Rapidity dependence of Bose-Einstein correlations at SPS energies S. Kniege 1, C. Alt1, T. Anticic2, B. Baatar3, D. Barna4, J. Bartke5, L. Betev6, H. Bialkowska7, C. Blume1, B. Boimska7, M. Botje8, J. Bracinik9, R. Bramm1, P. Buncˇic´1,6, V. Cerny9, P. Christakoglou10, 6 0 O. Chvala11, J.G. Cramer12, P. Csató4, P. Dinkelaker 1, V. Eckardt 13, 0 D. Flierl 1, Z. Fodor 4, P. Foka 14, V. Friese 14, J. Gál 4, M. Gaz´dzicki 1,15, 2 V. Genchev16, G. Georgopoulos10, E. Gładysz 5, K. Grebieszkow 17, n a S. Hegyi 4, C. Höhne 18, K. Kadija 2, A. Karev 13, M. Kliemant 1, J V.I. Kolesnikov 3, E. Kornas 5, R. Korus 15, M. Kowalski 5, I. Kraus 14, 8 M. Kreps 9, A. Laszlo 4, M. van Leeuwen 8, P. Lévai 4, L. Litov 19, 1 B. Lungwitz 1, M. Makariev 19, A.I. Malakhov 3, M. Mateev 19, 1 G.L. Melkumov 3, A. Mischke 14, M. Mitrovski 1, J. Molnár 4, v 4 St. Mrówczyn´ski15, V. Nicolic12, G. Pálla 4, A.D. Panagiotou10, 2 D. Panayotov 19, A. Petridis 10, M. Pikna 9, D. Prindle 20, F. Pühlhofer18, 0 1 R. Renfordt 1, C. Roland 21, G. Roland 21, M. Rybczyn´ski15, A. Rybicki 5,6, 0 A. Sandoval 14, N. Schmitz 13, T. Schuster 1, P. Seyboth 13, F. Siklér 4, 6 0 B. Sitar 9, E. Skrzypczak 17, G. Stefanek 15, R. Stock 1, C. Strabel 1, / x H. Ströbele 1, T. Susa 2, I. Szentpétery4, J. Sziklai 4, P. Szymanski 15,15, e V. Trubnikov 15, D. Varga 4, M. Vassiliou 10, G.I. Veres 4,21, - l c G. Vesztergombi 4, D. Vranic´ 14, A. Wetzler 1, Z. Włodarczyk15 and u J. Zimányi 4 n : v i 1FachbereichPhysikderUniversität,Frankfurt,Germany. X 2RudjerBoskovicInstitute,Zagreb,Croatia. r 3JointInstituteforNuclearResearch,Dubna,Russia. a 4KFKIResearchInstituteforParticleandNuclearPhysics,Budapest,Hungary. 5InstituteofNuclearPhysics,Cracow,Poland. 6CERN,Geneva,Switzerland. 7InstituteforNuclearStudies,Warsaw,Poland. 8NIKHEF,Amsterdam,Netherlands. 9ComeniusUniversity,Bratislava,Slovakia. 10DepartmentofPhysics,UniversityofAthens,Athens,Greece. 11InstituteofParticleandNuclearPhysics,CharlesUniversity,Prague,CzechRepublic. 12NuclearPhysicsLaboratory,UniversityofWashington,Seattle,WA,USA. 13Max-Planck-InstitutfürPhysik,Munich,Germany. 14GesellschaftfürSchwerionenforschung(GSI),Darmstadt,Germany. 15InstituteofPhysicsS´wietokrzyskaAcademy,Kielce,Poland. 16InstituteforNuclearResearchandNuclearEnergy,Sofia,Bulgaria. 17InstituteforExperimentalPhysics,UniversityofWarsaw,Warsaw,Poland. 18FachbereichPhysikderUniversität,Marburg,Germany. 19AtomicPhysicsDepartment,SofiaUniversitySt.KlimentOhridski,Sofia,Bulgaria. 20UniversityofHouston,Houston,TX,USA. 21MIT,Cambridge,USA. Abstract. Thisarticleisdevotedtoresultsonp −-p −-Bose-EinsteincorrelationsincentralPb+Pb collisions measured by the NA49 experiment at the CERN SPS. Rapidity as well as transverse momentumdependencesof thecorrelationlengthswillbe shownforcollisionsat 20A,30A,40A, 80A,and158AGeVbeamenergy.OnlyaweakenergydependenceoftheradiiisobservedatSPS energies.Thek-dependenceofthecorrelationlengthsaswellasthesingleparticlem-spectrawill t t becomparedtomodelcalculations.Therapiditydependenceisanalysedinarangeof2.5unitsof rapiditystartingatthecenterofmassrapidityateachbeamenergy.Thecorrelationlengthsmeasured inthelongitudinallycomovingsystemshowonlyaweakdependenceonrapidity. Keywords: Bose-Einsteincorrelations,HBT PACS: 25.75.Gz 1. INTRODUCTION The measurement of correlations of identical bosons in heavy ion collisions provides a unique tool to investigate the space time evolution of the particle emitting source. Bose-Einstein correlations are observed as an enhancement of the yield of pairs of particles with small relative momenta. Measurements of the range and strength of the correlationsinmomentumspaceallowtoderivetheextensionofthesourceincoordinate space. Due to space momentum correlations in expanding sources the correlations do not reflect the whole extensions of the source. In such a scenario, the study of the correlations in different regions of phase space helps to understand the evolution of the source. While the dependence of the correlation lengths on the mean transverse momentum k = 1|~p +~p | of the pairs reflects the transverse expansion dynamics t 2 t,1 t,2 of the source the dependence on the pair rapidityY = 1log E1+E2+pz,1+pz,2 , which is 2 (cid:16)E1+E2−pz,1−pz,2(cid:17) measured in the center of mass system, should shed light on the profile of the source in longitudinaldirection.ThelargeacceptanceoftheNA49experimentallowsustoobtain acomprehensivepictureofthedynamicalevolutionofthesource. The article is organized as follows: A brief survey of the experiment, the construction of the correlation function and the fit method are presented in section 2. In section 3, crucialsystematicuncertaintiesintheanalysisduetodetectoreffectsarediscussed.The resultsonthek -aswellastheY-dependenceofthecorrelationlengthsarepresentedin t section4and compared tomodelcalculations. 2. EXPERIMENTAL SETUP AND ANALYSIS NA49 [1] is a fixed target experiment located at the CERN SPS comprising four large- volumeTimeProjectionChambers(TPC), twoofwhicharelocatedinsidethemagnetic field of two superconducting dipole magnets (Figure 1). The TPCs are read out at 90 (MTPC)and72(VTPC)padrowsresultinginaverygooddeterminationofthemomen- tum of the traversing particles. A zero degree calorimeter at the downstream end of the experimentis used to trigger on the centrality of the collisions.The data presented here correspond to the 7.2% most central events for data samples taken at 20A, 30A, 40A, 13 m TOF-GL MTPC-L VERTEX MAGNETS TOF-TL BEAM VCAL X TARGET VTPC-1 VTPC-2 TOF-TR RCAL COLL MTPC-R TIME PROJECTION CHAMBERS CALORIMETER TOF-GR FIGURE1. NA49detectorsetup. 80A,and158AGeVbeamenergy.Byscalingthemagneticfielditwaspossibletoobtain asimilarcoverageofphasespacerelativetothecenterofmassrapidityforthedifferent beam energies. Measuring the specific energy loss dE/dx ofcharged particles in thegas of the TPCs with a resolution of 3-4% allows particle identification. However, due to ambiguitiesinparticleidentificationbyspecificenergylossmeasurementsincertainre- gions of phase space, negativehadrons rather than identified negativepions are studied inthisanalysis. The correlation function is constructed as the ratio of a distribution of the momentum differenceofpairsfromthesameevent(signal)and amixedeventbackgrounddistribu- tion (background). Following the approach of Pratt and Bertsch [2, 4] the momentum difference is decomposed into a component parallel to the beam axis q and two long components in the transverse plane q and q with q defined parallel, and q out side out side perpendicularto k . Thecorrelationfunctionisparameterised by aGaussianfunction t C (q) =1+l ·exp(−R2 q2 −R2 q2 −R2 q2 −2R2 q q ) (1) 2 BP out out side side long long outlong out long and the parameters R , R , R , R , and l are determined by a fit to the out side long outlong measured correlation function. The Coulomb repulsion of the particles is accounted for by weighting the theoretical Bose-Einstein correlation function C (q) by a fac- 2 BP tor F(q ,<r>) [3] in the fit procedure. The weight is determined by the invariant mo- inv mentum difference q of the pair and the mean pair separation <r> of the particles in inv the source. According to [3] this quantity can be derived from the extracted radii. We therefore determine the source parameters as well as the value of <r> in an iterative fit-procedure. Forfollowingfit functionwasused: C (q) =n{p·(C (q) ·F(q,<r>))+(1−p)}. (2) 2 f 2 BP Thecontaminationofthesamplewithpairsofnon-identicalparticlesandpairs ofpions from long lived resonances or weak decays is accounted for by a purity factor p which is determined by a VENUS/GEANT simulation. The fit parameter n is introduced to account for the different statistics in signal and background distributions. Beside the uncertainties which arise due to the construction of the correlation function and the fit formalism there are further detector related effects which will be discussed in the next section. 