Spin alignment of vector mesons by second-order hydrodynamic gradients
Avdhesh Kumar, Di-Lun Yang, Philipp Gubler
Abstract
Starting with the polarization dependent Wigner function of vector mesons, we derive an expression for the 00--component (${\ensuremath{\rho}}_{00}$) 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 ${\ensuremath{\rho}}_{00}$ for $\ensuremath{\phi}$ and ${K}^{*0}$ mesons resulting from distribution gradients in Au-Au collisions with $\sqrt{{s}_{NN}}=130\text{ }\text{ }\mathrm{GeV}$ at midrapidity. Our results for the transverse momentum dependence indicate that the deviations of ${\ensuremath{\rho}}_{00}$ 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 (${\ensuremath{\phi}}_{q}$) dependence suggest that such deviations have a $\mathrm{cos}(2{\ensuremath{\phi}}_{q})$ structure with opposite sign for $\ensuremath{\phi}$ and ${K}^{*0}$. Our finding may be considered as a baseline for probing spin-alignment mechanisms beyond hydrodynamic gradients.