Boissevain, J G

Bøggild, H

Cherney, M

Dodd, J

Esumi, S C

Fabjan, Christian Wolfgang

Fields, D E

Franz, A

Hansen, K H

Holzer, B

Humanic, T J

Jacak, B V

Jayanti, R

Kalechofsky, H

Kobayashi, T

Kvatadze, R A

Lee, Y Y

Leltchouk, M

Lörstad, B

Maeda, N

Medvedev, A

Miake, Y

Miyabayashi, A

Murray, M

Nishimura, S

Noteboom, E

Pandey, S U

Piuz, François

Polychronakos, V

Potekhin, M V

Poulard, G

Sakaguchi, A

Sarabura, M

Shigaki, K

Simon-Gillo, J

Sondheim, W E

Spegel, M

Sugitate, T

Sullivan, J P

Sumi, Y

van Hecke, H

Willis, W J

Wolf, K

Physics Letters B

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN{PPE/94{17721 November 1994Directional dependence of the pion source inhigh-energy heavy-ion collisionsH. Bggild1, J. Boissevain2, M. Cherney3, J. Dodd4, S. Esumi5, C.W. Fabjan6, D. E. Fields2,A. Franz6, K.H. Hansen1, B. Holzer6, T. J. Humanic7, B.V. Jacak2, R. Jayanti7;8,H. Kalechofsky8;a, T. Kobayashi9;b, R. Kvatadze6;c, Y.Y. Lee8;d, M. Leltchouk4, B. Lorstad10,N. Maeda5, A. Medvedev4, Y. Miake11;e, A. Miyabayashi10, M. Murray12, S. Nishimura5,E. Noteboom3, S.U. Pandey7, F. Piuz6, V. Polychronakos11, M. Potekhin4, G. Poulard6,A. Sakaguchi5, M. Sarabura2, M. Spegel6, K. Shigaki9;f, J. Simon-Gillo2, W. Sondheim2,T. Sugitate5, J. P. Sullivan2, Y. Sumi5, H. van Hecke2, W.J. Willis4and K.Wolf12Abstract++and   correlations from 200 GeV per nucleon S + Pb collisions and ++correlations from 450 GeV p + Pb collisions measured by the focusing spectrometerof CERN experiment NA44 are presented. The large data set which emphasizes smallvalues of momentum dierence allows multi-dimensional analysis along with the moretraditional one-dimensional parameterization to characterize the pion emission source.It is found that the three radius parameters are similar and large compared to theprojectile radius. This can be explained by pion scattering in the nal state hadronicsystem.( To Be Submitted to Physics Letters B.)1Niels Bohr Institute, DK-2100 Copenhagen, Denmark.2Los Alamos National Laboratory, Los Alamos, NM 87545, USA.3Creighton University, Omaha, NE 68178, USA.4Columbia University, New York, NY 10027, USA.5Hiroshima University, Higashi-Hiroshima 724, Japan.6CERN, CH-1211 Geneva 23, Switzerland.7Ohio State University, Columbus, OH 43210, USA8University of Pittsburgh, Pittsburgh, PA 15260, USA.9National Laboratory for High Energy Physics, Tsukuba 305, Japan.10University of Lund, S-22362 Lund, Sweden.11Brookhaven National Laboratory, Upton, NY 11973, USA.12Texas A&M University, College Station, TX 77843, USA.aNow at University of Geneva.bNow at Riken Linac Laboratory, Riken, Saitama 351-01, Japan.cVisitor from Tbilisi State University, Tbilisi, Rep. of Georgia.dNow at GSI Laboratory, Darmstadt, Germany.eNow at Tsukuba University, Tsukuba 305, Japan.fUniversity of Tokyo, Tokyo 113, Japan.1 INTRODUCTIONTwo-particle intensity interferometry can provide information on the space{timeextent of the particle-emitting source [1, 2, 3, 4], and shed light on the dynamical evolutionof heavy-ion collisions. In particular, intensity interferometry provides information on thetime span of particle emission, which in the case of a rst order phase transition in a QGPcan be long compared to the equivalent spatial extent of the source [5, 10]. Such studiesrequire good momentum resolution and high statistics, especially at small momentumdierences.NA44 is optimized for the study of identied single- and two-particle distributionsat mid-rapidity. The spectrometer is a focusing spectrometer, a design which optimizesthe acceptance for pairs of particles with small momentum dierence. This allows smallstatistical