Toward an Effective Field Theory for Cold Compressed Baryonic Matter

This is an extended version of the note taken by the first author (W.-G.P.) on a lecture given by the second author (M.R.) as a first part of the series on "Hadronic Matter Under Extreme Conditions," the principal theme of the WCU-Hanyang Program. It covers the attempts to go in a framework anchored on effective field theory of QCD from zero density to the nuclear matter density and slightly beyond, with the ultimate goal of arriving at the density relevant to compact stars, including chiral phase transition and quark matter. The focus is on the conceptual aspects rather than detailed "fitting" of the data on the kinds of physics that are being addressed to in radioactive-ion-beam machines in operation as well as in project (such as `KoRIA' in Korea) and will be explored at such forthcoming accelerators as FAIR/GSI. The approach presented here is basically different from the standard ones found in the literature in that the notion of hidden local symmetry -- which underlies the chiral symmetry of the strong interactions -- and its generalization to dual gravity description involving infinite tower of hidden gauge fields are closely relied on.Comment: 25 pages, 12 figures, WCU lecture note prepared for the review section of MPL

The Inhomogeneous Phase of Dense Skyrmion Matter

It was predicted qualitatively in ref.[1] that skyrmion matter at low density is stable in an inhomogeneous phase where skyrmions condensate into lumps while the remaining space is mostly empty. The aim of this paper is to proof quantitatively this prediction. In order to construct an inhomogeneous medium we distort the original FCC crystal to produce a phase of planar structures made of skyrmions. We implement mathematically these planar structures by means of the 't Hooft instanton solution using the Atiyah-Manton ansatz. The results of our calculation of the average density and energy confirm the prediction suggesting that the phase diagram of the dense skyrmion matter is a lot more complex than a simple phase transition from the skyrmion FCC crystal lattice to the half-skyrmion CC one. Our results show that skyrmion matter shares common properties with standard nuclear matter developing a skin and leading to a binding energy equation which resembles the Weiszaecker mass formula.Comment: 8 figures, 14 page

Dilaton-Limit Fixed Point in Hidden Local Symmetric Parity Doublet Model

We study nucleon structure with positive and negative parities using a parity doublet model endowed with hidden local symmetry (HLS) with the objective to probe dense baryonic matter. The model -- that we shall refer to as "PDHLS model" for short -- allows a chiral-invariant mass of the nucleons unconnected to spontaneously broken chiral symmetry which comes out to be m_0 ~ 200 MeV at tree level from fitting to the decay width of the parity doubler, N(1535), to nucleon-pion and nucleon axial coupling g_A=1.267. The presence of a substantial m_0 that remains non-vanishing at chiral restoration presents a deep issue for the origin of the nucleon mass as well as will affect nontrivially the equation of state for dense baryonic matter relevant for compact stars. We construct a chiral perturbation theory at one-loop order and explore the phase structure of the model using renormalization group equations. We find a fixed point that corresponds exactly to the "dilaton limit" at which the HLS vector mesons decouple from the nucleons before reaching the vector manifestation fixed point. We suggest that cold baryonic system will flow to this limit as density increases toward that of chiral restoration.Comment: 22 pages, 6 figure

Conformal anomaly and the vector coupling in dense matter

We construct an effective chiral Lagrangian for hadrons implemented by the conformal invariance and discuss the properties of nuclear matter at high density. The model is formulated based on two alternative assignment, "naive" and mirror, of chirality to the nucleons. It is shown that taking the dilaton limit, in which the mended symmetry of Weinberg is manifest, the vector-meson Yukawa coupling becomes suppressed and the symmetry energy becomes softer as one approaches the chiral phase transition. This leads to softer equations of state (EoS) and could accommodate the EoS without any exotica consistent with the recent measurement of a $1.97 \pm 0.04\,M_\odot$ neutron star.Comment: v2:10 pages, 2 figures, typos corrected, a rough estimate of m0 adde

Nuclear structure in Parity Doublet Model

Using an extended parity doublet model with the hidden local symmetry, we study the properties of nuclei in the mean field approximation to see if the parity doublet model could reproduce nuclear properties and also to estimate the value of the chiral invariant nucleon mass $m_0$ preferred by nuclear structure. We first determined our model parameters using the inputs from free space and from nuclear matter properties. Then, we study some basic nuclear properties such as the nuclear binding energy with several different choices of the chiral invariant mass. We observe that our results, especially the nuclear binding energy, approach the experimental values as $m_0$ is increased until $m_0=700$ MeV and start to deviate more from the experiments afterwards with $m_0$ larger than $m_0=700$ MeV, which may imply that $m_0=700$ MeV is preferred by some nuclear properties.Comment: 8 pages, 2 figure

Scale-Chiral Symmetry, Proton Mass and Sound Velocity in Compact-Star Matter

Revised for submission to journalWith a light dilaton $\sigma$ and the light-quark vector mesons $V=(\rho,\omega)$ incorporated into an effective scale-invariant hidden local symmetric Lagrangian, scale-chiral symmetry -- hidden in QCD -- arises at a high density, $n_{1/2}$, as an "emergent" symmetry, a phenomenon absent in standard chiral perturbative approaches but highly relevant for massive compact stars. What takes place as the density increases beyond $n_{1/2}\sim 2n_0$ in compressed baryonic matter is (1) a topology change from skyrmions to half-skyrmions, (2) parity doubling in the nucleon structure, (3) the maximum neutron star mass $M\simeq 2.05 M_{\odot}$ and the radius $R\simeq 12.19$ km and (4) the sound velocity $v_s^2/c^2\simeq 1/3$ due to the "vector manifestation (VM)" fixed point of $\rho$ and a "walking" dilaton condensate, which is intricately connected to the source of the proton mass