Fluctuations in “Brown-Rho scaled” chiral Lagrangians

Abstract

We develop arguments for ``mapping'' the effective chiral Lagrangian whose parameters are given by ``Brown-Rho'' (BR) scaling to a Landau Fermi-liquid fixed-point theory for nuclear matter in describing fluctuations in various flavor (e.g., strangeness) 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 (quarkonium) degree of freedom with the heavy (gluonium) degree of freedom integrated out. The large anomalous dimension ${d}_{\mathrm{an}}\ensuremath{\approx}5/3$ 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.