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Symmetry
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Chiral Symmetry in Physics
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Chiral Symmetry in Physics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 22714

Special Issue Editor

Prof. Dr. Dubravko Klabučar

E-Mail Website
Guest Editor
Department of Physics, University of Zagreb, Bijenicka c. 32, HR-10000 Zagreb, Croatia
Interests: particle physics, especially hadron physics and QCD
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetries have always been inspiring intellectually and aesthetically. In particular, importance of chiral symmetry has been overwhelming in modern physics - both as a guiding principle and as a practical tool for extracting the essentials of complicated emergent phenomena in several areas of physics.

Its breaking and its restoration, as well as its relation with axial UA(1) symmetry of QCD, provide many unifying themes of nuclear and particle physics, both in vacuum and in media with nonvanishing temperature and/or density.

The phenomenology of hadrons, the observable bound states of confined QCD fields, is dominated by approximate chiral symmetry and by its large dynamical breaking, which is responsible for almost all visible mass in the Universe.

This Special Issue thus invites especially contributions studying chiral symmetry and its dynamical breaking consistently related to anomalous UA(1) breaking and to confinement, another crucial feature of QCD.

Nevertheless, it remains open also to contributions from other pertinent areas, from condensed matter to physics beyond Standard Model to biophysics to quantum computers, whereby chiral symmetry exhibits the unity of physics.

Prof. Dr. Dubravko Klabučar
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • symmetry breaking: spontaneous, dynamical and explicit
  • Goldstone modes
  • nonperturbative dynamical mass
  • quark-antiquark condensate
  • nonperturbative QCD
  • chiral phase transition
  • chiral symmetry restoration

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Published Papers (7 papers)

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Research

Jump to: Review

8 pages, 259 KiB  
Article
Multifarious Roles of Hidden Chiral-Scale Symmetry: “Quenching” gA in Nuclei
by Mannque Rho
Symmetry 2021, 13(8), 1388; https://doi.org/10.3390/sym13081388 - 30 Jul 2021
Cited by 7 | Viewed by 1343
Abstract
I discuss how the axial current coupling constant gA renormalized in scale symmetric chiral EFT defined at a chiral matching scale impacts on the axial current matrix elements on beta decays in nuclei with and without neutrinos. The “quenched” gA observed [...] Read more.
I discuss how the axial current coupling constant gA renormalized in scale symmetric chiral EFT defined at a chiral matching scale impacts on the axial current matrix elements on beta decays in nuclei with and without neutrinos. The “quenched” gA observed in nuclear superallowed Gamow–Teller transitions, a long-standing puzzle in nuclear physics, is shown to encode the emergence of chiral-scale symmetry hidden in QCD in the vacuum. This enables one to explore how trace-anomaly-induced scale symmetry breaking enters in the renormalized gA in nuclei applicable to certain non-unique forbidden processes involved in neutrinoless double beta decays. A parallel is made between the roles of chiral-scale symmetry in quenching gA in highly dense medium and in hadron–quark continuity in the EoS of dense matter in massive compact stars. A systematic chiral-scale EFT, presently lacking in nuclear theory and potentially crucial for the future progress, is suggested as a challenge in the field. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
13 pages, 791 KiB  
Article
Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics
by David Blaschke, Kirill A. Devyatyarov and Olaf Kaczmarek
Symmetry 2021, 13(3), 514; https://doi.org/10.3390/sym13030514 - 21 Mar 2021
Cited by 1 | Viewed by 2166
Abstract
In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that [...] Read more.
In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with O(αs) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
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10 pages, 259 KiB  
Article
Perturbative RG Analysis of the Condensate Dependence of the Axial Anomaly in the Three-Flavor Linear Sigma Model
by Gergely Fejős
Symmetry 2021, 13(3), 488; https://doi.org/10.3390/sym13030488 - 16 Mar 2021
Cited by 1 | Viewed by 1572
Abstract
Coupling of ‘t Hooft’s determinant term is investigated in the framework of the three-flavor linear sigma model as a function of the chiral condensate. Using perturbation theory around the minimum point of the effective action, we calculate the renormalization group flow of the [...] Read more.
Coupling of ‘t Hooft’s determinant term is investigated in the framework of the three-flavor linear sigma model as a function of the chiral condensate. Using perturbation theory around the minimum point of the effective action, we calculate the renormalization group flow of the first field-dependent correction to the coupling of the conventional UA(1) breaking determinant term. It is found that, at low temperatures, mesonic fluctuations make the anomaly increase when the chiral condensate decreases. As an application, we analyze the effect at the zero temperature nuclear liquid–gas transition. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
35 pages, 2694 KiB  
Article
Empirical Consequences of Emergent Mass
by Craig D. Roberts
Symmetry 2020, 12(9), 1468; https://doi.org/10.3390/sym12091468 - 7 Sep 2020
Cited by 73 | Viewed by 4221
Abstract
The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The [...] Read more.
The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The source of all these things can be traced to emergent mass, which might itself be QCD’s self-stabilising mechanism. A background to this perspective is provided, presenting, inter alia, a discussion of the gluon mass and QCD’s process-independent effective charge and highlighting an array of observable expressions of emergent mass, ranging from its manifestations in pion parton distributions to those in nucleon electromagnetic form factors. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
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22 pages, 2369 KiB  
Article
Two-Pole Structures in QCD: Facts, Not Fantasy!
by Ulf-G. Meißner
Symmetry 2020, 12(6), 981; https://doi.org/10.3390/sym12060981 - 8 Jun 2020
Cited by 69 | Viewed by 4127
Abstract
The two-pole structure refers to the fact that particular single states in the spectrum as listed in the PDG tables are often two states. The story began with the Λ ( 1405 ) , when in 2001, using unitarized chiral perturbation theory, it [...] Read more.
The two-pole structure refers to the fact that particular single states in the spectrum as listed in the PDG tables are often two states. The story began with the Λ ( 1405 ) , when in 2001, using unitarized chiral perturbation theory, it was observed that there are two poles in the complex plane, one close to the K ¯ p and the other close to the π Σ threshold. This was later understood combining the SU(3) limit and group-theoretical arguments. Different unitarization approaches that all lead to the two-pole structure have been considered in the mean time, showing some spread in the pole positions. This fact is now part of the PDG book, although it is not yet listed in the summary tables. Here, I discuss the open ends and critically review approaches that cannot deal with this issue. In the meson sector, some excited charm mesons are good candidates for such a two-pole structure. Next, I consider in detail the D 0 * ( 2300 ) , which is another candidate for this scenario. Combining lattice QCD with chiral unitary approaches in the finite volume, the precise data of the Hadron Spectrum Collaboration for coupled-channel D π , D η , D s K ¯ scattering in the isospin I = 1 / 2 channel indeed reveal its two-pole structure. Further states in the heavy meson sector with I = 1 / 2 exhibiting this phenomenon are predicted, especially in the beauty meson sector. I also discuss the relation of these two-pole structures and the possible molecular nature of the states under consideration. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
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Review

