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 phi and K-*0 mesons resulting from distribution gradients in Au-Au collisions with root s(NN) = 130 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 (phi(q)) dependence suggest that such deviations have a cos(2 phi(q)) structure with opposite sign for phi and K-*0. Our finding may be considered as a baseline for probing spin-alignment mechanisms beyond hydrodynamic gradients.