Spin polarization of $\Lambda$ hyperon has been observed by STAR in non-central heavy-ion collisions [1,2,3]. Among these measurements, the global polarization reflects the bulk-averaged value of the vorticity, while the local polarization probes more detailed structure of the vorticity field.
We have studied the $\Lambda$ polarization in heavy-ion collisions using a multi-phase transport (AMPT) model. The results show that:
- The value of global polarization decreases with increasing collision energy . This is in agreement with the measurement [1,2].
- Because of the non-uniform transverse expansion of the fireball, it can produce transverse vorticity circling the beam direction and further generate transverse local polarization .
- The result for the longitudinal local polarization  is consistent with the hydrodynamic calculation. However, these calculations have an opposite sign comparing to the experiment measurement .
To resolve this sign puzzle, we further study the effect of feed-down decay on local $\Lambda$ polarization . We develop a theoretical framework to study how spin polarization is transferred from parent to daughter particle in two-body decay. After Monte-Carlo simulation, we find that the feed-down effect suppresses the primordial $\Lambda$ polarization, but can not flip the sign.
 STAR collaboration, Nature 548 (2017) 62-65.
 STAR collaboration, Phys.Rev. C98 (2018) 014910.
 STAR collaboration, arXiv:1905.11917.
 Hui Li, Long-Gang Pang, Qun Wang, and Xiao-Liang Xia, Phys.Rev. C96 (2017) no.5, 054908.
 Xiao-Liang Xia, Hui Li, Zebo Tang, and Qun Wang, Phys.Rev. C98 (2018) 024905.
 Xiao-Liang Xia, Hui Li, Xu-Guang Huang, and Huan Zhong Huang, arXiv:1905.03120, submitted to Phys.Rev.C.