Quark matter under rotation in the NJL model with vector interaction

We study the chiral phase transition of quark matter under rotation in two-flavor Nambu--Jona-Lasinio (NJL) model. It is found that, in the rotating frame, the angular velocity plays the similar role as the baryon chemical potential and suppresses the chiral condensate, thus the chiral phase transition shows a critical end point not only in the temperature-chemical potential $T-\mu$ plane, but also in the temperature-angular momentum $T-\omega$ plane. One interesting observation is that in the $T-\mu$ plane, the presence of the angular momentum only shifts down the critical temperature $T^E$ of the CEP and does not shift the critical chemical potential $\mu^E$, and in the $T-\omega$ plane, the increase of the chemical potential only shift down the critical temperature $T^E$ and does not change the critical angular momentum $\omega^E$. The phase structure in the $T-\mu$ plane is sensitive to the coupling strength in the vector channel, while the phase structure in $T-\omega$ plane is not. It is also observed that the rotating angular velocity suppresses the kurtosis of the baryon number fluctuations, while it enhances the pressure density, energy density, the specific heat and the sound velocity.