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

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 $\alpha_{{\rm sh}}$) 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.