The N umber-of- C onstituent- Q uark Scaling of Elliptic Flow at 9.2GeV AuAu Collisions

1. The Number-of-Constituent-Quark Scaling of Elliptic Flow at 9.2GeV AuAu Collisions Kejun Wu, Feng Liu, Nu Xu Institute of Particle Physics Huazhong Normal University wukj@iopp.ccnu.edu.cn

2. Outline Motivation Results and Discussions MC Simulation versus Experimental Data NCQ Scaling of v2 from AMPT&UrQMD When/Where does the partonic medium form? Summary wukj@iopp.ccnu.edu.cn

3. NCQ=3 NCQ=2 Motivation QCD Phase diagram partonic phase Cross-over hadronic phase The essential degrees of freedom at hadronization seem to be effective constituent quarks that have developed a collective flow during the partonic evolution.  RHIC beam energy scan program : ----- Search for the critical point. ----- Draw the QCD phase boundary. NCQ-scaling == partonic degrees of freedom? wukj@iopp.ccnu.edu.cn

4. MC vs. Experimental data (Provided by S.S. S)  Only 3k good events for the experimental data. Difficult to conclude which MC model is best suitable. wukj@iopp.ccnu.edu.cn

5. v2 of all Charged Hadrons • About 3M, 1M, 5M and 5M events for UrQMD v2.3 , RQMD v2.4, AMPT v2.1 with string melting and default minimum bias calculations. • Small physical variances between RQMD and UrQMD.  A maximum value of v2 is reached in mid-rapidity at 8~9fm (about 40%).  v2 : AMPT with string melting > AMPT default > UrQMD >RQMD. wukj@iopp.ccnu.edu.cn

6. NCQ Scaling of v2 in AMPT  Crossing and subsequent splitting between meson and baryon at pT~1.2GeV Only for AMPT with string melting  like hydrodynamic behavior mass ordering at pT<1GeV  Obvious particles type dependence: NCQ Scaling at pT>1GeV Why is the NCQ scaling of v2 presented in the AMPT with string melting? wukj@iopp.ccnu.edu.cn

7. Difference for Two AMPT Versions tiny Zi-Wei Lin,Che Ming Ko,etc., Phys.Rev.C 72,064901(2005), “Multiphase transport model for relativistic heavy ion collisions”  The quark coalescence mechanism leads to the v2 NCQ scaling. One can download and use freely the codes such as AMPT RQMD UrQMD ART and HING. http://karman.physics.purdue.edu/OSCAR/models/list.html wukj@iopp.ccnu.edu.cn

8. NCQ Scaling of v2in RQMD/UrQMD  like hydrodynamic behavior mass ordering at pT<1GeV  Rough particles type dependence: NCQ scaling at pT>1GeV Only hadronic interactions ->NCQ scaling The NCQ scaling is not unique feature of quark recombination/coalescence! Also see J. Phys. G: Nucl. Part. Phys. 32 (2006) 1121–1129 Anisotropic flow at RHIC: How unique is the number-of-constituent-quark scaling wukj@iopp.ccnu.edu.cn

9. Where was v2 Formed? Hadronic Rescattering Effect • The rescattering is the key of the v2 development. • No repulsive vector interactions, no flow. wukj@iopp.ccnu.edu.cn

10. When was v2 Formed? •  Earlier freeze-out particles have larger v2. •  Lower pt particles tend to freeze out later. • v2 decreases <-- the coordinate space anisotropy was diluted. • High pt pions v2 saturate and tend to reflect the earlier stage. • The wiggle should due to the excessive expand of the radial flow. wukj@iopp.ccnu.edu.cn

11. Time Evolution of the Medium Pions Pions 0~5 fm/c, target and projectile penetrate at each other, the initial strings are excited. 5~9 fm/c, vast inelastic collisions and produced particles from the string fragmentation. Pions are absorbed by the spectators in the reaction plane. 9~12 fm/c, pressure gradient builds up quickly. At ~12 fm/c, △v2 reaches to maximum. 12~20 fm/c, the coordinate space is more spherical and △v2 decreases gradually. 20 fm/c~, particles freeze out. v2 doesn’t change. pre-hadronic stage pre-equilibrium stage wukj@iopp.ccnu.edu.cn

12. When does v2 NCQ Scaling Come from? v2/nq (%) pre-hadronic stage pre-equilibrium stage • Early string fragmentation and hadronic interactions -> v2 NCQ scaling • The mechanisms of string fragmentation and excitation are called. is given approximatively by the constituent quark model. wukj@iopp.ccnu.edu.cn

13. Where does v2 NCQ Scaling Come from? Final elliptic flow: Y.Lu,F.Liu,N.Xu.etc., J. Phys. G: Nucl. Part. Phys. 32 (2006) 1121–1129, “Anisotropic flow at RHIC: How unique is the number-of-constituent-quark scaling” denotes the hyper-surface where hadrons are emitted. In the low pt region, the frequent rescatterings among hadrons can lead to the like hydrodynamic mass ordering. In the high pt region(pt>1GeV/c), particles early freeze out and lack the hydrodynamics development, and the details of the interaction cross-sections are most important. In UrQMD,the hadronic cross sections can be described by the detailed balance and parameterized by AQM. Additive Quark Model cross section only depends on the quark-content of the colliding hadrons K. Goulianos, Phys.Rep.101,169(1983), “Diffractive interactions of hadrons at high energies” Color Strings and ropes -excitation and -fragmentation S.A.Bass, M.Belkacem,etc., Nucl-th/9803035, “Microscopic Models for Ultrarelativistic Heavy Ion Collisions” wukj@iopp.ccnu.edu.cn

14. Summary • Due to large statistical uncertainties, it is too early to conclude if the AMPT and the hadronic transport model are suitable to reproduce the experimental data of AuAu 9.2GeV. • In those models, v2 is formed in the pre-equilibrium stage when the frequent rescatterings among hadrons or partons lead to the effective development of pressure gradient. • The NCQ scaling of v2 is not unique as a signature for deconfinement. Hadronic interactions can quantitatively reproduce the scaling. The scaling is independent on the colliding energy. • - URQMD: the v2 NCQ scaling arises from the hadronic cross sections, parameterized by the additive quark model. • - AMPT: the scaling is due to the quark coalescence. • High statistics is required for v2 in the future experiments. • To measure v2 of the multi-strange hadrons ( ) or resonance hadrons ( ) wukj@iopp.ccnu.edu.cn

15. ThankYou wukj@iopp.ccnu.edu.cn