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1、1 31 ? 1 12 2007 c 12 ? p U ? n ? ? ? n HIGHENERGYPHYSICSANDNUCLEARPHYSICS Vol. 31, No. 12 Dec., 2007 Eccentricities of Flow - Elliptic Flow Fluctuations and Evidence for Transverse Localization in the Initial State of the Matter in Relativistic Heavy Ion Collisions* S.Manly8;1)(for the PHOBOS Colla
2、boration) PHOBOS Collaboration B.Alver4B.B.Back1M.D.Baker2M.Ballintijn4D.S.Barton2R.R.Betts6R.Bindel7W.Busza4 Z.Chai2V.Chetluru6E.Garc a6T.Gburek3K.Gulbrandsen4J.Hamblen8I.Harnarine6 C.Henderson4D.J.Hofman6R.S.Hollis6R.Ho ly nski3B.Holzman2A.Iordanova6J.L.Kane4 P.Kulinich4C.M.Kuo5W.Li4W.T.Lin5C.Loiz
3、ides4S.Manly8A.C.Mignerey7R.Nouicer2 A.Olszewski3R.Pak2C.Reed4E.Richardson7C.Roland4G.Roland4J.Sagerer6I.Sedykh2 C.E.Smith6M.A.Stankiewicz2P.Steinberg2G.S.F.Stephans4A.Sukhanov2A.Szostak2 M.B.Tonjes7A.Trzupek3G.J.van Nieuwenhuizen4S.S.Vaurynovich4R.Verdier4G.I.Veres4 P.Walters8E.Wenger4D.Willhelm7F.
4、L.H.Wolfs8B.Wosiek3 K.Wo zniak3S.Wyngaardt2B.Wys louch4 1 (Physics Division, Argonne National Laboratory, Argonne, IL 60439-4843, USA) 2 (Chemistry and C-A Departments, Brookhaven National Laboratory,Upton, NY 11973-5000, USA) 3 (Institute of Nuclear Physics PAN,Krak ow, Poland) 4 (Laboratory for Nu
5、clear Science, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA) 5 (Department of Physics, National Central University, Chung-Li) 6 (Department of Physics, University of Illinois at Chicago, Chicago, IL 60607-7059, USA) 7 (Department of Chemistry and Biochemistry, University of M
6、aryland, College Park, MD 20742, USA) 8 (Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA) Abstract Recent measurements of event-by-event elliptic fl ow in Au+Au collisions at s NN=200GeV exhibit large relative fl uctuations of about 40%50%. The data are well de
7、scribed by fl uctuations in the shape of the initial collision region, as estimated event-by-event with the participant eccentricity using Glauber Monte Carlo. These results, combined with the demonstrated participant eccentricity scaling of the elliptic fl ow across nuclear species, constitute evid
8、ence of transverse granularity in the initial matter production in these collisions. Key words elliptic fl ow, fl uctuation, event-by-event 1Introduction Elliptic fl ow (v2) is one of the key observables in the understanding of the dynamics of heavy ion col- lisions. The observation of a signifi can
9、t azimuthal anisotropy in the momentum and/or spatial distribu- tions of the detected particles relative to the reaction plane, is direct evidence of interactions between the Received 25 June 2007 *Supported by U.S. DOE Grants DE-AC02-98CH10886, DE-FG02-93ER40802, DE-FG02-94ER40818, DE-FG02-94ER4086
10、5, DE-FG02-99ER41099, and DE-AC02-06CH11357, by U.S. NSF Grants 9603486, 0072204, and 0245011, by Polish KBN Grant 1-P03B-062-27 (2004-2007), by NSC of Taiwan Contract NSC 89-2112-M-008-024, and by Hungarian OTKA Grant F049823 1)E-mail:steven.manlyrochester.edu 1133 1136 1134p U ? n ? ? ? n( HEP & N
11、P )131? initially produced particles in heavy ion collisions. These interactions must occur at relatively early times, since expansion of the source rapidly reduces the magnitude of the spatial asymmetry. Typically, the connection between the initial and fi nal-state anisotropy is provided by hydrod
12、ynamical models that relate a given, initial source shape to the distribution of produced particles. In such calcula- tions, it is common to use smooth, event-averaged, initial conditions. However, event-by-event fl uctua- tions in the shape of initial interaction region must not be neglected. As a
13、means to quantify the eff ect of initial-state eccentricity fl uctuations, PHOBOS has introduced the “participant eccentricity” 1, 2, ?part= q (2 yy2xx)2+42xy 2 yy+2xx , where 2 ab=habihaihbi are the per-event (co-) vari- ances of the participant nucleon position distributions in the transverse plan
14、e. The magnitude and shape of ?partas a function of centrality were found to be ro- bust to variations of the Glauber parameters. Fluctuations in the shape of the initial state in- teraction region might be expected to be more pro- nounced for smaller species and for more peripheral events. This is
15、borne out by the data, where a strik- ing agreement between the elliptic fl ow signals in Cu+Cu and Au+Au data as a function of central- ity is obtained when scaled by the participant ec- centricity, v2/h?parti1, 2.The agreement is not as good when scaled by the commonly used eccentricity, = 2 y 2 x
16、 2 y+2x , that does not take into account initial state fl uctuations. Given the obvious importance of fl uctuations in the initial state to the fi nal elliptic fl ow measurement, PHOBOS recently developed a new technique to mea- sure dynamical fl ow fl uctuations in our data3, 4. The new analysis and results stemming from it are sum- marized below. 2Elliptic fl ow fl uctuationsanalysis technique and results The PHOBOS fl ow fl uctuations analysis extracts the fl
