颗粒性粒子发射源的视像 (Imaging) 分析

1. 颗粒性粒子发射源的视像(Imaging)分析 1,2 2 2 张卫宁 杨志滔 任延宇 • 大连理工大学 物理与光电工程学院 • 2) 哈尔滨工业大学物理系 Phys. Rev. C80 (2009) 044908

2. 得到的定量结果 是模型依赖的。 一、引 言 强度干涉学(HBT)已被广泛应用于获取高能重离子碰撞产生的粒子发射源的时空信息。 在高能重离子碰撞的传统强度干涉学分析中，人们是对实验(或模拟)产生的2粒子(如2π)关联函数用参量化的公式进行拟合，得到有关时空结构定量结果。例如，一维高斯参量化公式拟合，

3. + 0  - - 对这样的非高斯源，高斯拟合得到的源半径 不能反映源的空间特征，得到的 参量也会畸变。 在高能重离子碰撞产生的π发射源可能并不是简单的高斯分布。例如，为解释实验观察上小的λ参量，人们提出了源的Core-Halo分布模型；为解释RHIC的HBT之谜，提出了颗粒源模型。

4. π对质心系中相对动量和坐标 笛卡尔谐函数基 由视像分析得到的 是模型无关的，从中获取的有关源的定量信息也与模型无关。因而适合用于对非高斯源的分析。 视像分析可以从关联函数 得到相对源函数 ，(一维, Brown & Danielewicz; 三维, Danielewicz & Pratt)。

5. Imaging Model-independent 二、源的模型无关特征量 之前对实验imaging的研究主要集中于对源函数形状的讨论和利用参数化函数拟合imaged sources。 S. S. Afanasiev et al., (PHENIX Collaboration), Phys. Rev. Lett. 100, 232301 (2008) S. S. Adler et al., (PHENIX Collaboration), Phys. Rev. Lett. 98, 132301 (2007) Zhi-Tao Yang, Wei-Ning Zhang, L. Huo, Jing-Bo Zhang, J. Phys. G36, 015113 (2009)

6. 定义相对距离r的n阶矩 r 的各阶“矩”是描述发射源的模型无关的特征量。

7. 对静态源的分析表明：对非高斯源，视像法得到的 更接近于真实值， 能更好地体现非高斯源在大 r 的分布，而 反映了源分布与高斯分布的差异。 对高斯源 引入

8. QGP在接近相变时快速增加的体粘滞性 PRC77 (2008) 034903 三、改进的QGP颗粒源模型 形成QGP颗粒源的可能因素： 大的初始涨落+快速膨胀+表面张力效应 NeXus PRC74 (2006) 024908

9. 过去QGP颗粒源的结果： ( W. N. Zhang, Y. Y. Ren, C. Y. Wong, PRC74, 024908, 2006) V2 随 PT增加 V2 饱和

10. 中心快度区域（| y |< ym ) 速度 假定系统在 碎裂，颗粒的初始速度为 颗粒按流体力学演化，初始半径满足高斯分布 ，初始位置分布满足 对模型的改进： 初始颗粒的速度满足Bjorken条件 初始颗粒的大小满足高斯分布 考虑了直接产生和衰变产生的介子

11. π介子冻结温度满足分布 模型参量： 态方程

12. 四、颗粒源的多维视像分析 一维视像

13. X方向有长的尾巴, 随kT增加, 与y方向不同. Z方向小kT有长的尾巴。 三维视像 x — out 方向，y — side 方向，z — long 方向，kT=|p1T - p2T|/2

14. 引入 定义 i 方向 n 阶矩 考虑了洛仑兹变换后，颗粒源的视像结果R与传统HBT的半径结果符合，且可以解释HBT实验的半径结果。

15. 与传统的强度干涉学相比，视像法得到的源函数 S(r) 具有模型独立的特性。从原函数可以得到 r 的各阶矩，它们是描述粒子发射源时空和相干性的模型独立的特征量。 颗粒源模型能够再现实验HBT的主要特性。 对颗粒源的视像分析表明，相对原函数在out方向的分布要比side方向宽，其 值随粒子对横动量的增加而增加。而在long方向，小横动量时相对原函数有长的尾巴。在考虑了洛仑兹收缩后，视像分析的结果与通常HBT分析的结果相符。 我们的研究表明，与零阶矩相关的 给出有关源相干性的信息，与一阶矩有关的 给出源的平均尺寸，而 可以反映源分布与高斯分布的差异。对非高斯源，这些模型独立的特征量比通常HBT的结果更能反映源的实际情况。 五、总 结

16. Thank you!

17. ---------------------------------------------------------------------- Report of the Referee -- CJ10161/Zhang ---------------------------------------------------------------------- This is an interesting paper that expounds on some long-standing ideas about how droplets or granularity might manifest themselves in correlation measurements. The methods well surpass the quality of previous analyses, and warrant publication in PRC. The authors might want to reference some older papers which present the same ideas, but certainly do not compete with the present paper in their sophistication, e.g., S.Pratt, PRC49, 2722 (1994). The paper is clear and easy to read. I recommend publishing without changes, unless the authors wish to add reference to the paper above.

18. 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)

19. 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!

20. 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 )

21. 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 !

22. 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.

23. 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.

24. 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.

25. 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).

26. 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.

27. 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.

28. 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”.

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

31. 高能重离子碰撞系统演化 碎裂信号 碎裂机制

33. Intensitive interferometry（HBT） X1 X2

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

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

36. 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）

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

38. 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!