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Light mesons $(\sigma, \pi^0, \pi^\pm)$ are investigated in$T-\mu_B-\mu_I-eB$ space by using a two-flavor NJL model, which are related tothe chiral symmetry restoration and pion superfluid phase transition. In$T-\mu_B-eB$ space, during the chiral restoration process, the mass ofpseudo-Goldstone mode $\pi^0$ keeps increasing, together with the sudden massjump. At the critical end point region, $\pi^0$ meson has a very sharp butcontinuous mass increase, together with a sudden mass jump at the Motttransition, and in the first order chiral phase transition region nearby, weobserve twice $\pi^0$ mass jumps, induced by the Mott transition and quark massjump, respectively. The mass of Higgs mode $\sigma$ first decreases and thenincreases associated with the chiral symmetry restoration, and shows a jump atthe first order chiral phase transition. We plot the chiral phase diagram interms of the change of quark mass, the Mott transition of $\pi^0$ and theminimum mass of $\sigma$. Due to the explicit breaking of chiral symmetry inphysical case, the chiral restoration phase boundaries in $T-\mu_B$ plane fromthe order parameter and meson side are different from each other. In $T-\mu_I$plane, the competition between pion superfluid phase transition and chiralsymmetry restoration under magnetic fields is studied in terms of the Goldstonemode $\pi^+$ and the pseudo-Goldstone mode $\pi^0$. The separation of the twophase boundaries is enhanced by the external magnetic field. Different from thetwice mass jumps of $\pi^0$ in the first order chiral phase transition region,the $\pi^+$ meson displays several mass jumps in the chiral crossover region.At the critical end point, $\pi^+$ also shows very sharp but continuous masschanges, together with a mass jump at the Mott transition.

Light mesons around critical end points in $T-\mu_B-\mu_I-eB$ space