The linear meson model and chiral perturbation theory

Jungnickel, D.-U.; Wetterich, C.

doi:10.1007/s100520050161

Cited by 18 publications

(27 citation statements)

References 8 publications

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“…Upcoming studies will also shed more light on the relation to ChPT, where this work can be understood as an extension of Refs. [5,6]. In particular, it would be very interesting if the computed low-energy couplings of the QMM and related effective theories, like the extended LSM [31], are consistent with the low-energy limit of QCD (the latter is formalized by means of the LECs in ChPT).…”

Section: Discussionmentioning

confidence: 99%

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Dynamical generation of low-energy couplings from quark-meson fluctuations

2019

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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 σπ interactions as well as σ 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.

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Section: Discussionmentioning

confidence: 99%

“…After its calculation from the FRG flow, the effective action of the QMM has been reduced to an effective pion action by integrating out the σ field, similarly to Refs. [5,6]. In this action, the higher-derivative terms are parametrized by the low-energy couplings of the O(4)…”

Section: Introductionmentioning

confidence: 99%

Dynamical generation of low-energy couplings from quark-meson fluctuations

2019

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“…In general, the Euclidean Lagrangian of the mesonic sector with a global chiral U (N f ) L × U (N f ) R flavor symmetry has the form [32][33][34]…”

Section: U (1)a-symmetry Breaking In Chiral Modelsmentioning

confidence: 99%

Fluctuations and the axial anomaly with three quark flavors

Mitter

Schaefer

2014

Phys. Rev. D

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The role of the axial anomaly in the chiral phase transition at finite temperature and quark chemical potential is investigated within a non-perturbative functional renormalization group approach. The flow equation for the grand potential is solved to leading-order in a derivative expansion of a three flavor quark-meson model truncation. The results are compared with a standard and an extended mean-field analysis, which facilitates the exploration of the influence of bosonic and fermionic fluctuations, respectively, on the phase transition. The influence of U(1)_A-symmetry breaking on the chiral transition, the location of a possible critical endpoint in the phase diagram and the quark mass sensitivity is studied in detail.Comment: 12 pages, 11 figures, accepted versio

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“…It is an effective model for dynamical chiral symmetry breaking below a scale Λ ≃ 1.5 GeV, where a description of QCD in terms of hadronic degrees of freedom is valid. Although the linear sigma-model by itself is not compatible with the low-energy ππ-scattering data, due to the presence of quarks the low energy constants of chiral perturbation theory are reproduced [16].…”

Section: Renormalization Group Flow Equationsmentioning

confidence: 86%

Volume Dependence of the Pion Mass from Renormalization Group Flows

Klein¹,

Braun²,

Pirner³

2005

AIP Conference Proceedings

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We investigate finite volume effects on the pion mass and the pion decay constant with renormalization group (RG) methods in the framework of a phenomenological model for QCD. An understanding of such effects is important in order to interpret results from lattice QCD and extrapolate reliably from finite lattice volumes to infinite volume. We consider the quark-meson-model in a finite Euclidean 3+1 dimensional volume. In order to break chiral symmetry in the finite volume, we introduce a small current quark mass. In the corresponding effective potential for the meson fields, the chiral O(4)-symmetry is broken explicitly, and the sigma and pion fields are treated individually. Using the proper-time renormalization group, we derive renormalization group flow equations in the finite volume and solve these equations in the approximation of a constant expectation value. We calculate the volume dependence of pion mass and pion decay constant and compare our results with recent results from chiral perturbation theory in finite volume.Comment: 9 pages, 3 figures, talk given at "Hadronic Physics 2004 - Joint meeting Heidelberg-Liege-Paris-Rostock", to appear in the proceedings, AIP conference serie

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The linear meson model and chiral perturbation theory

Cited by 18 publications

References 8 publications

Dynamical generation of low-energy couplings from quark-meson fluctuations

Dynamical generation of low-energy couplings from quark-meson fluctuations

Fluctuations and the axial anomaly with three quark flavors

Volume Dependence of the Pion Mass from Renormalization Group Flows

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