1. 1 Transport description of viscous effects Che-Ming Ko Texas A&M University  Introduction  A multi-phase transport (AMPT) model  Anisotropic flow - Elliptic flow - Higher-order anisotropic flow - Rapidity dependence - System size dependence - Flavor dependence  Summary Collaborators: Lie-wen Chen (SJTU), Zie-wei Lin (Univ. Alabama), Bin Zhang (Arkansas State Univ.)

2. 2 Zhang, Gyulassy & Ko, PLB 455, 45 (1999) Elliptic flow from parton cascade Based on Zhang’s parton cascade (ZPC) (CPC 109, 193 (1998)) using minijet partons from HIJING for Au+Au @ 200 AGeV and b=7.5fm v 2 of partons is sensitive to their scattering cross section

3. 3  Using α s =0.5 and screening mass μ=gT≈0.6 GeV at T≈0.25 GeV, then 1/2 ≈4.2T≈1 GeV, and pQCD gives σ≈2.5 mb and a transport cross section  σ=6 mb → μ≈0.44 GeV, σ t ≈2.7 mb  σ=10 mb → μ≈0.35 GeV, σ t ≈3.6 mb Zhang’s parton cascade (ZPC) Bin Zhang, Comp. Phys. Comm. 109, 193 (1998)

4. 4 A multiphase transport (AMPT) model Default: Lin, Pal, Zhang, Li &Ko, PRC 61, 067901 (00); 64, 041901 (01); 72, 064901 (05); http://www-cunuke.phys.columbia.edu/OSCAR  Initial conditions: HIJING (soft strings and hard minijets)  Parton evolution: ZPC  Hadronization: Lund string model for default AMPT  Hadronic scattering: ART  Convert hadrons from string fragmentation into quarks and antiquarks  Evolve quarks and antiquarks in ZPC  When partons stop interacting, combine nearest quark and antiquark to meson, and nearest three quarks to baryon (coordinate-space coalescence)  Hadron flavors are determined by quarks’ invariant mass String melting: PRC 65, 034904 (02); PRL 89, 152301 (02)

5. 5  Based on coordinate-space coalescence  Need string melting and large parton scattering cross section  Mass ordering of v 2 at low p T as in ideal hydrodynamic model Lin & Ko, PRC 65, 034904 (2002) Elliptic flow from AMPT σ p = 6 mb

6. 6 Coalescence model Quark distribution function Spin-color statistical factor e.g. Coalescence probability function PRL 90, 202102 (2003); PRC 68, 034904 (2003) Number of hadrons with n quarks and/or antiquarks For baryons, Jacobi coordinates for three-body system are used.

7. 7 Momentum-space coalescence model Including 4 th order quark flow Meson flow Baryon flow Kolb, Chen, Greco, & Ko, PRC 69 (2004) 051901

8. 8 Data can be described by a multiphase transport (AMPT) model Data Parton cascade Higher-order anisotropic flow Momentum-space coalescence Chen, Ko, & Lin, PRC 69, 031901 (04)

9. 9 Strange quarks from AMPT Chen & Ko, PRC 73, 044903 (2006)

10. 10 Phi & Omega flows same for phi & Omega but different from quark instead of 1.1 and 0.7 from dynamical coalescence model Chen & Ko, PRC 73, 044903 (2006)

11. 11 satisfied for large phi and Omega sizes of 4.5 fm Flows of phi & Omega with large sizes

12. 12 Pseudorapidity dependence of v 1 and v 2  String melting describes data near mid-rapidity (|  |<1.5)  At large rapidity (|  |>3), hadronic picture works better Chen, Greco, Ko & Koch, PLB 605, 95 (2005)

13. 13 System size dependence of elliptic flow Chen & Ko, nucl-th/0505044 v 2 is proportional to size of colliding system

14. 14 Elliptic flow in collisions of asymmetric systems Compared to symmetric collisions  Directed flow v 1 is stronger  Elliptic flow v 2 is more sensitive to parton cross section  Both directed and elliptic flows are asymmetric in forward and backward rapidities

15. 15 Quark elliptic flow from AMPT  P T dependence of charm quark v 2 is different from that of light quarks.  At high p T, charm quark has similar v 2 as light quarks.  Charm elliptic flow is also sensitive to parton cross sections

16. 16 Charm elliptic flow from AMPT Zhang, Chen & Ko, PRC 72, 024906 (05)  Current light quark masses are used in AMPT. Charmed meson elliptic flow will be larger if constituent quark masses are used.  To increase v 2 at low p t requires going beyond parton cascade. 15 10 5 0 -5

17. 17 Summary  Elliptic flow is sensitive to parton scattering cross section  The AMPT model with string melting can reproduce observed large elliptic flow and mass ordering at low p T with large parton cross section ( quasi bound states in QGP and/or multiparton dynamics gg↔ggg?)  Observed hadron v 4 ≈1.2v 2 2 is reproduced with parton v 4 ≈v 2 2  v 1 and v 2 at midrapidity requires formation of partonic matter, while those at large rapidity is consistent with a hadronic matter  AMPT predicts: - v 2 scales with the size of colliding system - Stronger v 1 and more sensitivity of v 2 to parton cross section in asymmetric than symmetric collisions, and both show forward-backward asymmetry in rapidity  Observed large charmed meson flow requires large charm quark scattering cross section (resonance effect?)