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Description
This work focuses on the existence of pion condensate in neutron star matter based on a parity doublet model. Parity doublet model is a model that explains the hadron mass as two parts: one part is generated by spontaneous breaking of chiral symmetry and the other is an invariant mass that does not depend on the breaking of chiral symmetry and is called a chiral invariant mass $m_0$. A pion serves as psedo-Numbu-Goldstone boson associated with spontaneous chiral symmetry breaking and has a small mass. According to Bose-Einstein condensate theory, in nuclear matter, pion condensate could occur when the isospin chemical potential is large enough. In this study, we determine the phase transition line from normal phase to pion condensate phase on the $\mu_B-\mu_I$ plane, where $\mu_B$ is the baryon number chemical potential and $\mu_I$ is the isospin chemical potential. The result shows that in low density neutron star matter, pion condensate is unlikely to occur.