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

## TL;DR

This paper investigates how the Dirac sea influences pion propagation in asymmetric nuclear matter, comparing non-chiral and chiral models, and providing analytical results for effective pion masses and dispersion relations.

## Contribution

It introduces a comprehensive analysis of Dirac sea effects on pion propagation in ANM using both non-chiral and chiral effective theories with analytical solutions.

## Key findings

- Mode splitting for charged pions in ANM
- Dirac sea significantly affects pion effective masses
- Analytical dispersion relations derived under HNL approximation

## Abstract

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 non-chiral model where one starts with pseudoscalar (PS) $\pi$N coupling and the pseudovector (PV) representation is obtained via suitable non-linear 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 re-defining the field parameters as done in the modern effective field theory approach developed recently. The results are compared with the previous calculations for the case of symmetric nuclear matter (SNM). Closed form analytical results are presented for the effective pion masses and dispersion relations by making hard nucleon loop (HNL) approximation and suitable density expansion.