In-plane transverse polarization in heavy-ion collisions

TL;DR

This paper derives an analytical expression for the in-plane spin polarization $P^{x}$ in heavy-ion collisions within an extended blast-wave framework and validates it against (3+1)D hydrodynamic simulations. The approach leverages perturbation in small transverse anisotropies and a flow-momentum correspondence to obtain $P^{x}$ alongside $P^{z}$ and $P^{y}$, highlighting that $P^{x}$ shares the same order of magnitude as $P^{y}$ and is driven by directed flow. Hydro results indicate significant contributions from temperature gradients in shaping $P^{x}$, leading to sign differences with the blast-wave predictions and a small net signal due to cancellations among large sources. The findings offer testable predictions for $P^{x}$ and call for experimental measurements to complete the spin-polarization picture in heavy-ion collisions.

Abstract

We give an analytical expression for the in-plane polarization $P^{x}$, in heavy-ion collisions that has, to our knowledge, not been measured in heavy-ion collision experiments. We also carry out a numerical study of $P^{x}$ using a hydrodynamic model simulation as a cross-check for the analytical formula. It is found that if the temperature-gradient contribution is neglected the simulation result for $P^{x}$ qualitatively agrees with the analytical one. The prediction of $P^{x}$ can be tested in experiments and will contribute to provide a complete and consistent picture of spin phenomena in heavy-ion collisions.

Figures (11)

• Figure 1: The transverse spin polarization vector $\mathbf{P}_{T}(\phi_{p})$ in Eq. (\ref{['eq:transverse-spin']}).
• Figure 2: Vector plot of $\mathbf{P}_{T}(\phi_{p})$ with arrow and length on a circle varying with $\phi_{p}$.
• Figure 3: The model fit to elliptic flow data of light particles in 10-80% central Au+Au collisions at 200 GeV with the values of $\rho_2$ and $\epsilon$ listed in Table \ref{['tab:centrality-para']}.
• Figure 4: The results for $P^{z}$ (left panel) and $P_{H}\equiv-P^{y}$ (right panel) as functions of $\phi_{p}$ following Eq.(\ref{['eq:integrated-pol']}). The black solid lines represent the calculated results based on analytical formulas.
• Figure 5: The calculated results for $\left\langle P^{z}\sin(2\phi_{p})\right\rangle$ and $P_{H}$ as functions of $p_{T}$ from Eq. (\ref{['eq:pol-xyz-pt']}). The polarization at 20-60% and 20-50% is calculated by the total particle-production weighted average.