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 pionlike excitations, may be relevant in neutron-rich matter encountered in core-collapse supernovae and neutron star mergers. We find, as previously expected, that the ${\ensuremath{\pi}}^{\ensuremath{-}}$ mass increases with density and precludes $s$-wave condensation at ${n}_{B}\ensuremath{\lesssim}{n}_{\mathrm{sat}}$, where ${n}_{\mathrm{sat}}\ensuremath{\approx}0.16\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$ is the nuclear saturation density, and the mass of the ${\ensuremath{\pi}}^{+}$ mode decreases with density. The uncertainty in these predictions increases rapidly for ${n}_{B}\ensuremath{\gtrsim}{n}_{\mathrm{sat}}$ because low-energy constants associated with the two-pion-two-nucleon operators in chiral perturbation theory are poorly constrained. These uncertainties are especially large in symmetric nuclear matter and should be included in the analysis of pion-nucleus interactions at low-energy and pionic atoms. In neutron-rich matter, accounting for the self-energy difference between neutrons and protons related to the nuclear symmetry energy has several effects. It alters the power counting of certain higher-order contributions to the pion self-energy. Previously unimportant but attractive diagrams are enhanced, resulting in a modest reduction of the pion masses. Furthermore, in the long-wavelength limit, a collective mode with the quantum numbers of the ${\ensuremath{\pi}}^{+}$ appears.