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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 1086

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)

25 pages, 521 KiB

Open AccessFeature PaperArticle

Mapping Topology of Skyrmions and Fractional Quantum Hall Droplets to Nuclear EFT for Ultra-Dense Baryonic Matter

by Mannque Rho

Symmetry 2022, 14(5), 994; https://doi.org/10.3390/sym14050994 - 12 May 2022

Cited by 5 | Viewed by 3457

Abstract

We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are “local flavor symmetry” of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden “quantum scale symmetry” with an IR fixed point with a “genuine dilaton (GD)” characterized by non-vanishing pion and dilaton decay constants. Both the skyrmion topology for

N_{f} \geq 2

baryons and the fractional quantum Hall (FQH) droplet topology for

N_{f} = 1

baryons are unified in the “homogeneous/hidden” Wess–Zumino term in the hidden local symmetry (HLS) Lagrangian. The possible indispensable role of the FQH droplets in going beyond the density regime of compact stars approaching scale-chiral restoration is explored by moving toward the limit where both the dilaton and the pion go massless. Full article

(This article belongs to the Special Issue The Nuclear Physics of Neutron Stars)

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19 pages, 719 KiB

Open AccessReview

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 14 | Viewed by 2064

Abstract

We review a new development on the possible direct connection between the topological structure of the

N_{f} = 1

baryon as a FQH droplet and that of the

N_{f} \geq 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

N_{f} = 1

baryon as a FQH droplet and that of the

N_{f} \geq 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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8 pages, 259 KiB

Open AccessArticle

Multifarious Roles of Hidden Chiral-Scale Symmetry: “Quenching” g_A in Nuclei

by Mannque Rho

Symmetry 2021, 13(8), 1388; https://doi.org/10.3390/sym13081388 - 30 Jul 2021

Cited by 8 | Viewed by 1566

Abstract

I discuss how the axial current coupling constant

g_{A}

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”

g_{A}

observed [...] Read more.

I discuss how the axial current coupling constant

g_{A}

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”

g_{A}

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

g_{A}

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

g_{A}

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)

19 pages, 909 KiB

Open AccessArticle

Genuine Dilatons in Gauge Theories

by R. J. Crewther

Universe 2020, 6(7), 96; https://doi.org/10.3390/universe6070096 - 10 Jul 2020

Cited by 33 | Viewed by 2990

Abstract

A genuine dilaton

σ

allows scales to exist even in the limit of exact conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP)

α_{IR}

through dimensional transmutation. These large scales at

α_{IR}

can be separated from [...] Read more.

A genuine dilaton

σ

allows scales to exist even in the limit of exact conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP)

α_{IR}

through dimensional transmutation. These large scales at

α_{IR}

can be separated from small scales produced by

θ_{μ}^{μ}

, the trace of the energy-momentum tensor. For quantum chromodynamics (QCD), the conformal limit can be combined with chiral

S U (3) \times S U (3)

symmetry to produce chiral-scale perturbation theory

χ

_{σ}

, with

f_{0} (500)

as the dilaton. The technicolor (TC) analogue of this is crawling TC: at low energies, the gauge coupling

α

goes directly to (but does not walk past)

α_{IR}

, and the massless dilaton at

α_{IR}

corresponds to a light Higgs boson at

α ≲ α_{IR}

. It is suggested that the

W^{\pm}

and

Z^{0}

bosons set the scale of the Higgs boson mass. Unlike crawling TC, in walking TC,

θ_{μ}^{μ}

produces all scales, large and small, so it is hard to argue that its “dilatonic” candidate for the Higgs boson is not heavy. Full article

(This article belongs to the Special Issue Spontaneous Breaking of Conformal Symmetry)

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