Buschbeck, Brigitte

Lipa, P

Mandl, F

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and Experiment, Divonne - Les—Bains, France, Plenum, N.Y. OCR Output*to be published in Proc. of Nato Advanced Research Workshop on Hot Hadronic Matter: TheoryA QU $5 ScQQto U1Z>those of Lund-strings alone.discuss a possible improvement by including low py clustering effects in addition toour understanding of the dynamics of multiparticle production is still insumcient. Wein pp reactions at collider energy. A comparison with Monte Carlo models shows thatcorrelation functions over a wide range of invariant mass 50 GeV 2 M 2 0.2809 GeVBy using the recently developed technique of correlation integrals we measuredABSTRACTNikolsdorfcrg. 18, A—1050 WienOsterr. Akadcmic der WissenschaftcnInstitut fiir Hochcnergicphysik derB. Buschbcck and P. Lipa (UA1), F. Mandl (DELPHI)NEW DEVELOPMENTS IN CORRELATION STUDIES*October 1994HEPHY—PUB 613/94(work of E. Berger et al.6 should be mentioned here as an exception. OCR Outputthe normalization included always some arbitrariness and has been an unsolved problem. An early*Q2 has been used frequently in the past, e.g. when measuring Bose—Einstein correlations, however,lant correlation functions.to extend the event mixing technique to the numerator for estimating the cumuthe event mixing technique,4to find the proper normalizatiorf by justifying and quantifying mathematicallyQQ + 4m? can be analysed,like the four momentum transfer Qfz : -—(p1 — pz) and the invariant mass Mand to integrate over all distinct locations in phase space; therefore, new variablesto choose differences of phase space variables between particles (e.g. 6y = yl — y2)The crucial steps leading to the correlation integrals have been:and new tools, the correlation integrals,3`5 are available now.(FM) on the magnitude of phase space bins,1 correlation studies have developed rapidly2Peschanski in 1986 have proposed to study the dependence of the factorial momentsin high energy reactions, they are dimcult to measure. However, since Bialas andvaluable information on the multiparticle system; Because of their high dimensionalityIn principle, the correlation functions both of lower and higher orders provideINTRODUCTIONthose of Lund-strings alone.discuss a possible improvement by including low py clustering effects in addition toour understanding of the dynamics of multiparticle production is still insufhcient. Wein pp reactions at collider energy. A comparison with Monte Carlo models shows thatcorrelation functions over a wide range of invariant mass 50 GeV 2 M 2 0.2809 GeVBy using the recently developed technique of correlation integrals we measuredABSTRACTNikolsdorferg. 18, A—105O WienOsterr. Akademie der WissenschaftenInstitut fiir Hochcnergicphysik derB. Buschbeck and P. Lipa (UA1), F. Maud] (DELPHI)NEW DEVELOPMENTS IN CORRELATION STUDIESllln case of exception, this will be indicated in the text or figure caption. OCR Output§for details of data selection seesffor details of data selection seelOther recent applications of correlation integrals are summarized in_ p1®p1(M)dM Z <TL>l lll QMIDAX· p2(M)dM = < n(n -1) > in SZ (3)MHIGXThe normalization condition1T, fo P1 ® P1(M MM 2 ( )F M _ f$P2(M)dM2( ) — *"‘_‘—T‘MIIwill use also the integral respresentation, the momentsstructure of correlations shows up. Beside the differential representation in eqn.(1) weof single particle spectrum p1(P), in the ratio of iig.1b this has cancelled out and themagnitude!) over the whole mass range which are due to phase space and the shapeshown in fig.1b. Whereas both quantities in iig.1a show large variations (four orders ofThe numerator and the denominator of eqn.(1) are shown in fig.1a. The ratio isthe pseudorapidity interval ——3 f n §_ 3 and py > 0.15 GeV/cland 0; the inclusive and event cross sections. The integration region Sl in our case iswith P being the 3—m0menta and E the corresponding energies with pion mass, amdm (i1,?>`2) (E1 + 1202 - {15} + E2)2O'] dp#1 (5*) I d3O'inc)O-I d 51 52.pi (F152) Ld“°‘¤¤¤¤pr ® MM) NPI · dfpz · P1 @1) 0 (F2) 6 (M - m ($1%))MM) ;2dP1‘dP2‘P233 (I"1,I’i2)6(M —· m (51752))TAM) (1)pi épi(M)p (M)M > 0.2809.moments ) (i = 2-5) depending on the invariant mass M over a wide range 50 2investigate in the following the differential density correlation function r2(M) and the\/E = 90 GeV from the DELPHI experiment§ are presented for comparison. We will630 GeV, measured in the UA1 detector;. In one distinct case, c"’e” reactions atThe data sample consists of 160.000 non—single diHractive pp reactions at \/EDATA, DEFINITIONS AND GENERAL FEATUREScorrelations. This is the aim of the present contributionlcan help to get more sensitive information on the dynamical origin of multiparticleNow we are in the position to apply these tools to the data, to sec whether theynear unity. OCR Output*In case of full phase