In hydrodynamic picture of heavy ion collisions, local thermal vorticity of the QGP fluid leads to polarization of nonzero spin hadrons produced out of it . The nonzero polarization of $\Lambda$ hyperons has been recently discovered by STAR in non-central Au-Au collisions in RHIC Beam Energy Scan program .
We further study the predictions of the hydrodynamic model for different components of the $\Lambda$ polarization in the framework of 3-dimensional viscous hydrodynamic model with UrQMD initial state, and demonstrate that:
at RHIC Beam Energy Scan energies, the global polarization $P$ of produced Lambda is directed along the total angular momentum of the fireball (perpendicular to reaction plane). $P$ decreases with collision energy from 1.7 to 0.2% , in agreement with STAR results . The global $\Lambda$ polarization further decreases towards LHC energies,
at full RHIC and LHC energies, the dominant component of polarization is the one in the beam direction. This component has a quadrupole structure in transverse momentum plane. Its amplitude $f_2$ shows a mild decrease with collision energy, and it is thus detectable at LHC enegries.
We show that different components of polarization are driven by different properties of the hydrodynamic expansion: whereas the global polarization $P$ is a result of initial shear flow in the reaction plane, $f_2$ is driven by anisotropy of the transverse expansion (which is also responsible for elliptic flow $v_2$). Polarization component in the beam direction is a generic effect present even in a simple 2-dimensional hydrodynamic calculation with longitudinal boost invariance .
 F. Becattini, V. Chandra, L. Del Zanna, E. Grossi, Ann. Phys. 338 (2013) 32.
 STAR collaboration, Nature 548 (2017), 62–65
 I. Karpenko, F. Becattini, Eur. Phys. J. C (2017) 77: 213.
 F. Becattini, Iu. Karpenko, arXiv:1707.07984, accepted to Phys.Rev.Lett.
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