We present measurements of elliptic flow and event-by-event fluctuations
established by the PHOBOS experiment. Elliptic flow scaled by participant
eccentricity is found to be similar for both systems when collisions with the
same number of participants or the same particle area density are compared. The
agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence
that the matter is created in the initial stage of relativistic heavy ion
collisions with transverse granularity similar to that of the participant
nucleons. The event-by-event fluctuation results reveal that the initial
collision geometry is translated into the final state azimuthal particle
distribution, leading to an event-by-event proportionality between the observed
elliptic flow and initial eccentricity.Comment: To appear in the proceedings of the Lake Louise Winter Institute
  2007. The proceedings of the institute will be published by World Scientifi

Alver, B.

Back, B. B.

Baker, M. D.

Ballintijn, M.

Barton, D. S.

Nouicer, R.

English

arXiv

We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity

UNT (University of North Texas) Digital Library

BNL-79569-2007-CP Elliptic Flow, Initial Eccentricity and Elliptic Flow Fluctuations in Heavy Ion Collisions at m I C  Rachid Nouicer for the PHOBOS Collaboration Presented at the Lake Louise Winter Institute 2007 Alberta, Canada February 19 - 24,2007 Physics Department Heavy Ion Research Group Brookhaven National Laboratory P.O. Box 5000 Upton, NY 1 1973-5000 www.bnl.gov Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-ACOZ 98CH10886 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. This preprint is intended for publication in a journal or proceedings. Since changes may be made before publication, it may not be cited or reproduced without the author's permission. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. July 30, 2007 18:32 Proceedings Trim Size: 9in x 6in RNouicer'LLWI07'Proc ELLIPTIC FLOW, INITIAL ECCENTRICITY AND ELLIPTIC FLOW FLUCTUATIONS IN HEAVY ION COLLISIONS AT RHIC RACHID NOUICER for the PHOBOS Collaboration Brookhaven National Laboratory, Physics Department E-mail: rachid.nouicerObnl.gov B.ALVER4,B.B.BACK1,M.D.BAKER2,M.BALLINTIJN4,D.S.BARTON2,R.R.BETTS6, A.A.BICKLEY7,R.BINDEL7,W.BUSZA4,A.CARROLL2,Z.CHAI2,M.P.DECOWSKI4,E.GARCiA6 , T.GBUREK3,N.GEORGE2,K.GULBRANDSEN4,C.HALLIWELL6, J.HAMBLEN8 ,M.HAUER2, C.HENDERSON4,D. J.HOFMAN6,R.S.HOLLIS6,B.HOLZMAN2,A.IORDANOVA6,J.L.KANE4, N.KHAN8,P.KULINICH4,C.M.KUO5,W.LI4,W.T.L1N5 ,C.LOIZIDES4,S.MANLY8 ,A.C.MIGNEREY7, R.NOUICER2~6,A.OLSZEWSKI3,R.PAK2,C.REED4,C.ROLAND4,G.ROLAND4,J.SAGERER6, H.SEALS2,1.SEDYKH2,C.E.SMITH6 ,M.A.STANKIEWICZ2 ,P.STEINBERG2 ,G.S.F.STEPHANS4, A.SUKHANOV2,M.B.TONJES7,A.TRZUPEK3,C.VALE4 ,G. J.VAN NIEUWENHUIZEN4, S.S.VAURYNOVICH4,R.VERDIER4,G.I.VERES4,P.WALTE~8,E.WENGER4,F.L.H.WOLFS8, B.WOSIEK3,K.WOZNIAK3,B.WYS10UCH4 Argonne National Laboratory, Argonne, IL 60439-4843, USA Brookhaven National Laboratory, Upton, N Y  11973-5000, USA Institute of Nuclear Physics, Krako'w, Poland Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA National Central University, Chung-Li, Taiwan University of Illinois at Chicago, Chicago, IL 60607-7059, USA University of Maryland, College Park, MD 20742, USA University of Rochester, Rochester, N Y  14627, USA We present measurements of elliptic flow and event-by-event fluctuations estab- . lished by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the mat- ter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctu- ation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity. 1 July 30, 2007 18:32 Proceedings Trim Size: 9in x 6in 0.1 0.1 " ' I  ~ " I ' " I " ' / " ' I ' " _  - a ) 0 Track-based200GeV' 0 Hit-basedZOOGeV - t Hit-based624GeV 0 Hit-based224GeV . 0.05 0.08 - Preliminary '. : >" 0.06; 11s; .O v bQ.