Spin alignment of vector mesons by second-order hydrodynamic gradients

Avdhesh Kumar, Di-Lun Yang, and Philipp Gubler 2024 Physical Review D 109 054038

Starting with the polarization dependent Wigner function of vector mesons, we derive an expression for the 00–component (ρ_{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 ρ_{00} 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 ρ_{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 (ϕ_{q}) dependence suggest that such deviations have a cos(2ϕ_{q}) 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.