The study of the differences of the fragmentation of quarks and gluons to
jets of hadrons gives insight into the fundamental structure of QCD. Results
from different approaches to properties of quarks and gluons are shown. The
colour factor ratio $C_A/C_F$ is measured in agreement with the QCD prediction.
Identified particles in quark and gluon jets are investigated, revealing no
overproduction of isoscalar $\eta^0$ and $\phi(1020)$ in gluon jets, but an
excess of protons.Comment: Submitted to the proceedings of the XXIX International Symposium on
  Multiparticle Dynamics (ISMD99), Providence, 6 pages including 6 figures
  Version 2 with additional reference

Siebel, Martin

English

arXiv

The study of the differences of the fragmentation of quarks and gluons to jets of hadrons gives insight into the fundamental structure of QCD. Results from different approaches to properties of quarks and gluons are shown. The colour factor ratio $C_A/C_F$ is measured in agreement with the QCD prediction. Identified particles in quark and gluon jets are investigated, revealing no overproduction of isoscalar $\eta^0$ and $\phi(1020)$ in gluon jets, but an excess of protons

Siebel, M

CERN Document Server

QUARK AND GLUON JET PROPERTIES AT LEPMARTIN SIEBELDep. of Physics, University of Wuppertal, Gaußstraße 20, D-42097 Wuppertal,GermanyE-mail: Martin.Siebel@cern.chThe study of the differences of the fragmentation of quarks and gluons to jets ofhadrons gives insight into the fundamental structure of QCD. Results from differentapproaches to properties of quarks and gluons are shown. The colour factor ratioCA/CF is measured in agreement with the QCD prediction. Identified particles inquark and gluon jets are investigated, revealing no overproduction of isoscalar η0and φ(1020) in gluon jets, but an excess of protons.1 IntroductionIn QCD there are three fundamental vertices representing the three and thefour gluon coupling and the coupling of a fermionic current to a gluon. Ne-glecting the four gluon coupling which is of O(α2s) there are three fundamentalprocesses described by these vertices: The radiation of a gluon by a quark(q ! qg) or by another gluon (g ! gg) and the splitting of a gluon into aquark-antiquark pair (g ! qq). The probability of these processes is given bythe splitting kernels which take the kinematics into account and are propor-tional to the colour factors CF , CA and TF respectively. The colour factorsare the structure constants of the SU(3) colour symmetry group of QCD,vividly speaking, they take care of the bookkeeping of undetermined colourflows in these processes. As the main contribution to particle production inhadronic events is due to the radiation of gluons, it is to be expected thatthe dierences of the properties of jets initiated by quarks to those of jetsinitiated by gluons are in terms of the ratio CA/CF . The assumption of localparton-hadron duality (LPHD) gives rise to the hope that these perturbativelycalculated dierences can be observed in the hadronic nal state.2 Experimental accessTo get information about gluons, events with three jets are used, as theycontain exactly one gluon jet. The jets of a hadronic three jet event arenumbered according to their energy with jet 1 being the most energetic onewhile angles between jets are numbered according to the jet opposite of theangle. There are three dierent ways of getting information about quarks andgluons out of hadronic three jet events presented here. In the jet analysis2,59911018: submitted to World Scientific on November 16, 1999 110-11100 0.5 1 1.5 2 2.5 3gincl. jetsuds jetsJetset 7.4Herwig 5.9Ariadne 4.08AR-2AR-3pT(p<4 GeV/c)[GeV/c]1 Ndnch.dpT(a) OPAL11.522.530 0.5 1 1.5 2 2.5 3gincl./uds jetsJetset 7.4Herwig 5.9Ariadne 4.08AR-2 AR-3pT(p<4 GeV/c)[GeV/c]1 Ndnch.dpTRg/q  (b) OPALFigure 1. pT -distributions (upperplot) and the ratio gluon/quark ofthe distributions (lower plot)00.20.40.60.811.20 20 40 60 80 100 120<Nch,cone> for symmetric three jet eventsDataFit with free normalisationθ1[o]<Nch,cone> DELPHIFit rangeFigure 2. The multiplicity within a 30◦-coneperpendicular to the event plane as functionof the event topologysingle jets taken from three jet events are looked at. Gluon jets are identiedusing an anti-tagging technique in events with primary b-quarks. Informationabout light quark jets is obtained by subtracting the properties of gluon jetsfrom a sample of unidentied jets. Approximately 142.000 identied gluonjets enter this analysis. As the dynamical scale for a single jet the so calledhardness scale κh = Ejet sin θmin is used, where θmin represents the smaller ofthe two angles adjacent to a jet. Although this is a problem which, in principle,involves two scales, κH proves to be an appropriate choice to reduce this to aone scale problem. The jets entering this analysis cover the dynamical range ofapproximately κh = 6GeV . . . 