Hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions

We perform a systematic study of the spin polarization of hyperons in heavy ion collisions using the music hydrodynamic model with a multiphase transport preequilibrium dynamics. Our model calculations nicely describe the measured collision energy, centrality, rapidity, and $p_T$ dependence of the $\mathrm{\Lambda }$ polarization. We also study and predict the global spin polarization of ${\mathrm{\Xi }}^{-}$ and ${\mathrm{\Omega }}^{-}$ as a function of collision energy, which provides a baseline for the studies of the magnetic moment, spin, and mass dependence of the spin polarization. For the local spin polarization, we calculate the radial and azimuthal components of the transverse $\mathrm{\Lambda }$ polarization and find specific modulating behavior which could reflect the circular vortical structure. However, our model fails to describe the azimuthal-angle dependence of the longitudinal and transverse $\mathrm{\Lambda }$ polarizations, which indicates that the hydrodynamic framework with the spin Cooper-Frye formula under the assumption of thermal equilibrium of the spin degree of freedom needs to be improved.

Figure 1

(a) Global $\mathrm{\Lambda }$ polarization along the $-y$ direction as a function of collision energy. (b) Centrality dependence of global $\mathrm{\Lambda }$ polarization in $27A$ GeV Au $+$ Au collisions. The kinematic cut for panels (a) and (b) are $0.4<p_T<3$ GeV, $\left|Y\right|<1$, and $0.4<p_T<3.0$ GeV, $\left|\eta \right|<1$, respectively. The calculated spin polarization is for primary $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$. The STAR data are taken from Ref. [4] (As the hyperon decay parameter ${\alpha }_{\mathrm{\Lambda }}$ is updated, here and in the following figures, the published STAR results are scaled by a factor of 0.87 [74].

Figure 2

Global spin polarization of $\mathrm{\Lambda }, {\mathrm{\Xi }}^{-}$, and ${\mathrm{\Omega }}^{-}$ in Au $+$ Au collisions at various collision energies. The kinematic setup is the same as that in Fig. 1. The STAR data are taken from Ref. [74]. For the measurements in $200A$ GeV and $27A$ GeV Au $+$ Au collisions, the centrality is $20–80\%$ and $20–50\%$, respectively. For the AMPT $+$ MUSIC calculations, the centrality is $20–50\%$.

Figure 3

(a) Transverse momentum and (b) pseudorapidity dependence of $\mathrm{\Lambda }$ polarization along the $-y$ direction in $200A$ GeV Au $+$ Au collisions at 20–60% centrality and in $27A$ GeV Au $+$ Au collisions at 15–75% centrality. The STAR data are taken from Refs. [5, 79].

Figure 4

(a) Distribution of $P_y$ on the $p_x\text{−}Y$ plane in momentum space. (b)–(d) Transverse spin polarization ${\mathit{P}}_{\perp }$ at midrapidity ($Y=0$), at backward rapidity ($Y=-2$), and at forward rapidity ($Y=2$) in $19.6A$ GeV Au $+$ Au collisions at $20–50\%$ centrality, calculated with AMPT $+$ music.

Figure 5

The azimuthal-angle $\varphi$ dependence of the (a) radial ($r$) and (b) azimuthal ($\varphi$) components of the transverse spin polarization ${\mathit{P}}_{\perp }$ in momentum space at forward rapidity, backward rapidity, and midrapidity, calculated with AMPT $+$ music.

Figure 6

Azimuthal distribution of (a) $P_{-y}$ and (b) ${\langle cos\left({\theta }_p^{*}\right)\rangle }^{\mathrm{sub}}$ in $200A$ and $19.6A$ GeV Au $+$ Au collisions at $20–50\%$ centrality. In panel (b), the calculated $P_z$ is scaled by a factor of 0.33 to make the comparison more explicit. The STAR data are taken from Refs. [6, 8].

Figure 7

The distribution of $P_y$ and $P_z$ at midrapidity in the transverse $p_x-p_y$ plane in $19.6A$ GeV Au $+$ Au collisions, calculated with AMPT $+$ music with and without initial flow.

Figure 8

Contributions of $P_z$ from AMPT $+$ music calculations: (a) total $P_z$, (b) the nonrelativistic contribution, and (c) and (d) Thomas-precession contributions in Eq. (12).

Figure 9

(a) Pseudorapidity distribution of all charged hadron and (b) transverse momentum spectra of pions and protons in $200A$ and $19.6A$ GeV Au $+$ Au collisions. The experimental data are from the PHOBOS, PHENIX, and STAR Collaborations [84, 85, 86].

Figure 10

Differential elliptic flow $v_2\left(p_T\right)$ of pions and protons in $200A$ GeV and $19.6A$ GeV Au $+$ Au collisions. The experimental data are from PHENIX and STAR Collaborations [87, 88].

Figure 11

(a) Energy-dependent global $\mathrm{\Lambda }$ polarization, calculated with AMPT [24] and AMPT $+$ music. (b) Hadronization distribution from AMPT and the freeze-out hypersurface from the AMPT $+$ music hydrodynamic model.