Effects of the Dirac sea on pion propagation in asymmetric nuclear matter

We study pion propagation in asymmetric nuclear matter (ANM). One of the interesting consequences of pion propagation in ANM is the mode splitting for the different charged states of pions. First we describe the pion-nucleon dynamics using the nonchiral model in which one starts with pseudoscalar pi N coupling, and the pseudovector representation is obtained via suitable nonlinear field transformations. For both of these cases, the effect of the Dirac sea is estimated. Subsequently, we present results using the chiral effective Lagrangian where the short-distance behavior (Dirac vacuum) is included by redefining the field parameters as done in the modern effective field theory approach developed recently. The results are compared with previous calculations for symmetric nuclear matter. Closed form analytical results are presented for the effective pion masses and dispersion relations by making a hard nucleon loop approximation and suitable density expansion.