Low-energy limit of the O(4) quark-meson model from the functional renormalization group approach

Jürgen Eser,Florian Divotgey,Mario Mitter,Dirk H Rischke

doi:10.1103/physrevd.98.014024

Abstract

We compute the low-energy limit of the $O(4)$-symmetric quark-meson model as an effective field theory for Quantum Chromodynamics within the Functional Renormalization Group (FRG) approach. In particular, we analyze the renormalization group flow of momentum-dependent pion self-interactions beyond the local potential approximation. The numerical results for these couplings obtained from the FRG are confronted with a recent tree-level study. Additionally, their effect on the wave-function renormalization and the curvature masses is investigated.

Highlights

The fundamental dynamics of the strong interaction is described by quantum chromodynamics (QCD)
The relevant flavor symmetry is given by SUðNfÞL × SUðNfÞR, the so-called chiral symmetry, which is further broken both explicitly and spontaneously
The experimentally observed hadrons can be grouped into the irreducible representations of SUðNfÞV ≡ SUðNfÞLþR, but not into those of SUðNfÞL × SUðNfÞR

Summary

Introduction

The fundamental dynamics of the strong interaction is described by QCD. In the case of Nf massless quark flavors, the classical Lagrangian of QCD possesses a globalSUðNfÞL × SUðNfÞR × Uð1ÞL × Uð1ÞR flavor symmetry.Due to an anomaly [1], the Uð1ÞL × Uð1ÞR part of the symmetry is broken to Uð1ÞV ≡ Uð1ÞLþR, which corresponds to quark number conservation. In the case of Nf massless quark flavors, the classical Lagrangian of QCD possesses a global. SUðNfÞL × SUðNfÞR × Uð1ÞL × Uð1ÞR flavor symmetry. Due to an anomaly [1], the Uð1ÞL × Uð1ÞR part of the symmetry is broken to Uð1ÞV ≡ Uð1ÞLþR, which corresponds to quark number conservation. The relevant flavor symmetry is given by SUðNfÞL × SUðNfÞR, the so-called chiral symmetry, which is further broken both explicitly and spontaneously. The experimentally observed hadrons can be grouped into the irreducible representations of SUðNfÞV ≡ SUðNfÞLþR, but not into those of SUðNfÞL × SUðNfÞR. This signals the spontaneous breakdown of chiral symmetry to its diagonal flavor subgroup SUðNfÞV. An immediate consequence of this symmetry-breaking mechanism is the occurrence of

Methods

Results

Conclusion