Probing vorticity structure in heavy-ion collisions by local <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Λ</mml:mi></mml:math> polarization

Abstract

We study the local structure of the vorticity field and the $\mathrm{\ensuremath{\Lambda}}$ polarization in Au+Au collisions in the energy range $\sqrt{{s}_{\mathrm{NN}}}=7.7--200\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$ and Pb+Pb collisions at $\sqrt{{s}_{\mathrm{NN}}}=2760\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$ using a multiphase transport model. We focus on the vorticity field arising from the nonuniform expansion of the fireball, which gives the circular structure of the transverse vorticity ${\mathbf{\ensuremath{\omega}}}_{\ensuremath{\perp}}=({\ensuremath{\omega}}_{x},{\ensuremath{\omega}}_{y})$ around the $z$ direction as well as the quadrupole pattern of the longitudinal vorticity ${\ensuremath{\omega}}_{z}$ in the transverse plane. As a consequence, the three components of the polarization vector $\mathbf{P}=({P}_{x},{P}_{y},{P}_{z})$ for $\mathrm{\ensuremath{\Lambda}}$ hyperons show harmonic behaviors as $\mathrm{sgn}(Y)sin{\ensuremath{\phi}}_{p}$, $\ensuremath{-}\mathrm{sgn}(Y)cos{\ensuremath{\phi}}_{p}$, and $\ensuremath{-}sin(2{\ensuremath{\phi}}_{p})$, where ${\ensuremath{\phi}}_{p}$ and $Y$ are the azimuthal angle and rapidity in momentum space. These patterns of the local $\mathrm{\ensuremath{\Lambda}}$ polarization are expected to be tested in future experiments.