The Fate of Hadron Masses in Dense Matter: Hidden Local Symmetry and Color Flavor Locking

The notion that hadron masses scale according to the scaling of the quark condensate in hadronic matter, partly supported by a number of observations in finite nuclei, can be interpreted in terms of Harada-Yamawaki's ``vector manifestation" (VM) of chiral symmetry. In this scenario, near chiral restoration, the vector meson masses drop to zero {\it in the chiral limit} with vanishing widths. This scenario appears to differ from the standard linear sigma model scenario. We exploit a link between the VM and color-flavor locking inferred by us from lattice data on quark number susceptibility (QNS) measured as a function of temperature to suggest that local flavor symmetry gets mapped to color gauge symmetry at the chiral phase transition.Comment: 5 pages, revised with title change, sharpened arguments and updated reference

Double Decimation and Sliding Vacua in the Nuclear Many-Body System

We propose that effective field theories for nuclei and nuclear matter comprise of "double decimation": (1) the chiral symmetry decimation (CSD) and (2) Fermi liquid decimation (FLD). The Brown-Rho scaling recently identified as the parametric dependence intrinsic in the "vector manifestation" of hidden local symmetry theory of Harada and Yamawaki results from the first decimation. This scaling governs dynamics down to the scale at which the Fermi surface is formed as a quantum critical phenomenon. The next decimation to the top of the Fermi sea where standard nuclear physics is operative makes up the Fermi liquid decimation. Thus nuclear dynamics is dictated by two fixed points, namely, the vector manifestation fixed point and the Fermi liquid fixed point. It has been a prevalent practice in nuclear physics community to proceed with the second decimation only, assuming density independent masses. We show why most nuclear phenomena can be reproduced by theories using either density-independent, or density-dependent masses, a grand conspiracy of nature that is an aspect that could be tied to the Cheshire-Cat phenomenon in hadron physics. We identify what is left out in the Fermi liquid decimation that does not incorporate the CSD. Experiments such as the dilepton production in relativistic heavy ion reactions, which are specifically designed to observe effects of dropping masses, could exhibit large effects from the reduced masses. However they are compounded with effects that are not directly tied to chiral symmetry. We discuss a recent STAR/RHIC observation where BR scaling can be singled out in a pristine environment.Comment: Latex, 9 figures; based on version prepared for Phys. Re

Matching the QCD and Hadron Sectors and Medium Dependent Meson Masses; Hadronization in Relativistic Heavy Ion Collisions

The recent developments on the "vector manifestation" of chiral symmetry by Harada and Yamawaki provide a compelling evidence for, and "refine," the in-medium scaling of hadronic properties in dense/hot matter (call it ``BR scaling") proposed by the authors in 1991. We reinterpret the Harada-Yamawaki result obtained in a Wilsonian renormalization-group approach to hidden local symmetry theory matched to QCD at near the chiral scale in terms of the Nambu-Jona-Lasinio model and predict that the vector meson mass in medium should scale m_\rho^\star/m_\rho\sim (\la\bar{q}q\ra^\star/\la\bar{q}q\ra)^{1/2} from $n=0$ up to $\sim n=n_0$ (where $n_0$ is nuclear matter density) and then go over to the linear scaling m_\rho^\star/m_\rho\sim \la\bar{q}q\ra^\star/\la\bar{q}q\ra up to the chiral transition density $n_c$ at which the mass is to vanish (in the chiral limit) according to the vector manifestation fixed point. In the regime of the linear scaling above $n_0$, the (vector) gauge coupling constant should fall linearly in \la\bar{q}q\ra^\star, vanishing at the critical point, with the width of the vector meson becoming steeply narrower. We suggest the in-medium vector meson mass, {\em both} parametric and pole, which goes smoothly to zero with increasing density, to be an order parameter for chiral symmetry restoration. Some issues related to recent RHIC observations are qualitatively discussed in the appendices. Our main conclusion that follows from these considerations is that the movement towards chiral restoration can be reliably described in Nambu-Jona-Lasinio mean field, with constituent quarks as variables, although there is probably density discontinuity following chiral restoration.Comment: Contribution to the Hidenaga Yamagishi Commemorative Volume edited by E. Witten and I.Zahe

On the Manifestation of Chiral Symmetry in Nuclei and Dense Nuclear Matter

This article reviews our view on how chiral symmetry, its pattern of breaking and restoration under extreme conditions manifest themselves in the nucleon, nuclei, nuclear matter and dense hadronic matter. Topics treated are nucleon structure in terms of chiral symmetry, "first-principle" (QCD) calculations of the properties of finite nuclei effectuated by embedding the ``standard nuclear physics approach" into the framework of effective field theories of nuclei with predictions for certain astrophysical processes, a reinterpretation of the Brown-Rho (BR) scaling that implements chiral symmetry property of baryon-rich medium \`a la "vector manifestation" of hidden local symmetry, evidences for BR scaling in nuclear processes at normal nuclear matter density and at higher density, the notion of "broadband equilibration" in heavy-ion processes, and the role of strangeness in the formation of compact stars and their collapse into black-holes. We revisit the "Cheshire-Cat phenomenon" recently revived in the form of "quark-hadron continuity" in mapping low-density structure of hadrons to high-density structure of quarks and gluons and suggest how color-flavor locking in terms of QCD variables and hidden local symmetry in terms of hadronic variables may be connected and how BR scaling could fit into this "continuity" scheme.Comment: 103 pages, latex, 14 figures; Physics Reports; references updated and new developments adde

Strangeness Equilibration at GSI Energies

We develop the notion of "broad-band equilibration" in heavy-ion processes involving dense medium. Given density-dependent \Km-masses we show that the equilibration at GSI energies claimed to hold in previous treatments down to $\sim \rho_0/4$, can be replaced by a broad-band equilibration in which the \Km-meson and hyperons are produced in an essentially constant ratio independent of density. There are experimental indications that this also holds for AGS energies. We then proceed to argue that {\it both} $K^+$ and $K^-$ must get lighter in dense medium at some density $\rho >\rho_0$ due to the decoupling of the vector mesons. As a consequence, kaon condensation in compact stars could take place {\it before} chiral restoration since the sum of bare quark masses in the kaon should lie below $\mu_e$. Another consequence of the decoupling vector interactions is that the quasi-particle picture involving (quasi)quarks, presumably ineffective at low densities, becomes more appropriate at higher densities as chiral restoration is approached.Comment: 16 pages, latex with 2 eps figures. Abstract rewritten and references update

A Schematic Model For Density-Dependent Vector Meson Masses

A schematic two-level model consisting of a "collective" bosonic state and an "elementary" meson is constructed that provides interpolation from a hadronic description (a la Rapp/Wambach) to B/R scaling for the description of properties of vector mesons in dense medium. The development is based on a close analogy to the degenerate schematic model of Brown for giant resonances in nuclei.Comment: 20 pages, latex with 8 figures: Talk given by GEB at AIP Klaus Kinder-Geiger Memorial Meeting, 3 October 199