scholarly journals Aspects on Effective Theories and the QCD Transition

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 945
Author(s):  
Angel Gómez Nicola
Keyword(s):  
Phase Diagram ◽  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Chiral Symmetry ◽  
Current Knowledge ◽  
Chiral Symmetry Restoration ◽  
Chiral Perturbation ◽  
Ward Identities ◽  
Hadron Gas ◽  
Effective Theories

We review recent advances in the understanding of the Quantum Chromodynamics (QCD) transition and its nature, paying special attention to the analysis of chiral symmetry restoration within different approaches based on effective theories. After presenting some of the main aspects of the current knowledge of the phase diagram from the theoretical, experimental and lattice sides, we discuss some recent problems where approaches relying on effective theories have been particularly useful. In particular, the combination of ideas such as Chiral Perturbation Theory, unitarity and Ward Identities allows us to describe successfully several observables of interest. This is particularly relevant for quantities expected to be dominated by the light meson components of the hadron gas such as the scalar and topological susceptibilities. In addition, ward identities and effective Lagrangians provide systematic results regarding chiral and U ( 1 ) A partner degeneration properties which are of great importance for the interplay between those two transitions and the nature of chiral symmetry restoration. Special attention is paid to the connection of this theoretical framework with lattice simulations.

scholarly journals The Leutwyler–Smilga relation on the lattice

2019 ◽  
Vol 35 (01) ◽  
pp. 1950346 ◽  
Author(s):  
Gernot Münster ◽  
Raimar Wulkenhaar
Keyword(s):  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Effective Action ◽  
Lattice Spacing ◽  
Chiral Perturbation ◽  
Quark Masses

According to the Leutwyler–Smilga relation, in Quantum Chromodynamics (QCD), the topological susceptibility vanishes linearly with the quark masses. Calculations of the topological susceptibility in the context of lattice QCD, extrapolated to zero quark masses, show a remnant nonzero value as a lattice artefact. Employing the Atiyah–Singer theorem in the framework of Symanzik’s effective action and chiral perturbation theory, we show the validity of the Leutwyler–Smilga relation in lattice QCD with lattice artefacts of order a2 in the lattice spacing a.

scholarly journals COMPACT STARS IN HADRON AND QUARK-HADRON MODELS

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1455-1462 ◽  
Author(s):  
S. SCHRAMM ◽  
V. A. DEXHEIMER
Keyword(s):  
Phase Diagram ◽  
Neutron Star ◽  
Chiral Symmetry ◽  
Degrees Of Freedom ◽  
Dense Matter ◽  
Compact Stars ◽  
Chiral Symmetry Restoration ◽  
Hybrid Star ◽  
Nonlinear Realization ◽  
Model Approach

We investigate strongly interacting dense matter and neutron stars using a flavor-SU(3) approach based on a nonlinear realization of chiral symmetry. We study chiral symmetry restoration and the equation of state of stellar matter and determine neutron star properties using different sets of degrees of freedom. Finally, we include quarks in the model approach. We show the resulting phase diagram as well as hybrid star solutions for this model.

scholarly journals CHIRAL PERTURBATION THEORY WITH NUCLEONS

1992 ◽  
Vol 01 (03) ◽  
pp. 561-601 ◽  
Author(s):  
Ulf-G. Meißner
Keyword(s):  
Perturbation Theory ◽  
Chiral Symmetry ◽  
Chiral Perturbation Theory ◽  
Chiral Limit ◽  
Nuclear Forces ◽  
Chiral Perturbation ◽  
Chiral Structure ◽  
Quark Masses ◽  
Alternative Approach ◽  
Working Out

I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external momenta and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward–identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the method. Some processes which are discussed are threshold photopion production, low-energy Compton scattering off nucleons, πN scattering and the σ–term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon.

scholarly journals QCD beyond diagrams

2021 ◽  
Vol 36 (21) ◽  
pp. 2130012
Author(s):  
Michael Creutz
Keyword(s):  
Perturbation Theory ◽  
Symmetry Breaking ◽  
Quantum Chromodynamics ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Strong Interactions ◽  
Quark Confinement ◽  
Mass Generation ◽  
Diagrammatic Perturbation Theory

Quantum chromodynamics (QCD), the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation and chiral symmetry breaking. This paper is a colloquium level overview of the framework for understanding how these effects come about.

scholarly journals Hidden Local Symmetry and Effective Chiral Theory for Vector and Axial-vector Mesons

2007 ◽  
Vol 22 (07n10) ◽  
pp. 683-698 ◽  
Author(s):  
B. A. Li ◽  
Y. L. Wu
Keyword(s):  
Perturbation Theory ◽  
Chiral Symmetry ◽  
Chiral Perturbation Theory ◽  
Covariant Derivative ◽  
Local Symmetry ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Chiral Theory ◽  
Basic Parameters ◽  
Chiral Lagrangian

