Flow Fluctuations in the AMPT model

1. 2009 威海高能物理暑期论坛暨“RHIC 物理和 CSR 强子物理”: (I.2) 集体流(Flow) Flow Fluctuations in the AMPT model Lie-Wen Chen (陈列文) (上海交通大学物理系，粒子物理宇宙学研究所-INPAC) Collaborators: Che Ming Ko (TAMU) Na Li (CCNU) Nu Xu (LBNL)

2. Contents • Anisotropic Flows • Anisotropic Flows in the AMPT model • Fluctuation of Anisotropic Flows • Summary

3. py px z y x Anisotropic flowsvn Sine terms vanish because of the symmetry Anisotropic flows Spatial anisotropy Momentum anisotropy

4. Zhang/Gyulassy/Ko, PLB455, (1999)45 Good probe of early pressure, thus properties (EOS) of matter formed in early stage of heavy-ion collisions !

5. Almost linearly Anisotropic Flows in the AMPT Model I: Valence Quark Number Scaling of Elliptic Flow Latest data (see, e.g., M. Issah and A. Taranenko, arXiv:nucl-ex/0604011) Very good scaling is observed for Pressure gradients Collective transverse kinetic energy of emitted particles

6. Almost linearly AMPT: Valence quark number scaling

7. STAR Collaboration, PRL 92, 062301 (2003) results for all charged particles, minimum bias values from Au+Au@200 AGeV II. Scaling of Hadron Higher-Order Anisotropic Flows

8. AMPT: Scaling relation among hadron hgher-order vn’s AMPT model can describe the higher-order anisotropic flow Chen/Ko/Lin,PRC69, 031901(R) (2004) Charged hadrons

9. III. Pseudorapidity dependence of anisotropic flows Chen/Greco/Ko/Kolb,PLB605, 95 (2005) • AMPT with string melting (10 mb) can describe the data around midrapidity but overestimate the data at larger rapidities • Default AMPT can describe the data at large rapidities

10. IV. V2 at LHC • Compared with the v2 at RHIC, the meson v2 enhances while baryon v2 reduces (radial flow effects?)

11. Initial spatial anisotropy x Pressure gradient anisotropy Anisotropic flows Fluctuation of Anisotropic Flows • Factor of fluctuations: • particle density n (initial physical state) • transverse size R (collisional geometry) • eccentricity εpart (collisional geometry) • collision dynamics … The initial state and the dynamics are never perfectly smooth and they fluctuate from one event to the other, which will cause fluctuations of anisotropic flows. The fluctuations of anisotropic flows reflect both the initial variation of the eccentricity caused by the quantum nature of the elementary collisions, and the dynamic evolution of the system. It provides a promising probe to extract crucial information on early dynamics in high-energy nuclear collisions.

12. P. Sorensena for the STAR Collaboration, arXiv: 06120221v2 Eccentricity fluctuations vs. v2 fluctuation Participant eccentricity: Standard eccentricity: B. Alver et al., PRL98, (2007) The fluctuations of participant eccentricity can fit the data

13. R. Nouicer for the PHOBOS Collaboration, arXiv: 0707.4424v1 Eccentricity fluctuations vs. v2 fluctuation The agreement between the Glauber model and data may suggests that the fluctuations of elliptic flow primarily reflect fluctuations in the initial state geometry and are not affected strongly by the later stages of the collision.

14. Eccentricity fluctuations vs. v2 fluctuation Effects of different initial states Wounded nucleons/Binary collisions Color Glass Condensate Drescher and Nara, PRC76:041903,2007 W. Broniowski, PoSCPOD07:014,2007 Different initial states produce different fluctuations of participant eccentricity

15. v2 fluctuation from the AMPT model • Larger parton cross sections lead to smaller relative v2 fluctuations • Lower collision energy causes lager relative v2 fluctuations (smaller particle number density leads to larger fluctuations)

16. v2 fluctuation from the AMPT model • Two event samples with 325,460 and 693,705 events are generated respectively. Track Cut: |η|<1 , charge particles. • The AMPT with string melting reproduce the data value of v2 better than the default version. The relative v2 fluctuation in both of two versions are over estimate the fluctuation than data. • String melting - increasing the partonic interactions leads to stronger collective flow v2 (partonic collectivity) and reduce the fluctuation (thermalization). By Na Li

17. Partonic effects and flavor dependence of v2 fluctuation • Fluctuation has been already developed during the partonic stage ! • Particle with larger mass has larger fluctuation (number density of particles with larger mass is smaller)! • Coalescence essentially does not affect relative v2 fluctuation

18. Why does the AMPT model overestimate v2 fluctuation? Try the same way to calculate the anisotropic flows as in experiments Experimental reaction plane Poskanzer and Voloshin PRC58, 1671 (1998) Reaction plane resolution:

19. Why does the AMPT model overestimates v2 fluctuation? Ideal reaction plane from AMPT Experimental reaction plane data • Using experimental RP significantly reduces v2 fluctuation, especially for light system Cu + Cu ! • Lighter system has larger v2 fluctuation !

