4. Experimental measure and expectations 5. Summary and conclusions A test of hydrodynamic behavior in the formed matter of relativistic heavy ion collisions Wang Meijuan, Liu Lianshou, and Wu Yuanfang IOPP, Huazhong Normal University, Wuhan, China Motivation A new measure --- neighboring angular-bin multiplicity corr. pattern 3. A demonstration --- the pattern of Au + Au coll. at 200 GeV generated by transport models 4. Experimental measure and expectations 5. Summary and conclusions First, why we need such a test, and how the test should be. Then I suggest a new measure. In the following, using the transport model, I will demonstrate what interesting physics can be revealed by the pattern. In the fourth part, I will talk how to experimentally measure the pattern and what we can expect from coming experiments. 2008.5.24 LHC -- IOPP

« Perfect liquid », « sQGP » ! 1. Motivation: ★ New form of a quark-gluon plasma is formed at RHIC ► Large energy density achieved ► Jet energy loss in matter ► Collective behaviour observed The mass-dependence of v2 at pT < 2 GeV shows qualitatively agreement with ideal hydrodynamic flow. As we know, It is commonly believed that new form of matter has been formed at RHIC. Among these three main evidences, it is just because the observed collective behavior, or, the mass dependence of v_2 at low pt region shows qualitatively agreement with ideal hydrodynamic. We refer the formed matter as perfect liquid, or strong coupling quark-gluon plasma. However, there are still many uncertain problems in hydrodynamics. « Perfect liquid », « sQGP » ! M. Gyulassy, L. McLerran, Nucl. Phys. A750, 30-63(2005); B. Muller, Annu. Rev. Nucl. and Part. Phys.,1(2006). K. Adcox et al. (PHENIX Coll.), Nucl. Phys. A757, 184-283(2005); John Adams et al. (STAR Coll.), Nucl. Phys. A757, 102-183(2005); 2008.5.24 LHC -- IOPP

1. Motivation: ★ Uncertain problems of idea hydrodynamics EP side: ● Quantitatively fit the mass dependence of v2 . ● Centrality dependence of v2 /(nqε) vs. KET/nq for Au + Au at 200GeV. STAR, PRC 77, 054971(2008). ● Cu + Cu collisions at 200 GeV. PHENIX, PRL 98, 162301(2007); PHOBOS, PRL 98, 242302(2007). TH side: Hydrodynamics ● early ( fm/c) thermalization ● Absent of viscosity Azimuthal anisotropy arising from ridges without rapid thermalization In experimental side, if we remember that Hydrodynamics in fact still can not quantitatively fit the mass dependence of v_2. This has been stressed in the white papers of four RHIC experiments,. Hydrodynamics also fail to describe the new data related to flow from STAR, Phenix and PHOBOS , that has been mentioned in Nu’s talk in this workshop. In the theory side, hydrodynamics requires early thermal equilibrium and absent of viscosity. Both of these are hard to understand. (The smallest viscosity will reduce flow in 25-30%.) So two new theoretical treatments without hydrodynamics appear recently. They get good agreement with data as well. In fact, there are efforts alone the non-equilibrium line in the early time too. Sergei Voloshine gave a list about achievements, difficulties and expectations in his talk at last QM. (It is found that azimuth quadrupole spectrum isolated from v2(pt) in Au +Au colli. comes from soft component of N-N coll. No evidence for thermalized system or for medium properties without viscosity Azimuth quadrupole spectrum, Thomas A. Trainor, arXiv: 0803.4002.) They found that v2 in cu+cu (copper + copper) coll. ) is unexpected as large as Au + Au collisions . KE (transverse kinetic energy) scaling is better than former pt scaling , This is still not fully understood. R. C. Hwa, arXiv: 0708.1508; R. C. Rudy, C. B.Yang, arXiv: 0801.2183. Relativistic nucleus-nucleus collisions without hydrodynamics D. V. Anchishkin, S. N. Yezhov, arXiv: 0804.1745. T. S. Biro and B. Muller, Phys. Lett. B 578, 78(2004); M. Asakawa, S. A. Bass, B. Muller, and C. Nonaka, arXiv: 0803.2449; S. A. Voloshin, arXiv: 0805.1351. 2008.5.24 LHC -- IOPP

