\begin{document}$ (\sigma, \pi^0, \pi^\pm) $\end{document} are investigated in \begin{document}$ \mu_B-T-eB $\end{document} and \begin{document}$ \mu_I-T-eB $\end{document} spaces using a two-flavor NJL model and used to determine chiral symmetry restoration and the pion superfluid phase transition. In \begin{document}$ \mu_B-T-eB $\end{document} space, during the chiral symmetry restoration process, the mass of the pseudo-Goldstone mode \begin{document}$ \pi^0 $\end{document} increases, with sudden jumps. At the critical end point, the \begin{document}$ \pi^0 $\end{document} meson exhibits a sharp but continuous mass increase, with a sudden mass jump at the Mott transition. In the nearby first order chiral phase transition region, we observe two \begin{document}$ \pi^0 $\end{document} mass jumps, one induced by the Mott transition and the other by the quark mass jump. The mass of the Higgs mode σ first decreases and then increases with chiral symmetry restoration, only showing a jump at the first order chiral phase transition. We plot a chiral phase diagram in terms of the change in quark mass, the Mott transition of the pseudo-Goldstone mode \begin{document}$ \pi^0 $\end{document}, and the minimum mass of the Higgs mode σ. Owing to explicit breaking of chiral symmetry in the physical case, the chiral restoration phase boundaries on the \begin{document}$ \mu_B-T $\end{document} plane from the order parameter side and meson side are different. The \begin{document}$ \pi^0 $\end{document} and σ mass jumps will be helpful to the experimental search for the chiral phase diagram and critical end point. On the \begin{document}$ \mu_I-T $\end{document} plane, the competition between the pion superfluid phase transition and chiral symmetry restoration under magnetic fields is studied in terms of the Goldstone mode \begin{document}$ \pi^+ $\end{document} and pseudo-Goldstone mode \begin{document}$ \pi^0 $\end{document}. In contrast to the two mass jumps of \begin{document}$ \pi^0 $\end{document} in the first order chiral phase transition region, the \begin{document}$ \pi^+ $\end{document} meson displays several mass jumps in the chiral crossover region. At the critical end point, \begin{document}$ \pi^+ $\end{document} also has sharp but continuous mass change, with a mass jump at the Mott transition. The isospin symmetry is strict, and the pion superfluid phase transition is uniquely determined by the massless Goldstone mode \begin{document}$ \pi^+ $\end{document}. The separation of chiral restoration and the pion superfluid phase boundaries is enhanced by the external magnetic field."> Light mesons and phase structures in <i>μ</i><sub><i>B</i></sub>-<i>T</i>-<i>eB</i> and <i>μ</i><sub><i>I</i></sub>-<i>T</i>-<i>eB</i> spaces -
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