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. Phenomenologically, we find that the dissipative contributions have the potential to generate substantial spin alignment and give rise to complex behaviors, providing insights that may help explain the puzzling phenomena observed in experiments.