Does the formed matter at RHIC really behave like hydrodynamic flow ? 1. Motivation: ★ Arising question Does the formed matter at RHIC really behave like hydrodynamic flow ? So the question arise, Does the formed matter at RHIC really behave like hydrodynamic flow? How can we answer the question. Obviously, it is useless to have more interpretations without hydrodynamic. Only new experimental evidence can clarify the debate. Then what kind of experimental evidence can help us to definitely answer the question? 2008.5.24 LHC -- IOPP

Elliptic Flow Parameter v2 1. Motivation: ★ Observed evidence Elliptic Flow Parameter v2 coordinate-space-anisotropy  momentum-space-anisotropy py px y x Z : beam direction Then let’s first see what experimental observable we have up to now. In fact , what we observed up to now is only the second coefficient of Fourier expansion of azimuthal distributions. It describes the anisotropic distribution of transverse momentum. Such a dis. is supposed to be driven by pressure gradient in coordinate space due to eccentricity of initial overlap zone. However, this global measure itself is not able to tell if this pressure gradient is the only driver of anisotropic dis., since it does not contain the information of intrinsic interactions of the formed matter. So v-2 is insufficient in judging whether the formed matter behaves like hydrodynamic flow or not. out-of-plane direction in-plane direction v2 can not provide information on intrinsic interaction of formed matter! 2008.5.24 LHC -- IOPP

1. Motivation: ★ Solusion Examing intrinsic interaction of the formed matter ! To find experimentally who really drivers elliptic flow ! If initial anisotropic pressure gradient is the only driver of elliptic flow, the intrinsic interaction should have the same anisotropy as its azimuthal distribution, i.e., in-plane like. (2) Otherwise, the interaction pattern should be different from its azimuthal distribution. In order to answer the question, we have to exam the intrinsic interaction of the formed matter, namely, to say to find experimentally who really drives elliptic flow. As we know, in hydrodynamics, the pressure gradient that drives elliptic flow is directly linked to the collective kinetic energy of the emitted particles. If it is the only driver,…. Then the next question is how to measure the intrinsic interaction. A spatial-dependent bin-bin correlation should be help, and therefore is called for. The correlation between each cell of observed system should provide us such kind of information. So a spatial-dependent bin-bin correlation is called for. How to measure the intrinsic interaction ? A spatial-dependent bin-bin correlation is called for ! 2008.5.24 LHC -- IOPP

1. Motivation: ★ Conventional measures ▲ 2, or 3-particle correlations Average corr. of two particles separated by a certain angle, no matter where the two particles are in the azimuthal space. So no information on intrinsic spatial interaction! ▲ bin-bin correlations Spatially averaged bin-bin corr. in exploring self-similar fractality, where the system is supposed to be homogeneous, and only scaling in the shrinking of phase space is concerned. Let’s first see what we have at market. One is 2, 3 , or 4 particle correlations. For 2-particle correlation, it measures the correlation of two particles separated by….. Where, no matter where the two particles are, as long as they are separated in the same azimuthal angle, they contribute to the correlation. So the information on …. does not contain in the measure. A other measure is bin-bin correlation. It is originally suggested in exploring self-similar fratality, Where the system is supposed to be homogeneous and the scaling of correlation in the shrinking of phase space is concerned. Now we face a high anisotropic system in relativistic heavy ion collision, we need a spatial-dependent bin-bin correlation pattern. These two old measures and concerns are helpless. Let me introduce the our new measure. They can not provide preferential direction of intrinsic interactions ! 2008.5.24 LHC -- IOPP

