Wang Meijuan Liu Lianshou Wu Yuanfang IOPP， Huazhong Normal University

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1 Wang Meijuan Liu Lianshou Wu Yuanfang IOPP， Huazhong Normal University
Is there hydrodynamic flow at RHIC? Wang Meijuan Liu Lianshou Wu Yuanfang IOPP， Huazhong Normal University Motivation Neighboring angular-bin multiplicity correlation pattern in transport models Anisotropic correlation coefficient（ACC） Summary 3.引入各项异性关联系数.

2 1. Motivation Some form of a quark-gluon plasma is formed at RHIC, and one of the evidences is the anisotropic collective flow behavior observed. The successful hydrodynamic description on the observed mass dependence of v2 at pt < 2GeV shows that observed dense matter behaves like a perfect fluid, and is referred as sQGP. Experimentally ： Hydrodynamic model can still not quantitatively fit the observed mass dependence of v2 for Cu+Cu data. PRL98, (2007) 相对论重离子碰撞实验表明在RHIC能区产生了QGP，其中证据之一就是观测到了各项异性集体流. 实验上，流体力学模型并不能很好的吻合Cu+Cu数据，特别在中心碰撞中，实验数据的结果比流体力学模 型预言的要大很多。 理论上：流体力学有一前提，就是要达到局域热平衡；很难找到这么一物理过程能让系统在如此的时间 尺度达到热化。另外没有粘滞性的流体在理论上并不好理解。 目前也有很多别的非热平衡的一些方法，它们也能很好的和RHIC数据作比较。 Theoreticallly： local thermal equilibrium is required. Viscosity=0 is hard to be understood. However 2019/1/13 NanJing

3 1. Motivation The main experimental physical quantity v2 ：
1）it only globally characterizes the possible direction and strength of anisotropic distribution. 2) The intrinsic interaction of final state particles is absent. 2-particle azimuthal corr. the average correlation of two particles separated by a certain angle, no matter where the two particles are in the whole azimuthal space. 被流体力学模型研究的一主要实验观测量是v_2, 。。。，它是一整体观测量，末态粒子的 内部作用不可现。 2-particle 轴相角关联是一个很不错的物理量,给出了很多物理信息,比如Au+Au背靠背关联的 消失之类的,但是它是相隔某个间隔的两粒子的平均关联的结果, 只关心其相对位置.而不管这 两粒子的具体位置. 所以….,但是对于高度各项异性的物理系统, 位置相关的信息应该还是很重要的,不能被简单 的平均掉! How the particles in different azimuthal directions interact with each other can not be drawn from them either. 2019/1/13 NanJing

4 2. Introduction of the corr. pattern
A spatial-dependent neighboring correlation pattern is suggested: Wu Yuanfang, Lianshou Liu, Yingdan Wang, Yuting Bai and Hongbo Liao, Phys. Rev. E71, (2005). m: the sequence number of bins nm: the multiplicity in the mth angular bin 1 2 M …… 2π A typical spatial distri. of two bin corr. is drawn. i.e.If the particles are produced independently, then <nm nm+1>=<nm> <nm+1>, Cm,m+1 vanishes. How the nearby particles correlate with each other in different directions of azimuthal space can be measured! 除以…,这是在作一规一化,除去了多重数的影响.让其能给更好地给出关联信息! 。。。 这儿我们取得是50,那么m可以从1取到49,这样我们就可以清楚的看到… 如果粒子独立产生，bin-bin之间的关联信息消失。 It’s a good observable for tracing the interaction among different azimuthal directions in relativistic heavy ion collision. 2019/1/13 NanJing