*.: 0.04 0.02; . cu+cu PHOBOS i -0.05: 0 ' ' '20' ' 40' ' '6ti ' '80' ' I00 ' ' -0.1 RNouicer'LLWI07'Proc 0-25% most central 1 Mid-rapidity region - ti 1 , 4 4 4  4 'I A FiredTarget Coilider Experiments Expcrimenb ' ih. EOS i A E895 I t  Q NA49 *PHENlX OPHOBOS A CERES ' " " 1 1 "  ' " 1 ( 1 ' 1 '  2 Figure 1. Panel a) v2 versus Npart for Au+Au and Cu+Cu collisions at 6 = 22.4, 62.4 and 200 GeV. Panel b) the dependence of v2 on beam energy for mid-central Au+Au collisions. We add to this plot PHOBOS published data for Au+Au at 6 = 19.6, 62.4, 130 and 200 GeV. The bars in the plots represent statistical errors. 1. Introduction Elliptic flow has been studied extensively in nucleus-nucleus collisions at SPS and RHIC as a function of pseudorapidity, centrality, transverse mo- mentum and center-of-mass energy l ~ ~ ,  One of the most striking observa- tions at RHIC is a strong event anisotropy in non-central collisions 3, which is generated through the elliptically deformed overlap region of the collid- ing nuclei, resulting in an eccentric distribution of matter and anisotropic pressure gradients in the early stages of the expansion '. From a micro- scopic point of view this strong collective anisotropy is best described under the assumption of extremely strong rescattering 5 ,  strong enough in fact to reach the limit of continuum dynamics. To achieve such a strong conver- sion of anisotropies from coordinate to momentum space, rescattering has to be strong at very early times and local thermalization has to occur while the geometric deformation of the source is still large '. In this work, the comparison of the data from Cu+Cu and Au+Au collisions measured by PHOBOS experiment at  RHIC provides new information on the interplay between initial collision geometry (initial eccentricity) and initial particle density in determining the observed final state flow pattern. Studies from PHOBOS have pointed out the importance of fluctuations in the initial- - I I July 30, 2007 18:32 Proceedings Trim Size: Sin x 6in RNouicer'LLWI07'Proc 3 state geometry for understanding the large Cu+Cu v2 value. 2. Elliptic Flow PHOBOS has measured elliptic flow as a function of pseudorapidity, cen- trality, transverse momentum, center-of-mass energy 7,819 and, recently, nuclear species lo. In particular, the measurements of elliptic flow as a function of centrality provide information on how the azimuthal anisotropy of the initial collision region drives the azimuthal anisotropy in particle pro- duction. In figure la ,  we show the centrality dependence of v2 at midrapid- ity (171 < 1) for Cu+Cu at 6 = 22.4,62.4 and 200 GeV collision energies, as obtained from our hit-based and track-based analysis methods 8,10. A substantial flow signal is measured in Cu+Cu at, three energies, even for the most central events. The strength of Cu+Cu v2 signal is surprising in light of expectations that the smaller system size would result in a much smaller flow signal I1. Figure. l b  shows the dependence of v2 on beam en- ergy 12. We add to this plot PHOBOS published data for Au+Au at & = 19.6, 62.4, 130 and 200 GeV '. At low fixed target energies (&- 3 GeV), particle production is enhanced in the direction orthogonal to the reaction plane, and v2 is negative. This is due to the effect that the spec- tator parts of the nuclei block the matter in the direction of the reaction plane. At higher center of mass energies, these spectator components move away sufficiently quickly, and therefore particle production is enhanced in the reaction plane, leading to v2 > 0. This phenomenon is expected in hydrodynamic scenarios in which the large pressure gradients within the reaction plane drive a stronger expansion. However, the most important observation is that, up to the highest center of mass energies at RHIC, the observed asymmetry v2 continues to grow. It would be interesting to see whether this tendency is confirmed by the LHC data. 3. Initial Eccentricity In order to distinguish collision dynamics from purely geometrical effects, it has been suggested that the measured v2 should be scaled by the eccentric- ity of the nuclear overlap area 13. The PHOBOS collaboration has shown that for small systems or small transverse overlap regions, event-by-event fluctuations in the shape of the initial collision region affect the elliptic flow: Monte Carlo Glauber (MCG) studies have shown that the fluctuations in the nucleon positions frequently create a situation' where the minor axis of the overlap ellipse of the participant nucleons is not aligned with the I July 30, 2007 18:32 Proceedings Trim Size: 9in x 6in - e -  - 30; c )  * e e rn 46 *O: eo 1 -19. ,ol % d o  A 0 .  