We present the effective chiral Lagrangian of mesons (peusodoscalars, vectors and axial-vectors) obtained in the chiral limit by using two approaches. The first approach is based on symmetries: the explicit global chiral symmetry and hidden local chiral symmetry. In this approach, it is noticed that there are in general fourteen interacting terms up to the dimension-four of covariant derivative for meson fields rather than the usual eleven interacting terms given in literature from hidden local symmetry approach. Of particular, the additional terms are found to be very important for understanding the vector meson dominance and providing consistent predictions on the decay rates of a1 → γπ and a1 → ρπ as well as for resulting a consistent effective chiral Lagrangian with chiral perturbation theory. The second approach is motivated from the chiral symmetry of chiral quarks and the bound state solutions of nonperturbative QCD at low energy and large Nc. The second approach is more fundamental in the sense that it is based on the QCD Lagrangian of quarks and only relies on two basic parameters in addition to the ones in the standard model. As a consequence, it allows us to extract, in terms of only two basic parameters, all the fourteen parameters in the more general effective Lagrangian constructed from symmetries in the first approach. It is surprising to note that except the necessity of three additional new interacting terms introduced in this paper, the resulting values of the coupling constants for other three interacting terms at the dimension-four are also quite different from the ones given in the literature. It is likely that the structures of the effective chiral Lagrangian for the dimension-four given in the literatures by using hidden local symmetry are incomplete and consequently the resulting coulpings are not reliable. It is shown that the more general effective chiral Lagrangian given in the present paper shall provide a more consistent prediction for all the low energy phenomenology of ρ - a1 system and result in a more consistent description on the low energy behavior of light flavor mesons. Its fourteen parameters up to the dimension-four of covariant derivative may be uniquely determined from the effective chiral theory based on the second approach, which is consistent with the chiral perturbation theory.

scholarly journals Contribution of QCD condensates to the OPE of Green functions of chiral currents

2019 ◽  
Vol 199 ◽  
pp. 05025
Author(s):  
Tomáš Kadavý ◽  
Karol Kampf ◽  
Jiří Novotný
Keyword(s):  
Perturbation Theory ◽  
Operator Product Expansion ◽  
High Energy ◽  
Operator Product ◽  
Green Functions ◽  
Chiral Perturbation ◽  
Unknown Parameters ◽  
Energy Behaviour ◽  
Intrinsic Parity ◽  
Effective Theories

A framework of operator product expansion (OPE) allows us to study high-energy behaviour of Green functions. A calculation of such Green functions within chiral perturbation theory (χPT) or resonance chiral theory (RχT) and subsequent matching of the result to the OPE enables us to determine constraints for unknown parameters of the effective theories. We present such procedure for Green functions in the odd-intrinsic parity sector of QCD.

scholarly journals QCD phase diagram from chiral symmetry restoration: analytic approach at high and low temperature using the Linear Sigma Model with Quarks

2018 ◽  
Vol 64 (3) ◽  
pp. 302 ◽  
Author(s):  
Luis Hernandez ◽  
Alejandro Ayala ◽  
Saul Hernandez-Ortiz
Keyword(s):  
Phase Diagram ◽  
Chiral Symmetry ◽  
Low Temperatures ◽  
Sigma Model ◽  
Chemical Potential ◽  
Linear Sigma Model ◽  
Transition Line ◽  
Chiral Symmetry Restoration ◽  
Qcd Phase Diagram ◽  
End Point

We use the linear sigma model with quarks to study the QCD phase diagram from the point of view of chiral symmetry restoration. We compute the leading order effective potential for high and low temperatures and finite quark chemical potential, up to the contribution of the ring diagrams to account for the plasma screening effects. We fix the values of the model couplings using physical values for the input parameters such as  the vacuum pion and sigma masses, the critical temperature at vanishing quark chemical potential and the conjectured end point value of the baryon chemical potential of the transition line at vanishing temperature. We find that the critical end point (CEP) is located at low temperatures and high quark chemical potentials $(\mu^{\text{CEP}}>320\ {\mbox{MeV}},T^{\text{CEP}}<40\ {\mbox{MeV}})$.

Renormalisation II: Improving perturbation theory

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Perturbation Theory ◽  
Critical Phenomena ◽  
Renormalisation Group ◽  
Green Functions ◽  
Ward Identities ◽  
Generating Functional ◽  
Vacuum Polarisation ◽  
Quantum Action ◽  
Effective Theories

This chapter introduces the quantum action as the generating functional of 1PI Green functions. The Ward identities of QED are derived and the vacuum polarisation is calculated. The renormalisation group equations are introduced. Critical phenomena and Wilsonian effective theories are discussed.

scholarly journals Aspects of Chiral Symmetry

1997 ◽  
Vol 06 (02) ◽  
pp. 203-249 ◽  
Author(s):  
Volker Koch
Keyword(s):  
Perturbation Theory ◽  
Chiral Symmetry ◽  
Nuclear Physics ◽  
Sigma Model ◽  
Heavy Ion ◽  
Nonlinear Sigma Model ◽  
Chiral Perturbation ◽  
Ion Collisions ◽  
Linear And Nonlinear ◽  
Ultrarelativistic Heavy Ion Collisions

This article is an attempt to a pedagogical introduction and review into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.

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