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We propose an improved quark coalescence model for spin alignment of vectormesons and polarization of baryons by spin density matrix with phase spacedependence. The spin density matrix is defined through Wigner functions. Withinthe model we propose an understanding of spin alignments of vector mesons$\phi$ and $K^{*0}$ (including $\bar{K}^{*0}$) in the static limit: a largepositive deviation of $\rho_{00}$ for $\phi$ mesons from 1/3 may come from theelectric part of the vector $\phi$ field, while a negative deviation of$\rho_{00}$ for $K^{*0}$ may come from the electric part of vorticity tensorfields. Such a negative contribution to $\rho_{00}$ for $K^{*0}$ mesons, incomparison with the same contribution to $\rho_{00}$ for $\phi$ mesons which isless important, is amplified by a factor of the mass ratio of strange to lightquark times the ratio of $\left\langle \mathbf{p}_{b}^{2}\right\rangle $ on thewave function of $K^{*0}$ to $\phi$ ($\mathbf{p}_{b}$ is the relative momentumof two constituent quarks of $K^{*0}$ and $\phi$). These results should betested by a detailed and comprehensive simulation of vorticity tensor fieldsand vector meson fields in heavy ion collisions.

Improved quark coalescence model for spin alignment and polarization of hadrons