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 the polarization signals for $\Lambda$ hyperons and possible spin alignment signals for $\phi$ mesons. In this paper, 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 $|\eta|< \sim \!\! 1.3$ will generate a larger value for the extracted $\rho_{00}$ parameter for $\phi$ mesons and $p_H$ parameter for $\Lambda$ hyperons. A finite $p_T$ coverage also affects the extracted parameters. As a result, a finite coverage can lead to an artificial deviation from 1/3 on the extracted $\rho_{00}$ as well as a small deviation from 0 for the extracted $p_H$ even if there were no polarization. Therefore proper corrections should be made to the experimental observables before one can reliably quantify the global polarization.