Shear-Induced Spin Polarization in Heavy-Ion Collisions

We study the spin polarization generated by the hydrodynamic gradients. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. We obtain the explicit expression for SIP using the quantum kinetic equation and linear response theory. Based on a realistic hydrodynamic model, we compute the differential spin polarization along both the beam direction $\widehat{z}$ and the out-plane direction $\widehat{y}$ in noncentral heavy-ion collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$, including both SIP and thermal vorticity effects. We find that SIP contribution always shows the same azimuthal angle dependence as experimental data and competes with thermal vorticity effects. In the scenario that $\mathrm{\Lambda }$ inherits and memorizes the spin polarization of a strange quark, SIP wins the competition, and the resulting azimuthal angle dependent spin polarization $P_y$ and $P_z$ agree qualitatively with the experimental data.

Figure 1

Spin polarization as a function of azimuthal angle ${\varphi }_p$ along $z$ and $y$ directions, induced by hydrodynamic gradients for $\mathrm{\Lambda }$ hyperon and strange quarks at the freeze-out surface: colored curves show effects from vorticity, temperature gradient, and shear stress tensor (i.e., the SIP), corresponding to the first, second, and third terms in Eq. (3), respectively. The effects of thermal vorticity are given by the sum of vorticity and temperature gradient effects and have been studied by many others. SIP is the new effect studied in this Letter and competes with the thermal vorticity effects.

Figure 2

Spin polarization of $\mathrm{\Lambda }$ hyperon (left) and strange quark (middle) along $z$ (upper) and $y$ (lower) directions induced by the combined effects of the shear stress tensor and thermal vorticity (solid curves) and by thermal vorticity effects only (dashed curves) on the freeze-out surface. Right: the replotted experimental data in Refs. [5, 7]. The $P_z$ is converted using $P_z=⟨\cos {\theta }_p^{*}⟩/[{\alpha }_H⟨(\cos {\theta }_p^{*}{)}^2⟩]$ assuming zero error in the denominator. The results for strange spin polarization illustrate the anticipated qualitative behavior in the strange memory scenario, i.e.; the memory of strange quark polarization is preserved in the measured $\mathrm{\Lambda }$ polarization.

Figure 3

The comparison between strange quark and $\mathrm{\Lambda }$ hyperon spin polarization in lab and particle rest frame.