The recent results on hadron multiplicities in heavy and light quark
fragmentation, multiplicity local fluctuations and multiparticle correlations
submitted to the Conference are reviewed.Comment: 5 pages, 4 eps figs. Talk given at the 31st International Conference
  on High Energy Physics (ICHEP02), Amsterdam, The Netherlands, 24-31 July
  2002. To appear in the Proceeding

Abbiendi

Abreu

De Wolf

Dremin

Edward K.G. Sarkisyan

Feng

Khoze

English

arXiv

The recent results on hadron multiplicities in heavy and light quark fragmentation, multiplicity local fluctuations and multiparticle correlations submitted to the Conference are reviewed

Sarkisyan-Grinbaum, E

CERN Document Server

1Multiplicities, fluctuations and correlationsEdward K.G. SarkisyanabyaEP Division, CERN, CH-1211 Geneva 23, SwitzerlandbPhysics Department, University of Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, BelgiumThe recent results on hadron multiplicities in heavy and light quark fragmentation, multiplicity local fluctuationsand multiparticle correlations submitted to the Conference are reviewed.1. IntroductionOne of the most important observables in par-ticle production processes is multiplicity, i.e. thenumber of particles (mostly, hadrons) producedin the collision [1]. The multiplicity dependenceon the energy scale, species of particles, eventflavour content are among the main predictions ofthe theory of strong interactions, quantum chro-modynamics (QCD) [1,2]. On the other hand,the multiplicity is used to select or to describeevents, e.g. as a trigger for specic processes, asan input for kinematic variables’ spectra. Thedistribution of multiplicity, its mean value andmultiplicity fluctuations are the essential charac-teristics of the collision dynamics. However, themultiplicity distribution tells us just about theaveraged, integrated numbers, while deeper in-formation comes from the moments of the distri-bution, which measure particle correlations, i.e.probe the interaction dynamics [3].Here, I report on the multiplicity flavourdependence3, on the analyses of local multiplic-ity fluctuations and multiparticle correlations4.These studies provide us with details of stronginteractions and allow us to estimate the level of∗Talk given at the 31st International Conference on HighEnergy Physics (ICHEP 2002), Amsterdam, The Nether-lands, 24 – 31 July 2002†Electronic address: sedward@mail.cern.ch3Other aspects of multiplicity studies such as multiplic-ity energy dependence, 3-jet multiplicity, multiplicities ofquark and gluon jets etc. are reviewed by M. Siebel [4].4Bose-Einstein correlation studies are reviewed by Sˇ.Todorova-Nova´ [5].the applicability of QCD, based on the partonicpicture, to the production of hadrons which arethe experimentally observed objects.2. Denitions and notations [1,3]The multiplicity distribution, or the densityn, of multiplicity n of particles with kinematicvariables p1; p2; : : : ; pn is dened by the inclusiveprobability spectrum,n(p1; p2; : : : ; pn) =1Nevdn(p1; p2; : : : ; pn)dp1dp2    dpn ;where Nev is the number of events.As it follows from this formula, the single parti-cle distribution 1(p1) gives an average multiplic-ity, hni = ∫ 1(p1)dp1, while integration of theq-particle densities leads to the unnormalised qthorder factorial moments,fq =∫1(p1; p2 : : : pn)dp1dp2   dpn(1)= hn(n− 1)    (n− q + 1)i  hn[q]i :The normalised factorial moments are then de-ned as Fq = fq=hniq.The q-particle densities give us a way tostudy particle correlations described by the q-particle correlation functions, (factorial) cumu-lants, Cq(p1; : : : ; pq). The cumulants vanishwhenever one of their arguments is statisticallyindependent, i.e. these functions measure gen-uine q-particle correlations.The cumulants are constructed from the mul-tiplicity densities, e.g.C1(p1) = 1(p1);2C2(p1; p2) = 2(p1; p2)− 1(p1)1(p2);C3(p1; p2; p3) = 3(p1; p2; p3)−∑(3)1(p1)2(p2; p3) + 21(p1)1(p2)1(p3) : (2)These functions, being properly normalised, areused to study multiparticle correlations in dier-ent kinematic variables.In studies of local fluctuations and correlations,i.e those in phase-space bins, one uses the bin-averaged factorial moments and cumulants. Thephase space is divided into M bins of equal size,so that hnmi is the number of particles in the mthbin. Then, the