Preliminary results on pion-pion Bose-Einstein correlations in central Pb+Pb collisions measured by the NA49 experiment are presented. Rapidity as well as transverse momentum dependence of the HBT-radii are shown for collisions at 20, 30, 40, 80, and 158 AGeV beam energy. Including results from AGS and RHIC experiments only a weak energy dependence of the radii is observed. Based on hydrodynamical models parameters like lifetime and geometrical radius of the source are derived from the dependence of the radii on transverse momentum

Collaboration, NA49

Kniege, Stefan

English

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:nucl-ex/0403034 v1   17 Mar 2004Rapidity and transverse momentum dependence ofπ−π− Bose-Einstein correlations measured at 20, 30,40, 80, and 158 A·GeV beam energyS. Kniege9,∗, C. Alt9, T. Anticic21, B. Baatar8,D. Barna4, J. Bartke6, L. Betev9,10,H. Bia  lkowska19, A. Billmeier9, C. Blume9, B. Boimska19, M. Botje1, J. Bracinik3,R. Bramm9, R. Brun10, P. Bunˇ ci´ c9,10, V. Cerny3, P. Christakoglou2, O. Chvala15,J.G. Cramer17, P. Csat´ o4, N. Darmenov18, A. Dimitrov18, P. Dinkelaker9,V. Eckardt14, G. Farantatos2, P. Filip14, D. Flierl9, Z. Fodor4, P. Foka7,P. Freund14, V. Friese7, J. G´ al4, M. Ga´ zdzicki9,12, G. Georgopoulos2, E. G  ladysz6,K. Grebieszkow20, S. Hegyi4, C. H¨ ohne13, K. Kadija21, A. Karev14, M. Kliemant9,V.I. Kolesnikov8, T. Kollegger9, E. Kornas6, R. Korus12, M. Kowalski6, I. Kraus7,M. Kreps3, M. van Leeuwen1, P. L´ evai4, L. Litov18, B. Lungwitz9, M. Makariev18,A.I. Malakhov8, C. Markert7, M. Mateev18, B.W. Mayes11, G.L. Melkumov8,C. Meurer9, A. Mischke7, M. Mitrovski9, J. Moln´ ar4, St. Mr´ owczy´ nski12, G. P´ alla4,A.D. Panagiotou2, D. Panayotov18, A. Petridis2, M. Pikna3, L. Pinsky11,F. P¨ uhlhofer13, J.G. Reid17, R. Renfordt9, A. Richard9, C. Roland5, G. Roland5, M.Rybczy´ nski12, A. Rybicki6,10, A. Sandoval7, H. Sann7, N. Schmitz14, P. Seyboth14,F. Sikl´ er4, B. Sitar3, E. Skrzypczak20, G. Stefanek12, R. Stock9, H. Str¨ obele9,T. Susa21, I. Szentp´ etery4, J. Sziklai4, T.A. Trainor17, D. Varga4, M. Vassiliou2,G.I. Veres4,5, G. Vesztergombi4, D. Vrani´ c7, A. Wetzler9, Z. W  lodarczyk12 I.K. Yoo16,J. Zaranek9, J. Zim´ anyi4(NA49 Collaboration)1NIKHEF, Amsterdam, Netherlands.2Department of Physics, University of Athens, Athens, Greece.3Comenius University, Bratislava, Slovakia.4KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary.5MIT, Cambridge, USA.6Institute of Nuclear Physics, Cracow, Poland.7Gesellschaft f¨ ur Schwerionenforschung (GSI), Darmstadt, Germany.8Joint Institute for Nuclear Research, Dubna, Russia.9Fachbereich Physik der Universit¨ at, Frankfurt, Germany.10CERN, Geneva, Switzerland.11University of Houston, Houston, TX, USA.12Institute of Physics ´ Swietokrzyska Academy, Kielce, Poland.13Fachbereich Physik der Universit¨ at, Marburg, Germany.14Max Planck Institut f¨ ur Physik, Munich, Germany.15Institute of Particle and Nuclear Physics, Charles University, Prague, Czech Re public.16Department of Physics, Pusan National University, Pusan, Republic of Korea.17Nuclear Physics Laboratory, University of Washington, Seattle, WA, USA.18Atomic Physics Department, Soﬁa University St. Kliment Ohridski, Soﬁa, Bulgaria.19Institute for Nuclear Studies, Warsaw, Poland.20Institute for Experimental Physics, University of Warsaw, Warsaw, Poland.21Rudjer Boskovic Institute, Zagreb, Croatia.* parallel talk presented at Quark Matter 2004Abstract: Preliminary results on π−π− Bose-Einstein correlations in central Pb+Pbcollisions measured by the NA49 experiment are presented. Rapidity as well astransverse momentum dependence of the HBT- radii are shown for collisions at 20,30, 40, 80, and 158 A·GeV beam energy. Including results from AGS and RHICexperiments only a weak energy dependence of the radii is observed. Based onhydrodynamical models parameters like lifetime and geometrical radius of the sourceare derived from the dependence of the radii on transverse momentum.1. IntroductionThe objective of HBT analysis is to obtain information about the spatial and temporalevolution of high energy collisions by means of two particle Bose Einstein correlations.Two particle correlations in general lead to a diﬀerence between the product ofsingle particle distributions P(1)P(2) and the corresponding two particle