Recent results on jet and inclusive charged particle production in hadronic
e+e- interactions are reviewed.Comment: 5 pages, to appear in the proceedings of the EPS/HEP-2001 conference,
  Budapest, Hungar

Vossebeld, J. H.

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arXiv

Joost Vossebeld

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Jets and multiplicities in $e^+e^-$

Recent results on jet and inclusive charged particle production in hadronic e+e- interactions are reviewed.Recent results on jet and inclusive charged particle production in hadronic e+e- interactions are reviewed

Vossebeld, Joost H.

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 hep2001International Europhysics Conference on HEPPROCEEDINGSJets and Multiplicities in e+e−Joost VossebeldCERN, CH-1211 Geneva 23, SwitzerlandE-mail: Joost.Vossebeld@cern.chAbstract: Recent results on jet and inclusive charged particle production in hadronice+e− interactions are reviewed.1. IntroductionThe production of jets and hadrons in e+e− interactions provides a suitable laboratory tostudy quantum chromodynamics. Both the coupling strength and the group structure ofthe theory can be determined. We discuss a number of recent measurements concerningjet and hadron production. These include a determination of the strong coupling constant,αs, from 4-jet rates[1], two studies of 4-jet angular correlations[2, 3], in which αs and thecolour factors, CA and CF , are determined, a study of charged particle multiplicity in 3-jetevents[4] and two helicity analyses of charged hadron production[5, 6].2. Determination of αs from 4-jet ratesIn a recent study[1] DELPHI has measured n-jet rates, Rn, as a function of the jet resolu-tion parameter ycut, at centre-of-mass energies in the range 89-207 GeV, using various jetalgorithms. The 4-jet rate, R4, is compared to NLO QCD predictions[7] to determine αs.As there are expected to be considerable higher order contributions, still missing in thesepredictions, in particular due to large logarithmic terms, DELPHI uses the method of scaleoptimisation when determining αs. This implies that both αs and the renormalisation scaleparameter xµ =µ2RQ2are varied when tting the NLO predictions to the data. It is arguedthat the obtained optimal scale, xoptµ , accounts for missing higher order contributions.Fig. 1 shows the result for R4 based on the Durham[8] jet algorithm, atps = 91 GeV,compared to tted theory predictions. The tted value for the strong coupling constantis: αs(MZ) = 0.1178  0.0012(exp.) 0.0023(had.) 0.0014(scale) and the correspondingoptimal scale: xoptµ = 0.015. The low value obtained for the scale suggests that missinghigher orders are indeed important. The scale uncertainty on αs is determined by varying∗Speaker. hep2001International Europhysics Conference on HEP Joost Vossebeldxµ between12xoptµ and 2xoptµ , yielding a smaller uncertainty than obtained with the conven-tional variation of xµ between14 and 4. The obtained αs value is in good agreement witha similar ALEPH[9] result, obtained using resummed NLO predictions.Using R4 measurements from dierent centre-of-10-310-210-1R4fit rangeDelphipreliminaryxµ=1xµopt10 -3 10 -2DurhamycutFigure 1: Durham R4 distributionatps = 91 GeV compared to ttedNLO predictions with a xed or a t-ted scale.mass energies, DELPHI has also studied the scaledependence of αs, nding good agreement with therunning behaviour predicted in QCD.3. Determination of αs, CA and CF from4-jet angular correlationsOPAL[2] and ALEPH[3] have recently presented stud-ies of angular correlations in 4-jet events atps =91 GeV. A combined t of theory predictions to thesecorrelations and to jet rates is used to determine αs,CA and CF . The theory predictions[7, 10] comparedto are to NLO accuracy for the angular correlationsand to resummed NLO accuracy for the jet rates.In both the OPAL and the ALEPH studies the theory predictions have been ttedsimultaneously to 4 angular variables, to R4 and, in the OPAL study, also to the dier-ential 2-jet rate, D2. The 4-jet angles measured are the Bengtsson-Zerwas[11] angle, χBZ ,the modied Nachtmann-Reiter[12] angle, NR, the Ko¨rner-Schierholtz-Willrodt[13] angle,KSW , and the angle between the two lowest energy jets, α34. Fig. 2 shows these anglesas measured by OPAL, compared to the tted NLO predictions.The t results obtained by OPAL are: αs(MZ) = 0.120  0.011  0.020, CA = 3.02 0.25  0.49, CF = 1.34  0.13  0.22, and by ALEPH: αs(MZ) = 0.119  0.006  