Centrality Dependence of Two-Particle Correlations in Heavy Ion Collisions
CCentrality Dependence of Two-Particle Correlations in Heavy IonCollisions
George S.F. Stephans for the PHOBOS collaborationB.Alver , B.B.Back , M.D.Baker , M.Ballintijn , D.S.Barton , S.Basilev , B.D. Bates ,R.Baum , B.Becker , R.R.Betts , A.Białas , A.A.Bickley , R.Bindel , W.Bogucki ,A.Budzanowski , W.Busza , A.Carroll , M.Ceglia , Z.Chai , Y.-H.Chang , A.E.Chen ,V.Chetluru , T.Coghen , C.Conner , W.Czy˙z , B.Dabrowski , M.P.Decowski , M.Despet ,P.Fita , J.Fitch , M.Friedl , K.Gałuszka , R.Ganz , E.Garc´ıa , T.Gburek , N.George ,J.Godlewski , C.Gomes , E.Griesmayer , K.Gulbrandsen , S.Gushue , J.Halik , C.Halliwell ,J.Hamblen , P.Haridas , I.Harnarine , A.S.Harrington , M.Hauer , A.Hayes ,G.A.Heintzelman , C.Henderson , D.J.Hofman , R.S.Hollis , R.Hoły´nski , B.Holzman ,A.Iordanova , E.Johnson , J.L.Kane , J.Katzy , N.Khan , W.Kita , J.Kotuła , H.Kraner ,W.Kucewicz , P.Kulinich , C.M.Kuo , C.Law , J.W.Lee , M.Lemler , W.Li , J.Ligocki ,W.T.Lin , C.Loizides , S.Manly , D.McLeod , J.Michałowski , A.C.Mignerey ,J.M¨ulmenst¨adt , M.Neal , A.Noell , R.Nouicer , A.Olszewski , R.Pak , I.C.Park , M.Patel H.Pernegger , M.Plesko , C.Reed , L.P.Remsberg , M.Reuter , E.Richardson , C.Roland ,G.Roland , L.Rosenberg , D.Ross , J.Ryan , J.Sagerer , A.Sanzgiri , P.Sarin , P.Sawicki ,J.Scaduto , H.Seals , I.Sedykh , J.Shea , J.Sinacore , W.Skulski , C.E.Smith ,M.A.Stankiewicz , S.G.Steadman , P.Steinberg , M.Stodulski , Z.Stopa , A.Straczek ,M.Strek , A.Sukhanov , K.Surowiecka , A.Szostak , J.-L.Tang , R.Teng , M.B.Tonjes ,A.Trzupek , C.Vale , G.J.van Nieuwenhuizen , S.S.Vaurynovich , R.Verdier , G.I.Veres ,B.Wadsworth , P.Walters , E.Wenger , D.Willhelm , F.L.H.Wolfs , B.Wosiek , K.Wo´zniak ,A.H.Wuosmaa , S.Wyngaardt , B.Wysłouch K.Zalewski , J.Zhang , P. ˙Zychowski Argonne National Laboratory, Argonne, IL 60439, USA Brookhaven National Laboratory, Upton, NY 11973, USA Institute of Nuclear Physics, Krak´ow, Poland Jagellonian University, Krak´ow, Poland Massachusetts Institute of Technology, Cambridge, MA 02139, USA National Central University, Chung-Li, Taiwan University of Illinois at Chicago, Chicago, IL 60607, USA University of Maryland, College Park, MD 20742, USA University of Rochester, Rochester, NY 14627, USA
Abstract
Data from the PHOBOS detector have been used to study two-particle correlations over a broadrange of pseudorapidity. A simple cluster model parameterization has been applied to inclusivetwo-particle correlations over a range of centrality for both Cu + Cu and Au + Au collisions at √ s NN =
200 GeV. Analysis of the data for Au + Au has recently been extended to more peripheralcollisions showing that the previously-observed rise in cluster size with decreasing system sizeeventually reaches a maximum value. Model studies have been used to quantify the significante ff ect of limited detector acceptance on the extracted cluster parameters. In the case of Au + Au,correlations between a trigger particle with p T > . a r X i v : . [ nu c l - e x ] F e b arge phase-space coverage of the PHOBOS detector has enabled a quantitative understandingof the so-called ‘ZYAM’ parameter used in the subtraction of the contribution of elliptic flow tothese triggered correlations.Studies of single-particle distributions extracted using data from ultra-relativistic heavy ioncollisions have provided a wealth of information concerning the global properties of these inter-actions. Two-particle correlations can provide more detailed information, in particular probingthe characteristics of the particle production process itself. The PHOBOS detector at the Rela-tivistic Heavy Ion Collider (RHIC) has been used to study correlations in which both particlesin a pair are chosen from the inclusive distribution [1, 2] as well as those in which inclusiveparticles are correlated with a trigger particle selected to have p T > . + Au and Cu + Cu at √ s NN =