20. System size dependence of v2 revisited Chen/Ko, PLB634, 205(2006) Try experimental reaction plane Ideal reaction plane from AMPT Using experimental RP significantly increases v2 for light system Cu + Cu, and Au+Au and Cu+Cu have similar v2 vs. pT, which is consistent with data

21. pT dependence of v2 fluctuation Ideal reaction plane from AMPT Experimental reaction plane • Using experimental RP significantly reduces v2 fluctuation, especially for light system Cu + Cu ! • Lighter system has larger v2 fluctuation !

22. Rapidity dependence of v2 fluctuation Ideal reaction plane from AMPT Experimental reaction plane • Using experimental RP significantly reduces relative v2 fluctuation, especially for light system Cu + Cu ! • Lighter system has larger v2 fluctuation !

23. v4 fluctuation v4 fluctuation is significantly larger than v2 fluctuation ! Naively, from coalescence argument, one expect: However, the fluctuations are dominated by the fluctuations of initial state rather than coalescence. W. Broniowski, PoSCPOD07:014,2007 arXiv:0709.0123

24. v2 fluctuation from other dynamical models NeXSPheRIO Predictions from dynamical models UrQMD S. Vogel et al., nucl-th/0703031 Hama et al., arXiv:0711.4544

25. Summary • Increasing partonic interactions leads to stronger collective flow v2 and reduce the relative fluctuation due to thermalization • Particle with larger mass has larger relative v2 fluctuation • The coalescence process essentially does not change the relative v2 fluctuations • The experimental reaction plane method should be used in AMPT model to compare with the observed v2 relative fluctuation

26. The End Thank you !

28. A Brief Review of the AMPT Model Four important components are needed to be included for a general model at RHIC:Initial Condition, Partonic Stage, Hadronization/QCD phase transition, and Hadronic Interactions AMPT(A Multi-Phase Transport) model • Initial Condition for Particle and Energy Production: • Soft Strings and Hard Minijets from HIJING • Partonic Stage with EOS: • Parton cascade • Hadronization/QCD phase transition: • String fragmentation or Quark Coalescence • Hadronic Interactions • Hadron cascade Two versions: Default AMPT and AMPT with string melting A useful model for investigating reaction dynamics at RHIC: Zhang,Ko,Li&Lin, PRC61; Zhang,Ko,Li,Lin&Sa,PRC62; Lin,Pal,Ko,Li&Zhang,PRC64; Lin&Ko,PRC65; Zhang,Ko,Li,Lin&Pal,PRC65; Pal,Ko&Lin,NPA707; Lin,Ko&Pal,PRL89; Lin&Ko,PRC68; Pal,Ko&Lin,NPA730; Chen,Ko&Lin,PRC69; Chen,Greco,Ko,Kolb, PLB605; Lin/Ko/Li/Zhang/Pal, PRC72 Zhang/Chen/Ko, PRC72; Chen/Ko, PLB634; Chen/Ko, PRC73; Chen/Ko, PRC73……

29. The Default AMPT model The Default AMPT model can describe the rapidity distributions and transverse momentum spectraat RHIC(Zhang,Ko,Li&Lin, PRC61;Zhang,Ko,Li,Lin &Sa,PRC62; Lin,Pal,Ko,Li&Zhang,PRC64) Wang&Gyulassy,PRD43,44,45 Zhang, CPC82 Freezeout:last coll. Decay all resonances; Final particle spectra Li&KoPRC52

30. AMPT model with String Melting AMPT model with String Melting can describe the measured strong elliptic flow and pion HBT at RHIC(Lin&Ko, PRC65, Lin,Ko,Pal,PRL89) Wang&Gyulassy,PRD43,44,45 Zhang, CPC82 Freezeout:last coll. Partonic effects become much more important !! Decay all resonances; Final particle spectra Li&KoPRC52

31. String melting and Quark Coalescence in AMPT String melting: Excited strings (Lund-)Fragment into hadrons, and then melt into quarks according to hadron valence structure: • Quark Coalescence in AMPT model: • When the partonic interactions stop (last collision of parton), all partons must be converted to hadrons (hadronization). A simple quark coalescence model is used for hadronization: • Nearest quarks form a hadron • Determine Flavor according to quarks’ invariant mass • Most hadrons in Pythia are included: