The polarization of the $\Lambda$ and $\overline{\Lambda}$ hyperons along the beam direction has been measured in proton-lead (pPb) collisions at a center-of-mass energy per nucleon pair of 8.16 TeV. The data were obtained with the CMS detector at the LHC and correspond to an integrated luminosity of 186.0 $\pm$ 6.5 nb$^{-1}$. A significant azimuthal dependence of the hyperon polarization, characterized by the second-order Fourier sine coefficient $P_{z,s2}$, is observed. The $P_{z,s2}$ values decrease as a function of charged particle multiplicity, but increase with transverse momentum. A hydrodynamic model that describes the observed $P_{z,s2}$ values in nucleus-nucleus collisions by introducing vorticity effects does not reproduce either the sign or the magnitude of the pPb results. These observations pose a challenge to the current theoretical implementation of spin polarization in heavy ion collisions and offer new insights into the origin of spin polarization in hadronic collisions at LHC energies.
The second-order Fourier sine coefficients of $\Lambda$, $\bar{\Lambda}$ and $\Lambda+\bar{\Lambda}$ polarizations along the beam direction as functions of $N_\mathrm{trk}^\mathrm{offline}$ in pPb collisions at 8.16 TeV.
The second-order Fourier sine coefficients of $\Lambda+\bar{\Lambda}$ polarization along the beam direction as functions of $p_{T}$ in pPb collisions at 8.16 TeV.
The second-order Fourier sine coefficients of $K_{S}^{0}$ polarization along the beam direction as functions of $N_\mathrm{trk}^\mathrm{offline}$ in pPb collisions at 8.16 TeV.
The $\Lambda$ ($\bar{\Lambda}$) hyperon polarization along the beam direction has been measured for the first time in Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV. The polarization dependence on the hyperons' emission angle relative to the second-order event plane exhibits a sine modulation, indicating a quadrupole pattern of the vorticity component along the beam direction. The polarization is found to increase in more peripheral collisions, and shows no strong transverse momentum ($p_T$) dependence at $p_T>1$ GeV/$c$. The magnitude of the signal is about five times smaller than those predicted by hydrodynamic and multiphase transport models; the observed phase of the emission angle dependence is also opposite to these model predictions. In contrast, blast-wave model calculations reproduce the modulation phase measured in the data and capture the centrality and transverse momentum dependence of the signal once the model is required to reproduce the azimuthal dependence of the Gaussian source radii measured via the Hanbury-Brown and Twiss intensity interferometry technique.
$\langle \cos\theta_p* \rangle$ of $\Lambda$ and $\bar{\Lambda}$ hyperons as a function of azimuthal angle $\phi$ relative to the second-order event plane $\Psi_2$ for 20%–60% centrality bin in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.
The second Fourier sine coefficient $\langle P_Z \sin(2\phi-2\Psi_2) \rangle$ of the polarization of $\Lambda$ and $\bar{\Lambda}$ along the beam direction as a function of the collision centrality in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.
The second Fourier sine coefficient $\langle P_Z \sin(2\phi-2\Psi_2) \rangle$ of the polarization of $\Lambda$ and $\bar{\Lambda}$ along the beam direction as a function of the collision centrality in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. Results updated with $\alpha_{\Lambda} = -\alpha_{\bar{\Lambda}} = 0.732$.
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