The mass of charged pions in neutron star matter

TL;DR

This paper investigates how charged pion masses change in neutron-rich matter using chiral perturbation theory, revealing density-dependent behaviors and uncertainties relevant for neutron star physics and nuclear interactions.

Contribution

It provides a detailed analysis of charged pion mass modifications in neutron-rich matter, including the effects of nuclear symmetry energy and collective modes, with quantified uncertainties.

Findings

$^-$ mass increases with density, preventing s-wave condensation below saturation density.

$^+$ mass decreases with density, and a collective mode of $^+$ appears at low wavelengths.

Uncertainties grow rapidly at densities above saturation, especially in symmetric nuclear matter.

Abstract

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 at $n_B\lesssim n_{\text{sat}}$, where $n_{\text{sat}} \simeq 0.16 \text{fm}^{-3}$ is the nuclear saturation density, and the mass of the $\pi^+$ mode decreases with density. The uncertainty in these predictions increases rapidly for $n_B \gtrsim n_{\text{sat}} $ because low energy constants associated with the two-pion-two-nucleon operators in chiral perturbation theory are poorly constrained. We find that 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 and result in a modest reduction of the pion masses. Furthermore, in the low-wavelength limit, a collective mode with the quantum numbers of the $\pi^+$ appears.