space, not shown here, the Fi values of e"'e' are even smaller and indeedtion (equivalence theoremlz).Giovanniui}1 They provide an equivalent and alternative parametrization of the multiplicity distribuThe factorial moments of the Neg. Bin. distribution have been evaluated already early by A.the following only pp reactions.even quantitatively by Monte Carlo models with QCD cascading, we will consider inDo we understand these features ? Since in e+ e` reactions they can be reproducedlong—range correlations are almost absent.only with a small amount to the overall multiplicity distribution and in this case, themultiplicity distribution in S). Again, the large short—range correlations do contributeshow small values at large M which is the signature of an (approximate) Poissonic"In contrast, the F} of e+e` reactions at LEP energy (open circles in iig.3) doto long-range correlations only.that multiplicity distributions in large phase space bins (like Q) are almost duebroad Negative Binomialll distribution. From the observations of item 1 we arguemultiplicity distribution in Q. The large values at higher orders i indicate aThe values Fi(Mmx), already reached at M z 50 GeV in fig.3, represent the> 1 in the whole range of M (kg = r2 — 1 > O, positive genuine correlations).the presence of long-range correlations. This is seen also in r2(M), which remainsIn Hg2 F2(M) decreases for small M $ 1 GeV but levels off at larger M because ofSimilar considerations hold for the higher moments shown in fig.3.2% to the value of F2(Mmax) which is reached already for M = 50 GeV in lig.2.responsible for this rise above the pedestrial value of rz rz 1.4 contribute less thenregion M < 1GeV (liglb). We evaluated from fig.1a that the number of pairsThe short-range correlationsm show up as rise of r2(M) with decreasing M in thetheir respective contributions to the multiplicity distribution in S2.In figs.l—3 we can read off the whole story of long- and short-range correlations andlation integrals.representation (black circles, eqn. of the second order correFig.2: Differential representation (open circles, eqn. and integralM(GeV)TO••••••OOOUOOO;t:••• 5 FOh'-. ?_6 F457.:6• F'2(M>O |'z(M)OCR OutputQ1,large mass which can be attributed to pairs of high py particles, 2) no reproduction OCR Output5.6 with two selections of pTmh_. We observe 1) an overestimation of correlations withadded as ”fl.118.l state interactions". Fig.4 shows a comparison of r2(M) with PYTHIAthus contains jet and resonance production. Bose-Einstein correlations have beenstrings spanned between the hard-scattered partons and beam remanents. PYTHIAand final state radiation is created. Each parton configuration hadronises via Lu.nd—multiplicity and the shape of the multiplicity distribution depend on pym. Initialcentrality of the reactions together with Poissonian fluctuations). Both, the meannumber of initial parton scatterings per event from one event to another (varyingpqym to 1.5-2 GeV / c. The broad multiplicity distribution is obtained by varying theto QCD. The description of inclusive event properties restricts the cut-off parametersection falling rapidly towards higher partonic transverse momentum pq- accordingreaction is initialised by a ha.rd-to—semihard parton—parton scattering with a crossPYTHIA}3 A high energy collision is viewed as a collision of two parton beams. EachA very detailed physical picture is contained in the Lund Monte Carlo programORIGIN OF CORRELATIONS IN hh REACTIONS ?HOW WELL DO WE UNDERSTAND THE DYNAMICALreactions (black circles) with e`*‘e' reactions (open circles).Fig.3: A comparison of correlation integrals = 2 — 5) of ppM(<;ev)10i = 3:2*o 0. 88O°"oo00o 8•••••••••••1 = 4o°Q°O••O •• 0•• O10g '•,• 1 = 5 ••••••••••••••••••15b 02025O DELPHI• UA130A 55framework of the Statistical Bootstrap Model has been given in ref.1 OCR Outputcarefully and tuned to observed rapidity correlations. A derivation of multiplicity distributions in thethe overall multiplicity distribution are put in ”by hand" only. However, clustering effects are created*GENCL does by far not contain a detailed physical picture like PYTHIA. Most observations, likepy z 0.5 GeV/c.verified that it is due to transverse momentum compensation between hadron pairs of relatively lowiThis structure is likely to be connected with the unknown transition region hard to soft. Westrong correlations at low mass 2 2 M 2 0.5 (not shown here). Since cluster effectsas expected and it does not repoduce the bump at 2 GeV either, but it producesUA5 cluster modelff GENCL}6 It turns out, that it underestimates high py effectsA first impression, what clustering effects may achieve, can be gained with theclusters or Hreballs on the other sideparton showering and string fragmentation on one side and the production of low pyor do we have to merge the two pictures: hard scattering processes with subsequentthis conference.15 Does the Lund-string alone really provide an alternative description,Convincing evidence for the existence of Hreballs has been reviewed by R. Hagedom atHow can we obtain a better agreement? Are there additional cluster effectsFig.4: Comparison of r2(M) in pp reactions with PYTHIA 5.6.M(GeV)101.11.2o°°°0°°o1.3 44<>O 4.4444M° Q 1+44444+°°°4M¢ “°§tééi¢¢++1.4 A •. • Al+ ·•••••••• An + Q Oi“••••++.. 