Local Spin Polarization in Anisotropic Gubser Flow: Suppression Mechanism and Formulation Dependence

Abstract

We analytically study the longitudinal spin polarization in relativistic heavy-ion collisions using a perturbed Gubser flow solution. In the large-system-size limit, we derive analytical expression of the local spin polarization along the beam direction. In our treatment, the contributions from thermal vorticity and thermal shear are of comparable magnitudes. The thermal vorticity yields the polarization with a sign opposite to that observed experimentally, while the thermal shear counteracts this effect, helping recover the desired sign. We find that the choice of the reference unit vector aligned with the fluid velocity gives the experimentally observed sign only at low transverse momenta, whereas another formulation with the unit vector fixed along the laboratory time direction yields the desired sign for a wide range of transverse momenta. Notably, a recent formulation with the unit vector normal to the freeze-out hypersurface exhibits an exact cancellation between contributions from thermal vorticity and thermal shear at leading order in the large-system-size limit. We identify a general cancellation pattern with acceleration dominance, which is manifest particularly in the latter two formulations. Thus, the total polarization originates from non-acceleration effects, which need not be substantial even when the elliptic flow is finite, as clearly demonstrated in our analytical results. For comparison, we also discuss the spin polarization in the Hubble flow with rotation.