Integrated Azimuthal Correlations in Nucleus-Nucleus Collisions at CERN SPS
IIntegrated Azimuthal Correlationsin Nucleus–Nucleus Collisions at CERN SPS ∗ Katarzyna Grebieszkow
Faculty of Physics, Warsaw University of Technology,ul. Koszykowa 75, PL - 00-662 Warsaw, Poland andStanis(cid:32)law Mr´owczy´nski
Institute of Physics, Jan Kochanowski University,ul. ´Swi¸etokrzyska 15, PL - 25-406 Kielce, Polandand National Centre for Nuclear Research,ul. Ho˙za 69, PL - 00-681 Warsaw, Poland (Received October 21, 2011)
Azimuthal correlations of particles produced in nucleus-nucleus colli-sions at CERN SPS are discussed. The correlations quantified by the inte-gral measure Φ are shown to be dominated by effects of collective flow.PACS numbers: 25.75.-q, 25.75.Gz
1. Introduction
There are various sources of azimuthal correlations of particles producedin relativistic heavy-ion collisions. One mentions here jets and minijetsresulting from (semi-)hard parton-parton scattering and collective flow dueto the cylindrically asymmetric pressure gradients, see the review articles [1]and [2], respectively. More exotic sources of correlations are also possible.As argued in [3], the plasma instabilities, which occur at an early stage ofcollisions, can generate the azimuthal fluctuations. Except the dynamicallyinteresting mechanisms, there are also rather trivial effects caused by decaysof hadronic resonances or by energy-momentum conservation.Several methods has been developed to study fluctuations on event-by-event basis. In particular, the so-called measure Φ proposed in [4] was used ∗ Presented by St. Mr´owczy´nski at the HIC-for-FAIR Workshop & XXVIII Max-BornSymposium ‘Three Days on Quarkyonic Island’, Wroc(cid:32)law, Poland, May 18-21, 2011. (1) a r X i v : . [ nu c l - t h ] O c t Phi-phi-Wroclaw printed on October 14, 2018 to measure the transverse momentum [5, 6] and electric charge fluctuations[7]. The measure proved to be very sensitive to dynamical correlations andit was suggested to apply it to study azimuthal ones [8]. Such an analysisis underway using experimental data accumulated by the NA49 and NA61Collaborations and some preliminary results are already published [9].The fact that the measure Φ is sensitive to correlations of various originis advantage and disadvantage at the same time. A signal of correlations canbe rather easily observed but it is difficult to disentangle different contribu-tions. For this reason we studied in [10] how various sources of azimuthalcorrelations contribute to the measure Φ. And here we make use of the study[10] to interpret the preliminary experimental results [9]. We show that theobserved integrated correlations are mostly generated by the collective flow.
2. Measure Φ
Let us first introduce the correlation measure Φ. One defines the variable z def = x − x , where x is a single particle’s characteristics such as the parti-cle transverse momentum, electric charge or azimuthal angle. The overlinedenotes averaging over a single particle inclusive distribution. In the subse-quent sections, x will be identified with the particle azimuthal angle φ andthe fluctuation measure will be denoted as Φ φ . The event variable Z , whichis a multiparticle analog of z , is defined as Z def = (cid:80) Ni =1 ( x i − x ), where thesummation runs over particles from a given event. By construction, (cid:104) Z (cid:105) = 0,where (cid:104) ... (cid:105) represents averaging over events (collisions). The measure Φ isfinally defined as Φ def = (cid:115) (cid:104) Z (cid:105)(cid:104) N (cid:105) − (cid:113) z . (1)It is evident that Φ = 0, when no inter-particle correlations are present.The measure also possesses a less trivial property - it is independent of thedistribution of the number of particle sources if the sources are identicaland independent from each other. Thus, the measure Φ is ‘blind’ to theimpact parameter variation as long as the ‘physics’ does not change with thecollision centrality. In particular, Φ is independent of the impact parameterif the nucleus-nucleus collision is a simple superposition of nucleon-nucleoninteractions.
3. Experimental data
As already mentioned, the NA49 Collaboration undertook an effort tostudy Φ φ in nucleus-nucleus collisions at CERN SPS and some preliminaryresults are already published [9]. In Fig. 1 we show Φ φ as a function of the hi-phi-Wroclaw printed on October 14, 2018 φ as a function of the number of wounded nucleons for positively andnegatively charged particles produced in various colliding systems: p+p, C+C,Si+Si and Pb+Pb at 158A GeV. number of wounded nucleons for positively and negatively charged particlesproduced in various colliding systems (p+p, C+C, Si+Si and Pb+Pb) at158 GeV per nucleon which is the top SPS energy. In the case of Pb+Pbcollisions, a whole sample of events was split into six centrality classes. Themeasurement was performed in a rather limited domain of rapidity whichin the laboratory frame is 4 . ≤ y π ≤ .
