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.
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