in simple models for higher-lying states as well as by taking realistic steps beyond the rainbow-ladder truncation. The aims of the project fit well into the frame of present and future research at the Institut für Physik at the University of Graz. Progress toward these aims will contribute to various aspects of the current research in the field as well as the research of the different groups (few-body systems, lattice gauge theory, and Dyson-Schwinger- equation studies of QCD Green functions) at the institute.

Dyson-Schwinger equations (DSEs) are a nonperturbative continuum approach to quantum chromodynamics (QCD). Hadrons are studied in this framework of infinitely many coupled integral equations with the help of a coherent truncation scheme. In particular, the solution of the quark Dyson-Schwinger equation and the Bethe- Salpeter equation for a quark-antiquark system are used to describe mesons in a Poincaré-covariant way. Chiral symmetry and its dynamical breaking are incorporated model-independently via the axial-vector Ward-Takahashi identity. This leads to exact results like a massless pion in the chiral limit. While realistic models in rainbow-ladder truncation have been used successfully to study pseudoscalar and vector meson ground- and recently radially excited states, axial-vector mesons are not described satisfactorily in this truncation. Simple exploratory studies beyond rainbow-ladder approximation indicate that such steps involving realistic models will lead to improved descriptions of axial-vector mesons and reliable predictions about the so-called "exotic`` mesons. These, in contrast to a quantum mechanical framework, arise naturally as quark-antiquark bound states in a DSE approach. Furthermore, recent studies of pseudoscalar meson radial excitations have shown that investigations of the spectra and properties of these states can restrict models of the quark-(anti)quark interaction at large distances and thereby provide insight into the confinement mechanism. The aim of this project is to study these possibilities in detail, both in simple models for higher-lying states as well as by taking realistic steps beyond the rainbow-ladder truncation. The aims of the project fit well into the frame of present and future research at the Institut für Physik at the University of Graz. Progress toward these aims will contribute to various aspects of the current research in the field as well as the research of the different groups (few-body systems, lattice gauge theory, and Dyson-Schwinger- equation studies of QCD Green functions) at the institute.