uncertainties in the two-particle correlation function in the region of the sig-nal from Bose{Einstein correlations. We present the study of three components of themomentum dierence which are sensitive to the space{time character of the collision dy-namics. Results from the one-dimensional analysis are also presented in order to makecomparisons with other experiments and to observe trends in data sets.2 THE EXPERIMENTAL SET-UPThe focusing spectrometer of the NA44 experiment has been described in detailelsewhere [7]. Two dipole magnets and three quadrupoles create a magnied image of thetarget in the spectrometer. Only one charge sign can be detected in the spectrometer at atime. The momentum range selected in this analysis covers a band of  20% around thenominal momentum setting of 4 GeV/c. The beam rate and time-of-ight start signal forthe sulphur beam are determined using a Cherenkov beam counter with time resolutionof approximately 35 ps [8]; for the proton beam a scintillator interaction counter is used.A silicon pad detector is used to measure the charged-particle multiplicity distributionwith 2 azimuthal acceptance in the pseudorapidity range 1:8 <  < 3:3.The spectrometer uses three highly segmented scintillator hodoscopes [9] for trackingand time-of-ight measurements. In this analysis we use the time measured between thelast hodoscope and the start counter for time-of-ight with total resolution  100 ps.Together with the two gas Cherenkov counters this provides good particle identication.3 DATA ANALYSISTwo spectrometer settings are needed to optimize the acceptance and resolution.The `horizontal' spectrometer setting optimizes the acceptance in pxand pzwhile the`vertical' setting optimizes the acceptance in pyand pz, where z is along the incidentbeam. The pair statistics for various data sets are listed in Table 1.Data Horizontal VerticalS + Pb ! +++X 114,000 87,000S + Pb !   +X 60,000 {p + Pb ! +++X 160,000 132,000Table 1: Pair Statistics for various Data sets.The single-particle acceptance curves for both the horizontal and vertical settingsare shown in Figs. 1a and 1b. The rapidity range spanned is 3.2 to 4.2 and the pTrangecovered is from 0.0 to 0:6 GeV/c. For the sulphur beam at 200 GeV per nucleon the lead1target was 2 mm thick while for the proton beam at 450 GeV the target was 10 mm lead.The most central 3% of the events have been selected based on Si counter multiplicityinformation. Particles are identied based on the Cherenkov signal and the mass spectrumconstructed from momentum and time-of-ight. Fig. 1c shows the measured mass-squareddistribution. Contamination of  events by  K and other particles such as electrons,which are rejected by the second Cherenkov counter, is less than 1%.The raw correlation function is determined usingCraw(~k1;~k2) =R(~k1;~k2)B(~k1;~k2); (1)where~kiare the particle momenta. The `real distribution' R(~k1;~k2) is the distribution ofthe relative momentum in an event. The `background distribution' B(~k1;~k2) is generatedas follows: for each event in R(~k1;~k2), ten pairs of events are selected randomly to form thebackground pairs. In these pairs, one particle in each event is selected randomly to create anew `event' for the B(~k1;~k2) distribution. As in the real distribution, events from B(~k1;~k2)are subjected to the same analysis procedures. Distortions of the correlation functiondue to nal state Coulomb interactions [6], residual background corrections [11, 12] andmomentum smearing are treated as in [7].The measured two-particle correlation is related to the true correlation byCcorr(~k1;~k2) = Craw(~k1;~k2)KSPC(~k1;~k2)Kacceptance(~k1;~k2) ; (2)where KSPC(~k1;~k2) corrects