Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 8439

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Institut de Physique Theorique, Universite Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France
Interests: theoretical nuclear; hadron physics
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Guest Editor
Institute of Theoretical Physics, University of Wroclaw, 50-137 Wrocław, Poland
Interests: high energy particle physics; nuclear physics
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Special Issue Information

Dear Colleagues,

In shifting from dilute baryonic systems to superdense astrophysical systems on the verge of gravitational collapse, ranging from few-nucleon nuclei to infinite nuclear matter and superdense compact star matter, in the pursuit of strong interaction QCD with its UV completion, one would move from a pionless effective theory with only nucleons to a chiral effective field theory with both nucleons and pions. This provides stunningly simple proof of Weinberg’s “Folk Theorem” on EFT, which remains valid until the latter breaks down at densities near n_{cross-over}~ (2–3) times the normal nuclear matter density n_0. The scale for the breakdown is the mass of the lowest vector mesons ρ and ω identified as the (hidden) local fields and that of the dilaton D as the (hidden) scale field. At this scale, it is futile to attempt to precisely identify their microscopic structure in terms of the QCD variables. Hence, this cross-over regime is currently an almost entirely uncharted domain and will be addressed in the Special Issue by confronting the astrophysical observables coming from gravity waves, among other associated concepts. The theoretical approach will involve various hidden symmetries, some explicitly associated with the gauge theory QCD but more likely emergent in the strong intricate fermionic (nuclear and/or constituent quark) correlations involving the relevant hadron degrees of freedom in the background of a sliding vacuum. The relevant topics are highlighted in the keywords; they promise to be rich in surprises, not always ensuing from the inherent symmetries of QCD proper but possibly resembling what is taking place in condensed matter systems. The theoretical strategy requires both bottom–up and top–down approaches to the topology changes between solitons, quantum Hall droplets, Fermi liquids, and non-Fermi liquids, etc., moving across the cross-over density.

Prof. Dr. Mannque Rho
Prof. Dr. Chihiro Sasaki
Guest Editor

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Keywords

  • superdense matter
  • topology changes
  • baryon parity-doublet symmetry
  • Cheshire cat mechanism
  • hadron-quark duality
  • emergent hidden symmetries
  • Weinberg’s folk theorem
  • generalized Hohenberg-Kohn density functional
  • Landau–Migdal Fermi liquid
  • un-Fermi liquids
  • speed of sound
  • conformal symmetry
  • color superconductivity
  • neutron superfluidity

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Related Special Issue

Published Papers (6 papers)

