Spin polarization of $\mathrm{\Lambda }$ hyperons along beam direction in p+Pb collisions at $\sqrt{s_{NN}}=8.16$ TeV using hydrodynamic approaches

We have implemented the 3+1 dimensional CLVisc hydrodynamics model with TRENTO-3D initial conditions to investigate the spin polarization of $\mathrm{\Lambda }$ hyperons along the beam direction in p+Pb collisions at $\sqrt{s_{NN}}=8.16$ TeV. Following our previous theoretical framework based on quantum kinetic theory, we consider three different scenarios: $\mathrm{\Lambda }$ equilibrium, $s$ quark equilibrium, and iso-thermal equilibrium scenarios. We have computed the second Fourier sine coefficients of spin polarization along the beam direction, denoted as $⟨P_z\sin 2({\phi }_p-{\mathrm{\Psi }}_2)⟩$, with ${\phi }_p-{\mathrm{\Psi }}_2$ being the azimuthal angle relative to the second-order event plane ${\mathrm{\Psi }}_2$, as functions of multiplicity, transverse momentum and pseudo-rapidity in the three scenarios. Additionally, we have also computed the spin polarization along the beam direction, $P_z$, as a function of the azimuthal angle. We find that the spin polarization induced by thermal vorticity always provides an opposite contribution compared to the shear-induced polarization in p+Pb collisions. The total spin polarization computed by the current hydrodynamic model disagrees with the data measured by LHC-CMS experiments. Our findings imply that other non-flow effects may play a crucial role in p+Pb collisions.