New results on interface effects and correlations are reviewed, including
Fermi-Dirac and Bose-Einstein correlations in hadronic Z0 decays at LEP1.Comment: 3 pages, 3 figures, ICHEP conference, Tampere, July 199

Thomson, E. J.

English

arXiv

New results on interface effects and correlations are reviewed, including Fermi-Dirac and Bose-Einstein correlations in hadronic Z0 decays at LEP1.New results on interface effects and correlations are reviewed, including Fermi-Dirac and Bose-Einstein correlations in hadronic Z0 decays at LEP1

Thomson, Evelyn J.

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arXiv:hep-ex/9911014   12 Nov 1999NewresultsoninterferenceeectsandcorrelationsEJThomsonPhysicsDepartment,ImperialCollegeofScience,TechnologyandMedicine,PrinceConsortRoad,LONDONSW72AZ,UKE-mail:evelyn.thomson@cern.chAbstractNewresultsoninterferenceeectsandcorrelationsarereviewed,includingFermi-DiracandBose-EinsteincorrelationsinhadronicZ0decaysatLEP1.1.IntroductionStudiesofBose-Einstein(BE)correlationsofiden-ticalbosonsandofFermi-Dirac(FD)correlationsofidenticalfermionsproducedinhighenergycolli-sionsprovidemeasurementsofthedistributionsofparticlesourcesinspaceandtime.Thesecorre-lationsoriginatefromthesymmetrizationoranti-symmetrizationofthetwo-particlewavefunctionsofidenticalparticlesandleadtoanenhancementorasuppressionofparticlepairsproducedclosetoeachotherinphasespace.Thestrengthoftwo-particleBEorFDcorrelationeectscanbeex-pressedintermsofatwo-particlecorrelationfunc-tionC(p1;p2)denedas:C(p1;p2)=P(p1;p2)=Po(p1;p2)wherep1andp2arethefour-momentaoftheparticles,P(p1;p2)isthemeasureddierentialcross-sectionforthepairsandPo(p1;p2)isthatofareferencesample,whichisfreeofBEorFDcorrelationsbutotherwiseidenticalinallaspectstothedatasample.ThemainexperimentaldicultyistodeneanappropriatereferencesamplePo(p1;p2)inordertodeterminethatpartofP(p1;p2)whichcanbeattributedtotheBEorFDcorrelations.ThecorrelationfunctionCisusuallymeasuredasafunctionoftheLorentzinvariantQ,withQ2= (p1 p2)2.ForQ2=0,theeectsofBEorFDcorrelationsreachtheirextremevalues.Section2describesanewresultonFDcorrelationsinandpairs.Section3discussesnewresultsonmulti-dimensionalBEcorrelationsin++and  pairs.Section4summarisesothernewresultsandsection5presentsconclusions.2.FDcorrelationsinandpairsALEPHhavemeasuredthetwo-particlecorrelationfunctionof(,)pairs[1],usingthreedierentreferencesasshowningure1.AllthreereferencesrelytosomeextentonaproperdescriptionofthehadronizationprocessbyMonteCarlo.ReferenceAassumesthedierentialcross-sectionofsimulated(,)intheJETSETMonteCarlo.ReferencesBandCareobtainedbythetechniqueofeventmixing,wherepairsof'sor'sareconstructedbypairingeachorwiththe'sor'sofallotherevents.However,thismethodremovesnotonlypossibleFDorBEcorrelations,butitalsoaectsallothercorrelationsascanbeseenfromgure2,wherethecosineoftheangle1;2betweentheormomentaintheZ0restframeisplotted.In00.5 1ALEPHA)C(Q)00.5 1B)00.5 1012345678910Q [GeV]C)Figure1.CorrelationfunctionC(Q)forthe(,)pairsusingdierentreferencesamples:A)MonteCarlo,B)mixedeventdoubleratioandC)mixedeventswithreweightedcos1;2distribution.ThecurvesrepresenttheresultsoftsusingtheGoldhaberparameterisation[1].2the unmixed events most pairs are produced back toback, whereas the distribution for the mixed sampleis completely symmetric. This leads to a shift in theQ distribution for the mixed pairs towards lowervalues of Q. To overcome this problem, the doubleratio of the cross sections is commonly used and thisgives reference B:C(Q) =P (Q)dataP (Q)data;mixP (Q)MCP (Q)MC;mixSince the symmetrization of the