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%\title{Measurements of Global and Local Polarization of Hyperons in 200 GeV Isobar Collisions and First Order Flow Vector Dependence of $\Lambda$ Global Polarization in 19.6 GeV Au+Au Collisions from STAR}
%\title{Measurements of Hyperons Polarization in Heavy-Ion Collisions at $\sqrt{s_{NN}}= 200, 19.6$ GeV from STAR}

\title{Hyperon Polarization in Isobar Collisions and Correlation of Global Polarization with Directed Flow from STAR}

\author{Xingrui Gou and Kosuke Okubo for the STAR Collaboration }
\date{}


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\noindent The observation of hyperon polarization has revealed the existence of large vorticities in the medium created by heavy-ion collisions. Global polarization indicates vorticities perpendicular to the reaction plane due to the system's orbital angular momentum, while local polarization indicates vorticities along the beam direction due to anisotropic transverse expansion of the medium.
With the high-statistics data collected by the STAR experiment for isobar Ru+Ru and Zr+Zr collisions at $\sqrt{s_{\mathrm{NN}}} = 200$ GeV, we present the measurements of global polarization for $\Lambda$, $\bar{\Lambda}$, and $\Xi^{\pm}$ as a function of centrality, transverse momentum, pseudorapidity, and azimuthal angle relative to the event plane.
These measurements allow us to study possible magnetic field driven effects through the polarization difference between Ru+Ru and Zr+Zr, owing to a larger magnetic field expected in the former. 

\noindent Furthermore, the first measurements of $\Lambda$ hyperon local polarization along the beam direction relative to the second and third-order event planes in isobar collisions will be presented. Comparisons with previous measurements in Au+Au and Pb+Pb collisions at RHIC and the LHC will be performed to gain important insights into the collision system size and energy dependence of the vorticities in heavy-ion collisions. 

\noindent Previous measurements have shown a similar trend in the energy dependence between the global polarization and the slope of directed flow, suggesting a strong correlation between the initial tilt of the system and the vorticity\cite{v1dependence}. 
For the first time, this correlation is investigated, and the dependence of the $\Lambda$ global polarization as well as directed flow on the first-order flow vector ($q_1$) is presented in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}} = 19.6$ GeV.


\begin{thebibliography}{}
%\cite{LocalPolaritionpaper}.
%\bibitem{LocalPolaritionpaper}STAR Collaboration, Hyperon polarization along the beam direction relative to the second and third harmonic event planes in isobar collisions at $\sqrt{s_{NN}}$ = 200 GeV, 	arXiv:2303.09074.
%\bibitem{v1dependence}Vorticity and particle polarization in heavy ion collisions (experimental perspective), EPJ Web Conf. 171 (2018) 07002.
\bibitem{v1dependence}S. A. Voloshin, EPJ Web Conf. 171 (2018) 07002.
\end{thebibliography}
 
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