Probing vorticity structure in heavy-ion collisions by local Λ polarization

We study the local structure of the vorticity field and the polarization in Au+Au collisions in the energy range s₍₍=7. 7--2000. 28em{0ex}GeV and Pb+Pb collisions at s₍₍=27600. 28em{0ex}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 {}_= (ₗ, ₘ) around the z direction as well as the quadrupole pattern of the longitudinal vorticity ₙ in the transverse plane. As a consequence, the three components of the polarization vector P= (Pₗ, Pₘ, Pₙ) for hyperons show harmonic behaviors as sgn (Y) sin₏, -sgn (Y) cos₏, and -sin (2₏), where ₏ and Y are the azimuthal angle and rapidity in momentum space. These patterns of the local polarization are expected to be tested in future experiments.