Particle Spin in a Nuclear Vortex: Why the Sign Doesn't Add Up express
When two heavy nuclei collide in an accelerator, a tiny fireball of quark-gluon plasma is born — a special state of matter where quarks and gluons are not confined inside particles. As it expands and cools, the emitted particles often come out "spinning"—their spins align along the beam direction. Physicists call this longitudinal polarization. For a long time, it was thought that the culprit was plasma vorticity: its rotation transfers to spin, just as water spins a twig in a whirlpool.
But calculations gave the wrong sign of polarization compared to experiment. The authors of the new work took an exact solution for the plasma expansion, the Gubser flow with a small perturbation, and analytically computed the contributions of two effects: thermal vorticity (rotation) and thermal shear (layers of plasma sliding past each other). It turned out that these contributions are nearly equal in magnitude but opposite in sign. Vorticity gives a plus, shear gives a minus, and together they almost cancel each other out. The remainder determines the final polarization.
An important nuance: the result depends on which direction is taken as a reference when measuring spin. If you align with the particle's own velocity, the correct sign is obtained only for slow particles. If you fix the axis along laboratory time, the sign matches experiment over a wide range of velocities. And in a formulation where the axis is perpendicular to the freeze-out surface of the plasma, vorticity and shear cancel each other completely. The authors showed a general pattern: at leading order, polarization is determined not by acceleration but by other effects, and these can be noticeable even with strong elliptic flow.
Original abstract
as written by the authors arXiv:2608.03945v1
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.
The fireball in nuclear collisions expands almost like the Universe after the Big Bang — physicists even use a Hubble-like expansion solution to describe its behavior.