Pion properties in isospin-asymmetric nuclear matter using in-medium chiral perturbation theory

TL;DR

This paper uses in-medium chiral perturbation theory to analyze how pion properties like mass and decay constant vary with density and isospin asymmetry in nuclear matter, revealing splitting among the three pions.

Contribution

It provides a detailed calculation of in-medium pion properties considering isospin asymmetry, including a derived in-medium Gell-Mann--Oakes--Renner relation.

Findings

Pion properties split into three values in asymmetric matter.

Pion masses and decay constants depend on density and neutron-proton ratio.

The in-medium Gell-Mann--Oakes--Renner relation is validated within the model.

Abstract

We compute the density dependence of in-medium pion properties, such as mass, wave function renormalization, and decay constant in the correlation function approach, and how they change under the influence of isospin-asymmetric nuclear matter. To this end, we use in-medium chiral perturbation theory to compute the relevant Feynman diagrams up to two-loop diagrams. Our results show that the isospin asymmetry of the nuclear matter splits these quantities into three separate values, corresponding to the three pions. Consequently, the tendency of each in-medium pion mass, wave function renormalization, and decay constant is dependent on the density and the neutron-to-proton ratio $\rho_n/\rho_p$ of nuclear matter. We also derive an in-medium Gell-Mann--Oakes--Renner relation which is valid for isospin-asymmetric nuclear matter and investigate to what extent it holds within our calculations.