Pion Elliptic Flow and Interferometry for a Granular Source of QGP Droplets

1. Pion Elliptic Flow and Interferometry for a Granular Source of QGP Droplets Wei-Ning Zhang, Yan-Yu Ren, Cheuk-Yin Wong Phys. Rev. C74, 024908(2006)

2. I. Motivations Recently, there has been much progress in explaining RHIC’ data. However, there are many unsolved problems. Hydrodynamical model is successful in many aspects of high-energy heavy-ion collisions. Its calculations agree well with the RHIC’ data of elliptic flow v2 at low pT (<2 GeV). However, it can not be used to explain the saturation of v2 at high pT and the HBT puzzle RO/RS≈1. How to explain both the elliptic flow and HBT measurements at RHIC consistently?

3. O Xd fm ρ( Xd ) II. A Review for Our Past Work on HBT Puzzle A model of granular source of QGP droplets. The droplets evolve hydrodynamically. (W.N. Zhang, M.J. Efaaf, C.Y.Wong, PRC70, 024903,2004.) Rout / Rside ≈1

4. Static granular source O Xd fm ρ( Xd ) Expanding granular source out

5. Our new work: The old work: Only a simple spherical granular source with a constant radial droplet v. Consider a more reasonable 3D granular source model; the droplets expand anisotropicly. We investigate Ro, Rs, and Rl as a function of KT; We investigate v2 and pT spectra of granular source also. Did not study HBT radii as a function of KT. The QGP produced in collisions at RHIC has very high density & liquid properties. Its expansion may be unstable  fragmentation + surface tension  Granular Droplets! Where does a granular structure come from? Is it from first-order phase transition only?

6. III. Granular Source of QGP Droplets • The early system (QGP) produced in the Au + Au collisions at RHIC may be a strongly coupled medium with a very high energy density. It is thermalized at a very early time before 1 fm/c. • The expansion of the system after that time may be unstable. Many effect (the large fluctuations of initial energy distribution, surface tension, sound noise of large magnitudes accompanying a highly explosive expansion, and phase transition) may lead to a fragmentation of the very high density system and the production of a granular source when it expands to vacuum. • Although a granular structure was suggested earlier as the signature of a first-order phase transition, the occurrence of granular structure may not be limited to a QGP medium characterized by a first-order phase transition.

7. Initial State Effect (a) In many simulations of the heavy ion collision on an event-by-event basis, the initial energy density is far from being uniform and there are large fluctuations of the initial density distribution. (a) Y. Hama, QM2005 talk, hep-ph /0510096; (b) H.J. Drescher et al., PRC65,054902,2002. (NeXus model) (b) These large density fluctua-tions in the transverse direc-tion, together with the surface tension effects may lead to formation of granular droplets!

8. Model Calculation Averaging Results Model Calculation Physics Results Averaging Comparing with experiments Fragmentation and formation of granular droplets

9. π Z 2 —— shell factor Based on the above picture, we use a granular source model to des-cribe the system after fragmenta-tion. Assume the droplets initially distribute in a shell of disk with anisotropic velocity (i = x, y, z ). We use relativistic hydrodynamics with the EOS of entropy density to describe the evolution of single droplet as we did. The evolution of the granular source is obtained by superposing all of the droplet evolutions.

10. Fig. 1: Pion spectra of transverse momentum. (PHENIX Collab., PRC69, 034909, 2004.)

11. IV. Elliptic Flow In the region pT< 2GeV, v2 increases with pT as usual. In the region pT >2GeV, v2 of granular source decreases with pT . The decrease is sensitive to parameter bz. bz<<bT —different initial dynamical in L and T directions! (PHENIX Collab., PRL91, 182301, 2003.)

12. V. HBT Results

13. Rout and Rlong increase with rd. If increaseing ∆Rt , the varia-tions of Rside & Rout with pT will become flat. Small rd — small lifetime. small ∆Rt — large absorption? effect of early explosive expansion? (PHENIX, PRL93, 152302, 2004; STAR, PRC71, 044906, 2005.)

14. VI. Conclusions • Although a granular structure was suggested earlier as the signature of a first-order phase transition, there are additional initial state effects and dynamical granular instability due to surface tension may lead to a granular source. • The pion transverse momentum spectra, elliptic flow, and HBT radii for granular sources are in good agreement with the data of \sqrt{SNN}=200 GeV Au +Au collisions at RHIC.

15. In low pT region (<2GeV/c), elliptic flow reflects the aniso-tropic initial dynamical conditions in transverse directions. • In large pT region (>2GeV/c), the decrease of v2 is sensitive to bz, the result bz<<bT reflects different initial dynamical condi-tions between transverse and longitudinal directions. • The pion-emitting sources produced in the collisions at RHIC have short a lifetime and a shell configuration.

16. Thank you! • Unstable expansion may be a more general case in the expansion with the so high density difference. • So, it is possibly a granular source! • To find more evidences for the granular structure!

17. Thank you!

18. 强度干涉学（HBT） X1 X2

19. 强度干涉学（HBT） 假定 源半径， 源寿命 | p1 ─ p2| , | E1 ─ E2|

20. Side方向 q = p1 - p2 p1 K = p1 + p2 p2 Z Out方向 ( VK · q , K / VK ( 强度干涉学（HBT）

21. side R out R 1) Relatively small changes of the radii as a function of E K. Adcox et al., Phys. Rev. Lett. 88, 192302 (2002) RHIC的HBT之谜（1）

22. Predictions of Hydrodynamic model 2) Rout/ Rside≈1 K. Adcox et al., Phys. Rev. Lett. 88, 192302 (2002) RHIC的HBT之谜（2）

23. QGP颗粒源 高密度QGP 流体动力学方程 物态方程 初始条件 X ≥ Q QGP颗粒源模型对HBT之谜的解释

24. ( ( QGP颗粒源模型对HBT之谜的解释 单个QGP颗粒的源的结果

25. O Xd QGP颗粒源的结果 fm ρ( Xd ) 膨胀QGP颗粒源的结果 out 方向 QGP颗粒源模型对HBT之谜的解释

26. STAR Preliminary The QGP Fingerprint at RHIC = Bulk collective flow PQCD(T) Hadronization via quark coalescence: v2 of a hadron at a given p is the partonic v2 at p/n scaled by the # of quarks (n). Occurrence of hydrodynamical flow can be understood if the medium is a medium with the equation of state of the quark-gluon plasma.

27. V. Elliptic Flow where φis particle azimuthal angle with respect to the reaction plane. Choosing the direction of x-axis in the reaction plane and the direction of y-axis out of the reaction plane, In our calculations, we use the same cut, |η|<0.35 as in the experiments of PHENIX. (PHENIX Collab., PRL91, 182301, 2003.)

28. The pattern of v2 as a function of pT varies with bT, bz, and ∆aT after <aT> and az being fixed at the values determined by pion pT spectra. In the region pT<2GeV, v2 increases with pT as usual. However, in the region pT>2GeV we find that v2 of the granular source decreases with pT.The decrease is sensi-tive to bz. The curvature of v2 in the region pT<2GeV is much sensitive to the value of bT. Finally we find the curve of v2 for the parameters bT=0.70, bz=0.01, and ∆aT=0.08 agrees with the experimental data very well. bz<<bT —different initial dynamical in L and T direction!