Global polarization of $Λ$ hyperons and its sensitivity to equations of state in low-energy heavy-ion collisions

Abstract

Significant global polarization of $Λ$ hyperons along the direction of the orbital angular momentum has been measured in non-central heavy-ion collisions where the equation of state (EOS) of the produced dense matter is expected to change from intermediate to low colliding energies. We study the sensitivity of the global $Λ$ polarization to EOS in heavy-ion collisions within the SMASH transport model. Among the three different EOS we considered, only the hadron resonance gas (HRG) describes the experimental data well at low colliding energies even when it is below the $Λ$ production threshold in nucleon-nucleon collisions. The polarization induced by thermal vorticity as a function of centrality, rapidity, and transverse momentum at $\sqrt{s_{NN}} = 3$ GeV in Au+Au collisions is shown to agree well with the experimental data. Our study also indicates a possible peak in the global $Λ$ polarization around $\sqrt{s_{NN}} = 2.4$ GeV in Au+Au collisions. Furthermore, we find that the rapidity and transverse momentum-dependent helicity polarization induced by thermal vorticity vanishes due to space-reversal symmetry.

Figures (6)

• Figure 1: An example of extracting the temperature $T$ as a function of energy density $\epsilon$ at a specific net baryon density $n_{B}=0\; \text{fm}^{-3}$ or $n_{B}=0.2\; \text{fm}^{-3}$. The gray dashed, blue dash-dotted, and green solid lines represent the extracted temperature using the HotQCD EOS, NEOS-BQS EOS and HRG EOS, respectively. The top-left subplot shows $\epsilon/T^4$ as a function of $T$ for the three EOS.
• Figure 2: Global polarization of $\Lambda$ hyperons as a function of collision energy in Au+Au collisions by using the SMASH model. The gray dashed, blue dash-dotted, and green solid lines represent the results with HotQCD, NEOS-BQS, and HRG EOS, respectively. The red markers denote experimental data from the STAR STAR:2023eck and HADES HADES:2022enx collaborations. The purple point corresponds to $\sqrt{s_{NN}} = 2m_{N}$, the threshold energy where no collisions occur, resulting in vanishing vorticity and polarization. The kinematic cuts applied to $\Lambda$ hyperons are consistent with those used in the experimental measurements: $p_{T} \in [0.2, 1.5]$ GeV and $y_{cm} \in [-0.5, 0.3]$ at $\sqrt{s_{NN}} = 2.4$ GeV; $p_{T} \in [0.7, 2.0]$ GeV and $y_{cm} \in [-0.2, 1]$ for $2.4 < \sqrt{s_{NN}} < 7.7$ GeV; and $p_{T} \in [0.5, 6.0]$ GeV with $y_{cm} \in [-1, 1]$ at $\sqrt{s_{NN}} = 7.7$ GeV.
• Figure 3: The energy-weighted $\langle\varpi_{zx}\rangle_{max}$ component of thermal vorticity at space rapidity $\eta = 0$ as a function of collision energy $\sqrt{s_{NN}}$. The color assignment is the same as in Fig. \ref{['fig:energy']}.
• Figure 4: Polarization of $\Lambda$ hyperons along the $y$ direction as a function of centrality at $\sqrt{s_{NN}} = 3$ GeV in Au+Au collisions. The green solid line represents results computed using the HRG EOS. The red markers denote experimental data from the STAR STAR:2023eck collaboration. The kinematic region of $\Lambda$ hyperons is the same as that in Fig. \ref{['fig:energy']}.
• Figure 5: Polarization of $\Lambda$ hyperons along the $-y$ direction $-P_y$ and helicity polarization of $\Lambda$ hyperons as a function of rapidity $y_{cm}$ in $0$–$50\%$ centrality Au+Au collisions at $\sqrt{s_{NN}} = 3$ GeV. The green solid line and brown dashed line represent results for $-P_y$ and helicity polarization, respectively. The red markers denote experimental data from the STAR collaboration STAR:2023eck. We have chosen the HRG EOS at $b = 5$ fm and take $p_T > 0.7$ GeV for $\Lambda$ hyperons.