distributionP(1,2). The symmetrisation of the two particle wave function for bosons results in anenhancement of pairs with small relative momenta of the particles. We construct thecorrelation function C2(q) as the normalised ratio of a distribution of the momentumdiﬀerence of true pairs S(q) and a mixed event background distribution B(q):C2(q) =P(1,2)P(1)P(2)= N ·S(q)B(q). (1)Due to space momentum correlations in an expanding source the measuredcorrelations do not reﬂect the whole extension of the source. This enables us tostudy the space time evolution of the source by analysing the correlation function indiﬀerent bins of mean transvere momentum kt and pair rapidity Y :kt =12|  pt,1 +   pt,2| , Y =12log￿E1 + E2 + pz,1 + pz,2E1 + E2 − pz,1 − pz,2￿. (2)-0.1 0.1 -0.1 0.1 0.11.01.11.20.91.01.11.21.30.9qside qout qlongqside qout qlongq(GeV/c)b)a)C2(q)  20 AGeVC2(q)  30 AGeV￿          0.2 0.3 0.4 0.12468102468100.2 0.3 0.4 0.1kt(GeV/c)R(fm)R(fm)Ycm-bins 0.0 - 0.40.4 - 0.80.8 - 1.21.2 - 1.61.6 - 2.0Rside RoutRlong RoutlongFigure 1 : Projections of the 3-dimensional correlation function and thecorresponding ﬁts of eqn.4 (solid lines)onto the components qside, qout, andqlong for 20 (a) and 30 A·GeV (b) in thekt-bin (0.0-0.1) GeV/c at midrapidity.Projection range : 0.03 GeV/c.Figure 2 : Rapidity and transversemomentum dependence of the HBT-radii Rside, Rout, Rlong and Routlongfor 30 A·GeV beam energy.2. Experiment and AnalysisNA49 [1] is a ﬁxed target experiment located at the CERN SPS which comprisesfour large volume Time Projection Chambers (TPC). A zero degree calorimeter atthe downstream end of the experiment is used to trigger on the centrality of thecollisions. ‘The data presented here correspond to the 7.2% most central events for20, 30, 40, and 80 A·GeV and the 10% most central events for 160 A·GeV. Measuringthe speciﬁc energy loss dE/dx of charged particles in the gas of the TPC’s allowsfor particle identiﬁcation with a resolution of 3 4%. However, due to ambiguities inparticle identiﬁcation by speciﬁc energy loss measurements in certain regions of phasespace negative hadrons rather than identiﬁed negative pions are used for the analysis.The limited two track resolution of the detector is taken into account by rejectingpairs with an average distance of particles less than 2.0 cm in the signal  as well asin the background distribution. Following the approach of Pratt and Bertsch [2] themomentum diﬀerence is decomposed into a component parallel to the beam axis qlongand two components in the transverse plane qout and qside. Where qout is deﬁnedparallel, and qside perpendicular to kt. The correlation function is parametrised by agaussianC2(q)th = 1 + λ · exp(−R2oq2o − R2sq2s − R2l q2l − 2R2olqoql) (3)and the parameters Rout, Rside, Rlong, Routlong, and λ are determined by a ﬁt tothe measured correlation function. The calculations are done in the longitudinal restframe of the pair (LCMS) where the crossterm Rol is supposed to vanish at midrapidity under the assumption of a longitudinally boost invariant expansion [3]. Fora chaotic source the parameter λ is expectd to be unity and C2(q)th should reachthe value 2 for q → 0. However, due to contaminations of the sample with non pionsand pions from long lived resonances or weak decays, the height of the measuredcorrelation function is reduced. To account for this eﬀect we weight C2(q)th by afactor p determined by simulations, which corresponds to the fraction of correlatedpairs in the sample. Another major eﬀect determining the shape of the measuredcorrelation function is the Coulomb interaction of charged particles. It is accountedfor by a factor W(q,rm), so that the ﬁnal ﬁt function is given by:C2(q)f = p · (C2(q)th · W(q,rm)) + (1 − p). (4)The Coulomb weight W(q,rm) depends on the momentum diﬀerence q as well as onthe mean pair separation rm of the particles in the source. It is calculated using amethod derived by Sinyukov et al [4] which also provides a prescription to derivethe value of rm from the extracted source parameters Rout,Rside, and Rlong. Wetherefore determine the source parameters as well as the value of rm in an iterativeﬁt procedure. The sample was divided into 5 bins in kt in the range 0.0 0.5 GeV/c.In longitudinal direction the binsize was chosen to be 0.4 (20, 30, 40 A·GeV) and0.5 (80, 160 