Initial spin fluctuations in heavy-ion collisions and where to find them

TL;DR

The paper addresses whether spin can be present and fluctuate in the initial conditions of heavy-ion collisions. It introduces a Glauber Monte Carlo–inspired model that assigns spin projections to participant nucleons to generate a fluctuating midrapidity spin density ${\cal S}({\bf x})$, leading to event-by-event polarization ${\cal P}$ with ${\rm std}({\cal P}) \propto 1/\sqrt{N_{ m part}}$ and a larger signal in smaller systems. A key contribution is the proposed observable $v_\Lambda^2 = \langle {\cal P}^2 \rangle$, extracted from two-particle spin correlations of $\Lambda$ hyperons via $D = 3 \langle \cos(\Delta\theta) \rangle$ and $v_\Lambda^2 = \frac{3}{\alpha_1\alpha_2}\langle D \rangle$, which ties initial-spin fluctuations to final-state measurements. The work suggests that initial-spin fluctuations would be detectable at percent levels and potentially long-range, offering a new probe of spin conservation, early-time dynamics, and the spin structure of nuclei, with the strongest signals expected in small systems like O+O and robustness across beam energies.

Abstract

Collective spin phenomena in the final states of heavy-ion collisions are typically understood to originate from vorticity and shear in the quark-gluon plasma. Here, we ask whether spin could already be present in the initial condition of the collisions. In particular, we argue that if a spin density exists at the beginning of the QGP expansion, it should experience event-by-event fluctuations due to the finite number of participant nucleons. In this contribution, we propose a simple model of fluctuating spin initial conditions for event-by-event spin hydrodynamics based on the Glauber Monte Carlo paradigm. We postulate that, if the net spin of the events is conserved from the initial to the final state, then initial state fluctuations of spin should manifest in specific spin correlations of $Λ$ hyperons. Within our picture, we predict that this signal is much larger in central O+O collisions than in central Pb+Pb collisions.

Figures (2)

• Figure 1: Left: Transverse view of an O+O collision at $\sqrt{s_{\rm NN}}=5$ TeV. Each nucleon in the colliding ions is assigned a random spin projection, either up or down. Since $^{16}$O has $J=0$ in the ground state, it contains $A/2$ spin-up and $A/2$ spin-down nucleons. The spins are aligned along a random quantization axis. Colored arrows represent participant nucleons. Right: The corresponding spin density, $\mathcal{S}({\bf x})$, as defined in Eq. (\ref{['eq:Sdens']}). Here, the spin profile of each participant, $w_s({\bf x})$, is modeled as a two-dimensional Gaussian with width 0.5 fm, and $S_0=1$. The event shown yields $\int_{\bf x} \mathcal{S}({\bf x})=- \,\hbar/2$ and $\mathcal{P}=-0.034$.
• Figure 2: Left: Standard deviation of the polarization parameter, $\mathcal{P}$, as defined by Eq. (\ref{['eq:P']}) with $S_0=1$, in PB+Pb collisions (circles) Xe+Xe collisions (squares), and O+O collisions (Triangles) as a function of the collision centrality. Right: Xe+Xe (squares) and O+O (triangles) results normalized by the Pb+Pb result, and rescaled by a factor $\sqrt{208/A}$, where $A$ is either 129 or 16.