Practical Considerations for Measuring Global Spin Density Matrix Elements of Vector Mesons in Heavy-Ion Collisions

TL;DR

The paper addresses measuring global spin density matrix elements $ρ_{00}$ and off-diagonal $ρ_{mm'}$ for vector mesons in heavy-ion collisions, where a traditional 1D analysis can bias $ρ_{00}$ if off-diagonal SDMEs are nonzero. It introduces a two-dimensional angular distribution framework that enables simultaneous extraction of $ρ_{00}$ and off-diagonal SDMEs, with analytic corrections for event-plane resolution modeled by $R_m$ and rotation $R_x(ΔΨ_m)$ between reaction- and event-plane frames, and validates the approach with large-scale Monte Carlo simulations under realistic detector effects including $p_T$ resolution. The results show that neglecting event-plane smearing biases the SDMEs in 1D analyses, while the 2D method faithfully recovers the input SDMEs; an iterative $p_T$-resolution correction further ensures convergence to the true values. Overall, the work provides practical, bias-minimizing procedures to measure all five SDMEs, enabling robust access to local spin correlations and spin hydrodynamics in the quark-gluon plasma and informing CME-related observables.

Abstract

The STAR Collaboration has reported a significant $φ$-meson global spin alignment ($ρ_{00}$) signal in Au+Au collisions at $\sqrt{s_{NN}}\leq62$ GeV by measuring the polar angle distribution of $φ$-meson daughters with respect to the orbital angular momentum (OAM) 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 polar and azimuthal angle distribution. This method allows simultaneous extraction of $ρ_{00}$ and off-diagonal spin density matrix elements (SDMEs), providing unique access to local quark-antiquark spin correlations and spin hydrodynamics in quark-gluon plasma (QGP). The new 2D method also removes potential biases from non-zero off-diagonal SDMEs on $ρ_{00}$ with the 1D method. A detailed procedure to correct for detector acceptance and resolution effects is also presented and validated by simulation studies.

Figures (4)

• Figure 1: Global frame coordinate system: $\vec{p}_{d}$ is the momentum of a daughter particle in the vector meson's rest frame.
• Figure 2: 2-dimensional event plane resolution corrected results with and without event plane smearing: Blue points correspond to using the reaction plane yield correction and the orange points correspond to the event plane yield correction.
• Figure 3: 1-dimensional and 2-dimensional event plane resolution correction: Blue points correspond to using the 1-dimensional method and orange points correspond the 2-dimensional method.
• Figure 4: $p_{T}$ resolution correction with iterative method: The blue circles correspond to $p_{T}$ smearing off in the correction procedure. Yellow squares correspond to the first attempt (iteration 0) at correcting the $p_{T}$ resolution effect using isotropic $\cos{\theta^{\ast}},\beta$ MC. The cyan triangles and pink crosses correspond to the first and second iteration of input MC $\rho$ parameters, respectively.