normalised bin-averaged factorialmoment is dened via Eq. (1) averaged over bins,Fq(M) =1MM∑m=1fq(m)hnmiq 1MM∑m=1hn[q]m ihnmiq : (3)These factorial moments have been exten-sively used to extract the non-statistical (non-Poissonian) fluctuations in many types of colli-sions [3]. Such fluctuations lead to the power-lawscaling of factorial moments as a function of Mcalled the intermittency phenomenon.In analogy with Eq. (3), Eqs. (2) are averagedto the bin-averaged normalised cumulants,Kq(M) =1MM∑m=1hk(m)q ihnmiq ; (4)where k(m)q are the Mueller moments, the func-tions of unnormalised moments fq(m), Eq. (1),k1 = hnmi; k(m)2 = hn[2]m i − hnmi2;k(m)3 = hn[3]m i − 3 hn[2]m ihnmi + 2 hnmi3: (5)3. Hadronisation of heavy and light quarksIn this Section, I consider the recent results onhadron multiplicities from fragmentation of heavyand light quarks [6{8]. The study of the quarkcontent in multiparticle production provides oneof the basic tests of QCD. The results from LEPare of a special interest since they cover a widecentre-of-mass energy region and can be directlycompared with QCD which is mostly predictableat the asymptotic energies [2].-50510152020 40 60 80 100 120 140 160 180 200 220OPAL Preliminary√s (GeV)δ blDELCO/Mark II/TPCTASSOTOPAZOPALMark IISLDDELPHIQCD MLLAQCD upper limitNaïve ModelAverage measurementFigure 1. The dierence in the mean chargedmultiplicities, bl, between heavy and light quarkpairs as a function of centre-of-mass energy. Thedashed-dotted line is the combined result from allmeasurements, see Ref. [8] for more details.In Refs. [6] and [8], a study of the fragmen-tation of heavy b-quark and light quarks (l =u, d, s) is performed. The measurements of thedierence in charge particle multiplicities, bl =hnbb¯i − hnl¯li, for bb and ll events in e+e− anni-hilation at the centre-of-mass energies above theZ0 peak are carried out. The ndings are com-pared to the theoretical predictions of QCD andto a more phenomenological (the so-called na¨ve)model (for review, see Ref. [2]). The QCD calcu-lations predict energy-independent behaviour ofthe multiplicity dierence bl, while in the na¨vemodel one expects the decrease with increasingenergy. The latter is connected with the assump-tion that the hadron multiplicity accompanyingthe heavy hadrons in bb events is the same as themultiplicity in ll events at the energy left to thesystem once the heavy quarks have fragmented.The dierence between the heavy and lightmean quark-pair multiplicities obtained by DEL-PHI at 206 GeV is bl = 4:50  1:05(stat) 0:52(syst) [8], while OPAL nds bl = 3:44 0:40(stat) 0:79(syst) in the energy range of 130{ 206 GeV [8]. The dierence in the values isconnected with some dierences in the data pro-cessing procedure. In the meantime, the results ofthe energy-dependence is found to be the same for3the both studies: the mean multiplicity dierenceis energy-independent and favours the QCD pre-dictions while it is inconsistent with the flavour-independent na¨ve model (Fig. 1). Also in agree-ment with QCD is the ratio between light quarkmultiplicities, hnii : hnji  1, where i,j =fu,d,sg,as obtained by OPAL at the Z0 peak energy [7].To note is that the hnui and hndi are highly sta-tistically anti-correlated (−90%) which is due totheir fractions in K-mesons.4. Scaling of local fluctuations in hadronicZ0 decaysDuring the last decades, the phase-space lo-cal multiplicity fluctuations are actively studiedin many reactions, from leptonic to nuclear colli-sions, and the intermittency scaling of the fluctu-ations has been established [3].All the studies show that the intermittency ismore pronounced in high dimensions, while in onedimension (e.g., in rapidity) the eect is dilutedby projection onto one dimension. This leads toflattenning of the factorial moments. Such a be-haviour is well understood from a QCD partonshower which is a three-dimensional branchingand naturally leads to the fractality. The bestarea to study the eect and its connection withQCD is given by e+e− annihilation, where suchinvestigations has been performed earlier [3,9,10]and new analysis is carried out by L3 [11].The L3 analysis gives us further hints about theintermittency origin, which is currently far fromunderstanding. The new study employs the factthat so far the fluctuations in many dimensionswere studied with the same number M of binsin each dimension/direction. This leads to self-similar fractals, i.e. the fluctuations in any direc-tion are assumed to be the same, or isotropic.In case when the dynamics in dierent direc-tions are not equivalent, the fluctuations becomeanisotropic and this tells us about the self-affinity[12]. A self-ane behaviour has been observedin hadronic interactions [12], while a self-similarscaling has been qualitatively conrmed in e+e−annihilation [10]. In terms of factorial moments,Eq.