200 GeV [2]. The average numberof emitted particles (cluster size, K e ff ) and their spread in pseudorapidity (cluster width, δ ) wereextracted for interactions over a range of centrality. It was found that the cluster sizes are quitelarge and increase with decreasing system size. Comparing results for Au + Au and Cu + Cu, simi-lar cluster sizes are observed for collisions at the same fraction of the total inelastic cross section,as opposed to systems with the same number of participants. The left panel of Fig. 1 shows datafor the cluster sizes versus centrality in Au + Au which have recently been extended to more pe-ripheral collisions. The rise in cluster size is seen to saturate and possibly even begin to decreasein the most peripheral collisions. Continuation of this trend might result in values for the clustersize close to that seen for p + p collisions which is shown by the gray band in the figure. σ / σ e ff ∞ | < η | K PHOBOS Au+Au 200 GeVPHOBOS Au+Au 200 GeV, PRELIMINARYPHOBOS p+p 200GeVAMPT Au+Au 200 GeV
Cluster size |<3) η Measured cluster width (| | < o ve r f u ll acc . η R a t i o | -1 eff ∞ |< η | K -1 eff|<3 η | K ICM K=2.00ICM K=3.00ICM K=4.00ICM K=5.00HIJING AuAuHIJING CuCuAMPT AuAuAMPT CuCuPYTHIA
Figure 1: (color online) Left panel: Extracted cluster sizes, corrected for acceptance e ff ects, for Au + Au collisions at √ s NN =
200 GeV as a function of the fraction of the total inelastic cross section (equal to 1.0 for the most centralcollisions). Error bars include both statistical and systematic e ff ects. The gray band shows the acceptance-correctedcluster size for p + p collisions. The black line is the cluster size predicted by the AMPT model. Right panel: The ratioof the cluster size extracted using only the particles within a limited detector acceptance over the size found using allparticles is plotted for a variety of models as a function of the cluster width within the limited acceptance. Note that heavyion collisions at √ s NN =
200 GeV typically have measured cluster widths of about 0.7 − Model calculations were analyzed to study the e ff ect of limited detector acceptance on theextracted cluster parameters [2]. A range of very di ff erent models was studied, including bothsimple independent cluster production and more complicated dynamical calculations. Specifi-cally, the analysis determined the ratio of the cluster size extracted using a limited set of particlesover the size found using all particles. As shown in the right panel of Fig. 1, this ratio was verysimilar in all of the models when comparing systems with similar cluster width (i.e. the RMSof the separation in pseudorapidity between pairs of particles from a cluster). This result seemsintuitively reasonable since for broader particle emission from a particular cluster, it is more Preprint submitted to Nuclear Physics A October 31, 2018 ikely that one or more of the daughter particles will fall outside the detector acceptance. Whatwas not expected was the relatively large magnitude of the e ff ect even for the PHOBOS detectorwhich has the largest pseudorapidity acceptance at RHIC. In order to extract the correction toapply to experimental data, ratios were determined as a function of the cluster width found usingonly the restricted set of particles. For the typical cluster widths seen in heavy ion collisions at √ s NN =
200 GeV, a detector extending over | η | < K e ff − K e ff is the cluster size. Similar, although smaller, correction factors were found for the cluster width.Data from a detector with a pseudorapidity acceptance smaller than PHOBOS would have aneven more limited sensitivity to the e ff ect of this aspect of particle production.Correlations between a trigger particle with p T > . + Au at √ s NN =
