The STAR Collaboration has reported a significant $\varphi$-meson global spin alignment $\left({\rho }_{00}\right)$ signal in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}\le 62$ GeV by measuring the polar angle distribution of $\varphi$-meson daughters with respect to the orbital angular momentum direction of the collision system. In this paper, a new method is explored for studying vector-meson global spin alignment in heavy-ion collisions by examining the two-dimensional (2D) polar and azimuthal angle distribution. This method allows simultaneous extraction of ${\rho }_{00}$ and off-diagonal spin density matrix elements (SDMEs), providing unique access to local quark-antiquark spin correlations and spin hydrodynamics in quark-gluon plasma. The new 2D method also removes potential biases from nonzero off-diagonal SDMEs on ${\rho }_{00}$ with the 1D method. A detailed procedure to correct for detector acceptance and resolution effects is also presented and validated by simulation studies.

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• Relativistic heavy-ion collisions
• Vector mesons
• Spin
• Particle detectors