(3), the 3-dimensional moments are expectedto exhibit the intermittency property in e+e− col-1.101.201.301.401.50JETSET_BERandomized frameThrust frame F 2(y)JETSET_noBEL3 data (Preliminary)FitHERWIGMC1.051.101.15F 2(p t)1.051.101.151.201 10 40MF 2(φ)1 10 40M1 10 40MFigure 2. The 1-dimensional 2nd-order factorialmoments, Eq. (3), as a function of the number Mof bins in the randomised and the thrust framescompared to the Monte Carlo predictions withand without Bose-Einstein correlations. The tis given by the rst f-la of Eqs. (7). The be-haviour in the qq frame is similar to that in therandomised frame. See text and [11] for details.lisions when phase-space is partitioned isotropi-cally, while this scaling in hadronic interactionsonly occurs for anisotropic partitioning.In order to quantitatively study the observedisotropic fluctuations, the method of the Hurstexponent is used [12]. The Hurst exponent,Hab = ln Ma= lnMb; (6)is obtained from the t of the one-dimensionalsecond-order factorial moments,F2(Ma) = Aa + Ba M−γaa ) Hab =1 + γb1 + γa: (7)Here a, b are the directions of the (a; b) plane. Forthe isotropic dynamical fluctuations, Hab = 1,while Hab 6= 1 if the fluctuations are anisotropic.L3 uses rapidity y, azimuthal angle ’ andtransverse momentum pt { the variables oftenused in multiparticle studies { in the analysis.The variables are dened with respect to the410-1all chargeslike signsDATAPYTHIA+BE32PYTHIA no BEK 2 yOPAL10-11y×Φ×ln pT10-11K 310-111010-210-111 10 10 2K 410-210-111010 21 10MFigure 3. The all-charge and like-sign cumulants,Eq. (4), as a function of the number M of binsin rapidity and in three dimensions. The like-sign cumulants are compared to the Monte Carlopredictions with and without Bose-Einstein cor-relations. See text and Ref. [13] for more details.thrust axis, as well as the other two frames areconsidered: the randomised and the qq frames. Inthe former one, the ’-angles are randomly cho-sen being uniformly distributed in [0; 2], whilein the latter case one uses Monte Carlo to correctthe original thrust axis to the qq axis.The 3-dimensional factorial moments are foundto exhibit the intermittency scaling when phase-space is isotropically partitioned. This conrmsearlier indications for isotropic fluctuations ine+e− annihilations [9,10]. No sensitive dierencesin the dierent frames as well as no disagreementsbetween the data and Monte Carlos are observed.Fig. 2 shows the 2nd-order factorial momentsin one dimension, from which the quantitativetest of the isotropy of the fluctuations is madeusing Eqs. (7). The calculations of the Hurst ex-ponent give: Hab  1, a; b = fy; ’; ptg, i.e. dueto the denition of Eq. (6) one concludes aboutthe equivalence of the directions and about theisotropy of the fluctuations. The fluctuations in’ are nearly absent in the thrust frame. In allframes the data are well described by Jetset, whilesomewhat less well by Herwig. No sensitivity toBose-Einstein correlations is seen. From its study,L3 also concludes that there is the dependence onthe QCD dynamics which serves to decrease thefluctuations in the thrust frame.The 2-jet sub-samples are also analysed usingthe Durham jet algorithm. The fluctuations inthe 2-jet events show the self-ane (anisotropic)fluctuations. This looks like the hard gluon emis-sion leads to the isotropy.5. Multiparticle correlationsThe multiparticle correlation studies are per-formed for e+e− annihilations at the Z0 energy[13] and for pp annihilation at the incident mo-mentum of 22.4 GeV/c [14].Genuine multiparticle correlations in e+e− an-nihilations are studied by OPAL [13]. To extractthe correlations, the method of the bin-averagednormalised cumulants is used, see Eqs. (4){(5).In addition to the earlier analysis [10] of the cu-mulants of all charged particles (\all-charge cu-mulants"), OPAL