for the distortion of the single-particle spectrum due to resid-ual correlations, Kacceptance(~k1;~k2) is the correction for the distortion of the two-particlespectrum by the momentum resolution and the two-particle acceptance of the detectorsand Kcoulcorrects for the nal state Coulomb interactions. All three corrections, KSPC,Kacceptanceand Kcoul, depend on the source size and the tting results, so an iterativeapproach is required [7]. We do not consider screening eects due to particles of oppositecharge in a high-particle-density environment. Such eects are believed to have only asmall inuence on the Coulomb correction [13, 14].We use the following t functions:C(Qinv) = A(1 + e Q2invR2inv); Qinv=qQ2 Q20(3)C(QR=) = A(1 + e Q2R=R2R=); QR==qQ2+Q20(4)andC(Qto; Qts; Ql) = A(1 + e Q2toR2to Q2tsR2ts Q2lR2l) (5)WhereQ = j~p1  ~p2j; Q0= jE1  E2j (6)Fits in one dimension using eitherQinvorQR=inherently assume a spherical source.The interpretation of extracted parameters from the ts to Qinvor QR=are inuencedby Lorentz eects which vary for dierent particle species [15]. Our data permit analysisin three dimensions and enable better interpretation of the extracted parameters. Themomentum dierence of the particle pair is resolved into Qlparallel to the beam and QTperpendicular to the beam direction. QTis further resolved into a component Qtoparallel2to the pair momentum sum and Qtsperpendicular to the transverse pair momentum sum.Being parallel to the velocities of the particles, Qtois sensitive to the lifetime of the source[13]. The data are analyzed in the frame in which the z-component (pz= pz1+ pz2) ofthe pair momentum sum is zero. In this frame the lifetime information is coupled only toQto.The three-dimensional ts require data from both the horizontal and vertical spec-trometer settings. Bin sizes of 10 MeV/c have been used in this analysis. No bins wereexcluded while tting. Systematic errors on the t parameters are estimated by reanalyz-ing the data under two altered conditions. The conditions varied are: (i) rejecting trackswhich hit neighbouring slats on all three hodoscopes and (ii) degrading the momentumresolution by 10% (estimated maximum uncertainty). The estimated systematic errorsthus obtained are approximately equal to the statistical errors. Further details of thesystematic error analysis can be found elsewhere [16].4 Results and DiscussionFits to Qts,Qtoand Qlare performed on the S + Pb and p + Pb data sets; the resultsfor the three-dimensional ts from the horizontal and vertical spectrometer setting aresummarized in Table 2 and shown together with the data in Figure 2. The R parametersincrease from p+Pb collisions to S+Pb collisions and are larger than the correspondingR parameters from the kaon pairs for similar systems [7]. These trends are supportedby source parameters extracted from Qinvand QR=shown in Table 3 and Table 4. Theradius parameters from the R =  t for ++and   are similar, indicating that theCoulomb eects from excess charged particles such as protons are not signicant in S +Pb collisions. This trend is supported by the single-particle spectra of +and  , whichare found to be very similar [17].Our three-dimensional analysis of p+Pb and S+Pb data indicates that within rathersmall errorsRts Rto Rl: (7)These results may be interpreted in the following way: (i) a rst order phase transition,which would lead to Rtosignicantly larger than Rts[5, 10], is not borne out in our results;(ii) the lifetime parameter,  ,which represents the width of freezeout time distribution, isestimated from the static Gaussian model as = 1=qR2to R2ts(8)where  is the average transverse velocity of the particle pair; we