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113 pages, 1241 KiB  
Review
Introduction to Renormalization Theory and Chiral Gauge Theories in Dimensional Regularization with Non-Anticommuting γ5
by Hermès Bélusca-Maïto, Amon Ilakovac, Paul Kühler, Marija Mađor-Božinović, Dominik Stöckinger and Matthias Weißwange
Symmetry 2023, 15(3), 622; https://doi.org/10.3390/sym15030622 - 1 Mar 2023
Cited by 13 | Viewed by 5340
Abstract
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for γ5. One goal was to show how chiral gauge theories can be renormalized despite the spurious breaking [...] Read more.
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for γ5. One goal was to show how chiral gauge theories can be renormalized despite the spurious breaking of gauge invariance and how to obtain the required symmetry-restoring counterterms. A second goal was to familiarize the reader with the theoretical basis of the renormalization of chiral gauge theories, the theorems that guarantee the existence of renormalized chiral gauge theories at all orders as consistent quantum theories. Relevant topics include BPHZ renormalization, Slavnov–Taylor identities, the BRST formalism, and algebraic renormalization, as well as the theorems guaranteeing that dimensional regularization is a consistent regularization/renormalization scheme. All of these, including their proofs and interconnections, are explained and discussed in detail. Further, these theoretical concepts are illustrated in practical applications with the example of an Abelian and a non-Abelian chiral gauge theory. Not only the renormalization procedure for such chiral gauge theories is explained step by step, but also the results of all counterterms, including the symmetry-restoring ones, necessary for the consistent renormalization, are explicitly provided. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
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19 pages, 719 KiB  
Review
Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions: Topological Structure of Dense Matter
by Yong-Liang Ma and Mannque Rho
Symmetry 2021, 13(10), 1888; https://doi.org/10.3390/sym13101888 - 7 Oct 2021
Cited by 9 | Viewed by 1767
Abstract
We review a new development on the possible direct connection between the topological structure of the Nf=1 baryon as a FQH droplet and that of the Nf≥2 baryons (such as nucleons and hyperons) as skyrmions. This development [...] Read more.
We review a new development on the possible direct connection between the topological structure of the Nf=1 baryon as a FQH droplet and that of the Nf≥2 baryons (such as nucleons and hyperons) as skyrmions. This development suggests a possible “domain-wall (DW)” structure of compressed baryonic matter at high density expected to be found in the core of massive compact stars. Our theoretical framework is anchored on an effective nuclear effective field theory that incorporates two symmetries either hidden in the vacuum in QCD or emergent from strong nuclear correlations. It presents a basically different, hitherto undiscovered structure of nuclear matter at low as well as high densities. Hidden “genuine dilaton (GD)” symmetry and hidden local symmetry (HLS) gauge-equivalent at low density to nonlinear sigma model capturing chiral symmetry, put together in nuclear effective field theory, are seen to play an increasingly important role in providing hadron–quark duality in baryonic matter. It is argued that the FQH droplets could actually figure essentially in the properties of the vector mesons endowed with HLS near chiral restoration. This strongly motivates incorporating both symmetries in formulating “first-principles” approaches to nuclear dynamics encompassing from the nuclear matter density to the highest density stable in the Universe. Full article
(This article belongs to the Special Issue Chiral Symmetry in Physics)
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