5. It corresponds to the center-of-mass rapidity interval 1 . ≤ y ∗ π ≤ .
6. To determine particle’s rapidity thepion mass was assigned to all particles. The acceptance window in particle’stransverse momentum was fairly broad (0 . ≤ p T ≤ . /c ) but inazimuthal angle was incomplete, as in the NA49 measurement of transversemomentum fluctuations [5].As seen in Fig. 1, significant positive values of Φ φ are observed with amaximum at (cid:104) N w (cid:105) ≈
50 in Pb+Pb interactions. The correlations are verysmall for both the smallest and highest numbers of wounded nucleons. Onealso observes that Φ φ is higher for negative particles than for positive ones.Fig. 2 shows the energy dependence of Φ φ for the 7.2% most centralPb+Pb interactions. The produced particles were registered in the fixed Phi-phi-Wroclaw printed on October 14, 2018
Fig. 2. Φ φ as a function of the colliding center-of-mass energy of nucleon-nucleonsystem for positively and negatively charged particles produced in most centralPb+Pb collisions. interval of center-of-mass rapidity 1 . ≤ y ∗ π ≤ . φ for positive particlesare consistent with zero but for negative particles Φ φ is positive. No collisionenergy dependence of the correlations is observed.In Figs. 1 and 2 we also show predictions of the UrQMD model [11, 12].Since an orientation of the reaction plane is fixed for all collisions in themodel, it was randomly rotated to compare the model predictions with theexperimental data. As seen in Figs. 1 and 2, the model provides vanishingvalues of Φ φ within the experimental acceptance. Therefore, the mechanismresponsible for the correlation signal is either missing or not strong enoughin the UrQMD model.
4. Interpretation of experimental data
In our study [10] we considered separately the azimuthal correlationscaused by the collective flow, resonance decays, jets and transverse momen- hi-phi-Wroclaw printed on October 14, 2018 φ as a function of the number of wounded nucleons for positively andnegatively charged particles produced in various colliding systems: p+p, C+C,Si+Si and Pb+Pb at 158A GeV. The solid (dashed) line connects three pointswhich represent the collective flow effect for negative (positive) particles. tum conservation. In contrast to all other mechanisms under study, whichgenerate negative values of Φ φ , the collective follow produces positive val-ues. So, it is natural to expect that the correlations caused by the collectiveflow are responsible for the experimental signal seen in Figs. 1 and 2. Thefact that Φ φ almost vanishes for very central Pb+Pb collisions and p+pinteractions suggests the same.The collective flow quantified by the measure Φ φ was studied in [8].When the multiplicity distribution is poissonian, which is true in narrowcentrality classes, the measure was found to beΦ φ = (cid:115) π (cid:104) N (cid:105) S − π √ , (2)where S ≡ (cid:68) ∞ (cid:88) n =1 (cid:16) v n n (cid:17) (cid:69) . (3) Phi-phi-Wroclaw printed on October 14, 2018
Thus, Φ φ is fully determined by the average Fourier harmonics and averageparticle multiplicity.Because of incomplete experimental acceptance in azimuthal angle, weused a simple Monte Carlo model instead of the formula (2) to check whetherthe collective flow is indeed responsible for the correlation signal seen inFig. 1. Particle’s number distribution was poissonian with the average mul-tiplicities of positively and negatively charged particles which were measuredin a given acceptance window together with Φ φ for every centrality. Nega-tively charged particles were all pions but among positively charged particlesthere was a 15% admixture of protons. The estimate was based on predic-tions of the UrQMD model within the NA49 acceptance. The azimuthalangle of each particle was generated from the distribution P ( φ ) ∼ v cos( φ − φ R ) + 2 v cos(2( φ − φ R )) , (4)where 0 ≤ φ ≤ π ; the reaction plane angle φ R of a given event was gen-erated from the flat distribution. The Fourier harmonics v and v in therapidity domain of interest in central, mid-central and peripheral Pb+Pbcollisions at 158A GeV had been measured by the NA49 Collaboration [13].The higher Fourier harmonics v n with n ≥ φ in Fig. 3.As seen, the model fairly well estimates the observed Φ φ for both posi-tively and negatively charged particles. The main contribution to Φ φ comesfrom the directed flow represented by v . The difference of Φ φ for positiveand negative particles occurs because v of protons is significantly smallerthan that of pions [13].
5. Conclusions
The azimuthal correlations in nucleus-nucleus collisions at CERN SPS,which are quantified by the integral measure Φ φ , are strongly dominatedby the directed and elliptic flow generated in the collisions. In the forwardrapidity window under study, the directed flow is more important than theelliptic one. The difference of Φ φ for positive and for negative particles iscaused by a 15% admixture of protons among positive particles. Acknowledgments
Discussions with Wojciech Broniowski are gratefully acknowledged. Thiswork was partially supported by Polish Ministry of Science and Higher Ed-ucation under grants N N202 204638 and 667/N-CERN/2010/0. hi-phi-Wroclaw printed on October 14, 2018 REFERENCES [1] J. Casalderrey-Solana and C. A. Salgado, Acta Phys. Polon. B , 3731 (2007).[2] S. A. Voloshin, A. M. Poskanzer and R. Snellings, in Relativistic Heavy IonPhysics , Landold-B¨ornstein Volume I/23, edited by R. Stock (Springer, Berlin,2010).[3] St. Mr´owczy´nski, J. Phys. Conf. Ser. , 204 (2005).[4] M. Ga´zdzicki and St. Mr´owczy´nski, Z. Phys. C , 127 (1992).[5] T. Anticic et al. [NA49 Collaboration], Phys. Rev. C , 034902 (2004).[6] T. Anticic et al. [NA49 Collaboration], Phys. Rev. C , 044904 (2009).[7] C. Alt et al. [NA49 Collaboration], Phys. Rev. C , 064903 (2004).[8] St. Mr´owczy´nski, Acta Phys. Polon. B , 2065 (2000).[9] T. Cetner and K. Grebieszkow [for the NA49 Collaboration], J. Phys. Conf.Ser. , 012023 (2011).[10] T. Cetner, K. Grebieszkow and St. Mr´owczy´nski, Phys. Rev. C83 , 024905(2011).[11] S. A. Bass et al. , Prog. Part. Nucl. Phys. , 255 (1998).[12] M. Bleicher et al. , J. Phys. G G25 , 1859 (1999).[13] C. Alt et al. [NA49 Collaboration], Phys. Rev.