Scaling Of Chiral Lagrangians And Landau Fermi Liquid Theory For Dense Hadronic Matter

Abstract

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.