cos 1;2distributionis the main reason for the dierence in the Qdistributions of the mixed and original pairs,reference C is constructed from the mixed datasample, which is reweighted to reproduce thecos 1;2distribution from the original pairs obtainedfrom Monte Carlo.Independent of the reference sample used,C(Q) shows a decrease for Q < 2 GeV. If thisis interpreted as a FD eect, the size of thesource R estimated from C(Q) with a Goldhaberparameterisation is:R(;) = 0:11 0:02stat 0:01systfmThis is consistent with the result of the lessprecise but less model dependent measurement ofthe spin composition [2] of the (,) system,which can have a total spin of 0 or 1. Thespin 1 fraction, (Q), is expected to be 0.75 forALEPH(a)(b)0100200300400500Entries / 0.0501234-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Arbitrary unitscos Θ 1,2Figure 2. The histogram shows the cos 1;2distribution for a) the original (,) pairs from theMonte Carlo and b) for the mixed pairs of the samesample. Points in a) show the cos 1;2distribution ofthe data. The deviation of the Monte Carlo from dataat large cos 1;2is due to the FD eect.a statistical spin mixture ensemble. Since thetotal wave function for the fermion pair must beantisymmetric, the symmetric spin 1 wave functionmust be paired with the antisymmetric space wavefunction, and thus (Q) is expected to decrease to0 as Q goes to 0 due to FD statistics. ALEPHnds that  < 0:75 for Q < 2 GeV and  ' 0:75for Q > 2 GeV, as shown in Table 1. The size ofthe source R estimated from (Q) is R = 0:14 0:09stat 0:03systfm. For the  system, whichis free of FD correlations, the spin compositionmeasurements are consistent with  = 0.75 in theentire Q range studied. ALEPH also proves thatthis spin composition technique, previously shownto hold approximately for low values of Q, is infact valid for any value of Q. The results for (Q)are in agreement with previous measurements fromOPAL [3] and DELPHI [4].A comparison of this result with the measuredradii for identical charged pions [5] and kaons [6]:R(; ) = 0:65 0:04stat 0:16systfmR(K;K) = 0:48 0:04stat 0:07systfmindicates that the dimension of the source decreaseswith the increasing mass of the emitted particles.3. Multi-dimensional BE correlationsA recent model of BE correlations predicts thatthe longitudinal correlation length is dierent fromthe transverse one since momentum componentslongitudinal and transverse with respect tothe string direction are generated by dierentmechanisms [7]. To verify this prediction, OPAL [8],DELPHI [9] and L3 [10] have all investigated multi-dimensional BE correlations in hadronic Z0decaysin the so-called Longitudinally CoMoving System,which represents the local rest frame of the string.OPAL use a sample of opposite sign particlepairs to dene the reference for correlation functionC(Q) shown in gure 3(a). However, this referenceTable 1. The values of  for the (,) and samples.Q Range [GeV] (,) ()0.0 - 1.5 0:36 0:30 0:08 0:61 0:13 0:071.5 - 2.0 0:52 0:31 0:10 0:77 0:07 0:032.0 - 4.0 0:78 0:16 0:09 0:51 0:11 0:123also contains pairs coming from resonance decaysand from weakly decaying particles. In addition,the correlation function has to be normalisedand suers, at large four-momentum dierences,from long-range correlations due to energy andmomentum conservation. Therefore OPAL use alarge sample of Monte Carlo to dene a secondcorrelation function C0(Q) = Cdata=CMC, shown ingure 3(b). This correlation function is more relianton the Monte Carlo but is almost normalised witha reduced contamination from correlated