0.022,CA = 2.930.140.49, CF = 1.350.070.22, where the uncertainties are the statisticaland systematic uncertainties, respectively. In Fig. 3 68% condence level contours in the1/σ dσ/d(|cosχ BZ|)fit rangeOPAL dataNLO fitted|cosχBZ|00.511.522.530 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11/σ dσ/d(|cosΘNR|)fit rangeOPAL dataNLO fitted|cosΘNR|0.40.60.811.21.41.60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11/σ dσ/d(cosΦKSW)fit rangeOPAL dataNLO fittedcosΦKSW0.20.40.60.811.21.4-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 11/σ dσ/d(cosα34)fit rangeOPAL dataNLO fittedcosα3400.10.20.30.40.50.60.70.80.91-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 100.20.40.60.811 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25CA/CFT R/CFSU(4)ALEPH PRELIMINARY, 68% CL contour ALEPH-1997 OPAL-2001Figure 2: 4-jet angles measured by OPALatps = 91 GeV, compared to tted NLOpredictions.Figure 3: 68% condence level contours in(TRCF, CACF), compared to the expectated val-ues in various Lie group structures.{ 2 { hep2001International Europhysics Conference on HEP Joost Vossebeld(TRCF, CACF)plane are shown from the results presented here and from an earlier ALEPHstudy. The results are compared to the expected values for dierent group structures. Allresults agree well with the SU(3) group structure while several alternatives are disfavoured.4. Charged particle multiplicity in 3-jet eventsMultiplicity dierences in the fragmentation of quark and gluon jets are of great interestas they provide a direct measure of the colour factor ratio CACF . Most measurements of themultiplicity in gluon jets, however, rely on a jet algorithm to separate the gluon fragmen-tation products from those of the quarks in 3-jet events, rendering the obtained resultsbiased. Unbiased gluon jet multiplicity has so far only been measured in -decays[14, 15]and in e+e− 3-jet events, where the gluon is associated with the highest energy jet and it’sfragmentation products can therefore be separated in one hemisphere of the event[16].Recently a formalism[17] has been proposed (in MLLA[18]) to express the multiplicityin 3-jet events as a function of the unbiased gluon jet multiplicity and a biased quark jetmultiplicity, where the latter is dened as the multiplicity in hadronic e+e− events with nogluon radiation harder than the scale associated with the gluon jet in the 3-jet event.Nqq¯g = Nqq¯(Lqq¯, κ?Lu) +12Ngg(κ?Le) (4.1a)Nqq¯g = Nqq¯(L, κ?Lu) +12Ngg(κ?Lu) (4.1b)where L = ln sΛ2, Lqq¯ = lnsqq¯Λ2, κ?Lu = lnsqgsq¯gsΛ2, κ?Le = lnsqgsq¯gsqq¯Λ2and sij = (pi + pj)2. Thetwo alternative formulations reflect an ambiguity in dening the transverse momentum ofthe emitted gluon with respect to the qq system. In the same formalism both the biasedquark jet multiplicity and the energy dependence of the gluon jet multiplicity can be derivedfrom the inclusive multiplicity in hadronic e+e− events.In a recent analysis[4] the DELPHI collaboration161820222426283020 40 60 80 100 120θ1[o]NchNqqNqqgDelphiEden et al. (a)Eden et al. (b)DELPHIFigure 4: Charged particle multi-plicity in 3-jet events in bins of θ1,compared to predictions based onequations 4.1a and 4.1b.has measured the charged particle multiplicity in 3-jet events, in which the two lowest energy jets haveidentical angles with respect to the highest energy jet.In these so-called \Y" events all scales in equations4.1a and 4.1b are determined by the angle between thetwo lowest energy jets, θ1. The charged multiplicity in3-jet events as a function of θ1 is shown in Fig. 4. Thedata are compared to predictions based on the aboveformalism, where the normalisation of the gluon jetmultiplicity has been xed to the direct measurementof [14] and an additional oset is tted to the data toaccount for the bias in the multiplicity due to c and bquarks which are not considered in the formalism.The formalism (equation 4.1a) has also been usedto obtain a measurement of CACF which determines the{ 3 { hep2001International Europhysics Conference on HEP Joost Vossebeldratio of the energy slopes of the multiplicity in gluon and quark jets. DELPHI obtains:CACF= 2.221  0.032(stat.)  0.047(exp.)  0.058(had.)  0.075(theo.). In agreement withthe QCD expectation of 2.25. Recently DELPHI has extended this study to include alsoasymmetric 3-jet events, obtaining similar results.5. Helicity analysis of inclusive charged hadron productionThe inclusive hadron production cross section in e+e− annihilation can be expressed