e Au-AuZOOGeV 1 o c u - m z w c ~ v ~  :csoo" A ~ . A ~ ~ Z A G ~ V  - dy * C ~ . C ~ ~ ~ A G ~ V  - f i . l . l S x f i ( ~ < l )  4 Figure 2. Panel a) V Z / ( E ~ ~ ~ ~ )  versus Npart for Au+Au and Cu+Cu collisions at  fi = 200 GeV. Panel b) shows v2/(.spart) as func- tion of mid-rapidity (171 < 1) particle area density l/(S)(dN/dy) for Cu+Cu and Au+Au collisions. The bars in the plots represent the statistical errors. Panel c) correlation plot of midrapidity particle area density l/(S)(dN/dy) as function of RNouicer'LLWI07'Proc b )  0 62.4 GeV, Au+Au, hib 19.6 CeV, Au*Au, hits impact parameter vector. To account for this effect, PHOBOS has intro- duced the participant eccentricity defined as lo: &part = , where ozv = (zy) - (z)(y) is the covariance. This definition accounts for the nucleon fluctuations by quantifying the eccentricity event-by-event with respect to the overlap region of the participant nucleons. For com- parison of Au+Au and Cu+Cu collisions at several energies, figure 2a and 2b show V Z / ( E ~ ~ ~ ~ )  as a function of Npart and midrapidity particle area density, 1/(S) (dN/dy), respectively. Figure 2c shows that at given energy, 62.4 or 200 GeV, the AufAu and Cu+Cu collisions selected for the same value of Npart leads to the same value of midrapidity particle area density l/(S)(dN/dy) calculated in MCG. We observe in figure. 2a (2b) that the v2 scaled by Epart are similar for both Cu+Cu and Au+Au collisions at the same value of Npart (l/(S)(dN/dy) ). It should be noted that in figure 2b which has been introduced previously in Ref. 14, in the y-axis the va(r7) has been converted to v2(y) by scaling the data by factor 0.9 and also in the x-axis the dN/dy = 1.15 dN/dq at midrapidity region, 171 < 1. This simi- larity between Cu+Cu and Au+Au collisions is also observed as a function of transverse momentum as well as in a wide pseudorapidity range dFFzF&=g 15 . - - I I July 30, 2007 18:32 Proceedings Trim Size: 9in x 6in - RNouicer'LLWI07'Proc 5 Figure 3. Panel a) ("2) and panel b) uv2 versus Npart for Au+Au collisions at Js;;;; = 200 GeV. Boxes and gray bands show 90% C.L. systematic errors and the error bars represent 1-u statistical errors. The results are for 0 < 17 < 1 for the track-based method and 1171 < 1 for hit-based and event-by-event methods. Panel c) ~ 7 ~ ~ / ( 7 ~ 2 )  versus Npart for Au+Au collisions at Js;;;; = 200 GeV. Open squares show ufpart /(cpart) calculated in a Glauber MC. The bands show 90% C.L. systematics errors. 4. Elliptic Flow Fluctuations The apparent relevance of the participant eccentricity model in unify- ing the average elliptic flow results for Cu+Cu and Au+Au collisions leads naturally to consideration of the dynamical fluctuations of both the par- ticipant eccentricity itself as well as in the elliptic flow signal from data. Simulations of the expected dynamical fluctuations in participant eccen- tricity as a function of Npart were performed using the PHOBOS Monte Carlo Glauber based participant eccentricity model. Figure. 