Nuclear matter as a liquid phase of spontaneously broken semi-classical \(SU(2)_L \times SU(2)_R\) chiral perturbation theory: Static chiral nucleon liquids

We study effective field theories (EFT) of nuclear structure based on spontaneously broken global \(SU(2)_L\times SU(2)_R\) chiral symmetry of QCD with two massless quarks, i.e. \(SU(2)\chi PT\). For ground-state nuclei, this EFT enables expansion and truncation in inverse powers of \(\Lambda_{\chi...

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Bibliographic Details
Published in:arXiv.org 2021-12
Main Authors: Lynn, Bryan W, Coffey, Brian J, McGee, Kellen E, Starkman, Glenn D
Format: Article
Language:English
Subjects:
Asymmetry
Chiral dynamics
Conservation laws
Drops (liquids)
Empirical analysis
External pressure
Liquid phases
Nuclear matter
Nuclear structure
Nuclei (nuclear physics)
Nucleons
Nuclides
Perturbation theory
Pions
Quantum chromodynamics
Quarks
Solitary waves
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Summary:We study effective field theories (EFT) of nuclear structure based on spontaneously broken global \(SU(2)_L\times SU(2)_R\) chiral symmetry of QCD with two massless quarks, i.e. \(SU(2)\chi PT\). For ground-state nuclei, this EFT enables expansion and truncation in inverse powers of \(\Lambda_{\chi SB}\simeq 1 GeV\), with analytic operators renormalized to all loop orders. We derive the EFT Lagrangian to order \(\Lambda^0_{\chi SB}\). We show that \(SU(2)\chi PT\) of protons, neutrons and pions admits a semi-classical "Static Chiral Nucleon Liquid" (Static\(\chi\)NL) phase and that "Pion-less" \(SU(2)\chi PT\) emerges in this liquid: far-infrared pions decouple from Static\(\chi\)NL, vastly simplifying the derivation of saturated nuclear matter (the infinite liquid phase) and of finite microscopic liquid drops (ground-state nuclides). Static\(\chi\)NL are made entirely of nucleons with even parity, total spin zero, and even \(Z\) and \(N\); local expectation values for spin and momenta vanish. They explain the power of pion-less \(SU(2)\chi PT\) to capture experimental ground-state properties of certain nuclides, this explanation following directly from the global symmetries of QCD with two massless quarks. Mean-field Static\(\chi\)NL non-topological solitons are true solutions of \(SU(2)\chi PT\)'s semi-classical symmetries: they obey all CVC and PCAC conservation laws and they have zero internal and external pressure. The nuclear liquid-drop model and the semi-empirical mass formula emerge -- with correct nuclear density and saturation and asymmetry energies -- in an explicit Thomas-Fermi construction. We relate our work to compatible and complementary work in pionless and in halo/ cluster EFTs, also composed entirely of nucleons and applied to light (\(A\leq 6\)) nuclei, which might provide important (
ISSN:2331-8422