Medium Dependence of the Vector-Meson Mass: Dynamical and/or Brown-Rho Scaling?

We discuss the similarities and differences for the theories of Rapp, Wambach and collaborators (called R/W in short) and those based on Brown-Rho scaling (called B/R), as applied to reproduce the dileptons measured by the CERES collaboration in the CERN experiments. In both theories the large number of dileptons at invariant masses $\sim$~$m_\rho/2$ are shown to be chiefly produced by a density-dependent $\rho$-meson mass. In R/W the medium dependence is dynamically calculated using hadronic variables defined in the matter-free vacuum. In B/R scaling it follows from movement towards chiral symmetry restoration due to medium-induced vacuum change, and is described in terms of constituent (or quasiparticle) quarks. We argue that the R/W description should be reliable up to densities somewhat beyond nuclear density, where hadrons are the effective variables. At higher density there should be a crossover to constituent quarks as effective variables scaling according to B/R. In the crossover region, the two descriptions must be ``dual''.Comment: 13 pages LaTeX, incl. 5 eps-figures and appb.sty; Talk given at the Workshop on 'The Structure of Mesons, Baryons and Nuclei', Cracow, May 1998, in honor of J. Speth's 60th birthday, to be published in Acta Physica Polonica

A Schematic Model for ρ−a1\rho-a_{1} Mixing at Finite Density and In-Medium Effective Lagrangian

Based on schematic two-level models extended to $a_1$-meson degrees of freedom, we investigate possible mechanisms of chiral restoration in the vector/axial-vector channels in cold nuclear matter. In the first part of this article we employ the massive Yang-Mills framework to construct an effective chiral Lagrangian based on low-energy mesonic modes at finite density. The latter are identified through nuclear collective excitations of `meson'-sobar type such as $\pi\leftrightarrow [\Delta (1232)N^{-1}]\equiv\hat\pi$, type treatment the in-medium gauge coupling $\hat g$, the (axial-) vector meson masses and $\hat f_\pi$ are found to decrease with density indicating the approach towards chiral restoration phase in the language of in-medium effective fields. In the second part of our analysis, we evaluate the (first) in-medium Weinberg sum rule which relates vector and axial-vector correlators to the pion decay constant. Using in-medium $\rho$/$a_1$ spectral functions (computed in the two-level model) also leads to a substantial reduction of the pion decay constant with increasing density

Half-Skyrmions, Tensor Forces and Symmetry Energy in Cold Dense Matter

In a previous article, the 4D half-skyrmion (or 5D dyonic salt) structure of dense baryonic matter described in crystalline configuration in the large $N_c$ limit was shown to impact nontrivially on how anti-kaons behave in compressed nuclear matter with a possible implication on an "ice-9" phenomenon of deeply bound kaonic matter and condensed kaons in compact stars. We extend the analysis to make a further prediction on the scaling properties of hadrons that have a surprising effect on the nuclear tensor forces, the symmetry energy and hence on the phase structure at high density. We treat this problem relying on certain topological structure of chiral solitons. Combined with what can be deduced from hidden local symmetry for hadrons in dense medium and the "soft" dilatonic degree of freedom associated with the trace anomaly of QCD, we uncover a novel structure of chiral symmetry in the "supersoft" symmetry energy that can influence the structure of neutron stars.Comment: 8 pages, 4 figures; contents unchanged but expanded for a journa

The Instanton Molecule Liquid and "Sticky Molasses" Above T_c

The main objective of this work is to explore the evolution in the structure of the quark-antiquark bound states in going down in the chirally restored phase from the so-called "zero binding points" T_zb to the QCD critical temperature T_c at which the Nambu-Goldstone and Wigner-Weyl modes meet. In doing this, we adopt the idea recently introduced by Shuryak and Zahed for charmed $\bar c c$, light-quark $\bar q q$ mesons $\pi, \sigma, \rho, A_1$ and gluons that at T_zb, the quark-antiquark scattering length goes through infinity at which conformal invariance is restored, thereby transforming the matter into a near perfect fluid behaving hydrodynamically, as found at RHIC. We show that the binding of these states is accomplished by the combination of (i) the color Coulomb interaction, (ii) the relativistic effects, and (iii) the interaction induced by the instanton-anti-instanton molecules. The spin-spin forces turned out to be small. While near T_zb all mesons are large-size nonrelativistic objects bound by Coulomb attraction, near T_c they get much more tightly bound, with many-body collective interactions becoming important and making the $\sigma$ and $\pi$ masses approach zero (in the chiral limit). The wave function at the origin grows strongly with binding, and the near-local four-Fermi interactions induced by the instanton molecules play an increasingly more important role as the temperature moves downward toward T_c.Comment: Contribution to QM2004 proceedings, 4 page

Kaon Condensation in the Bound-State Approach to the Skyrme Model

We explore kaon condensation using the bound-state approach to the Skyrme model on a 3-sphere. The condensation occurs when the energy required to produce a $K^-$ falls below the electron fermi level. This happens at the baryon number density on the order of 3--4 times nuclear density.Comment: LaTeX format, 15 pages. 3 Postscript figures, compressed and uuencode

Quark Description of Hadronic Phases

We extend our proposal that major universality classes of hadronic matter can be understood, and in favorable cases calculated, directly in the microscopic quark variables, to allow for splitting between strange and light quark masses. A surprisingly simple but apparently viable picture emerges, featuring essentially three phases, distinguished by whether strangeness is conserved (standard nuclear matter), conserved modulo two (hypernuclear matter), or locked to color (color flavor locking). These are separated by sharp phase transitions. There is also, potentially, a quark phase matching hadronic K-condensation. The smallness of the secondary gap in two-flavor color superconductivity corresponds to the disparity between the primary dynamical energy scales of QCD and the much smaller energy scales of nuclear physics.Comment: 21 pages, 2 figure

Finite density and temperature in hybrid bag models

We introduce the chemical potential in a system of two-flavored massless fermions in a chiral bag by imposing boundary conditions in the Euclidean time direction. We express the fermionic mean number in terms of a functional trace involving the Green function of the boundary value problem, which is studied analytically. Numerical evaluations for the fermionic number are presented.Comment: 19 pages, 4 figure