as afunction of xp, the scaled momentum of the hadrons and θ, the angle of the hadrons withrespect to the electron beam:d2σhdxpd cos θ=38(1 + cos2 θ)dσhTdxp+34sin2 θdσhLdxp. (5.1)A transverse and a longitudinal component are distinguished, which can be separated bymeasuring the cos θ distribution. This separation is of interest because the relative size ofthe longitudinal component, which is associated with gluon radiation, provides a measureof the strong coupling constant. A prediction up to NLO in αs for the longitudinal fractionhas been given in [19]:σLσtot=αspi+α2spi2(13.583 − 1.028Nf + (0.167Nf − 2.750) ln Q2µ2). (5.2)In a recent DELPHI study[6] of10-210-111010 210 310-210-11xpF T DELPHI (preliminary)data, not clustereddata (ycut=0.912 GeV)data (ycut=1.290 GeV)data (ycut=2.040 GeV)10-510-410-310-210-111010 210-210-11xpF Ldata, not clusteredDELPHI (preliminary)data (ycut=0.912 GeV)data (ycut=1.290 GeV)data (ycut=2.040 GeV)Figure 5: Transverse and longitudinal fragmentationfunctions atps = 91 GeV using angles of individualhadrons or those of jets.hadronic e+e− interactions atps =91 GeV, transverse and longitudi-nal charged particle fragmentationfunctions have been determined fromthe cos θ distribution measured inbins of xp. To study possible hadro-nisation eects on the hadron an-gles, which are not accounted forin equation 5.2, alternative ways ofmeasuring these angles were tested,either using the angles of the hadronsthemselves or using the angles of thejets to which the hadrons are assigned. In the latter case jets were dened using dier-ent values of the non-scaled distance measure ycut. The obtained transverse and lon-gitudinal fragmentation functions are shown in Fig.5. Taking the measurements withycut = 1.290 GeV as the nominal results, DELPHI obtains the longitudinal fraction:σLσtot(MZ) = 0.0445  0.0006(stat.)  0.0060(syst.). Using equation 5.2 the correspondingvalue for αs is found to be: αs(MZ) = 0.1083  0.0012(stat.) 0.0119(syst.).In a similar analysis of data from the JADE experiment[5] the cos θ distribution wasmeasured for e+e− interactions at a mean centre-of-mass energy of 36.6 GeV. The longitu-dinal fraction was determined to be: σLσtot (36.6 GeV ) = 0.067  0.011(stat.)  0.007(syst.){ 4 { hep2001International Europhysics Conference on HEP Joost Vossebeldand the corresponding value of the strong coupling constant: αs(36.6 GeV) = 0.150 0.020(stat.) 0.013(syst.) 0.008(scale). Evolved up to MZ this corresponds to αs(MZ) =0.127+0.017−0.018, in agreement with the DELPHI result and with the world average value ofαs(MZ) (0.1184  0.0031[20]).6. SummaryVarious new results on jet and inclusive hadron production in e+e− annihilation have beenpresented. The measurements have been compared to higher order QCD predictions totest this theory and to extract it’s coupling constant and it’s colour factors. The obtainedresults for αs agree with results obtained in other measurements and the obtained valuesfor the colour factors agree with the values expected in QCD.References[1] DELPHI collaboration, DELPHI 2001-059.[2] G. Abbiendi et al. [OPAL Collaboration], Eur. Phys. J. C 20 (2001) 601.[3] ALEPH Collaboration, ALEPH-2001-042 (submitted to this conference).[4] DELPHI collaboration, DELPHI 2000-118 and DELPHI 2001-067.[5] M. Blumenstengel et al. [JADE Collaboration], Phys. Lett. B 517 (2001) 37.[6] DELPHI collaboration, DELPHI 2001-058.[7] Z. Nagy and Z. Trocsanyi, Phys. Rev. D 59 (1999) 014020.[8] S. Catani et al., Phys. Lett. B 269 (1991) 432.[9] ALEPH collaboration, ALEPH 2000-045.[10] Z. Nagy and Z. Trocsanyi, Phys. Rev. D 57 (1998) 5793.[11] M. Bengtsson and P.M. Zerwas, Phys. Lett. B 208 (1988) 306.[12] O. Nachtmann and A. Reiter, Z. Physik C 16 (1982) 45.[13] J.G. Ko¨rner, G. Schierholz and J. Willrodt, Nucl. Phys. B 185 (1981) 365.[14] M.S. Alam et al. [CLEO Collaboration], Phys. Rev. D 46 (1992) 4822.[15] M.S. Alam et al. [CLEO Collaboration], Phys. Rev. D 56 (1997) 17.[16] G. Abbiendi et al. [OPAL Collaboration], Eur. Phys. J. C 11 (1999) 217.[17] P. Eden and G. Gustafson, J. High Energy Phys. 9809 (1998) 015;P. Eden, G. Gustafson and V.A. Khoze, Eur. Phys. J. C 11 (1999) 345.[18] See e.g. Yu.L. Dokshitzer et al., Basics of Perturbative QCD, Ed. Frontieres, Gif-sur-Yvette,France, 1991.[19] P.J. Rijken and W.L. van Neerven, Phys. Lett. B 386 (1996) 422.[20] S. Bethke, J. Phys. G 26 (2000) R27.{ 5 {

Jets and multiplicities in e+e-

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