200 GeV over a range of centralities [3]. Aparticularly interesting feature of preliminary triggered correlations data from other experimentswas the so-called ‘ridge’, an enhancement at small relative azimuthal angle which was extendedin relative pseudorapidity compared to the same correlations from p + p interactions [4]. The η∆ -4 -2 0 2 η ∆ d c h d N t r i g N | < 1.0 φ∆ Near-side, |Au+Au 0-30% (PHOBOS)PYTHIA + 0.25 uncertainty vZYAM uncertainty Au + Au (cid:10) 200 GeV η∆ -4 -2 0 2 ) η ∆ a ( Centrality45-50%20-25%0-3%
PHOBOS preliminaryAu + Au 200 GeV
Figure 2: (color online) Left panel: Correlated particle yield for trigger particles with p T > . + Au collisions at √ s NN =
200 GeV as a function of relative pseudorapidity. Error bars are statistical errors andboxes represent the systematic error due to the uncertainty in the elliptic flow subtraction. The gray band shows thesystematic error due to the normalization between background and signal distributions. The dashed line shows thePYTHIA prediction for p + p at √ s =
200 GeV shifted up by a constant o ff set. Right panel: The normalization betweensignal and background distributions used in the elliptic flow subtraction for Au + Au collisions at √ s NN =
200 GeV inthree centrality ranges is plotted as a function of relative pseudorapidity. See text for discussion. unique feature of this analysis using PHOBOS data is the very broad accessible range in relativepseudorapidity between the two particles. Among other results, it was discovered that this ‘ridge’extends to the largest pseudorapidities analyzed. As shown in the left panel of Fig. 2, the dataare consistent with a constant height of the ridge over the entire range. The dashed line in thatpanel shows the PYTHIA prediction for p + p at the same center-of-mass energy shifted up by aconstant value of 0.25 associated particles per unit of relative pseudorapidity.In extracting the triggered correlation functions, it is necessary to subtract the e ff ect of ellipticflow as shown in Eq. 1 where the left side is the correlated particle density. The factor B ( ∆ η )is a normalization based on dN / d η ; s ( ∆ φ, ∆ η ) and b ( ∆ φ, ∆ η ) are the signal (pairs from a singleevent) and background (pairs from mixed events) distributions, respectively, both normalized tothe number of trigger events; and V ( ∆ η ) is a convolution of the elliptic flow magnitude for thetrigger and associated particles (see Ref. [3] for details).1 N trig d N ch ( d ∆ φ )( d ∆ η ) = B ( ∆ η ) · (cid:34) s ( ∆ φ, ∆ η ) b ( ∆ φ, ∆ η ) − a ( ∆ η )[1 + V ( ∆ η ) cos (2 ∆ φ )] (cid:35) . (1)In the absence of e ff ects which distort the relative normalization of the signal and backgrounddistributions, the factor a ( ∆ η ) would not be needed. The right panel of Fig. 2 shows the valueof a as a function of relative pseudorapidity for Au + Au collisions in several ranges of centrality.The data points were found by matching the uncorrected correlation function and the predictedflow signal using a variety of techniques [3], one of which was the so-called ZYAM or zero yieldat minimum [5]. In previous analyses, this adjustment was treated as a somewhat arbitrary value.3owever, the uniquely broad range of the PHOBOS detector allowed a quantitative understand-ing of the origin of this factor. Three features are clear in the right panel of Fig. 2, namely that a is typically very close to unity, that the deviation from one decreases for more central col-lisions, and that the dependence on relative pseudorapidity can be characterized as a Gaussianpeak on top of a constant value. The lines in the figure are the result of a fit to the full set of datapoints (i.e. all centralities and relative pseudorapidities) using a parameterization including bothconstant and Gaussian terms.The component of the a factor which is independent of pseudorapidity is due to a simpletrigger bias; events at the higher end of a centrality bin are more likely to contain the requiredtrigger