Tensor polarization and the dissipative damping of vector meson in QCD Medium

Abstract

Unexpectedly large and puzzling spin alignment, and thus tensor polarization, of vector mesons has been observed in heavy-ion collisions. Given that tensor polarization represents a fluctuation of spin, we derive, for the first time, a fluctuation-dissipation relation for tensor polarization, where the polarization is proportional to first-order hydrodynamic gradients (e.g., the shear-stress tensor), with dissipative coefficients depending on the particle's damping properties, as characterized by its spectral function. Employing relativistic hydrodynamics at finite density, we find that dissipative contributions can generate substantial spin alignment. We provide illustrative examples (by tuning one coefficients $α_{\rm sh}$) that generate a beam energy, $p_T$, and centrality dependence of spin alignment resembling those observed in experiments, offering insights into these puzzling phenomena and demonstrating its potential as a ``spectrometer" for in-medium vector mesons.

Figures (4)

• Figure 1: Compare to experimental data STAR:2022fan by tuning one parameter $\alpha_{\rm sh} (p,T)$($\alpha_{\rm sh} (\Delta m, \Gamma)$), using the same experimental cuts: (1) $\alpha_{\rm sh}$ for different cases and their $\rho_{00}$; (2) Beam energy dependence; (3) $p_T$ dependence; (4) Centrality dependence.
• Figure 2: (1) The $\alpha_{\rm sh}$ coefficients for different cases; (2) $p_T$-dependent $\rho_{00}$ for 'green' coefficients in (1); (3) $p_T$-integrated $\rho_{00}$ as a function of centrality; (4) illustration of $m_s$ change with centrality and freezeout $T$.
• Figure 3: The effects of the first three contributions ("0 order", "bulk", "shear") in Eq. (\ref{['eq_expand']}) with $\hat{y}$ (left) and $\hat{x}$ (right) as quantization axis and $\alpha_0=\alpha_{\text{sh}}=1$(Using unit coefficients to highlight the effects of the flow gradients). The final results should be scaled by the physical value of $\alpha_0$ and $\alpha_{\text{sh}}$.
• Figure 6: Centrality dependence with experimental data STAR:2022fanWilks:2025uzh at 62.4 GeV ($1^{\rm st}$ panel), 27 GeV ($2^{\rm nd}$ panel), 19.6 GeV ($3^{\rm rd}$ panel), and $\sqrt[3]{dN/d\eta}$ as a function of centrality from PHENIX data PHENIX:2015tbb ($4^{\rm th}$ panel). Width and mass shift can be fitted as universal functions: $\Delta m=(8.2-1.7\sqrt[3]{dN/d\eta}) +\rm const$ and $\Gamma= 200-19\sqrt[3]{dN/d\eta}$, where "const" can be fixed by $\rho_{00}$ at 20-60% for a given beam energy using the same experimental cuts. With the functional form fixed at $200$ GeV, the shape of the centrality dependence at all lower energies is a qualitative "quasi-prediction" from the proposed "centrality-freezeout correlation".