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Research

13 pages, 410 KiB  
Article
Parity Doubling in Dense Baryonic Matter as an Emergent Phenomenon and Pseudo-Conformal Phase
by Hyun Kyu Lee
Symmetry 2024, 16(12), 1598; https://doi.org/10.3390/sym16121598 - 30 Nov 2024
Viewed by 608
Abstract
The star matter composed of nucleons deep inside compact stars, such as neutron stars, is believed to be very dense, such that various types of new concepts and physical phenomena are naturally expected due to the nontrivial strong correlations between hadrons. The possibility [...] Read more.
The star matter composed of nucleons deep inside compact stars, such as neutron stars, is believed to be very dense, such that various types of new concepts and physical phenomena are naturally expected due to the nontrivial strong correlations between hadrons. The possibility of revealing the hidden scale symmetry in dense baryonic matter has been discussed recently, to uncover the pseudo-conformal phase in dense star matter. In the pseudo-conformal phase, the trace of the energy–momentum tensor becomes density-independent, and the speed of sound approaches the conformal velocity in scale symmetric matter. Interestingly, it is also observed that the effective nucleon mass becomes a density-independent finite quantity, which can be identified as the chiral invariant mass of the parity doublet model, indicating that the parity doubling is an emergent phenomenon. In this paper, we will discuss how parity-doubling symmetry emerges inside the core of a compact star as a consequence of the interplays between ω vector mesons and nucleons (or dilaton, χ, equivalently) and between the chiral symmetry and the scale symmetry. Full article
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33 pages, 700 KiB  
Article
Nuclear Matter and Finite Nuclei: Recent Studies Based on Parity Doublet Model
by Yuk-Kei Kong, Youngman Kim and Masayasu Harada
Symmetry 2024, 16(9), 1238; https://doi.org/10.3390/sym16091238 - 20 Sep 2024
Viewed by 1027
Abstract
In this review, we summarize recent studies on nuclear matter and finite nuclei based on parity doublet models. We first construct a parity doublet model (PDM), which includes the chiral invariant mass m0 of nucleons together with the mass generated by the [...] Read more.
In this review, we summarize recent studies on nuclear matter and finite nuclei based on parity doublet models. We first construct a parity doublet model (PDM), which includes the chiral invariant mass m0 of nucleons together with the mass generated by the spontaneous chiral symmetry breaking. We then study the density dependence of the symmetry energy in the PDM, which shows that the symmetry energy is larger for smaller chiral inavariant mass. Then, we investigate some finite nuclei by applying the Relativistic Continuum Hartree–Bogoliubov (RCHB) theory to the PDM. We present the root-mean-square deviation (RMSD) of the binding energies and charge radii, and show that m0=700 MeV is preferred by the nuclear properties. Finally, we modify the PDM by adding the isovector scalar meson a0(980), and show that the inclusion of the a0(980) enlarges the symmetry energy of the infinite nuclear matter. Full article
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19 pages, 6448 KiB  
Article
Constraints on Phase Transitions in Neutron Star Matter
by Len Brandes and Wolfram Weise
Symmetry 2024, 16(1), 111; https://doi.org/10.3390/sym16010111 - 18 Jan 2024
Cited by 16 | Viewed by 2159
Abstract
Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known [...] Read more.
Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known pulsars, the equation of state must be very stiff in order to ensure the stability of these extreme objects. This required stiffness limits the possible appearance of phase transitions in neutron star cores. For example, a Bayes factor analysis quantifies strong evidence for squared sound velocities cs2>0.1 in the cores of 2.1 solar-mass and lighter neutron stars. Only weak first-order phase transitions with a small phase coexistence density range Δρ/ρ<0.2 (at the 68% level) in a Maxwell construction still turn out to be possible within neutron stars. The central baryon densities in even the heaviest neutron stars do not exceed five times the density of normal nuclear matter. In view of these data-based constraints, much discussed issues such as the quest for a phase transition towards restored chiral symmetry and the active degrees of freedom in cold and dense baryonic matter, are reexamined. Full article
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13 pages, 295 KiB  
Article
On the Anomalous Dimension in QCD
by Koichi Yamawaki
Symmetry 2024, 16(1), 2; https://doi.org/10.3390/sym16010002 - 19 Dec 2023
Cited by 2 | Viewed by 1277
Abstract
The anomalous dimension γm=1 in the infrared region near the conformal edge in the broken phase of the large Nf QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for [...] Read more.
