Meson Resonances in a Dyson-Schwinger Approach

Modern hadron physics offers exciting challenges to both experiment and theory. The theoretical challenge is to calculate and explain the properties of hadrons from quantum chromodynamics (QCD). Confinement is an eminent property of quarks and gluons, which appears at large distances between quarks. To pin down its origin in QCD is difficult; one approach is to study the long-range part of the strong interaction between quarks, an investigation to be performed on extended systems, such as meson excitations. An important characteristic of meson excitations is their (hadronic) decay width, the property of a resonance. Dyson-Schwinger equations (DSEs) are a nonperturbative continuum approach to QCD. Hadrons are studied in this framework of infinitely many coupled integral equations with the help of a systematic, symmetry-preserving truncation scheme. In particular, the solution of the quark Dyson-Schwinger equation and the Bethe-Salpeter equation (BSE) for a quark-antiquark system are used to describe mesons in a quantum-field theoretical setting. In such a scheme all symmetries associated with conservation laws are preserved, e. g. chiral symmetry and its dynamical breaking are incorporated in a model-independent way via the axial-vector Ward-Takahashi identity. This leads to exact results like a massless pion in the chiral limit. The first step in such a scheme is the rainbow- ladder (RL) truncation. Realistic models in this truncation have been used successfully to study pseudoscalar and vector meson ground states. However, in order to satisfactorily describe states in other meson channels such as scalar or axial-vector mesons as well as radial excitations, terms beyond the RL truncation must be employed as well. A number of studies with simple models beyond RL truncation have demonstrated improvement and called for a more sophisticated study. While such a calculation would yield more reliable results, the explicit inclusion of hadronic decay channels in the kernel of a meson resonance`s Bethe-Salpeter equation is still neglected. This proposal aims at a more complete study, where both terms beyond RL truncation as well as explicit decay channels are included in the kernel of the BSE. The goal is to quantify the effects from such a procedure and to put them into perspective with respect to each other. This will produce reliable statements about the various excitations of meson ground states including those with "exotic" quantum numbers. As an intermediate step, the calculation of hadronic meson decay widths in an impulse approximation consistent with the RL truncation is planned. This technique will also be employed to study meson decays in finite-temperature QCD. Furthermore, the Bethe-Salpeter amplitude of the pion will be used to calculate hadronic contributions to quantum electrodynamics (QED) processes.

Modern hadron physics offers exciting challenges to both experiment and theory. The theoretical challenge is to calculate and explain the properties of hadrons from quantum chromodynamics (QCD). Confinement is an eminent property of quarks and gluons, which appears at large distances between quarks. To pin down its origin in QCD is difficult; one approach is to study the long-range part of the strong interaction between quarks, an investigation to be performed on extended systems, such as meson excitations. An important characteristic of meson excitations is their (hadronic) decay width, the property of a resonance. Dyson-Schwinger equations (DSEs) are a nonperturbative continuum approach to QCD. Hadrons are studied in this framework of infinitely many coupled integral equations with the help of a systematic, symmetry-preserving truncation scheme. In particular, the solution of the quark Dyson-Schwinger equation and the Bethe-Salpeter equation (BSE) for a quark-antiquark system are used to describe mesons in a quantum-field theoretical setting. In such a scheme all symmetries associated with conservation laws are preserved, e. g. chiral symmetry and its dynamical breaking are incorporated in a model-independent way via the axial-vector Ward-Takahashi identity. This leads to exact results like a massless pion in the chiral limit. The first step in such a scheme is the rainbow- ladder (RL) truncation. Realistic models in this truncation have been used successfully to study pseudoscalar and vector meson ground states. However, in order to satisfactorily describe states in other meson channels such as scalar or axial-vector mesons as well as radial excitations, terms beyond the RL truncation must be employed as well. A number of studies with simple models beyond RL truncation have demonstrated improvement and called for a more sophisticated study. While such a calculation would yield more reliable results, the explicit inclusion of hadronic decay channels in the kernel of a meson resonance`s Bethe-Salpeter equation is still neglected. This proposal aims at a more complete study, where both terms beyond RL truncation as well as explicit decay channels are included in the kernel of the BSE. The goal is to quantify the effects from such a procedure and to put them into perspective with respect to each other. This will produce reliable statements about the various excitations of meson ground states including those with "exotic" quantum numbers. As an intermediate step, the calculation of hadronic meson decay widths in an impulse approximation consistent with the RL truncation is planned. This technique will also be employed to study meson decays in finite-temperature QCD. Furthermore, the Bethe- Salpeter amplitude of the pion will be used to calculate hadronic contributions to quantum electrodynamics (QED) processes.