We investigate the influence of quark anomalous magnetic moments (AMMs) on the mass spectra of neutral pseudoscalar mesons ($\pi$, $K$, $\eta$, ${\eta }^{\prime }$) under external magnetic fields, finite temperatures, and quark chemical potentials using the three-flavor Nambu-Jona-Lasinio model. By incorporating AMMs at the quark level, we reveal that AMMs significantly alter the magnetic field dependence of constituent quark masses, inducing first-order phase transitions for light quarks at critical fields, while strange quarks exhibit nonmonotonic mass behavior. The inclusion of AMMs reshapes the QCD phase diagram, suppressing chiral transition temperatures, and the strong magnetic field shifts critical endpoints toward lower $\mu$ and higher $T$ without AMMs. The crossover phase transition without AMMs is replaced by a first-order transition with AMMs under strong fields. Moreover, the inverse magnetic catalysis (IMC) induced by the introduction of AMMs qualitatively aligns with the predictions of lattice QCD (LQCD) for the dependence of phase transition temperature on the magnetic field. For mesons, a larger AMM triggers abrupt mass collapses and enhances flavor spitting at zero $\mu$ and $T$ and accelerates chiral restoration for $K$ and $\eta$ mesons via thresholds tied to strange quark masses in finite $\mu$ and $T$. These findings underscore AMMs’ critical role in reconciling effective model predictions with LQCD results, particularly in reproducing IMC and explaining phase transition dynamics.

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• Effective field theory