The effect of hadronic scatterings on the measurement of vector meson spin alignments in heavy-ion collisions

Spin alignments of vector mesons and hyperons in relativistic heavy-ion collisions have been proposed as signals of global polarization. The STAR experiment first observed the begin{document}$ Lambda$end{document} polarization. Recently, the ALICE collaboration measured the transverse momentum (begin{document}$p_T$end{document}) and the collision centrality dependence of begin{document}$K^*$end{document}, and begin{document}$phi$end{document} spin alignments during Pb-Pb collisions at begin{document}$sqrt {{s_{{rm NN}}}}$end{document} = 2.76 TeV. A large signal is observed in the low begin{document}$p_T$end{document} region of mid-central collisions for begin{document}$K^*$end{document}, while the signal is much smaller for begin{document}$phi$end{document}, and these have not been understood yet. Since vector mesons have different lifetimes and their decay products have different scattering cross sections, they suffer from different hadronic effects. In this paper, we study the effect of hadronic interactions on the spin alignment of begin{document}$K^*$end{document}, begin{document}$phi$end{document}, and begin{document}$rho$end{document} mesons in relativistic heavy-ion collisions with a multi-phase transport model. We find that hadronic scatterings lead to a deviation of the observed spin alignment matrix element begin{document}$rho_{00}$end{document} away from the true value for begin{document}$rho$end{document} and begin{document}$K^*$end{document} mesons (with a bigger effect on begin{document}$rho$end{document}) while the effect is negligible for the begin{document}$phi$end{document} meson. The effect depends on the kinematic acceptance: the observed begin{document}$rho_{00}$end{document} value is lower than the true value when the pseudorapidity (begin{document}$eta$end{document}) coverage is small, while there is little effect when the begin{document}$eta$end{document} coverage is large. Hence, this study provides valuable information to understand the vector meson spin alignment signals observed during the experiments.