A·GeV) units of pair rapidity. An example for the projections of the3 dimensional correlation function and the corresponding ﬁts is given in Figure 1.3. ResultsThe data presented are not corrected for momentum resolution. The systematicerrors of the radii are about 0.5 fm. Since the Radii are measured in the LCMSonly a weak rapidity dependence of Rout, Rside, and Rlong is observed at all energies.However, the ﬁnite extension of the source leads to deviations from the expectedboost invariant expansion which shows up in an increase of the value of Routlong with0.1 0.2   0.3  0.4  0.1 0.2   0.3  0.4  0.1 0.2   0.3  0.4  0.1 0.2   0.3  0.4  0.1 0.2   0.3  0.4 246810246810Rlong (fm)20 AGeV 30 AGeV 80 AGeV 40 AGeV 160 AGeVkt(GeV/c)t = 7.3 fm/c t = 7.6 fm/c t = 7.9 fm/c t = 8.3 fm/c t= 8.1 fm/cRsideRoutRlongRside,out (fm)a)b)Figure 3 : kt-dependence of HBT-radii at midrapidity for central Pb-Pbcollisions at 20 to 160 A·GeV beam energy as measured by NA49. The solidlines correspond to ﬁts of eqns. 5 and 6 to Rlong and Rside, respectively.increasing rapidity as shown in Figure 2 for 30 A·GeV beam energy. Longitudinaland transverse expansion lead to a reduction of the correlation lengths with kt, whichis partly compensated by a superimposed thermal velocity ﬁeld. In case of a Bjorkenscenario the kt dependence of Rlong reﬂects the life time of the source [5]:Rlong = τf(Tf/mt)1/2 , mt = (m2π + k2t)1/2. (5)Under the assumption of a freezeout temperature Tf = 120 MeV a slight increase oflife time with energy is observed (Figure 3.a). Assuming a hydrodynamical modelwith transverse expansion characterized by a linear ﬂow proﬁle with rapidity ηf,the transverse geometrical radius Rgeo of the source can be extracted from the kt dependence of Rside [6]:Rside = Rgeo/(1 + mt · η2f/Tf)1/2. (6)From ﬁts to the data in Figure 3.b we obtain values for the geometrical radius Rgeoof about 7 9 fm, but we do not observe a signiﬁcant energy dependence. Anotherimportant parameter is the emission duration of the source which can be determinedby [7]: τ2 =1β2t(R2out − R2side) , βt ≈ktmt. (7)As seen in the panels of Figure 3.b the diﬀerence between Rout and Rside is positivefor all energies and the emission duration comes out to be about 3 4 fm/c.In summary the NA49 results only show a weak energy dependence of the extractedHBT radii and of the corresponding source parameters at SPS energies. This trendpersists if we include results from AGS and RHIC experiments as shown in Figure 4.We only see a slight rise of Rlong starting at SPS energies indicating an increase of  - p - - p     - -h -  h   p - p     - p - - p   E895  E895  E895  E895  E802  NA49  NA49 CERES NA49 CERES NA49 CERES NA49  STAR PHENIX2 AGeV 4 AGeV 6 AGeV 8 AGeV 11.6 AGeV 20 AGeV 30 AGeV 40 AGeV 160 AGeV 80 AGeV   =130GeVRside (fm)Rout (fm)Rlong (fm)0.2   0.4  0.2   0.4  0.2   0.4  0.2   0.4  0.2   0.4  0.2   0.4  0.2   0.4  0.2   0.4  0.2   0.4  0.2   0.4  0.2   0.4 kt(GeV/c)108642108642108642Figure 4 : Energy- and kt-dependence of the radii Rlong, Rside, and Rout forcentral Pb+Pb(Au+Au) collisions from AGS to RHIC experiments measurednear midrapidity.the life time of the source. Rside and Rout remain approximately constant over thewhole energy range.Acknowledgements: This work was supported by the US Department ofEnergy Grant DE FG03 97ER41020/A000, the Bundesministerium fur Bildung undForschung, Germany, the Polish State Committee for Scientiﬁc Research (2 P03B 13023, SPB/CERN/P 03/Dz 446/2002 2004, 2 P03B 04123), the Hungarian ScientiﬁcResearch Foundation (T032648, T032293, T043514), the Hungarian National ScienceFoundation, OTKA, (F034707), the Polish German Foundation, and the KoreaResearch Foundation Grant (KRF 2003 070 C00015).REFERENCES[1] S. V. Afanasiev et al (NA49 Collaboration), Phys. Rev. C 66 (2002) 054902[2] S. Pratt, Phys. Rev. C 33 (1986) 72[3] U. Heinz and U. Wiedemann, Phys. Rept. 319 (199) 145[4] Y. M. Synukov et al , Phys. Lett. B 432 (1998) 248[5] A. Makhlin and Y. M. Synukov, Z. Phys. C 39 (1988) 69[6] S. Chapman, J. Nix and U. Heinz, Phys. Rev. C 52 (1995) 2694[7] U. Heinz et al , Phys. Lett. B 382 (1996) 181

Rapidity and transverse momentum dependence of pion-pion Bose-Einstein correlations measured at 20, 30, 40, 80, and 158 AGeV beam energy

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