Probing vorticity structure in heavy-ion collisions by local $\Lambda$ polarization

TL;DR

This study investigates the local vorticity and $ ext{Lambda}$ polarization in heavy-ion collisions across various energies using the AMPT model, revealing harmonic polarization patterns linked to the vorticity structure.

Contribution

It introduces a detailed analysis of the local vorticity and polarization patterns in heavy-ion collisions, highlighting their harmonic behavior and potential for experimental testing.

Findings

Vorticity exhibits circular and quadrupole patterns in the fireball expansion.

Lambda polarization components show harmonic behaviors related to vorticity.

Predicted polarization patterns can be tested in future experiments.

Abstract

We study the local structure of the vorticity field and the $\Lambda$ polarization in Au+Au collisions in the energy range $\sqrt{s_{\mathrm{NN}}}=7.7$--$200$ GeV and Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2760$ GeV using A Multi-Phase Transport (AMPT) model. We focus on the vorticity field arising from the non-uniform expansion of the fireball, which gives the circular structure of the transverse vorticity $\boldsymbol{\omega}_{\perp}=(\omega_{x},\omega_{y})$ around the $z$ direction as well as the quadrupole pattern of the longitudinal vorticity $\omega_{z}$ in the transverse plane. As a consequence, the three components of the polarization vector $\mathbf{P}=(P_{x},P_{y},P_{z})$ for $\Lambda$ hyperons show harmonic behaviors as $\mathrm{sgn}(Y)\sin\phi_{p}$, $-\mathrm{sgn}(Y)\cos\phi_{p}$, and $-\sin(2\phi_{p})$, where $\phi_{p}$ and $Y$ are the azimuthal angle and rapidity in momentum space. These patterns of the local $\Lambda$ polarization are expected to be tested in future experiments.