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

The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling("BR scaling") and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. It is suggested that BR scaling gives the background around which the fluctuations are weak. A simple model with BR-scaled parameters is constructed and reproduces the properties of the nuclear ground state at normal nuclear matter density successfully. It shows that the tree level in the model Lagrangian is enough to describe the fluctuations around BR-scaled background. The model Lagrangian is consistent thermodynamically and reproduces relativistic Landau Fermi-liquid properties. Such points are important for dealing with hadronic matter under extreme condition. On the other hand it is shown that the vector current obtained from the chiral Lagrangian is the same as that obtained from Landau-Migdal approach. We can determine the Landau parameter in terms of BR-scaled parameter. However these two approaches provide different results, when applied to the axial charge. The numerical difference is small. It shows that the axial response is not included properly in the LandauMigdal approach. 6The 3-body contributions to the energy per nucleon vs. Fermi momentum in the FTS models. The short-dashed line represents the contribution of the φ 3 term in the FTS2 with the Q1 parameters. The long-dashed and the solid lines represent the contributions of the cubic terms (φω 2 and φ 3 ) in the FTS1 with the T1 parameters for d = 2.7. 7The comparison of CERES dilepton experiments and the theoretical predictions with the free-mass mesons and with scaled mass mesons. The figure comes from [61]. 45 8 The in-medium ρ-meson mass and Z factor obtained in [66] for Γ t = 0. 47 9 E/A − M vs. ρ for FTS1 theory ("T1" parameter), the "S3", "B1" and "B3" models defined in Table 4.

We discuss the Fermi-liquid properties of hadronic matter derived from a chiral Lagrangian field theory in which Brown-Rho (BR) scaling is incorporated. We identify the BR scaling as a contribution to Landau's Fermi liquid fixed-point quasiparticle parameter from "heavy" isoscalar meson degrees of freedom that are integrated out from a low-energy effective Lagrangian. We show that for the vector (convection) current, the result obtained in the chiral Lagrangian approach agrees precisely with that obtained in the semi-phenomenological Landau-Migdal approach. This precise agreement allows one to determine the Landau parameter that enters in the effective nucleon mass in terms of the constant that characterizes BR scaling. When applied to the weak axial current, however, these two approaches differ in a subtle way. While the difference is small numerically, the chiral Lagrangian approach implements current algebra and low-energy theorems associated with the axial response that the Landau method misses and hence is expected to be more predictive.

We show that effective chiral Lagrangians endowed with Brown-Rho scaling can be mapped to Landau Fermi-liquid fixed point theory in a way consistent with general constraints following from thermodynamics. This provides a unified scheme to treat, starting from normal nuclear matter, hadronic matter under extreme conditions that is encountered in relativistic heavy-ion collisions and in the interior of compact stars. *