nd that this time israther short, i.e. less than a few fermi/c.It is instructive to compare our measured Rtsparameter to the radius of the pro-jectile nucleus. The equivalent Gaussian radius is given by:Rgauss= 1:2A1=3=p5 fm (9)where A is the number of nucleons. The Rgaussfor sulphur and proton are 1.69 fm and0.44 fm respectively, both of which are considerably smaller than the measured Rts. Thisindicates considerable expansion of the source before freezeout.Some light can be shed on the above observations by comparison with the mi-croscopic simulation, RQMD, with which the space-time history of the particles can becalculated. Figure 4 shows comparison of our experimental correlation functions with3RQMD [18, 19, 20] for the S + Pb system. Reasonable agreement is seen with the data.The Rtsand Rtoparameters extracted from RQMD are also seen to be similar.Furthermore, it is possible to relate the space{time history of particles at freeze-out to the R parameters, including eects such as rescattering, resonance decays andacceptance of the experiment. This model can also be used for the physical interpretationof the extracted t parameters which are dierent from the actual radius and lifetimeof the source due to correlations between the particles' momentum and position. Thesecorrelations are induced by the expansion of the source driven by particle rescattering[21].Our RQMD calculations of Rts, which most closely reects the transverse sourcesize, yield 4.7  0.4 fm. This value is consistent with the measured Rts= 4.15  0.27 fm.We can also evaluate the RMS freezeout radius with RQMD by tting a Gaussian directlyto the particle position distribution at freezeout. For the y-pTregion of our measurements,the RQMD calculated RMS freezeout radius is 3.4 fm. This radius is considerably smallerthan the Rts. We can also evaluate with RQMD the lifetime parameter  by tting aGaussian directly to the particle freezeout time distribution. The width of the freezeouttime distribution is calculated to be  5fm/c. The dierences between the HBT extractedparameters, RtSand  from eq. 8, and the actual source parameters, the RMS freeze-out radius and  from RQMD, can be quantitatively understood as a consequence ofmomentum-position correlations [20].Other experimental evidence[22, 16, 23, 24] is also consistent with our interpretationof an expanding system. Data obtained at lower energies at the AGS [15] indicate smallerR parameters. This may reect the smaller number of particles produced at the lowerenergies, resulting in less secondary scattering after creation and consequently less sourceexpansion.5 CONCLUSIONSThe striking predictions of a possible phase transition are not seen in our data. TheRtsand Rtoparameters are similar. The radius parameters extracted for pions is largerthan that of the kaons for similar systems, which could be attributed to resonance decaysand rescattering in the source before freezeout. The radii we measure both for S + Pband p + Pb are larger than the projectile, indicating that there is an expansion of thehadronic nal state, in agreement with the fact that the radius parameters we measureare larger compared to the lower energy data.6 ACKNOWLEDGEMENTSThe NA44 Collaboration wishes to thank the sta of the CERN PS-SPS acceler-ator complex for their excellent work. We thank the technical sta at CERN and thecollaborating institutes for their valuable contribution. We are also grateful for the sup-port given by the W. M. Keck foundation; theOsterreichische Fond zur Forderung derWissenschaftlichen Forschung; the Science Research Council of Denmark; the JapaneseSociety for the Promotion of Science, and the Ministry of Education, Science and Culture,Japan; the Science Research Council of Sweden; the US Department of Energy; and theNational Science Foundation.4References[1] R. Hanbury-Brown and R. Q. Twiss, Nature 178 (1956) p. 1046.