Mass splitting of vector mesons and spontaneous spin polarization under rotation

In this study, we investigate the effect of rotation on the masses of scalar and vector mesons in the framework of the 2-flavor Nambu-Jona-Lasinio model. The existence of rotation produces a tedious quark propagator and a corresponding polarization function. By applying the random phase approximation, the meson mass is numerically calculated. It is found that the behavior of scalar and pseudoscalar meson masses under angular velocity ω is similar to that at a finite chemical potential; both rely on the behavior of the constituent quark mass and reflect the property related to chiral symmetry. However, vector meson ρ masses have a more profound relation to rotation. After analytical and numerical calculations, it turns out that at low temperature and small chemical potential, the mass for spin component of a vector meson under rotation exhibits a very simple mass splitting relation, similar to the Zeeman splitting of a charged meson under magnetic fields. Furthermore, the mass of the spin component of vector meson ρ decreases linearly with ω and reaches zero at, which indicates that the system will develop vector meson condensation and the system will be spontaneously spin-polarized under rotation.