2. A new measure ★ Neighboring angular-bin multiplicity corr. pattern: ● Two bin corr. m1, m2 : the positions of the two bins in phase space nm : the measured content in the mth bin It is a 3-dimentional plot ! ● Neighboring angular-bin multiplicity corr. pattern Wu Yuanfang, Lianshou Liu, Yingdan Wang, Yuting Bai and Hongbo Liao, PRE71, 017103 (2005). : multiplicity in mth bin. Two bin correlation in general is defined by this formula, where, m1 and m2,…. nm….. However, it is a 3-dim plot, it’s hard to get the information. We suggested to project this 3-d plot to very useful two ones in this paper, The main information will be clearly shown up. They are adjacent bin-bin correlation pattern and fixed bin to arbitary bin correlation pattern. Here I will only concentrate to adjacent bin-bin correlation pattern. It can be gotten if specify m1=m, m2=m+1 in general two bin corr., then it reduces to two adjacent bin correlation pattern. here we further specify the measured content in mth bin as multiplicity and divide 2pi azimuthal angle into M equal bins., Where phi=0 is the direction of reaction plane. So it measures spatial distribution of nearby particle correlation. : the direction of reaction plane. It measures the spatial distribution of nearby particles correlation 2008.5.24 LHC -- IOPP

2. A new measure ● Independent production If the particles are produced independently in the whole phase space, then: Where, multiplicity is produced by AMPT and its Φ dis. is randomly given according to cos(2Φ). Before we show that the pattern really measure the interesting physics, I first show how it look like for trivial case, namely, independent production. It is clear if nm and nm+1 are independent, the two bin correlation by definition is zero. Here I offer a cos(2phi) (flow) shaped phi-dis but its phi is random produced. It is gotten in this way. We first produce multiplicity of each event by AMPT, then randomly produce azimuthal angle of each particles according to cos(2phi). Here is its correlation pattern. We can see. It’s really flat. So the pattern measures correlation, or dependent production, or interaction. It does not influence by trivial shape effects of distribution. Tang Aihong private comm. No significant correlation in the case ! 2008.5.24 LHC -- IOPP

3. A demonstration ●Relativistic transport models: RQMD with hadron rescattering: A hadron-based transport model, where v2 > 0, but smaller than the data at RHIC. H. Sorge, Phys. Rev. C52, 3291 (1995); Y. Lu et al. nucl-th/0602009. AMPT with string melting : Parton cascade + hadron rescattering are both included. It reproduces v2 (pt) data at RHIC. As an example, I use relativistic transport model RQMD with … and AMPT with… to simulate the real data, And demonstrate what interesting physics can be revealed by our suggested pattern. Zi-Wei Lin, Che Ming Ko, Bao-An Li, Bin Zhang and Subrata Pal, Phys. Rev. C72, 064901 2008.5.24 LHC -- IOPP

3. A demonstration ★ Corr. pattern of Au + Au at 200 GeV given by RQMD & AMPT: ●Patterns of Au + Au at 200 GeV given by RQMD & AMPT: ☞ The corr. patterns from these two models are -cos2Φ (out-of-plane) like, opposite to cos2Φ (in-plane) like azimuthal distribution. Data sample is for …. Here is the results for minimun bias sample. We see that the correlation pattern …… This strange result imply that some… ▲ This shows that the formed matter is in fact drived toward out-of-plane direction, rather then in-plane direction ! ▲ Some unknown, or unexpected interactions exist in the formed matter. 2008.5.24 LHC -- IOPP

3. A demonstration ●Centrality dependence of the corr. patterns: 1. cos2Φ(in-plane) like in peripheral collisions 2. flat in mid-central collisions, 3. - cos2Φ(out-of-plane) like in near-central collisions. Here we give the results for these three typical centralities, we can see that Correlation pattern reveals that …. This also shows When in-plane driver dominate in peripheral collisions, the pattern is out-of-plane like, while when ….. It turns to … ▲ These reveal that two opposite intrinsic interactions coexist in the formed matter in these two models. ▲ This shows that anisotropic azimuthal distribution is not only driven by anisotropic expansion ! 2008.5.24 LHC -- IOPP