particle. As a result, the distribution of signal events within a given centrality bin isbiased towards the higher multiplicity end, as compared to the background events. By sim-ple combinatorics, this shift results in an artificial enhancement in the number of pairs at allrelative pseudorapidities. Both the magnitude and centrality dependence of this pseudorapidity-independent component of a can be reproduced quantitatively based on the widths and averageparticle multiplicities of the centrality bins used in this analysis.The Gaussian component is simply a reflection of the cluster-like particle-production pro-cesses discussed above, which impart a relative-pseudorapidity-dependent normalization be-tween the signal and background distributions. Both the Gaussian width and the centrality depen-dence of the Gaussian peak height found in fitting the a values are consistent with those foundin the inclusive two-particle analysis. Note that the definition of the δ parameter in Ref. [2]di ff ers from the width of the Gaussian in ∆ η found when fitting a by a factor of √
2. Com-paring inclusive and triggered correlations, the magnitude of the underlying cluster e ff ect is notnecessarily the same since in one case there is a requirement of a high transverse momentumtrigger particle. This di ff erence was reflected in the fit by a single overall normalization of theGaussian peak height. The centrality dependence of this peak amplitude includes the trivialmultiplicity-dependent dilution of correlated versus uncorrelated pairs. Note that the correlationfunctions used in the cluster analysis di ff er from those used in the triggered correlation study inthat this multiplicity-dependent dilution is explicitly removed in the cluster analysis (see Eq. 1of Ref. [2]). However, there is also the non-trivial centrality dependence of the cluster size itselfas seen in the left panel of Fig. 1 and described in detail in Ref. [2].These expectations for the characteristics of the a factor were not directly included in the fitalthough they did influence the choice of functions. As one example, the Gaussian amplitudeincluded an explicit (1 / multiplicity) dependence. Characteristics of the data, including a varyingcentrality bin width, precluded the use of a simple analytic form, although predictions could beeasily calculated bin by bin. The final results of the fits were compared to the predictions basedon the e ff ects discussed above and found to be in good quantitative agreement. As is clear in theright panel of Fig. 2 and as results from, among other e ff ects, the dramatic impact of detectoracceptance shown in the right panel of Fig. 1, this quantitative description of the various sourcesof o ff set between background and signal distributions in triggered correlations would not havebeen possible without the broad pseudorapidity coverage of the PHOBOS detector.In summary, PHOBOS data have been used to significantly enhance our knowledge of thenature of particle correlations in heavy ion collisions at the top RHIC energy. The data implythat particles are emitted from surprisingly large clusters with a non-trivial centrality dependencewhich has been recently extended towards smaller systems. The significant e ff ect of detectoracceptance, even in a detector as broad as PHOBOS, has been quantified. The ‘ridge’ at smallrelative azimuthal angle in triggered correlations has been found to extend over the full relativepseudorapidity range studied. Finally, the non-trivial normalization required when subtractingthe e ff ect of elliptic flow on two-particle correlations has been understood quantitatively. References [1] B. Alver et al. , Phys. Rev.
C 75 , 054913 (2007).[2] B. Alver et al. , arXiv:0812.1172 (2008).[3] B. Alver et al. , arXiv:0903.2811 (2009).[4] J. Putschke, J. Phys.
G34 , S679 (2007).[5] N. N. Ajitanand et al. , Phys. Rev. C , 011902 (2005)., 011902 (2005).