The mass of charged pions in neutron star matter

We examine the behavior of charged pions in neutron-rich matter using heavy-baryon chiral perturbation theory. This study is motivated by the prospect that pions, or pion-like, excitations, may be relevant in neutron-rich matter encountered in core-collapse supernovae and neutron star mergers. We find, as previously expected, that the $\pi^-$ mass increases with density and precludes s-wave condensation, and the mass of the $\pi^+$ mode decreases with increasing density. The energy difference between neutrons and protons in neutron-rich matter related to the nuclear symmetry energy alters the power counting. It enhances higher-order contributions to the pion self-energy. Previously unimportant but attractive diagrams are now enhanced. The net effect of this is the appearance of a new collective mode with the quantum numbers of the $\pi^+$, and a pronounced reduction of the $\pi^+$ mass.