Fluctuations and correlations of quark spin in hot and dense QCD matter

Abstract

In this work, we examine the impact of QCD phase transitions on the quark spin fluctuations and correlations. We propose the quark-antiquark correlation, which relates to the vector meson spin alignment and the $Λ-\barΛ$ correlation, can be used as a novel probe of the critical end point (CEP) in the QCD phase diagram. Using the Nambu-Jona-Lanisio model, we qualitatively study the properties of quark-antiquark spin correlations. Our findings reveal a peak structure near the CEP of the chiral phase transition, which may serve as an experimental signature of the CEP and account for the non-monotonic behavior of $φ$ meson alignment at low collision energies observed recently in experiments.

Figures (9)

• Figure 1: Upper panel: Quark-antiquark spin correlation $\langle P_{q}P_{\bar{q}}\rangle_{0}$ without critical fluctuation as a function of chemical potential. Lower panel: Quark-antiquark spin correlation $\langle P_{q}P_{\bar{q}}\rangle_{c}$ with critical fluctuation as a function of chemical potential at $r=0$. The angular velocity is chosen to be $\Omega=10$MeV.
• Figure 2: The density plot of the connected correlation $\langle P_{q}P_{\bar{q}}\rangle_c$ at $r=0$ with $\Omega=10$ MeV. The solid, dash and dot-dash line represent the hypothetical freezout line-1, 2, and 3 in Table \ref{['table:linepara']}, respectively. The red star stands for the CEP.
• Figure 3: $\delta\rho_{00}^\Omega$ at $r=0$ as a function of the collision energy $\sqrt{s}$ along the three different freezeout lines in Table. \ref{['table:linepara']}.
• Figure 4: A schematic figure including the critical fluctuation. The dashed line stands for $\rho_{00}=1/3$. The dashed dot line is based on the freezeout-3 and our argument. The solid line is from Ref. Sheng:2019kmk. The STAR data is from Ref. Wilks.
• Figure 5: Contribution of the thermodynamic fluctuations to the spin density matrix element $\delta\rho_{00}^\Omega$ as a function of the radial coordinate $r$ with several values of the angular velocity, where we have chosen a thermodynamic state in the phase diagram far away from the CEP with $T=85$ MeV and $\mu=250$ MeV.