The Λ Global Polarization with the AMPT model Hui Li ( 李慧 ) University of Science and Technology of China Cooperators: Xiao-Liang Xia, Long-Gang Pang, Qun Wang arxiv: 1704.01507
Outline Introduction The framework of global polarization Model setup Lambda polarization from vorticity Numerical results and discussion Summary
Introduction Consider non-central heavy ion collisions Large angular momentum spin-vorticity coupling L global polarization aligned with L Probe the vorticity and magnetic field of the rotational fluid Study the energy behavior of the global polarization signal Liang, Wang, PRL 94,102301(2005) Voloshin, nucl-th/0410089 Betz, Gyulassy, Torrieri, PRC 76, 044901(2007)
Rotation of Quark-Gluon Plasma Introduction y x z De-confinement Hadronization Scattering Time Initial conditions QGP Freeze-out
Introduction Angular Momentum over all regions Gao, Chen, Deng, Liang, Wang, Wang, PRC 77, 044902(2008) Jiang, Lin, Liao, PRC 94,044910(2016)
Introduction A positive polarization of lambda and anti-lambda; The polarization of lambda and anti-lambda is quite close within error bars (>7.7GeV); Decreasing behavior with energy. Aristova, Frenklakh, Gorsky, Kharzeev, arxiv:1606.05882 First evidence of the global hyperon polarization in HIC!
Introduction Upsal s talk in QM2017 STAR Collab.,1701.06657 ω y =(9±1)10 21 s 1 RHIC produces the fluid with highest vorticity!
Introduction Upsal s talk in QM2017 Solar subsurface flow 10 7 s 1 Supercell tornado cores 10 1 s 1 Rotating soap bubbles Super Fluid STAR Collab.,1701.06657 ω y =(9±1)10 21 s 1 10 2 s 1 10 7 s 1 RHIC produces the fluid with highest vorticity!
Introduction Properties of vorticity field Jiang, Lin, Liao, Phys.Rev. C94 (2016) Deng, Huang, Phys.Rev. C93 (2016)
Introduction Global polarization for spin ½ particle produced at hypersurface See also Becattini s talk where is the average number at hypersurface is the mean spin vector for one particle related to the thermal vorticity calculated by statistical-hydrodynamic model Becattini, Karpenko, Lisa, Upsal, Voloshin 1610.02506; Karpenko, Becattini, 1610.04717
Introduction Global polarization for spin ½ particle produced at hypersurface See also Becattini s talk where is the average number at hypersurface Karpenko s talk in QM 2017 is the mean spin vector for one particle related to the thermal vorticity calculated by statistical-hydrodynamic model UrQMD + vhlle + UrQMD Becattini, Karpenko, Lisa, Upsal, Voloshin 1610.02506; Karpenko, Becattini, 1610.04717
Lambda polarization from AMPT Why does the polarization show a decreasing behavior while the angular momentum increases with energy?
Model setup In our setup, global J and average spin vector point along (-y) direction The vorticity does not point along y everywhere. It has local structure The global polarization can be obtained by projecting the average spin vector onto the angular momentum, global polarization average spin vector -z Reaction Plane Λ -x y
Simulation Transport process: Participants Initial conditions Zhang s Parton Cascade A Relativistic Transport Model HIJING + ZPC + ART excited strings into partons till partons freeze out nearest partons coalesce into hadrons (resonance decay) Spectators Track the partons and hadrons position and momentum information u Find final-state particles (Λ hyperons) Lin, Ko, Li, Zhang, Pal, Phys. ReV. C 72, 064901 (2005) d s u d
Global polarization from AMPT Velocity: average all particles in cells over 10 6 events Cells:41 41 21 Vorticity: computed from velocity by finite-difference method (FDM) Non-relativistic vorticity: Vorticity tensor: Jiang, Lin, Liao, Phys.Rev. C94 (2016) Deng, Huang, Phys.Rev. C93 (2016)
Global polarization from AMPT Ensemble average of the spin vector Becattini, Piccinini, Ann. Phys.323 (2008) 2452 Becattini, Chandra, Zanna, Grossi, Annals Phys. 338, 32 (2013) Becattini, Inghirami, Eur.Phys.J. C75 (2015) no.9, 406 Fang, Pang, Wang, Wang, PRC 94, 024904(2016) thermodynamic equilibrium Boltzmann statistics limit Thermal vorticity:
Global polarization from AMPT Weak Decay: Λ p + π proton emission preferentially along Λ spin in Λ s rest frame In Lambda s rest frame Rest Frame C.M. Frame E p, p, m, are the energy, momentum and mass of Λ
Global polarization from AMPT The average spin vector in rest frame where the spin vector is The dominant term in is
Global polarization from AMPT with different impact parameters
Feed-down corrections
AMPT vs experiment 20%--50% Accounting for feed-down Au-Au 20%-50% with feed-down contributions included
Energy behavior of polarization Sideward deflection at 7.7 GeV Almost symmetric at 200 GeV due to the fast expansion b=7fm η <1
Vorticity field Energy behavior of polarization quadrupole structure opposite signs on opposite sides of x and η (200GeV) non-vanishing in the central region (7.7 GeV) y -y -y y
Number distribution of Λ hyperons the lambda number distribution at two energies net lambdas produced in the negative omega region (-y direction)
Summary We calculated the vorticity fields and the global polarization with AMPT. The result is consistent with the experimental data within error bars. The feed-down contributions suppress the result by 17%. We gave an explanation for the energy dependence of the global polarization. The expansion of the fireball at higher energies makes the global rotation and the sideward deflection less visible and less angular momentum is deposited in the mid-rapidity region.
Thank you!