5 2. Corr. pattern in transport models
RQMD with hadron rescattering: a hadron-based transport model; where v2 is smaller than the data at RHIC. H. Sorge, Phys. Rev. C52, 3291 (1995); Y. Lu et al. nucl-th/ AMPT with string melting: a multi-phase transport model, where parton cascade + hadron rescattering are both included. This model can reproduce v2 (pt) data at RHIC. 为了将关连花样应用到当前相对论重离子碰撞中, 我们选择了两种疏运模型作为例子. Zi-Wei Lin, Che Ming Ko, Bao-An Li, Bin Zhang and Subrata Pal, Phys. Rev. C72, 2019/1/13 NanJing

6 2. Corr. pattern in transport model
cos2Φ like pattern in peripheral coll. flat in mid-central coll. -cos2Φ like pattern in near-central coll. In Fig.(a) ： Corr. patterns from two models are –cos2Φ like, opposite to the well-known cos2Φ like azimuthal distribution. 在这张ppt中，我们给出了模型中一些关联花样的结果。(a)给出minibias的结果，空心点-RQMD，实心点-AMPT 两模型给出的结果都是-cos2phi, 和轴相角密度分布cos2phi刚好相反，或者说，粒子数多的方向，相邻两bin之间的 多重数关联弱，粒子数少的方向，两bin之间的多重数强。由此我们进一步分析了中心度的依赖，b-RQMD,c-AMPT 三个典型度中心度被选择，分别是边缘，半中心，中心碰撞区，我们发现一有趣的现象，。。。，事实上， 关联花样随着中心度的变化，由cos2phi渐变到-cos2phi，很明显。。。，类比于流的概念，我们将其分别称为 in-plane 关联花样，和out-of-plane关联花样。。。。在所有方向关联都是相等的，所以都是平的。 In Fig.(b)+Fig.(c) : two opposite trends dominate in peripheral and near-central collisions, which can be called as in-plane and out-of-plane corr. pattern respectively. In the mid-central collisions, the two trends turn to balance. 2019/1/13 NanJing

7 ? 2. Corr. pattern in transport model ☺ In-plane corr. pattern:
What is the physical origin of the two opposite trends ? ☺ In-plane corr. pattern: It is the same as in-plane flow, which is caused by anisotropic expansion in non-central collisions. ☺Out-of-plane corr. pattern : the anisotropic expansion and the late hadronization are impossible to produce strong correlations in out-of-plane directions. 这儿我们讲讲产生这两种相反趋势的物理原因。 对于in-plane corr. pattern： 它是由于非中心碰撞的各项异性扩展所导致。 对于out-of-plane corr. pattern, 各项异性扩展和强子化过程都不会在out-of-plane方向产生较强关联 仅仅初始碰撞粒子源在这个方向比较强。因为碰撞初期在out-of-plane方向有更多的核子参加反应， 从而能够在这些方向产生更强的相互作用。 Only the initial source anisotropy is preferential in these directions. A larger initial number of participant nucleons in the out-of-plane directions, which in turn generates stronger interaction in these directions. 2019/1/13 NanJing ? What is the physical origin of the two opposite trends

8 2. Corr. pattern in transport model
☺ Why the out-of-plane corr. patterns appear at near-central coll.? In peripheral collisions : The overlap zone is small, and so is the no. of participants; the diff. between two axes of overlap zone is large, and so is the difference of pressure gradient. The anisotropic expansion dominates the final observable,the effects of initial interaction in corr. patterns are hidden. In near-central collisions : 我们具体讲讲为什么out-of-corr.pattern出现在中心碰撞。在边缘碰撞中，两碰撞核的重叠区很小，参加反应的 核子数也很少，但是重叠区的两轴之间的区别很大，那么相应压力梯度也很大。这样，末态观测量主要被各项 异性扩展所主导，初始作用的效果被隐藏。 在中心碰撞中，这重叠区很多，参加反应的核子数很多，而此时两轴 之间的区别很小。所以这时初始作用很强能被显现出来，而各项异性扩展的效果不可现。 The overlap zone becomes large, and the diff. between two axes of overlap zone is small. The initial interactions are strong enough to show themselves up! 2019/1/13 NanJing

