Mass splitting of vector mesons and spontaneous spin polarization under rotation *

Abstract

Abstract 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.