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 (${\rho }_{00}$) 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 ${\rho }_{00}$ for $\varphi$ and $K^{*0}$ mesons resulting from distribution gradients in Au-Au collisions with $\sqrt{s_{NN}}=130\mathrm{GeV}$ at midrapidity. Our results for the transverse momentum dependence indicate that the deviations of ${\rho }_{00}$ 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 (${\varphi }_q$) dependence suggest that such deviations have a $\cos \left(2{\varphi }_q\right)$ structure with opposite sign for $\varphi$ and $K^{*0}$. Our finding may be considered as a baseline for probing spin-alignment mechanisms beyond hydrodynamic gradients.