Volume behavior of quark condensate, pion mass, and decay constant from Dyson-Schwinger equations

Luecker, Jan; Fischer, Christian; Williams, Richard

doi:10.1103/physrevd.81.094005

Cited by 45 publications

(37 citation statements)

References 51 publications

(87 reference statements)

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“…The results for periodic boundary conditions, on the other hand, are clearly incompatible with the ChPT results. A behavior similar to the one observed here has also been seen in Dyson-Schwinger calculations [33] and in quenched lattice simulations [34].…”

Section: The Quark-meson Modelsupporting

confidence: 74%

Finite-Volume Effects in Quantum Chromodynamics and Functional Renormalization Group Methods

Klein

2012

Few-Body Syst

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Quantum Chromodynamics (QCD) at finite temperature and density is currently a subject of great interest, due to both advances in experimental heavy-ion collisions and theoretical improvement of our understanding in recent years. Simulations of the theory on finite space-time lattices provide important theoretical advances. But in particular for investigating QCD phase transitions, finite quark masses and finite volumes in the simulations need to be taken into account. The investigation of finite-volume effects in QCD has a long tradition in the framework of chiral perturbation theory and random matrix theory and can provide useful tools for the analysis. With regard to a description of the chiral phase transition in QCD, it is very important to correctly take into account the effects of long-range fluctuations such as pions as the Goldstone bosons of spontaneous chiral symmetry breaking. It is natural to employ Renormalization Group methods for this purpose. Together with Hans-Jürgen Pirner, we have initiated work in this direction, and there has been an increasing interest in the investigation of such finite-volume effects. I will give an overview over recent developments.

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Section: The Quark-meson Modelsupporting

confidence: 74%

Finite-Volume Effects in Quantum Chromodynamics and Functional Renormalization Group Methods

Klein

2012

Few-Body Syst

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“…The comparison below L ≈ 2 − 3 fm is for illustrative purposes only, as the ChPT description is presumed to reach its limit of applicability. More recently, similar behavior has been observed in a calculation based on solutions of Dyson-Schwinger Equations (DSE) [135]. The authors attribute this to possible quenching effects, since the feedback of pions is not completely taken into account.…”

Section: Chiral Perturbation Theorysupporting

confidence: 69%

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

Klein

2017

Physics Reports

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Finite-volume effects in Quantum Chromodynamics (QCD) have been a subject of much theoretical interest for more than two decades. They are in particular important for the analysis and interpretation of QCD simulations on a finite, discrete space-time lattice. Most of these effects are closely related to the phenomenon of spontaneous breaking of the chiral flavor symmetry and the emergence of pions as light Goldstone bosons. These long-range fluctuations are strongly affected by putting the system into a finite box, and an analysis with different methods can be organized according to the interplay between pion mass and box size. The finite volume also affects critical behavior at the chiral phase transition in QCD. In the present review, I will be mainly concerned with modeling such finite volume effects as they affect the thermodynamics of the chiral phase transition for two quark flavors.I review recent work on the analysis of finite-volume effects which makes use of the quark-meson model for dynamical chiral symmetry breaking. To account for the effects of critical long-range fluctuations close to the phase transition, most of the calculations have been performed using non-perturbative Renormalization Group (RG) methods. I give an overview over the application of these methods to a finite volume. The method, the model and the results are put into the context of related work in random matrix theory for very small volumes, chiral perturbation theory for larger volumes, and related methods and approaches. They are applied towards the analysis of finite-volume effects in lattice QCD simulations and their interpretation, mainly in the context of the chiral phase transition for two quark flavors.

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“…Contrary to naive expectations, contributions from the zero-mode can enhance the chiral condensate in a finite volume, while for either choice of boundary condition chiral symmetry is restored in the small-volume limit and ultimately the condensate vanishes [31]. A similar effect in the pion mass has been observed in Dyson-Schwinger equations [72].…”

Section: Introductionmentioning

confidence: 79%

On the phase structure of QCD in a finite volume

2012

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The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.

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Volume behavior of quark condensate, pion mass, and decay constant from Dyson-Schwinger equations

Cited by 45 publications

References 51 publications

Finite-Volume Effects in Quantum Chromodynamics and Functional Renormalization Group Methods

Finite-Volume Effects in Quantum Chromodynamics and Functional Renormalization Group Methods

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

On the phase structure of QCD in a finite volume

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