9 2. Corr. pattern in transport models
If there is hydrodynamic flow, the system should be well thermalized and reach thermal equilibrium. Then all other interaction before anisotropic expansion should be forgotten! The out-of-plane corr. pattern is observed as the result of initial interaction before anisotropic expansion, i.e, a larger initial number of participant nucleons in the out-of-plane directions. This is out of the hydrodynamic expectation！ 我们知道，如果在RHIC能区存在流体力学的流的话，系统应该被热化，局域热平衡的条件应该达到。这样 系统在各项异性扩展之前的其他作用应该被忘记。 而在这儿，我们观测到了out-of-plane关联花样，它被认为是在各项异性扩展之前初始作用的结果，这和 流体力学模型是不相符的。所以研究RHIC和LHC的实验测量是很有必要的。 Measuring the corr. pattern by the data of RHIC and LHC is looking forward to！ 2019/1/13 NanJing

10 3. Anisotropic correlation coefficient
The correlation patterns are typical periodic function of azimuthal angle in periph.and central collisions, so it can be expanded by Fourier series： 1) Ψr is the direction of reaction plane, and is zero in model analysis, while in real exp. data analysis, it has to be determined event-by-event. 为了研究的方便，我们引入各项异性关联系数这一物理量。 类比于轴相角的密度分布展开，我们也将此变量傅立叶展开！我们已经看到关联花样是 轴相角的一典型周期函数。。。。 关联花样的曲线的周期大概是pi，所以傅立叶展开中的主要贡献来自第二项cos2(phi-psair) 它的系数u2的正负能给出关联花样的方向，大小能给出关联花样的数值，是一很方便的物理量 我们将其简成为ACC。 2) The main contribution in the expansion series comes from cos2(Φ-Ψr). 3) The coefficient u2 provides the preferential direction and strength of anisotropic correlation pattern. We specify it as anisotropic correlation coefficient (ACC). 2019/1/13 NanJing

11 3. The rapidity dependence of ACC
(+1, +5]；[-5,-1); [-1，+1] are chosen ,which correspond to forward, backward and central rapidity region. ACC is independent of the choice of rapidity and similar to that in whole rapidity space. 这儿我们给出的是u2在不同中心度的快度依赖，其中。。。三个典型的快度区间被选择。 很明显我们看到，。。。，所以。。。 So in finite rapidity range of current relativistic heavy ion exp., studying the corr. pattern and ACC is expectable. 2019/1/13 NanJing

12 4. Summary A spatially-dependent azimuthal multiplicity corr. pattern is suggested! There are two kinds of interactions at early stage of Au +Au collisions at √sNN =200GeV generated by the two models. a. one is in-plane preferential --- which is expected from anisotropic expansion due to initial eccentricity in non-central collisions. b. another new one is out-of-plane preferential --- which may be resulted from larger initial number of participant nucleons in these direction. The out-of-plane corr. pattern is observed as the result of initial interaction before anisotropic expansion. This is out of the hydrodynamic expectation！ 我们用模型观测到了200GeV Au+Au碰撞早期的两种相互作用。 一个是in-plane方向上的，由于非中心碰撞的各项异性扩展所致 另一个是out-of-plane，原因是在这些方向有更多的核子参加反应，而后在这些方向产生更强的相互作用 进一步的，我们指出了，系统各项异性扩展之前的相互作用在out-of-plane的关联花样中观测到，这和流体 力学模型的预言是不相符的。 所以在RHIC和LHC研究关联花样这一物理量是很有必要的。我们也模型给出了各项异性系数不依赖于快度 区间的选择。所以在当前重离子碰撞有限的快度区间范围，测量corr. Pattern是可行的。3KS！ Studying the corr. pattern of data of RHIC and LHC is looking forward to! i.e, ACC is independent of rapidity range, it is measurable in finite rapidity range of current relativistic heavy ion exp.. Thanks！ 2019/1/13 NanJing