The hadron-quark crossover equation of state (EOS) of neutron star (NS) matter is investigated by combining relativistic mean-field hadronic models with the Nambu-Jona-Lasinio model for quark matter. The vector and diquark coupling constants of the Nambu-Jona-Lasinio model are constrained using perturbative QCD (pQCD) calculations at high density through a scale-averaging likelihood approach, together with constraints from NS observations and the causality condition on the speed of sound. It is found that the diquark coupling is tightly constrained to $H\simeq 1.5G_s$, while the vector coupling is restricted to $G_v\lesssim 1.1G_s$ by the combined pQCD and astrophysical constraints. Crossover EOSs are constructed based on three hadronic relativistic mean-field parameter sets, and their thermodynamic properties, sound speed behavior, and trace anomaly are analyzed. The resulting EOSs are applied to calculate NS global and dynamical properties, including mass-radius relations, tidal deformabilities, and fundamental radial oscillation frequencies. Compared with pure hadronic EOSs, the hadron-quark crossover is shown to significantly enhance the maximum NS mass, particularly for softer hadronic EOSs, while remaining consistent with observational bounds. It is further shown that the fundamental radial oscillation frequencies predicted by different EOSs exhibit pronounced differences, especially for intermediate-mass NSs, indicating that radial modes may provide a sensitive probe of the internal composition of NSs. These results indicate that quantitative NS observables may provide potential signatures of quark matter in NS interiors.

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• Nuclear matter in neutron stars