[Paper Review] Proton Mass, Topology Change and Tensor Forces in Compressed Baryonic Matter

Mannque Rho|arXiv (Cornell University)|Jan 1, 2013

Quantum Chromodynamics and Particle Interactions29 references3 citations

TL;DR

This paper proposes that a substantial chirally invariant mass term ($m_0$) in the nucleon contributes significantly to the equation of state (EoS) of dense baryonic matter, stabilizing neutron stars against collapse. Using a dynamical hidden local symmetry (dHLS) framework, it shows that the proton mass origin—beyond chiral symmetry breaking—shapes neutron star maximum mass and topology, with implications for RAON and FAIR experiments.

ABSTRACT

This is a summary of the talks I gave at Korean Physical Society meeting (April 26, 2012, Daejeon, Korea) and the 4th Asian Triangle Heavy Ion Conference (ATHIC) (November 14, 2012, Pusan, Korea). They are based on the series of work done at Hanyang University in the World Class University III Program under the theme of "From Dense Matter to Compact Stars." The program was conceived and executed to understand highly compressed baryonic matter in anticipation of the forthcoming RIB machine "RAON" which is in construction in the Institute for Basic Science (IBS) in Korea. The problems treated ranged from the origin of the proton mass, topological structure of barynic matter, chiral symmetry and conformal symmetry to the EoS of nuclear matter and dense neutron-rich matter and to the maximum mass of neutron stars. The results obtained are new and intriguing and could have an impact on the novel structure of dense matter to be probed in the accelerators "RAON," FAIR etc. and in compact stars.

Motivation & Objective

• To understand the origin of the proton mass beyond chiral symmetry breaking in dense baryonic matter.
• To investigate how a chirally invariant mass term ($m_0$) affects the equation of state (EoS) of neutron-rich and compact-star matter.
• To resolve the tension between baryon and meson mass scaling under chiral restoration, particularly in the context of vector manifestation and hidden local symmetry.
• To assess the impact of topology change (e.g., half-skyrmion formation) on nuclear dynamics and neutron star structure.
• To connect theoretical predictions to upcoming experiments at RAON, FAIR, and space observatories probing dense matter.

Proposed method

• Uses a dynamical hidden local symmetry (dHLS) Lagrangian to describe baryons and mesons in medium, preserving QCD symmetries up to deconfinement.
• Applies the baryon parity-doublet model with a chirally invariant mass term $m_0$ to decouple nucleon mass from quark condensate scaling.
• Employs BLPR scaling to analyze nucleon mass evolution in dense matter, constrained by heavy-ion data and symmetry energy behavior.
• Introduces the role of dilaton and topology via half-skyrmion structures to explain stiffening of the EoS at $n_{1/2}$.
• Analyzes renormalization group flow of $ ho$ and $ u$-meson couplings to assess symmetry breaking in medium, particularly for $ ho$-meson at vector manifestation fixed point.
• Compares predictions with lattice QCD results and constituent quark model expectations to test consistency under chiral restoration.

Experimental results

Research questions

• RQ1 What is the origin of the proton mass if it is not solely due to spontaneous chiral symmetry breaking?
• RQ2 How does a chirally invariant mass term ($m_0$) influence the equation of state (EoS) of dense neutron-rich matter and neutron star maximum mass?
• RQ3 Why does the nucleon mass not drop below ~0.8$ m_N $ at $n_{1/2}$, despite chiral symmetry restoration?
• RQ4 Can the observed stiffening of the EoS at $n_{1/2}$ be explained by topology change (e.g., half-skyrmion formation) without violating constraints from heavy-ion data?
• RQ5 How do meson masses scale under chiral restoration, and can this be reconciled with baryon mass scaling in the dHLS framework?

Key findings

• The nucleon mass in dense matter cannot drop below approximately 0.8$ m_N $ at $n_{1/2}$ without destabilizing the EoS, implying a strong constraint on $m_0$.
• The $ ho$-nucleon coupling flows to the vector manifestation fixed point, suggesting spontaneous breaking of $U(2)$ symmetry in medium, while $ u$-coupling remains stable.
• A non-vanishing $m_0$ in the nucleon is required to stabilize the EoS and prevent unphysical repulsion, indicating a fundamental origin of proton mass independent of chiral condensate.
• Topology change via half-skyrmion formation at $n_{1/2}$ stiffens the EoS, counteracting the softening from kaon condensation, with net effect still uncertain.
• Meson masses, particularly $ ho$ and $ ho$-like states, are expected to vanish under chiral restoration due to vector manifestation, unlike baryons with large $m_0$.
• The constituent quark model may not hold in dense matter, as it would imply both baryons and mesons remain massive in the chiral limit, contradicting dHLS expectations.