Spin alignment of vector mesons by second-order hydrodynamic gradients

Kumar, A.*; Yang, D.-L.*; Gubler, P. 

Starting with the polarization dependent Wigner function of vector mesons, we derive an expression for the 00-component () 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 for and mesons resulting from distribution gradients in Au-Au collisions with GeV at midrapidity. Our results for the transverse momentum dependence indicate that the deviations of 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 dependence suggest that such deviations have a structure with opposite sign for and . Our finding may be considered as a baseline for probing spin-alignment mechanisms beyond hydrodynamic gradients.