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

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.