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

## TL;DR

This study explores how hydrodynamic effects influence the longitudinal spin polarization of $\\Lambda$ hyperons in high-energy nuclear collisions, analyzing the roles of thermal vorticity and shear tensor across different equilibrium assumptions.

## Contribution

It provides a detailed numerical analysis of spin polarization in Au+Au and p+Pb collisions using the CLVisc hydrodynamic model, considering multiple equilibrium scenarios.

## Key findings

- Thermal vorticity significantly affects spin polarization.
- The thermal-shear tensor also contributes to polarization.
- Results vary with collision system and equilibrium assumptions.

## Abstract

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.