Tensor spin polarization induced by curved freeze-out hypersurface

Abstract

We investigate how the curvature of the freeze-out hypersurface polarizes massive vector bosons in relativistic heavy-ion collisions. Starting from the Proca Lagrangian and using the Wigner function formalism, we perform a systematic gradient expansion to obtain a covariant spin-polarization tensor expressed in terms of hydrodynamic fields and the curvature tensor of the freeze-out hypersurface. Analytic results for Bjorken and Gubser flows show that curvature anisotropy generates a nonzero tensor polarization. For $\phi$ meson, we estimate the curvature contribution to its spin alignment as $ \delta\Theta_{yy} \sim -10^{-4} $ to $ -10^{-3} $. We also find that the curvature contribution grows as the system size decreases. A rough estimate for central O-O collisions gives a spin alignment of order $-10^{-2}$, suggesting that spin-alignment measurements in such small systems may provide a clean probe of this geometric effect.