IN-Medium Effective Chiral Lagrangian and the Pion Mass in Nuclear Matter

Abstract：

We argue that effective pion mass in nuclear matter obtained from chiral effective lagrangians is unique and does not depend on off-mass-shell extensions of the pion fields as e. g. the PCAC choice. How chiral perturbation theory can be applied to the analysis of s-wave pion propagation is discussed. We consider tree level lagrangians throughout, working to O(Q 2). We illustrate the results for homogeneous, isotropic, isospin symmetric and spin-unpolarized nuclear matter, and evaluate nucleon operators in the mean field approximation, such that the corresponding results hold modulo nuclear correlation corrections. The effective pion mass in isospin symmetric nuclear matter is predicted to increase slightly with increasing nuclear density, whereas the effective time-like pion decay constant and the magnitude of the density-dependent quark condensate decrease appreciably. We work out the in-medium pion mass, the effective pion decay constant, the in-medium quark condensate, the Gell-Mann-Oakes-Renner relation and the PCAC relation in nuclear matter. The in-medium GMOR relation as well as other in-medium identities are studied in addition. Finally, we discuss how the new developments about non-relativistic chiral lagrangians and generalizations to four-quark condensates constrain the structure of the in-medium chiral lagrangians, sevral constraints on effecttive lagrangians for the description of the pion propagation in isospin symmetric, isotropic and homogenous nuclear matter.