Effects of finite coverage on global polarization observables in heavy ion collisions

In non-central relativistic heavy ion collisions, the created matter possesses a large initial orbital angular momentum. Particles produced in the collisions could be polarized globally in the direction of the orbital angular momentum due to spin-orbit coupling. Recently, the STAR experiment has presented polarization signals for $\Lambda$ hyperons and possible spin alignment signals for $\phi$ mesons. Here we discuss the effects of finite coverage on these observables. The results from a multi-phase transport and a toy model both indicate that a pseudorapidity coverage narrower than $|\eta|< \sim 1$ will generate a larger value for the extracted $\phi$-meson $\rho_{00}$ parameter; thus a finite coverage can lead to an artificial deviation of $\rho_{00}$ from 1/3. We also show that a finite $\eta$ and $p_T$ coverage affect the extracted $p_H$ parameter for $\Lambda$ hyperons when the real $p_H$ value is non-zero. Therefore proper corrections are necessary to reliably quantify the global polarization with experimental observables.