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

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 ${\mathbf{\omega }}_{\perp }=({\omega }_x,{\omega }_y)$ 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 $\mathrm{sgn}(Y)\sin {\varphi }_p$, $-\mathrm{sgn}(Y)\cos {\varphi }_p$, and $-\sin (2{\varphi }_p)$, where ${\varphi }_p$ 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.

arXiv comment8 pages, 7 figures. One table, one figure and references added. Discussions in Sec III and IV improved. To appear in Phys. Rev. C

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