[2] G. Goldhaber et al., Phys. Rev. 120 (1960) p. 300.[3] M. Gyulassy and S.K. Kaumann and L.W. Wilson, Phys. Rev. C20 (1979) p. 2267.[4] B. Lorstad, Mod. Phys. A4 (1989) p. 2861.[5] G. Bertsch and G.E. Brown, Phys. Rev. C40 (1989) p. 1830.[6] S. Pratt, Phys. Rev. D33 (1986) p. 1314.[7] H. Becker et al., Phys. Lett. B302 (1993) p. 510.[8] N. Maeda et al., Nucl. Meth. Instr. A346 (1994) p. 132.[9] T. Kobayashi and T. Sugitate, Nucl. Inst. Meth. A287 (1990) p. 389.[10] S. Pratt, Phys. Rev. D33 (1986) p. 72.[11] W.A. Zajc et al., Phys. Rev. C29 (1984) p. 2173.[12] K. Kadija, Phys. Lett. B287 (1992) p. 362.[13] S. Pratt and T. Csorg}o and J. Zimanyi, Phys. Rev. C42 (1990) p. 2646.[14] M.G. Bowler, Z. Phys. C46 (1990) p. 305.[15] Y. Akiba et al., Phys. Rev. Lett. 70 (1993) p. 1057.[16] H. Beker et al., CERN{PPE/94{75 and Z. Phys. (in press) (1994).[17] H. Beker et al., Low pTphenomeanon in pA and AA collisions at mid-rapidity, 1994,to be published.[18] H. Sorge and H. Stocker and W. Greiner, Nucl. Phys. A498 (1989) p. 567.[19] J.P. Sullivan et al., Phys. Rev. Lett. 70 (1993) p. 3000.[20] D.E. Fields et al., 1994, to be published.[21] T.J. Humanic, Phys. Rev. C (in press) C50 (1994).[22] H. Beker et al., CERN{PPE/94{119 and submitted to Phys. Rev. Lett. (1994).[23] T. Alber et al., IKF{HENPG/9{94 (1994).[24] T. Alber et al., submitted to Phys. Rev. Lett. LBL{36062 (1994).5Data  RtsRtoRl2=DOFS + Pb ! +++X 0:56  0:02 4:15  0:27 4:02  0:14 4:73 0:26 1201=1415p + Pb ! +++X 0:41  0:02 2:00  0:25 1:92  0:13 2:34 0:36 1111=1152Table 2: Result of Gaussian parametrizations in Qts, Qtoand QlData  Rinv2=DOFS + Pb ! +++X 0:56  0:03 5:00  0:22 29=25S + Pb !   +X 0:42  0:02 4:00  0:27 19=25p + Pb ! +++X 0:38  0:03 2:89  0:30 16=25Table 3: Result of Gaussian parametrizations in QinvData  Rr=2=DOFS + Pb ! +++X 0:59  0:03 3:90  0:14 24=25S + Pb !   +X 0:62  0:03 3:64  0:18 15=25p + Pb ! +++X 0:41  0:03 2:35  0:23 23=25Table 4: Result of Gaussian parametrizations in QR=-0.100.10.23 3.25 3.5 3.75 4p T(GeV/c)Rapidity4GeV/c(Horizontal)a)-0.100.10.20.30.43 3.25 3.5 3.75 4p T(Gev/c)Rapidity4GeV/c(Vertical)b)01002003004000 0.25 0.5Mass2(GeV2/c4)Countsc)Figure 1: The NA44 acceptance and the measured mass squared as determined from themomentum and time of ight.60.811.21.41.61.80 100 200 300Qinv(MeV/c)C(Qinv)S + Pb → pi+pi+0.811.21.41.61.80 100 200 300Qinv(MeV/c)C(Qinv)S + Pb → pi-pi-0.811.21.41.61.80 100 200 300Qinv(MeV/c)C(Qinv)p + Pb → pi+pi+Figure 2: The Qinvplots from the horizontal setting of S + Pb and p + Pb interactions.00.20.40.60.811.21.41.61.820 50 100 150 200Qts(MeV/c)C20<QL,QTo<20 MeV/cVertical00.20.40.60.811.21.41.61.820 50 100 150 200Qto(MeV/c)C20<QL,QTs<20 MeV/cHorizontal00.20.40.60.811.21.41.61.820 50 100 150 200Ql(Mev/c)C20<QL,QTs<20 MeV/cHorizontalFigure 3: The Qts, Qtoand Qlprojections. The lines represent a Gaussian t to the datapoints. Error bars are statistical only.700.20.40.60.811.21.41.61.820 100 200 300Qinv(MeV/c)RQMDNA4400.20.40.60.811.21.41.61.820 50 100 150 200Qts(MeV/c)RQMDNA4400.20.40.60.811.21.41.61.820 50 100 150 200Qto(MeV/c)RQMDNA4400.20.40.60.811.21.41.61.820 50 100 150 200RQMDNA44Ql (MeV/c)Figure 4: Comparisons of data with RQMD of the correlation function for S + Pb inter-actions.8

Directional dependence of the pion source in high-energy heavy-ion collisions

Directional dependence of the pion source in high-energy heavy-ion collisions

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