Fluctuations in “Brown-Rho scaled” chiral Lagrangians

Abstract

We develop arguments for ''mapping'' the effective chiral Lagrangian whose parameters are given by ''Brown-Rho'' ͑BR͒ scaling to a Landau Fermi-liquid fixed-point theory for nuclear matter in describing fluctuations in various flavor ͑e.g., strangeness͒ directions. We use for this purpose the effective Lagrangian used by Furnstahl, Tang, and Serot that incorporates the trace anomaly of QCD in terms of a light-quark ͑quarkonium͒ degree of freedom with the heavy ͑gluonium͒ degree of freedom integrated out. The large anomalous dimension d an Ϸ5/3 for the scalar field found by Furnstahl et al. to be needed for a correct description of nuclear matter is interpreted as an indication for a strong-coupling regime and the ground state given by the BR-scaled parameters is suggested as the background around which fluctuations can be rendered weak so that mean-field approximation is reliable. We construct a simple model with BR-scaled parameters that provides a satisfactory description of the properties of matter at normal nuclear matter density. Given this, fluctuations around the BR-scaled background are dominated by tree diagrams. Our reasoning relies heavily on recent developments in the study of nucleon and kaon properties in normal and dense nuclear matter, e.g., nucleon and kaon flows in heavy-ion processes, kaonic atoms, and kaon condensation in dense compact-star matter. ͓S0556-2813͑97͒00810-8͔PACS number͑s͒: 24.85.ϩp, 12.39.Fe, 21.65.ϩf, 25.75.Ϫq

A new state of hadronic matter at high density

“…Including a ρ-meson mass shift to smaller values in the calculation of the relativistic transport theory, a good agreement of the theoretical predictions with the observed dilepton spectra in the S-Au collision is achieved [11]. The two approaches, one based on many-body correlations starting from strongly coupled hadrons whose properties are defined in matter-free space [6,7] (with broadening widths) and the other based on the notion of both bosonic and fermionic quasi-particles with parameters defined in a medium background field [12], somewhat contradictory to each other though they may appear to be, are probably related to each other when applied to the dilepton phenomena in question. Whether or not the two ways of looking at dense matter can be mapped to each other for other physical observables is not clear.…”

“…Let us look at the model (12) in Minkowski space. For this purpose, we integrate out the meson fields σ, π and V µ and perform the analytic continuation of the Euclidean quark theory to Minkowski space.…”

On the density-dependent hadron field theory at finite temperature and its thermodynamical consistency

“…In ref. [14] the authors proposed an effective Lagrangian whose parameters scale in nuclear medium according to the BR scaling. In its simplest version the Lagrangian in the MFA is [14,15] L =ψ [γ µ (i∂ µ − g * v (ρ) ω µ ) − M * (ρ) + hφ] ψ + 1 2 ∂ µ φ∂ µ φ − m * 2 φ (ρ)φ 2 − 1 4 ω µν ω µν + 1 2 m * 2 ω (ρ)ω µ ω µ .…”

Nuclear equation of state at high density and the properties of neutron stars

“…Theoretically, it is important to understand the decrease of vector coupling at high density. Contrast to heavy-ion reactions, in this line some works have been performed [19] and more to be required in details [20]. We show in Fig.…”