Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

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 Landau-Migdal approach.