Spin alignment of vector mesons by second-order hydrodynamic gradients

Starting with the polarization dependent Wigner function of vector mesons, we derive an expression for the 00--component (ρ₀₀) of spin density matrix in terms of the second order gradients of the vector meson distribution functions. We further apply a thermal model to analyze the transverse momentum and the azimuthal angle dependence of ρ₀₀ for φ and K*0 mesons resulting from distribution gradients in Au-Au collisions with √sNN=130 GeV at midrapidity. Our results for the transverse momentum dependence indicate that the deviations of ρ₀₀ from $1/3$ as the signal for spin alignment are greatly enhanced at large transverse momenta and have a strong centrality dependence while analysis of the azimuthal angle (φq) dependence suggest that such deviations have a cos(2φq) structure with opposite sign for φ and K*0. Our finding may be considered as a baseline for probing spin-alignment mechanisms beyond hydrodynamic gradients.