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: 15 July 2024 | Viewed by 2674

Special Issue Editor

Institut de Physique Theorique, Universite Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France
Interests: theoretical nuclear; hadron physics
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Special Issue Information

Dear Colleagues,

In going from dilute baryonic systems to super dense astrophysical systems on the verge of gravitational collapse, ranging from few-nucleon nuclei to infinite nuclear matter to superdense compact star matter, one moves, in pursuing the strong interaction QCD with its UV completion, from pionless effective theory with nucleons only to chiral effective field theory with nucleons and pions, until the latter breaks down at densities near (2–3) times the normal nuclear matter density n_0. The mass scale for the breakdown is of the lowest vector mesons \rho, \omega, and the dilaton with emergent local and global symmetries, respectively. At this scale, it is futile to bring in the microscopic degrees of freedom of QCD. This cross-over regime is, at present, more or less totally unknown. And this is the regime that this Special Issue will address. It will involve various hidden symmetries, some explicitly associated with the gauge theory QCD, but more likely emergent in the strong nuclear correlations involving the relevant degrees of freedom in the background of a sliding vacuum. What could be involved is listed in the key words. 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.

Prof. Dr. Mannque Rho
Guest Editor

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Keywords

  • super dense matter
  • topology change
  • hadron-quark continuity
  • IR fixed point
  • dilatons
  • vector manifestation
  • emergent hidden symmetries
  • chiral-scale effective field theory
  • generalized density-functional theory
  • Landau–Migdal Fermi-liquid theory
  • un-Fermi liquids

Published Papers (4 papers)

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Research

19 pages, 6448 KiB  
Article
Constraints on Phase Transitions in Neutron Star Matter
Symmetry 2024, 16(1), 111; https://doi.org/10.3390/sym16010111 - 18 Jan 2024
Cited by 1 | Viewed by 652
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
(This article belongs to the Special Issue Emergence of Symmetries in Strong Nuclear Correlations)
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13 pages, 295 KiB  
Article
On the Anomalous Dimension in QCD
Symmetry 2024, 16(1), 2; https://doi.org/10.3390/sym16010002 - 19 Dec 2023
Cited by 1 | Viewed by 497
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
(This article belongs to the Special Issue Emergence of Symmetries in Strong Nuclear Correlations)
14 pages, 344 KiB  
Article
Proving Rho Meson Is a Dynamical Gauge Boson of Hidden Local Symmetry
Symmetry 2023, 15(12), 2209; https://doi.org/10.3390/sym15122209 - 18 Dec 2023
Cited by 1 | Viewed by 543
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
(This article belongs to the Special Issue Emergence of Symmetries in Strong Nuclear Correlations)
9 pages, 277 KiB  
Article
Anomaly-Induced Quenching of gA in Nuclear Matter and Impact on Search for Neutrinoless ββ Decay
Symmetry 2023, 15(9), 1648; https://doi.org/10.3390/sym15091648 - 25 Aug 2023
Cited by 4 | Viewed by 492
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
(This article belongs to the Special Issue Emergence of Symmetries in Strong Nuclear Correlations)
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