Glashow-Weinberg relation in isospin-asymmetric nuclear matter

The conservation of the axial-vector currents in nuclear matter with finite isospin asymmetry $ρ_n/ρ_p$ is explored in this paper. In explicit calculations in the in-medium chiral perturbation theory, a charged pion becomes massive in isospin-asymmetric nuclear matter. In the presence of the massive charged pion, two components of the axial-vector current are not conserved from the two-loop order when applying the massive in-medium pion state. As a result, the in-medium Glashow-Weinberg relation for the charged pions cannot be derived in isospin-asymmetric nuclear matter from operator relations in quantum chromodynamics.