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

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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 8612

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Prof. Dr. Mannque Rho

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Institut de Physique Theorique, Universite Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France
Interests: theoretical nuclear; hadron physics
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Chihiro Sasaki

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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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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

Symmetries and Ultra Dense Matter of Compact Stars: Emergence of Duality in QCD in Symmetry

Published Papers (6 papers)

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Research

13 pages, 410 KiB

Open AccessArticle

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

Cited by 1 | Viewed by 620

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 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

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations)

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Figure 1

33 pages, 700 KiB

Open AccessArticle

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 1050

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

m_{0}

of nucleons together with the mass generated by the [...] Read more.

m_{0}

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

m_{0} = 700

MeV is preferred by the nuclear properties. Finally, we modify the PDM by adding the isovector scalar meson

a_{0} (980)

, and show that the inclusion of the

a_{0} (980)

enlarges the symmetry energy of the infinite nuclear matter. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations)

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19 pages, 6448 KiB

Open AccessEditor’s ChoiceArticle

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 2218

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 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

c_{s}^{2} > 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

Δ ρ / 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

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations)

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Figure 1

13 pages, 295 KiB

Open AccessArticle

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 1300

Abstract

The anomalous dimension

γ_{m} = 1

in the infrared region near the conformal edge in the broken phase of the large

N_{f}

QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for [...] Read more.

The anomalous dimension

γ_{m} = 1

in the infrared region near the conformal edge in the broken phase of the large

N_{f}

QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for

N_{f} = 8

and for

N_{c} = 3

. Recently, Zwicky made another independent argument (without referring to explicit dynamics) for the same result,

γ_{m} = 1

, by comparing the pion matrix element of the trace of the energy-momentum tensor

⟨π (p_{2}) | (1 + γ_{m}) \cdot \sum_{i = 1}^{N_{f}} m_{f} {\bar{ψ}}_{i} ψ_{i} | π (p_{1})⟩ = ⟨π (p_{2}) | θ_{μ}^{μ} | π (p_{1})⟩ = 2 M_{π}^{2}

(up to trace anomaly) with the estimate of

⟨π (p_{2}) | 2 \cdot \sum_{i = 1}^{N_{f}} m_{f} {\bar{ψ}}_{i} ψ_{i} | π (p_{1})⟩ = 2 M_{π}^{2}

through the Feynman–Hellmann theorem combined with an assumption

M_{π}^{2} \sim m_{f}

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 (p_{2}) | 2 \cdot \sum_{i = 1}^{N_{f}} m_{f} {\bar{ψ}}_{i} ψ_{i} | π (p_{1})⟩ = 2 M_{π}^{2} + [(1 - γ_{m}) M_{π}^{2} \cdot 2 / (1 + γ_{m})] = 2 M_{π}^{2} \cdot 2 / (1 + γ_{m}) \neq 2 M_{π}^{2}

in contradiction with his estimate, which is compared with

⟨π (p_{2}) | (1 + γ_{m}) \cdot \sum_{i = 1}^{N_{f}} m_{f} {\bar{ψ}}_{i} ψ_{i} | π (p_{1})⟩ = (1 + γ_{m}) M_{π}^{2} + [(1 - γ_{m}) M_{π}^{2}] = 2 M_{π}^{2}

(both up to trace anomaly), where the terms in

[]

are from the

σ

(pseudo-dilaton) pole contribution. Thus, there is no constraint on

γ_{m}

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

M_{π}^{2} \sim m_{f}^{2 / (1 + γ_{m})}

instead of

M_{π}^{2} \sim m_{f}

, we have the same result as ours in the broken phase. A further comment related to dChPT is made on the decay width of

f_{0} (500)

π π

for

N_{f} = 2

. It is shown to be consistent with the reality, when

f_{0} (500)

is regarded as a pseudo-NG boson with the non-perturbative trace anomaly dominance. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations)

14 pages, 344 KiB

Open AccessArticle

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 1123

Abstract

The rho meson has long been successfully identified with a dynamical gauge boson of Hidden Local Symmetry (HLS)

H_{local}

in the non-linear sigma model

G / H

gauge equivalent to the model having the symmetry

G_{global} \times H_{local}

, with [...] Read more.

The rho meson has long been successfully identified with a dynamical gauge boson of Hidden Local Symmetry (HLS)

H_{local}

in the non-linear sigma model

G / H

gauge equivalent to the model having the symmetry

G_{global} \times H_{local}

, with

G = [S U {(2)}_{L} \times S U {(2)}_{R}] ≃ O (4), H = S U {(2)}_{V} ≃ O (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 (N - 3) \times O (3)]

gauge equivalent to

O {(N)}_{global} \times {[O (N - 3) \times O (3)]}_{local}

, extrapolated to

N = 4

O {(4)}_{global} \times 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

Λ ≃ 4 π F_{π}

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

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations)

9 pages, 277 KiB

Open AccessArticle

Anomaly-Induced Quenching of g_A 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 1022

Abstract

How to disentangle the possible genuine quenching of

g_{A}

caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor

q_{s s b}

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

g_{A}

caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor

q_{s s b}

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

(1 - q_{s s b}) \neq 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

^{100}

Sn and in the spectral shape in the multifold forbidden

β

decay of

^{115}

In. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations)

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