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\title{Probing novel baryonic spin Hall effect using $\Lambda$ spin polarization at STAR}
\author{Qiang Hu  (for the STAR collaboration)\\
\\
Institute of Modern Physics Chinese Academy of Sciences, Lanzhou \\
 }		


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\section*{Abstract}

The Spin Hall Effect (SHE) is a generation of spin polarization for moving spin carriers in materials under an external electric field and is instrumental in investigating quantum effects in many-body systems~\cite{ref1}. Recent theoretical calculations indicate that the gradient of baryonic chemical potential (analogous to the electric field) can induce a sizeable spin Hall current in Au+Au collisions at $\sqrt{s_{NN}}$ $\sim$ 10 GeV. Furthermore, at the RHIC Beam Energy Scan (BES) energies, the sign as well as the pattern of energy dependence of the difference between the harmonics of spin polarization of $\Lambda$ and $\overline{\Lambda}$  hyperons, can be significantly different with and without the presence of baryonic spin Hall current~\cite{ref2,ref3,ref4}.

In this talk, we will present the harmonic coefficients of $\Lambda$ hyperons' spin polarization ($P_{x} sin(2\Delta\phi)$, $P_{y} cos(2\Delta\phi)$, $P_{z} sin(2\Delta\phi)$) as functions of transverse momentum, rapidity, and collision centrality in RHIC BES-II Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 14.6, 19.6, and 27 GeV. These measurements serve as the first experimental probe of the predicted baryonic SHE in heavy-ion collisions.


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\begin{thebibliography}{99}
\bibitem{ref1} Y. Kato el al, Science 306 (2004) 1910
\bibitem{ref2} S. Liu et al, JHEP 07 (2021) 181
\bibitem{ref3} B. Fu et al, Phys. Rev. Lett. 127 (2021) 142301
\bibitem{ref4} B. Fu et al, arXiv: 2201.12970 (2022)
\end{thebibliography}

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