Hydrodynamic effects on spin polarization along the beam direction in Au+Au and p+Pb collisions

We investigate hydrodynamic effects on the spin polarization of $\Lambda$ hyperons in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV and p+Pb collisions at $\sqrt{s_{NN}} = 8.16$ TeV using the CLVisc hydrodynamic framework. We present numerical results for the second Fourier sine coefficient of the longitudinal spin polarization, $\langle P_{z} \sin 2(\phi_{p} - \Psi_{2}) \rangle$, as a function of multiplicity (centrality) under three equilibrium scenarios: $\Lambda$ equilibrium, $s$-quark equilibrium, and isothermal equilibrium. We highlight the respective roles of thermal vorticity and the thermal-shear tensor in generating $\langle P_{z} \sin 2(\phi_{p} - \Psi_{2}) \rangle$ across collision systems and scenarios.