Event-by-event correlations between $\Lambda/\bar{\Lambda}$ polarization and CME observables in Au+Au collisions at $\sqrt{s_{NN}} = 27$ GeV from STAR*

Spin-orbit interactions cause a global polarization of $\Lambda/\bar{\Lambda}$ with the vorticity (total angular momentum) in the participant collision zone. The strong magnetic field mainly created by the spectator protons were predicted to lead to difference in the $\Lambda$ and $\bar{\Lambda}$ global polarization ($\Delta P = P_{\Lambda} - P_{\bar{\Lambda}} < 0$). On the other hand, the QCD predicts topological charge fluctuation in vacuum, resulting in a chirality imbalance, or parity violation in a local domain. This would give rise to an imbalanced left- and right-handed $\Lambda/\bar{\Lambda}$, $\Delta N= N_{\text{L}} - N_{\text{R}} \neq 0$, and a charge separation along the magnetic field, chiral magnetic effect (CME). The latter is characterized by the parity-even $\gamma$-correlator $\Delta\gamma$ and parity-odd sine coefficient $a_{1}$. While measurements of individual $\Delta P$, $\Delta\gamma$, and $a_{1}$ have not led to affirmative conclusions on the CME or the magnetic field, correlations among these observables may reveal new insights. We report exploratory measurements of event-by-event correlations between $\Delta P$ and $\Delta\gamma$, and between $\Delta N$ and $a_{1}$, by the STAR experiment in Au+Au collision at $27$ GeV.