3. A demonstration ★ Possible origins of out-of-plane preferential corr. pattern: (1) Missing parts from transport equation to idea hydrodynamics Non-linear collision terms Anisotropic geometry Out-of-plane correlation pattern More central collision, the larger the number of partons, and the stronger the contributions from collision terms. We are not completely clear how out-of-plane pattern comes. Here I would give a discussion for the possible ….. One possible reason is, it comes from the missing … This out-of-plane can only be observed at central collision, since more central collision, the larger number of parton, the stronger the contribution from non-equilibrium and no-linear collision terms. Li Jiarong, Liu Lianshou, Wu Yuanfang 2008.5.24 LHC -- IOPP

3. A demonstration → Anisotropic expansion (2) Initial interactions in geometric space (Meijuan Wang, Jiaxin Du, Wu Yuanfang) ●The evolution of AMPT Hadron (Hijing, PYTHIA) Parton Parton transport (ZPC) String melting Hadronization (Coalesce) Initial interaction → Anisotropic expansion Another reason is, it may comes from initial interaction, this interaction build up the pressure gradient that drive the elliptic flow. In order to trace this initial interaction, let’s go inside into the evolution processes of AMPT. 2008.5.24 LHC -- IOPP

Azimuthal corr. pattern 3. A demonstration ●Trace the pattern in the evolusion of AMPT Azimuthal corr. pattern in momentum space Initial eccentricity translates to pt space via transport equ.. (2)Both patterns appear simultaneously. (3) From parton to hadron, the patterns are unchanged, it shows no influence from hadronization . 2008.5.24 LHC -- IOPP

Azimuthal correlation pattern in coordinate space 3. A demonstration Azimuthal correlation pattern in coordinate space Corr. pattern is in-plane like for all centralities before transpt. (2) All patterns change to out-of-plane like as soon as start to transport, (???) and keep to be out-of-plane like. This maybe the origin of out-of-plane corr. pattern in pt space. 2008.5.24 LHC -- IOPP

4. Experimental measure and expectations ★ Fourier expansion of the correlation pattern: : the direction of reaction plane, zero in the model analysis, event- plane in real experimental data analysis. Anisotropic correlation coefficient (ACC) We have to do the average for all events. Patterns for different events should respect to the same direction, the best one is the reaction plane. : provides the preferential direction and strength of anisotropic correlation pattern. It makes systematic investigation of correlation pattern easily. 2008.5.24 LHC -- IOPP

4. Experimental measure and expectations ★ Rapidity dependence of ACC Three rapidity intervals: ☞u2 is independent of observed rapidity windows, in contrary to v2 . In finite rapidity ranges of current relativistic heavy ion experiments, studying the correlation pattern and ACC is expectable ! 2008.5.24 LHC -- IOPP

4. Experimental measure and expectations Case 1: As long as the observed correlation pattern are different from its azimuthal distribution, i.e., what we show by transport models, it would mean that the explanation of hydrodynamic flow has to be modified ! Case 2: If the experimentally measured correlation pattern has the same anisotropy as its azimuthal distribution, it will be a strong support to the current expectation, which means at intrinsic interaction level that the formed matter at RHIC indeed behaves like hydrodynamic flow ! 2008.5.24 LHC -- IOPP

谢 谢 ！ 5. Summary and conclusions ☞ It is argued that the observation of v2 alone is insufficient to assure whether the formed matter at RHIC behaves like hydrodynamic flow. Examining the intrinsic interaction of the formed matter should provide more definite judgment. ☞ A spatial-dependent azimuthal multiplicity corr. pattern is suggested. ☞ It shows clearly that there are two kinds of interactions at early stage of Au + Au coll. at 200 GeV, generated by RQMD and AMPT . ☞ The possibility of experimentally measuring the corr. pattern and ACC is discussed cf. arXiv: 0801.1149 arxiv: 0804.2932 谢 谢 ！ 2008.5.24 LHC -- IOPP 20