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\title{Significant charge splitting of rapidity-odd directed flow slope and its implication on electromagnetic effect in Au+Au, $^{96}_{44}$Ru+$^{96}_{44}$Ru, and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions from STAR}
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\centerline{Diyu Shen}

\section*{Abstract}
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Heavy-ion collisions can produce an ultra-strong magnetic field, the evolution of which was predicted to decrease (increase) the directed flow slope, $dv_1/dy$, for positively (negatively) charged particles \cite{Umut:2018,Umut:2014}. In this work, we study this effect with large statistics datasets accumulated for Au+Au, $^{96}_{44}$Ru+$^{96}_{44}$Ru, and $^{96}_{40}$Zr+$^{96}_{40}$Zr isobar collisions at $\sqrt{s_{NN}}=$ 200 GeV, and Au+Au collisions at $\sqrt{s_{NN}}=$ 27 GeV. 
The charge dependent $dv_1/dy$ splitting, $\Delta(dv_1/dy)$, will be presented for $\pi^{\pm}$, $K^{\pm}$, and (anti)proton. A finite $\Delta(dv_1/dy)$ between protons and anti-protons has been observed and it changes from positive to negative as a function of centrality from central to peripheral collisions. This is the first observation of a significant negative $\Delta(dv_1/dy)$ between proton and anti-protons. A similar decreasing trend of slope difference between $K^+$ and $K^-$ has also been observed in Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV and 27 GeV, and  in isobar collisions with less significance. The slope difference between $\pi^+$ and $\pi^-$ is negative and decreases as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}=$ 27 GeV, while no significant slope difference is observed in Au+Au and isobar collisions at $\sqrt{s_{NN}}=$ 200 GeV.  Our measurements of significant negative $\Delta(dv_1/dy)$ cannot be explained by conventional mechanisms (e.g. transported quarks), but qualitatively agree with the theoretical prediction with an ultra-strong electromagnetic field in peripheral collisions.  

\begin{thebibliography}{}
\bibitem{Umut:2018}
U. Gursoy, D. Kharzeev, E. Marcus {\it et al.} Phy.Rev.C, {\bf{98}} 055201 (2018).
\bibitem{Umut:2014}
U. Gursoy, D. Kharzeev and K. Rajagopal. Phy.Rev.C, {\bf{89}} 054905 (2014).
\end{thebibliography}{}

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