4 4l ld 40li · ;;l Ié.1.5 é'°°+4* me1.61.7A PYTHIA ,pt,,,,,=1.551.8O PYTHIA ,pt,,,,,=1.9O1.9• UA114the multiplicity and py dependence of short-range correlations.underestimation at low py /low multiplicity by PYTHIA has been observed also inA similar result: overestimation of correlations at high pT and high multiplicity, andof thc structure at 2 GeVH, and 3) an undemstimation of correlations at small mass.decay of clusters. OCR OutputBose—Einstein correlations. The rise in GENCL is entirely due to refelctions from theb) Comparison with the cluster model GENCL (squares) which does not containEinstein correlations (open circles and triangles respectively).a) Comparison with PYTHIA5 (py·_i_ : 1.9 GeV/c) including and excluding BoseFig.5: Comparison of r2(M) of like sign pairs (data: full circles) with Monte Carlo models;M (GeV)1 O.. 4 AA°°Z‘ + +*++ F, if i i . it••~¢O $l°+$¢r¢mO O •¢•, 5 fi '•4*2°s¤_¤aO •• We·51‘•1.6 1-+1.61.71.718,31.81.91.9production and decay of clusters /fireballs on the other.hard scattering processes with subsequent string fragmentation on one side and theof regarding string and cluster descriptions as alternatives, to merge the two pictures:hithero rmsatisfactory understanding of hh reactions, it could be necessary, insteadvariant mass to study the dynamical origin of particle production. To improve ourTo summarize, we found sensitive tools with the correlation integrals of instrong indication for the occurence of additional cluster effects (see fig.5b).provide a satisfactory description of the data in Hg.5, we sho11ld regard this as astructure and that also the Dual Parton Modelw with many short chains cannotopen circles). If it will turn out in the future that PYTHIA with changed stringcorrelations according to our present understanding (compare in £g.5a triangles withThe rise at large M observed in the data can neither be attributed to Bose—EinsteinEg.5a. Changing pym has similar eiets as in Eg.4, but does not improve the shape.pseudoskalars and tensors does not change the flat distribution for M > 0.8 GeV inpseudoskalas and vector multiplets are included. The additional inclusion of scalars,already at large M. This rise is not reproduced by PYTHIA (Hg.5a). By default onlyljke—sign pairs to demonstrate that there is a. rise of r2(M) of data (black circles)low pr particles (0.15 i py $ 0.3 GeV/4;) with PYTHIA and GENCL. We selectedshould show up more clearly at low pq-, we compared in HgS·5&,b & Subsamplc ofthe two—component Dual Parton Model”, SI-93-3.18. P. Aurenche et al., ”D'1`U.IET—93. Sampling inelastic pp and pp collisions according to17. G.J.H. Burgers, C. Fuglesang, R. Hagedorn and V. Kuvshinov, Z. Phys. C46 (1990) 465.16. GJ. Alner et al. (UA5), Nucl. Phys. B291 (1987) 445.15. R. Hagedorn, invited lecture, this conference.Y.F. Wu et al. (UA1—collab.), Acta Physica Slovaca V44 (1994) 141.14.. Albajar et al. (UA1-collab.), Nucl. Phys. B345 (1990) 1;13.. Sjostrand, Comp. Phys. Com. 82 (1994) 74.L. Diosi, Nucl. Instr. Meth. 138 (1976) 241.12.. Koba, Proc. of 1973 CERN-J NR School of Physics, CERN-Jellow Rep. 73-12;11.. Giovarmini, Lett. Nuovo Cimento 6 (1973) 514.10.. Neumeister et al., (UA1-collab.), Z. Phys. C60 (1993) 633.. Grassberger, Nucl. Phys. B120 (1977) 231.Ed. C. Paja.res (World Scientific).22. Internat. Symp. on Multiparticle Dynamics, Santiago de Compostela, Spain, 1992,. Mandl and B. Buschbeck, ”C0rrelation integal studies in DELPHI and UA1”, Proc.. Neumeister et al. (UA1-collab.), Z. Phys. C60 (1993) 633.E.L. Berger et al., Phys. Rev. D15 (1977) 206.H.C. Eggers et al., Phys. Rev. D48 (1993) 2040.H.C. Eggers et al., Phys. Lett. B301 (1993) 298.P. Lipa. et al., Phys. Lett. B285 (1992) 300.(1994) 199, P. Abreu et al. (DELPHI-collab.), Z. Phys. C63 (1994) 17.MPI-Pl1E/94-12 and N.M.Aga.babya.11 et al. (NA22/EHS—co1lab.), Phys. Lett. B328in Deep Inelastic Muon-Nucleon Scattering at 490 GeV” (Fermilab E665—collab.)Phys. Rep.; Some recent results are also given in ”Density and Correlation Integralsdyna.mics”, E.A. De Wolf, L.M. Dremin, W. Kittel, HEN—362 (1993), to appear infor a. review see ”Sca.ling Laws for density correlations and Huctuations in multiparticleA. Bialas and R. Peschanski, Nucl. Phys. B273 91986) 70; Nucl. Phys. B308 (1988) 857.REFERENCESWe gratefully acknowledge the helpful discussions with T. Sjostrand.Acknowledgements

New developments in correlation studies

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