Event-by-Event Two-Pion Correlations in Smoothed Particle Hydrodynamics

1. Event-by-Event Two-Pion Correlations in Smoothed Particle Hydrodynamics 1 1,2 Yan-Yu Ren and Wei-Ning Zhang • Department of Physics, Harbin Inst. of Tech. • 2) School of Physics & Optoelectronic, Dalian Univ. of Tech.

2. Outline: Motivations Space-time structure of SPH events · Single-event HBT correlation functions Observables for single-event HBT correlations Conclusions

3. nucleus nucleus Motivations The main physical goal of high energy heavy ion collisions is the study of the QGP. Hydrodynamics provides a direct link between the early state and final observables. Hydrodynamics has been extensively used in high energy heavy ion collisions.

4. The QGP Fingerprint at RHIC = Bulk collective flow PQCD(T) Occurrence of hydrodynamical flow can be understood if the medium is a medium with the equation of state of the quark-gluon plasma.

5. Predictions of Hydrodynamic model Rout / Rside ≈1 K. Adcox et al., Phys. Rev. Lett. 88, 192302 (2002) RHICHBT Puzzle

6. 2 O Xd ρ( Xd ) Rout / Rside ≈1 for a granular QGP droplet source The freeze-out time scales with the radius of the droplet. A smaller droplet radius rd has a smaller average freeze-out time, and smaller source lifetime τ. Granular Source of QGP droplets (W.N. Zhang, M.J. Efaaf, C.Y.Wong, PRC70, 024903,2004.)

7. 2 O Xd ρ( Xd ) Expanding granular source out Consider a source of QGP droplets distributed according to Static granular source Each droplet evolves hydrodynamically and emits pions at freeze-out.

8. a. Granular droplets may occur in first-order phase transitions The reason for the occurrence of Granular Source of QGP E.Witten, Phy. Rev D30, 272 (1984)

9. b. Initial State Effect (a) In high-energy heavy-ion collisons on an event-by-event basis, the initial transverse energy density is highly fluctuating (a)(NeXus) H.J. Drescher, F.M. Liu, S. Ostapchenko, T. Pierog, K. Werner, PRC65,054902,2002; (b) Y. Hama, QM2005 talk, hep-ph /0510096; (b) The large initial fluctuations of matter density, together with violent expansion and surface tension effects may lead to formation of granular droplets!

10. Dynamical expansion of a highly fluctuating distrbution may lead to droplet formation (or fragmentation) ( Highly fluctuating transverse density distribution ) ( Tubes of dense QGP matter ) ( Long tubes break up into droplets )

11. 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 first-order transition. There are additional initial state effects (large event-by-event fluctuations) and dynamical granular instability due to surface tension that may lead to a granular source. So, the examination of the space-time structure in event-by-event basis is important to understand the system evolution and the HBT puzzle.

12. Model Calculation Averaging Results Model Calculation Physics Results Averaging Comparing with experiments Why HBTPuzzle？ Fragmentation and formation of granular droplets The short lifetimes for granular sources are left from the averaging ---〉HBT puzzle !

13. Space-time structure of SPH event Smoothed Particle Hydrodynamics (SPH) can be used to treat the system evolution with large fluctuating initial conditions for investigating event-by-event attributes. C. Aguiar, T. Kodama, T. Osada, Y. Hama, J. Phys.G27,75,2001; Y. Hama, T. Kodama, O. Socolowski Jr, hep-ph/0407264; G.R. Liu, M.B. Liu 著, 韩旭, 杨刚, 强洪夫译《光滑粒子流体动力学》， 湖南大学出版社，2005. NEXSPHERIO is a SPH code with event-by-eventinitial conditions generated by NEXUS event simulator. It has been used in high energy heavy ion collisions. In this article we use NEXSPHERIO code to simulate the evolution of the system produced in the collisions of GeV Au+Au at RHIC.

14. EOS-I: First-order EOS-II: Cross-over

15. Transverse distributions of energy density of the events evolving with EOS-I ((a)--(d)) and EOS-II((a‘)--(d’)) atdifferent times forb=0 fm. The systems are inhomoge-neous in space and time both for the events evolving with the EOS-I and the EOS-II. There are many ``lumps“ in the systems. The lump loca-tions are different event-by-event.

16. Transverse distributions of energy density of the events forb=5 and 10 fm. The systems evolve with EOS-I ((a)--(d)) and EOS-II ((a')--(d')). The number of the lumps in the system decreases with impact parameter increasing. The systems evolving with the two kinds of EOSs have the similar space-time structure. We will consider only theEOS -II in our calculations later.

17. Single-event HBT correlation functions Single-events Mixed-events Two-pion correlation func-tions for the NEXSPHERIO events with different impact parameters. Tf =150 MeV. The correlation functions for single events exhibit fluctuations. The fluctua-tions are larger for bigger impact parameter. In longitudinal direction the correlation functions exhibit oscillations which can not be smoothed out by event mixing.

18. By applying an additional cut for the initial rapidity of the ``smoothed particles“, $\eta_0 >0$, we find that the osci-llations of the mixed-event correlation functions are smoo-thed out as shown in Fig. 5(c).

19. Observables for single-event HBT correlations We shown that the two-pion correlation functions of single vents exhibit event-by-event fluctuations. Because of statistics traditional HBT measurements are based on mixed-event analysis. The event-by-event fluctuations are smoothed out in this case. In order to observe the event-by-event fluctuations, we next investigate the distribution of the differences between the correlation functions of single and mixed events, with their errors as weights, dN/df, , i – side, out, long.

20. The distributions of f for 40 events with FIC & SIC. Fluctuating initial conditions (FIC) Smoothed initial conditions (SIC) Up panels: the distributions for FIC are much wider than the corresponding results for SIC. Down panels: one can also see the distributions for FIC are wider than those for SIF in this case.

21. Because of statistics, sometimes we have to reduce variable num-bers in analysis, although it will lose some details. (i – side, out, long, trans.) The distributions are good observables for the “granular source”.

23. Conclusions The systems produced in Au+Au collisions at RHIC energy are inhomogeneous due to the event-by-event fluctuating initial conditions. For this kind of source the two-pion HBT correlation func-tions of single-events exhibit fluctuations event-by-event. The distributions of the fluctuations between correlation func-tions of single and mixed events provide useful signals to de-tect the inhomogeneous particle-emitting sources produced in high energy heavy ion collisions. The study of the space-time structure in event-by-event basis is important to understand the system evolution and the HBT puzzle.

24. Thank you!

25. (W.N. Zhang, S.X. Li, C.Y.Wong, M.J. Efaaf, PRC71, 064908,2005.)

26. 高能重离子碰撞系统演化 碎裂信号 碎裂机制

28. Intensitive interferometry（HBT） X1 X2

29. Intensitive interferometry（HBT） radius， Life-time | p1 ─ p2| , | E1 ─ E2|

30. Side q = p1 - p2 p1 K = p1 + p2 p2 Z Out ( VK · q , K / VK ( Intensitive interferometry（HBT）

31. 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) RHICHBT Puzzle（1）

32. Predictions of Hydrodynamic model 2) Rout/ Rside≈1 K. Adcox et al., Phys. Rev. Lett. 88, 192302 (2002) RHICHBT Puzzle（2）

33. Unstable expansion may be a more general case in the expansion with the so high density difference between the QGP and vacuum and with the large- fluctuating initial density. • So, it is possibly a granular source!