3. SYSTEMATIC STUDIES 3.1. Two track resolution The momentum difference of a pair is closely related to the distance of the tracks traversing the detector. Bose-Einstein correlations are restricted to a narrow window in momentum difference, hence it is crucial to understand the two track resolution of the detector. The overlap of charge clusters induced at the pad planes of the TPCs can lead toanassignmentofpointstothewrongtrackorinanextremecasetocompletemerging oftwotracks.Inthiscase,apairwithsmallrelativemomentumwillbelostinthesignal distribution and the observable Bose-Einstein enhancement will be reduced. To study the impact of the limited two track resolution on the extracted radii, the distance of the trackswasmeasuredateachpadrowwherebothtrackslieinthesensitivevolumeofthe TPCs. Starting from the downstream end of the TPCs the distance of closest approach (dca)oftwotracksafteragivennumberofpassedpadrowsn wasdetermined.Pairs rows with a dca smaller than a given cut value dca were rejected both from the signal and cut thebackground distribution.Theimpactofa variationofthetwo parameters dca and cut n on the correlation function is shown in Figure 2. Requiring only small values of rows dca andn ,trackscanapproacheachotherverycloselyoveraconsiderablepartof cut rows thetrack length in theTPCs. In this case, track merging effects can lead to a significant loss of pairs in the signal. This effect is very pronounced at high transverse momenta and shows up in an undershoot of the projection of the correlation function onto q out (Figure 2a). Increasing the cut parameters, the influence of merging effects is reduced, the undershoot of the correlation function vanishes and the extracted radii vary only by lessthan0.2fm(Figure2b).Thiscanserveasanestimateofthesystematicerroronthe radiiduetothespecifictreatmentofthetwotrack inefficiencies inthisanalysis. Furthersystematicerrorsontheradiiariseduetouncertaintiesconcerningthetreatment of the Coulomb interaction (which can significantly influence the parameters R and out l ),themissingparticleidentification,thefinitemomentumresolutionofthedetectorand a) 158 AGeV kt=(0.3-0.4)GeV/c Y = 0.0-0.5 b) Rout dcacut= 1.6 cm dcacut= 2.2 cm 70 5.8 1.3 60 C(q)211..21 nrows= 10 nrows= 70 nrows 4500 55..46outR(fm) 30 1.0 20 5.2 10 0.9 -0.1 0.0 0.1 -0.1 0.0 0.1 1 1.4 1.8 2.2 2.6 3 qout(GeV/c) dcacut(cm) FIGURE2. a)Impactoftwotrackresolutioninefficienciesontheshapeofthecorrelationfunctionand b)fitresultsforR fordifferentcombinationsofthecutparametersdca andn . out cut rows the normalisation of the correlation function. The overall systematic error on the radii is not specified for each k -Y-bin but estimated to be smaller than 1 fm for all extracted t radii. 4. RESULTS 4.1. The k -dependence t Figure 3 presents the k -dependence of the radii at midrapidity.Radius and l param- t eters were obtained from fits of(2) to thecorrelation function in binsofY and k . Since t the influence of the finite momentum resolution was found to be small, no corrections were applied for this effect. The bin width in k was chosen to be 0.1 GeV/c and in- t creased to 0.2 GeV/c for the last bin ((0.4-0.6) GeV/c) to obtain sufficient statistics at all energies. A strong decrease of R with k is observed. R is slightly larger than long t out R for all energies indicating a finite duration of particle emission [4]. Also shown side in this picture is a fit of the k -dependence of the radii according to a blast wave pa- t rameterisation [5] of the source. In this model the source is treated as boost invariant in the longitudinal direction. In the transverse direction a box-shaped density profile and alinearly increasing flow profile is assumed. Space momentumcorrelations induced by flow reduce the measured correlation lengths. This effect is partly compensated in case of a superimposed thermal velocity field. Therefore ambiguities arise in the two model parameters temperature and flow, which can not be resolved by only analysing the k - t dependence of the radii. To resolve these ambiguities the single particle p -spectra of t protons and negativelycharged pions measured by NA49 were fitted to a parameterisa- tion derived from the same model. The lines in Figure 3 correspond to a combined fit to the radii and the particle p -spectra. As expected from the weak energy dependence t oftheradii onlysmallvariationsoftheextracted sourceparameters wereobserved.The extracted parameters were the temperature T, the maximum transverse flow rapidity r , the transverse geometrical radius R, the emission time t and the emission duration D t . The fit results are inserted in Figure 3. The temperature T slightly increases with the beam energy, transverse flow and geometrical radius stay approximately constant over the observed energy range. For the emission time we obtain values of 5.4 to 6.8 fm/c. The fit slightly overpredicts R at high k but still results in a finite emission duration side t of 2.2-3.2 fm/c. The fit might be further constrained by adding more particle spectra or byincludingcontributionsfrom resonancedecays inthemodel. 