Quark Anomalous Magnetic Moments and Neutral Pseudoscalar Meson Dynamics in Magnetized QCD Matter

Abstract: We investigate the influence of quark anomalous magnetic moments (AMM) on the mass spectra of neutral pseudoscalar mesons ($\pi$, $K$, $\eta$, $\eta^{'}$) under external magnetic fields, finite temperatures, and quark chemical potentials using the three-flavor Nambu-Jona-Lasinio (NJL) model. By incorporating AMM at the quark level, we reveal that AMM significantly alters the magnetic field dependence of constituent quark masses, inducing first-order phase transitions for light quarks at critical fields, while strange quarks exhibit non-monotonic mass behavior. The inclusion of AMM reshapes the QCD phase diagram, suppressing chiral transition temperatures and shifting critical endpoints (CEP) toward lower $\mu$ and $T$. Notably, crossover transitions observed without AMM are replaced by first-order transitions under strong fields, aligning with lattice QCD predictions for IMC. For mesons, AMM triggers abrupt mass collapses and enhances flavor mixing, accelerating chiral restoration for $K$ and $\eta$ mesons via thresholds tied to strange quark masses. The $\eta'$ meson, as a resonance state, shows suppressed mass growth and instability at strong fields, highlighting limitations in handling non-perturbative decay widths within the NJL framework. These findings underscore AMM critical role in reconciling effective model predictions with LQCD results, particularly in explaining IMC and phase transition dynamics.