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

Abstract

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 $μ_5$ and angular velocity $ω$ exert opposite effects on chiral symmetry breaking: $μ_5$ enhances the breaking, raising the pseudocritical temperature $T_{pc}$ and sharpening the phase transition, while $ω$ 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 $ω$ weakens progressively as $μ_5$ increases. The MSS predicts a monotonic increase of $T_{pc}$ with $μ_5$, 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.

Figures (6)

• Figure 1: Temperature dependence of the quark mass $M$ calculated using the MSS, with a fixed rotation radius $r = 0.1\,\text{Ge}{{\text{V}}^{\text{-1}}}$. Panel (a) shows the case of zero angular velocity ($\omega =0\ \text{GeV}$), while panel (b) corresponds to $0.45\ \text{GeV}$. The solid, dashed, and dot-dashed lines represent chiral chemical potentials ${{\mu }_{5}}=0.15\ \text{GeV}$, $0.3\ \text{GeV}$, and $0.45\ \text{GeV}$, respectively.
• Figure 2: Temperature dependence of the quark mass $M$, with a fixed rotation radius $r=0.1\,\text{Ge}{{\text{V}}^{\text{-1}}}$. Panel (a) corresponds to the case of vanishing chiral chemical potential (${{\mu }_{5}}=0\ \text{GeV}$), while panel (b) corresponds to finite chiral chemical potential (${{\mu }_{5}}=0.15\ \text{GeV}$). The solid, dashed, and dot-dashed lines denote angular velocities $\omega =0\ \text{GeV}$, $0.3\ \text{GeV}$, and $0.45\ \text{GeV}$, respectively.
• Figure 3: Temperature evolution of the derivative of the quark mass with respect to temperature, $dM/dT$. Panel (a) corresponds to vanishing chiral chemical potential (${{\mu }_{5}}=0\ \text{GeV}$), while panel (b) corresponds to ${{\mu }_{5}}=0.15\ \text{GeV}$. The solid, dashed, and dot-dashed lines represent angular velocities $\omega =0\ \text{GeV}$, 0.3 GeV, and 0.45 GeV, respectively.
• Figure 4: Pseudocritical temperature ${{T}_{\textrm{pc}}}$ of the chiral phase transition as a function of the chiral chemical potential ${{\mu }_{5}}$, calculated within the MSS at a fixed rotation radius. Three angular velocities are employed: $\omega =0\ \text{GeV}$ (black squares), $\omega =0.3\ \text{GeV}$ (red triangles), and $\omega =0.45\ \text{GeV}$ (blue circles).
• Figure 5: Pseudocritical temperature ${{T}_{\textrm{pc}}}$ of the chiral phase transition as a function of angular velocity $\omega$. The black squares, red triangles, and blue circles represent chiral chemical potentials ${{\mu }_{5}}=$ 0.0 GeV, 0.15 GeV, and 0.3 GeV, respectively.