Abstract
We discuss an approach for accessing bound state properties, like mass and decay width, of a theory within the functional renormalisation group approach. An important cornerstone is the dynamical hadronization technique for resonant interaction channels. The general framework is exemplified and put to work within the two-flavour quark-meson model. This model provides a low-energy description of the dynamics of two-flavour QCD with quark and hadronic degrees of freedom. We compare explicitly the respective results for correlation functions and observables with first principle QCD results in a quantitative manner. This allows us to estimate the validity range of low energy effective models. We also present first results for pole masses and decay widths. Next steps involving real-time formulations of the functional renormalisation group are discussed.
Highlights
The efforts of determining bound state properties in a quantum field theoretical approach date back to the seminal work of Bethe and Salpeter [1,2]
We have outlined an approach to the calculation of bound states within the Functional Renormalization Group
It is based on the procedure of dynamical hadronization, which comes with the great advantage that the information of bound states can be mapped to lower order n-point correlation functions in a systematic manner
Summary
The efforts of determining bound state properties in a quantum field theoretical approach date back to the seminal work of Bethe and Salpeter [1,2]. The study of highly relativistic bound states has been hampered by the fact that almost all quantitative nonperturbative methods rely on the Euclidean formulation of quantum field theory This implies that for determining bound state properties, the results for correlation functions have either to be continued to Minkowski space or have to be extracted from potentially subleading exponential tails of correlation functions. Such a unified approach resolves the challenge of self-consistent truncations, which is of crucial relevance in the DSE-BSE framework, by construction Another important ingredient is the fact, that the FRG has matured enough to sustain a systematic access to bound state properties. II dynamical hadronization within the FRG is briefly revisited Technical details as well as a comparison of results in different truncation levels are deferred to three appendixes
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