Chiral Phase Transition in Rotating Quark Matter with Chiral Imbalance: A Medium Separation Scheme Regularized NJL Model Study

We investigate the chiral phase transition in rotating quark matter with chiral imbalance using the two-flavor Nambu-Jona-Lasinio (NJL) model regularized by the Medium Separation Scheme (MSS). Our numerical calculations demonstrate that the chiral chemical potential $\mu_5$ and angular velocity $\omega$ exert opposite effects on chiral symmetry breaking: $\mu_5$ enhances the breaking, raising the pseudocritical temperature $T_{pc}$ and sharpening the phase transition, while $\omega$ suppresses the breaking, lowering $T_{pc}$ and smearing the transition. Notably, chiral imbalance buffers the rotation-induced softening of the phase transition-the suppression of $T_{pc}$ by $\omega$ weakens progressively as $\mu_5$ increases. The MSS predicts a monotonic increase of $T_{pc}$ with $\mu_5$, in qualitative agreement with LQCD, resolving the discrepancy found in traditional regularization. Furthermore, the rotational suppression of $T_{pc}$ exhibits strong radius dependence: larger rotation radii amplify the suppression due to enhanced spacetime curvature and centrifugal effects, and can even induce an abrupt drop in $T_{pc}$ in the high-rotation region. These findings clarify the interplay between rotation and chiral imbalance in modulating the QCD chiral phase transition and validate the MSS as a reliable regularization framework for such extreme systems.