The anomalous dimension γm=1 in the infrared region near the conformal edge in the broken phase of the large Nf QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for Nf=8 and for Nc=3. Recently, Zwicky made another independent argument (without referring to explicit dynamics) for the same result, γm=1, by comparing the pion matrix element of the trace of the energy-momentum tensor π(p2)|(1+γm)·i=1Nfmfψ¯iψi|π(p1)=π(p2)|θμμ|π(p1)=2Mπ2 (up to trace anomaly) with the estimate of π(p2)|2·i=1Nfmfψ¯iψi|π(p1)=2Mπ2 through the Feynman–Hellmann theorem combined with an assumption Mπ2mf characteristic of the broken phase. We show that this is not justified by the explicit evaluation of each matrix element based on the dilaton chiral perturbation theory (dChPT): π(p2)|2·i=1Nfmfψ¯iψi|π(p1)=2Mπ2+[(1γm)Mπ2·2/(1+γm)]=2Mπ2·2/(1+γm)2Mπ2 in contradiction with his estimate, which is compared with π(p2)|(1+γm)·i=1Nfmfψ¯iψi|π(p1)=(1+γm)Mπ2+[(1γm)Mπ2]=2Mπ2 (both up to trace anomaly), where the terms in [] are from the σ (pseudo-dilaton) pole contribution. Thus, there is no constraint on γm when the σ pole contribution is treated consistently for both. We further show that the Feynman–Hellmann theorem is applied to the inside of the conformal window where dChPT is invalid and the σ pole contribution is absent, and with Mπ2mf2/(1+γm) instead of Mπ2mf, we have the same result as ours in the broken phase. A further comment related to dChPT is made on the decay width of f0(500) to ππ for Nf=2. It is shown to be consistent with the reality, when f0(500) is regarded as a pseudo-NG boson with the non-perturbative trace anomaly dominance. Full article
14 pages, 344 KiB  
Article
Proving Rho Meson Is a Dynamical Gauge Boson of Hidden Local Symmetry
by Koichi Yamawaki
Symmetry 2023, 15(12), 2209; https://doi.org/10.3390/sym15122209 - 18 Dec 2023
Cited by 3 | Viewed by 1103
Abstract
The rho meson has long been successfully identified with a dynamical gauge boson of Hidden Local Symmetry (HLS) Hlocal in the non-linear sigma model G/H gauge equivalent to the model having the symmetry Gglobal×Hlocal, with [...] Read more.
The rho meson has long been successfully identified with a dynamical gauge boson of Hidden Local Symmetry (HLS) Hlocal in the non-linear sigma model G/H gauge equivalent to the model having the symmetry Gglobal×Hlocal, with G=[SU(2)L×SU(2)R]O(4),H=SU(2)VO(3). However, under a hitherto unproven assumption that its kinetic term is dynamically generated, together with an ad hoc choice of the auxiliary field parameter “a=2”, we prove this assumption, thereby solving the long-standing mystery. The rho meson kinetic term is generated simply by the large N limit of the Grassmannian model G/H=O(N)/[O(N3)×O(3)] gauge equivalent to O(N)global×[O(N3)×O(3)]local, extrapolated to N=4, O(4)global×O(3)local, with all the phenomenologically successful “a=2 results”, i.e., ρ-universality, KSRF relation, and the Vector Meson Dominance, realized independently of the parameter “a”. This in turn establishes validity of the large N dynamics at the quantitative level directly by the experiments. The relevant cutoff reads Λ4πFπ for N=4, which is regarded as a matching scale of the HLS as a “magnetic dual” to QCD. Skyrmion is stabilized by such a dynamically generated rho meson without recourse to the underlying QCD, a further signal of the duality. The unbroken phase with a massless rho meson may be realized as a novel chiral-restored hadronic phase in the hot/dense QCD. Full article
9 pages, 277 KiB  
Article
Anomaly-Induced Quenching of gA in Nuclear Matter and Impact on Search for Neutrinoless ββ Decay
by Mannque Rho
Symmetry 2023, 15(9), 1648; https://doi.org/10.3390/sym15091648 - 25 Aug 2023
Cited by 9 | Viewed by 1008
Abstract
How to disentangle the possible genuine quenching of gA caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor qssb from nuclear correlation effects is described. This is accomplished by matching the Fermi-liquid fixed point theory to [...] Read more.
How to disentangle the possible genuine quenching of gA caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor qssb from nuclear correlation effects is described. This is accomplished by matching the Fermi-liquid fixed point theory to the “Extreme Single Particle (shell) Model” (acronym ESPM) in superallowed Gamow–Teller transitions in heavy doubly-magic shell nuclei. The recently experimentally observed indication for (1qssb)0—that one might identify as “fundamental quenching (FQ)”—in certain experiments seems to be alarmingly significant. I present arguments for how symmetries hidden in the matter-free vacuum can emerge and suppress such FQ in strong nuclear correlations. How to confirm or refute this observation is discussed in terms of the superallowed Gamow–Teller transition in the doubly-magic nucleus 100Sn and in the spectral shape in the multifold forbidden β decay of 115In. Full article
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