Dilatons in Hidden Local Symmetry for Hadrons in Dense Matter

Abstract

With the explicit breaking of scale invariance by the trace anomaly of QCD rephrased in terms of spontaneous breaking, low-energy strong interaction dynamics of dense (and also hot) matter can be effectively captured by -- in addition to the Nambu-Goldstone bosons and the vector mesons -- two dilaton fields, the "soft" (${\chi }_s$) field that is locked to chiral symmetry and the "hard" (${\chi }_h$) field which remains unaffected by chiral symmetry. The interplay of the soft and hard dilatons plays a subtle role in how chiral symmetry is manifested in hot and/or dense matter. The scale anomaly in which the soft component intervenes vanishes at the chiral transition in a way analogous to the restoration of scale symmetry in the Freund-Nambu model, while that of the hard component remains broken throughout the QCD sector. Most remarkable of all is its role in the chiral anomaly sector through a "homogeneous Wess-Zumino (hWZ) term" of the form ${\omega }_{\mu }{B}^{\mu }$ on the structure of a single baryon as well as dense baryonic matter. It figures crucially in predicting a "Little Bag" for the nucleon and a "quarkyonic phase" in the form of a half-skyrmion matter at high density. We show how the vanishing of the vector-meson mass at the vector manifestation fixed point in hidden local symmetry theory can be related to the property of the "matter field" in the Freund-Nambu model that leaves scale symmetry invariant. The emerging structure of dense hadronic matter in the model so constructed suggests what could be amiss in describing dense matter in holographic dual QCD at its large $N_c$ and 't Hooft limit.

28 pages, 2 figures; additional references

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Cited by in corpus (21)

• Half-Skyrmions, Tensor Forces and Symmetry Energy in Cold Dense Matter
• An effective model for the QCD phase transitions at finite baryon density
• Dilaton-Limit Fixed Point in Hidden Local Symmetric Parity Doublet Model
• Conformal anomaly and the vector coupling in dense matter
• Interplay between ω-Nucleon Interaction and Nucleon Mass in Dense Baryonic Matter
• Half-Skyrmions and the Equation of State for Compact-Star Matter
• Dense baryonic matter in conformally-compensated hidden local symmetry: Vector manifestation and chiral symmetry restoration
• Hidden Local Symmetry and Infinite Tower of Vector Mesons for Baryons
• Kaons in Dense Half-Skyrmion Matter
• Holographic QCD Integrated back to Hidden Local Symmetry
• The phase structure of a chiral model with dilatons in hot and dense matter
• Flavor Symmetry and Topology Change in Nuclear Symmetry Energy for Compact Stars
• Dense Stellar Matter with Strange Quark Matter Driven by Kaon Condensation
• Toward an Effective Field Theory for Cold Compressed Baryonic Matter
• Dileptons Get Nearly "Blind" to Mass-Scaling Effects In Hot and/or Dense Matter
• Fractionized Skyrmions in Dense Compact-Star Matter
• Cold Dense Baryonic Matter and Compact Stars
• Proton Mass, Topology Change and Tensor Forces in Compressed Baryonic Matter
• Cold Compressed Baryonic Matter with Hidden Local Symmetry and Holography
• Dilatons for Dense Hadronic Matter
• Dilatons in Dense Baryonic Matter