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 v 2 at low p T (<2 GeV). However, it can not be used to explain the saturation of v 2 at high p T and the HBT puzzle R O /R S ≈1. How to explain both the elliptic flow and HBT measurements at RHIC consistently?

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

4. Static granular source O XdXd ρ( X d ) fm Expanding granular source out

5. The old work: Only a simple spherical granular source with a constant radial droplet v. Did not study HBT radii as a function of K T. Where does a granular structure come from? Is it from first-order phase transition only? Our new work: Consider a more reasonable 3D granular source model; the droplets expand anisotropicly. We investigate Ro, Rs, and Rl as a function of K T ; We investigate v 2 and p T spectra of granular source also. The QGP produced in collisions at RHIC has very high density & liquid properties. Its expansion may be unstable  fragmentation + surface tension  Granular Droplets!

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 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) (b) (a) Y. Hama, QM2005 talk, hep-ph /0510096; (b) H.J. Drescher et al., PRC65,054902,2002. (NeXus model) 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 Averaging Physics Results Fragmentation and formation of granular droplets Comparing with experiments

9. 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. —— shell factor π Z 2

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

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

12. V. HBT Results

13. R out and R long increase with r d. If increaseing ∆R t, the varia- tions of R side & R out with p T will become flat. Small r d — small lifetime. small ∆R t — 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{S NN }=200 GeV Au +Au collisions at RHIC.

15. In low p T region (<2GeV/c), elliptic flow reflects the aniso-tropic initial dynamical conditions in transverse directions. In large p T region (>2GeV/c), the decrease of v 2 is sensitive to b z, the result b z <<b T 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. X1 X2 强度干涉学（ HBT ）

19. 假定 源寿命源半径， | p 1 ─ p 2 |,| E 1 ─ E 2 |

20. 强度干涉学（ HBT ） V K · q, VKVK K / ( ( K = p 1 + p 2 p1p1 p2p2 Side 方向 Out 方向 Z q = p 1 - p 2

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

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

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

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

26. The QGP Fingerprint at RHIC = Bulk collective flow P QCD (T) STAR Preliminary Occurrence of hydrodynamical flow can be understood if the medium is a medium with the equation of state of the quark- gluon plasma. Hadronization via quark coalescence: v 2 of a hadron at a given p  is the partonic v 2 at p  /n scaled by the # of quarks (n).

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