4.2. Y-dependence The model described in section 4.1 is only applicable in case of a longitudinally boost invariant source. Under such conditions it is expected that the cross term R outlong vanishes [6]. Considering the systematic error of 1 fm this condition is fulfilled to good approximation at midrapidity. In Figure 4 the rapidity dependence of R , R , long side R , and R is shown at k =(0.0-0.1) GeV/c for the different beam energies. In out outlong t [7] the impact of a non-boost invariant expansion on the parameter R is studied. outlong 20A GeV 30A GeV 40A GeV 80A GeV 158A GeV 8.0 T (MeV) : m) 81.1 +/-2.2 91.7 +/-2.8 92.5 +/-2.3 99.9 +/-3.0 112 +/-6 f 6.0 ( g n4.0 o Rl2.0 ρ : 0.86 +/- 0.01 0.85 +/- 0.01 0.86 +/- 0.01 0.83 +/- 0.01 0.89 +/- 0.02 8.0 R (fm): ) 12.6 +/-0.2 12.0 +/-0.1 12.0 +/-0.1 11.7 +/-0.1 11.9 +/-0.1 m 6.0 f ( ut 4.0 o R 2.0 τ (fm/c): 8.0 m) 6.8 +/- 0.3 5.2 +/- 0.6 5.7 +/- 1.0 5.4 +/- 0.6 5.7 +/- 0.5 f 6.0 ( e d4.0 si ∆τ (fm/c): R 2.0 2.2 +/- 0.3 3.0 +/- 0.3 3.0 +/- 0.3 3.1 +/- 0.3 3.3 +/- 0.3 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 kt (GeV/c) FIGURE3. Thek-dependenceofR ,R ,andR atmidrapidity(0.0<Y <0.5)forthedifferent t side out long datasets(dots).Thelinescorrespondtoacombinedfitoftheblastwavemodeltotheradiiandthesingle particle p-spectra. t An increase of R with increasing rapidity is predicted due to the decrease of the outlong inclusive pion yields and is in agreement with the results for all energies. However a change in the longitudinal expansion dynamics which is indicated by the change in R is not reflected in the rapidity dependence of the other observables. R , outlong side which is supposed to determine the geometrical size of the source [8] does not change significantly with rapidity. R is approximately constant over the investigated rapidity out region. Only slight changes in R are observed. These are even less pronounced at long highertransversemomenta. Insummary,adistinctenergydependenceoftheradiiisnotobservedeventhoughthere is a dramatic change in the energy dependence of other hadronic observables like e.g. the kaon to pion ratio [9]. Furthermore the radii do not show a pronounced rapidity dependence, incontrastto theparticleyieldswhichdecrease stronglywithrapidity. ACKNOWLEDGMENTS This work was supported by the US Department of Energy Grant DE-FG03- 97ER41020/A000, the Bundesministerium fur Bildung und Forschung, Germany, the Virtual Institute VI-146 of Helmholtz Gemeinschaft, Germany, the Polish State CommitteeforScientificResearch(1P03B09729,1PO3B12129,2P03B04123),the 20A GeV 30A GeV 40A GeV 80A GeV 158A GeV 8.0 Routlong 6.0 4.0 2.0 8.0 6.0 4.0 Rlong ) m2.0 f ( R8.0 Rout 6.0 4.0 2.0 8.0 Rside 6.0 4.0 2.0 Ymid = 1.9 Ymid = 2.1 Ymid = 2.2 Ymid = 2.6 Ymid = 2.9 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 Y FIGURE4. RapiditydependenceofR ,R ,R ,andR atk=(0.0-0.1)GeV/cforthedifferent side out long outlong t beamenergies.ShownareaswellthemidrapidityvaluesY forthedifferentbeamenergies. mid HungarianScientificResearch Foundation(T032648,T032293,T043514),theHungar- ian National Science Foundation, OTKA, (F034707), the Polish-German Foundation, the Korea Research Foundation Grant (KRF-2003-070-C00015) and the Bulgarian NationalScienceFund (Ph-09/05). REFERENCES 1. S.Afanasievetal.,NIMA430(1999)210-244 2. S.Pratt,Phys.Rev.D33(1986)1314-1327 3. Yu.M.Sinyukovetal.,Phys.Lett.B432(1998)248-257 4. G.F.Bertsch,Nucl.Phys. A498 (1989)173c-180c 5. F.Retriere,M.Lisa,Phys.Rev.C70044907(2004) 6. S.Chapman,P.ScottoundU.Heinz,Phys.Rev.Lett74(1995)4400-4403 7. S.Chapman,P.ScottoundU.Heinz,Nucl.Phys.A590(1995)449c-452c 8. S.Chapman,J.NixandU.Heinz,Phys.Rev.C52(1995)2694-2703 9. M.Gazdzicki,J.Phys.G:Nucl.Part.Phys.30(2004)701-708