unlikecharge pairs. DELPHI and L3 both use eventmixing techniques to dene their references.OPAL and DELPHI parameterise the two-pioncorrelation function in two dimensions, while L3use three dimensions. OPAL also study a one-dimensional correlation function as a function of theangle between the two-pion momentum dierence,in the rest frame of the  system, and the thrustdirection. OPAL also check for any dependence onthe two-jet nature of the events.In all cases, a signicant dierence betweenthe transverse, rt, and longitudinal, rl, dimensionsis observed, indicating that the emitting sourceof pions has an elongated shape, with thelongitudinal dimension about 1.3 times larger thanthe transverse dimension. For instance, theparameter values obtained by tting an extendedGoldhaber parameterisation to the correlationfunction C0(Q) of OPAL are:rl= 0:935 0:013stat 0:026systfmrt= 0:720 0:009stat 0:044systfmrl=rt= 1:30 0:03stat 0:12syst0.2 0.40.6 0.81 1.21.4 1.61.8 20.20.40.60.811.21.41.61.82(a) (b)0.750.80.850.90.9511.051.10.2 0.40.6 0.81 1.21.4 1.61.8 20.20.40.60.811.21.41.61.820.911.11.21.31.4Figure 3. Two-dimensional BE correlation functionsplotted versus the two components of the momentumdierence, along the thrust axis, Ql, and transverse tothe same axis, Qt.4. Other resultsOPAL measure BE correlations in KKpairs [11], which conrms an earlier DELPHIresult [12], and implies that there must also besuch correlations in K0sK0spairs, making it unlikelythat previously observed threshold enhancementscan be attributed entirely to f0(980) production.SLD study correlations in rapidity between iden-tied charged hadrons and use the SLC electronbeam polarisation to tag the quark hemisphere ineach event, allowing the rst study of rapiditiessigned such that the positive rapidity is along thequark direction, which provides new insights intothe fragmentation process [13]. OPAL performa multidimensional study of local multiplicityuctuations and genuine multi-particle correlationsin terms of factorial moments and, for the rst timein e+e annihilation, factorial cumulants, up tofth order [14]. The Monte Carlo models JETSET7.4 and HERWIG 5.9 are found to reproduce thetrends but underestimate the magnitudes.5. Summary and conclusionsFD correlations have been clearly observed in(,) pairs by ALEPH using two dierenttechniques. A comparison of the source sizemeasured in systems of identical pions, kaonsand 's indicates that the source size decreasesas the mass of the emitted particles increases.Several studies of multidimensional BE correlationsby OPAL, DELPHI and L3 conrm a theoreticalprediction that the emitting source of pions hasan elongated shape, with a longitudinal dimensionabout 1.3 times larger than the transversedimension. This indicates that models based on theassumption of a spherical source are too simple.References[1] ALEPH Coll. Contribution 1 389[2] Alexander G and Lipkin H 1995 Phys. Lett. B352 162[3] OPAL Coll. 1996 Phys. Lett. B 384 377[4] DELPHI Coll. 1998 ICHEP98 proceedings[5] ALEPH Coll. 1992 Z. Phys. C 54 75[6] DELPHI Coll. 1996 Phys. Lett. B 379 330[7] Andersson B and Ringner M 1998 Nucl. Phys.B 513 627; Andersson B and Ringner M 1998Phys. Lett. B 421 283[8] OPAL Coll. Contribution 3 64[9] DELPHI Coll. Contribution 1 221[10] L3 Coll. Contribution 3 280[11] OPAL Coll. Contribution 3 65[12] DELPHI Coll. 1996 Phys. Lett. B 379 330[13] SLD Coll. Contribution 1 187[14] OPAL Coll. Contribution 3 64

New results on interference effects and correlations

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