3a shows the mean, (vz), and the standard deviation, o,,, of the elliptic flow parameter v2 at  midrapidity as a function of the number of participating nucleons, in Au+Au collisions at JSTNT; = 200 GeV for 6-45% most central events 17. The results for (v2) are in agreement with the previous PHOBOS v2 measurements ', which were obtained with the event-plane method for charged hadrons within 1171 < 1. The uncertainties in dN/dv and v2(17), as well as differences between HIJING and the data in these quantities, intro- duce a large uncertainty in the overall scale in the event-by-event analysis due to the averaging procedure over the wide pseudorapidity range. The event-plane method used in the previous PHOBOS measurements has been 16 proposed to be sensitive to the second moment, m, of elliptic flow . - - I I July 30, 2007 18:32 Proceedings Trim Size: 9in x 6in - RNouicer’LLWI07’Proc I - 6 The fluctuations presented in this work would lead to approximately 10% difference between the mean, (vq), and the RMS, m, of elliptic flow at a fixed value of Npart. Most of the scale errors cancel in the ratio, a,,/(vz), which defines “rela,tive flow fluctuations”, shown in figure. 3b as a function of the number of participating nucleons 17. We observe large relative fluc- tuations of approximately 40%. MC studies show that the contribution of non-flow correlations to the observed elliptic flow fluctuations is less than 2%. Figure 3c shows ~ , ~ , , ~ / ( ~ p ~ ~ t )  at fixed values of Npart obtained in a MC Glauber simulation. The 90% confidence level systematic errors are es- timated by varying Glauber parameters as discussed in Ref. lo. A striking agreement between the relative fluctuations in the Glauber model partici- pant eccentricity predictions and the observed elliptic flow fluctuations is seen over the full centrality range under study. The observed agreement suggests that the fluctuations of elliptic flow primarily reflect fluctuations in the initial state geometry and are not affected strongly by the later stages of the collision. 5. Summary We have performed a comprehensive examination of the elliptic flow of charged hadrons produced in Cu+Cu and Au+Au collisions at 6 = 19.6, 22.4, 64.4 and 200 GeV. We also presented the measurements of event-by-event fluctuations for Au+Au collisions at 6 = 200 GeV. The comparison of the data from Cu+Cu and Au+Au collisions provides new information illustrating that the participant.eccentricity is the relevant ge- ometric quantity for generating the azimuthal asymmetry leading to the observed flow. The magnitude of event-by-event fluctuations agree with predictions for fluctuations of’the initial shape of’ the collision region based on the Glauber model. These results provide qualitatively new information on the initial conditions of heavy ion collisions and the subsequent collective expansion of the system. References 1. C. Alt et al. Phys. Rev. C68 (2003) 034903 and references therein. 2. I. Arsene et al. Nucl. Phys. A 757 (2005) 1, B. B. Back et al. Nucl. Phys. A 757 (2005) 28, J. Adams et  al. Nucl. Phys. A757 (2005) 102 and K. Adcox et al. Nucl. Phys. A 757 (2005) 184. 3. K.H. Ackermann et al. Phys. Rev. Lett. 86 (2001) 402. 4. J.-Y. Ollitrault Phys. Rev. D46 (1992) 229. 5. D. Molnar and M. Gyulassey Nucl. Phys. A697 (2002) 495. - - I I July 30, 2007 18:32 Proceedings Trim Size: 9in x 6in - RNouicer'LLWI07'Proc 7 6. P.F. Kolb e t  al. Phys. Rev. C62 (2000) 054909. 7. B. B. Back et al. Phys. Rev. Lett. 89 (2002) 222301. 8. B. B. Back et al. Phys. Rev. Lett. 94 (2005) 122303. 9. B. B. Back e t  al. Phys. Rev C72 (2005) 051901(R). 10. B. Alver e t  al. Phys. Rev. Lett. 98 (2007) 242302. 11. L. W. Chen et al. Phys. Lett. B634 (2006) 205. 12. N. Borghini and U. Wiedemann (Private communication). 13. H. Sorge Phys. Rev. Lett. 82 (1999) 2048. 14. A. S. Voloshin e t  al. Phys. Lett. B474 (2000) 27. 15. R. Nouicer et al., J. Phys. G: Nucl. Part. Phys. 34 (2007) S887. 16. R.S. Bhalerao and J. Y. Ollitrault Phys. Lett. B641 (2006) 260. 17. B. Alver et al. arXiv:nucl-ex/0702036 (submitted to PRL, 2007). 

ELLIPTIC FLOW, INITIAL ECCENTRICITY AND ELLIPTIC FLOW FLUCTUATIONS IN HEAVY ION COLLISIONS AT RHIC.

Crossref

ELLIPTIC FLOW, INITIAL ECCENTRICITY AND ELLIPTIC FLOW FLUCTUATIONS IN HEAVY ION COLLISIONS AT RHIC

Elliptic Flow, Initial Eccentricity and Elliptic Flow fluctuations in
  Heavy Ion Collisions at RHIC

Elliptic Flow, Initial Eccentricity and Elliptic Flow fluctuations in Heavy Ion Collisions at RHIC

Abstract

Similar works

Full text

Available Versions

UNT (University of North Texas) Digital Library

Crossref