studies the cumulants of same-charge particles (\like-sign cumulants"). The in-vestigation is performed in rapidity y, azimuthalangle ’ and transverse momentum pt, the samevariables as in the above described L3 analysis,but the sphericity axis is used as a reference axis.Fig. 3 shows the all-charge and like-sign cumu-lants calculated in one (rapidity) and three di-mensions. Even in one dimension, positive gen-uine correlations of groups of two, three, four par-ticles are present. The cumulants exhibit a scal-ing behaviour, although in rapidity the saturationalready appears at the moderate bin sizes. Thelike-sign cumulants increase faster and drive theall-charge ones at small bins while the unlike-signcumulants are almost constant. This points tothe likely influence of Bose-Einstein correlations.The comparison between the data and MonteCarlo like-sign cumulants shows that the modeldescribes well the data when Bose-Einstein cor-relations are implemented. The same is true forthe all-charge cumulants (not shown here). This510-11102D     all charges     like signs3.2•K2   2.32•K22  (NB)K 33DOPAL(a)10-210-111010 210 -1 1K 4(b)13.7•K2   3.86•K23  (NB)K2Figure 4. The Ochs-Wosiek plot in two andthree dimensions for all-charge and like-sign cu-mulants. The dashed line shows the Negative Bi-nomial prediction. The solid line is a t, lnKq =aq + rq ln K2. See text and [13] for more details.is not the case of the L3 results where no dier-ence is found for the models with and withoutBose-Einstein correlations, see Fig. 2. To noteis that the OPAL data is described well in onedimension as well as in three dimensions.From Fig. 3, one can see that Bose-Einsteincorrelations which are implemented in the modelas the correlations of two identical particles andare pair-wise adjusted, well also describe the cu-mulants of q > 2. This suggests to consider theinterdependence of the 2nd- and higher-order cu-mulants, Fig. 4. The t akin to the Ochs-Wosiekone [3] gives the same parameter values for the all-charge and like-sign cumulants, while disagreeswith the Negative Binomial predictions.The multiparticle fluctuations are also studiedin [14] using the Serpukhov xed target pp an-nihilation data at 22.4 GeV/c. The dierentialspectra of k particles in pseudorapidity bins areanalysed relative to the similar background spec-tra. The dips in the distributions of such ratiosare found to be independent on the number k ofparticles,  1:8. The number of clusters is es-timated to be about 2-3 with two particles percluster in average. It is found that the data in thenon-annihilation channel is similar to that fromthe inelastic pp collisions at 69 GeV/c from thesame accelerator. These observations are treatedin frames of dierent mechanisms, e.g. a modelwith mesons emitted from intermediate nucleonisobars is suggested.I am thankful to the ICHEP02 Organising Com-mittee, to convenors of the QCD Session, and tomy colleagues at CERN and particularly in OPALfor giving me the opportunity to make this pre-sentation and for their kind help and support.REFERENCES1. I.M. Dremin, J.W. Gary, Phys. Rep. 349(2001) 301.2. V.A. Khoze, W. Ochs, Int. J. Mod. Phys. A12(1997) 2949.3. E.A. De Wolf, I.M. Dremin, W. Kittel, Phys.Rep. 270 (1996) 1.4. M. Siebel, Fragmentation of quarks and glu-ons, these Proceedings.5. S. Todorova-Nova, Bose-Einstein correlationsat LEP and HERA, these Proceedings.6. P. Abreu, A. De Angelis, DELPHI 2002-052CONF 586 (2002), ICHEP02 abs. 232;DELPHI Collaboration, P. Abreu et al., Phys.Lett. B479 (2000) 118.7. OPAL Collaboration, G. Abbiendi et al., Eur.Phys. J. C19 (2001) 257.8. OPAL Collaboration, Physics Note PN511(2002), ICHEP02 abs. 373.9. DELPHI Collaboration, P. Abreu et al., Nucl.Phys. B386 (1992) 471.10. OPAL Collaboration, G. Abbiendi et al., Eur.Phys. J. C11 (1999) 239.11. L3 Collaboration, L3 Note 2758 (2002),ICHEP02 abs. 494.12. Liu Feng, Liu Fuming, Liu Lianshou, Phys.Rev. D59 (1999) 114020 and refs. therein.13. OPAL Collaboration, G. Abbiendi et al.,Phys. Lett. B523 (2001)35, ICHEP02 abs.319.14. E.G. Boos et al., ICHEP02 abs. 37.

Multiplicities, fluctuations and correlations

Crossref

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.5601

Multiplicities, fluctuations and correlations

Abstract

Similar works

Full text

Available Versions

CERN Document Server

Crossref