Abstract
We extend our recent computation of the low-energy limit of the linear O(4) Quark-Meson Model. The present analysis focuses on the transformation of the resulting effective action into a nonlinearly realized effective pion action, whose higher-derivative interaction terms are parametrized by so-called low-energy couplings. Their counterparts in the linear model are determined from the Functional Renormalization Group flow of the momentum-dependent four-pion vertex, which is calculated in a fully O(4)-symmetric approximation by including also momentum-dependent {\sigma}{\pi} interactions as well as {\sigma} self-interactions. Consequently, these higher-derivative couplings are dynamically generated solely from quark and meson fluctuations, initialized at a hadronic scale. Despite our restriction to low-energy degrees of freedom, we find that the qualitative features of the fluctuation dynamics allow us to comment on the range of validity and on appropriate renormalization scales for purely pionic effective models.
Highlights
A time-honored possibility to study the low-energy regime of the theory of strong interactions, quantum chromodynamics (QCD), is given by effective field theories (EFTs)
In a recent work [4], we studied the low-energy limit of the Oð4Þ linear sigma models (LSMs) coupled to quarks, the so-called quarkmeson model (QMM), within the functional renormalization group (FRG) approach
We studied the low-energy limit of the Oð4Þ QMM within the FRG approach by transforming the corresponding effective action into an effective pion theory
Summary
A time-honored possibility to study the low-energy regime of the theory of strong interactions, quantum chromodynamics (QCD), is given by effective field theories (EFTs). In this approach, one investigates QCD-inspired effective models that describe the interactions of the relevant low-energy degrees of freedom (d.o.f.), namely, those of hadrons. In order to capture the low-energy dynamics of the strong interaction properly, the construction of these models is mainly based on the internal and spacetime symmetries of QCD and their possible breaking. In the context of low-energy models for QCD, the most central symmetry is given by the chiral SUðNfÞL × SUðNfÞR symmetry accidentally arising from the quark sector of the QCD Lagrangian.
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