29GeV . In the hemisphere analysis8 events areselected with a hard gluon initiating the most energetic jet. The gluon jet isdened by all particles in the hemisphere of the leading jet. This type of eventrequires both subleading jets to be tagged as b-quark jets successfully. Lightquark jets to compare with are dened by a whole hemisphere of an event.This procedure gives 439 gluon jets at an energy of 40.1GeV and quark jets at45.6GeV . Corrections for the dierence in energy are applied to the quark jets.In the symmetric event analysis2,3 complete three jet events are investigated.Only events with θ2 being equal to θ3 within small tolerances (1.25◦) areused so the whole event can be described by giving only θ1. No assignmentof particles to jets and no jet tagging is needed. A total of approximately162.000 symmetric events enter this analysis.9911018: submitted to World Scientific on November 16, 1999 23 ResultsAs stated above, the gluon bremsstrahlung is expected to be CA/CFtimes higher in gluon than in quark jets. This contrasts to the experimentalobservation of the ratio rch of the charged multiplicity in gluon jets over quarkjets to be below 1.5 as found over the whole scale range of the jet analysis2and 1.514 0.019 0.034 for the hemisphere analysis8. This dierence to thena¨ve expectation can be explained by higher order corrections and eects ofnite energy. Soft partons emitted at large pT cannot resolve single partonswithin the shower-evolution of a jet,[width=]pic3.epsFigure 3. The multiplicity of events at differ-ent energies (lower curve) leads to a predic-tion of the gluon contribution to multiplicityin three jet events (upper curve).so the eective colour charge emit-ting these particles is the one ofthe primary parton. Figure 1 showsthe pT distribution of soft parti-cles (jpj < 4GeV/c) in quark andgluon jets and the ratio of both in the lower plot as taken from thehemisphere analysis. For higher pT the ratio is in the expected rangeof CA/CF = 2.25. Monte-Carlo studies conrmed that this ratio in therange of 0.8GeV/c < pT < 3GeV/c reflects the colour factor ratio, yield-ing rch(jpj < 4GeV/c, 0.8GeV/c < pT < 3GeV/c) = 2.290.090.15 in goodagreement with the QCD expectation for CA/CF 8. The same idea is used ingure 2 from the event analysis. This plot shows the multiplicity within acone with xed opening angle of 30◦ perpendicular to the event plane. Theabscissa is the angle θ1 between jet 2 and 3. The plotted line is derived froma prediction by V.Khoze, W.Ochs and S.Lupia7 and parametrised byN qq¯g⊥ / 2 + cosθ12− cos θ1 − 1N2C(1 + cosθ12)(1)with only the normalisation left free3. The prediction describes the data well,giving evidence of coherent radiation within a three jet event. This providesa direct test of a perturbative calculation independent of fragmentation mod-els. Both approaches are complementary, as in the hemisphere analysis thetopology and therefore the colour charge separation is xed while partons ofdierent wavelengths and resolution capabilities have been investigated, whilein the symmetric event analysis the cone and therefore the phase space of thepartons remains xed and the separation of the colour charges is varied withthe topology.For the multiplicity of a hadronic three jet event there is a MLLA-prediction6 of the simple formNqq¯g(θ1) = Nqq¯(2E∗, pt1) +12Ngg(pt1) (2)9911018: submitted to World Scientific on November 16, 1999 3where coherence eects are taken into account by the used scales 2E∗ andpt1. As in the symmetric event analysis the event is described by only givingθ1, the two scales 2E∗ and pt1 can be expressed as functions of this angle.The contributions Nqq¯ and Ngg are correlated by a dierential equation in-cluding the colour factor ratio with corrections. Taking the parametrisationof Nqq¯(ps) from events at various beam energies and xing the only free pa-rameter left by a measurement of the gg-multiplicity by Cleo1, one gets anabsolute prediction of the topology dependence of the three jet multiplicity.This prediction is found to be in very good agreement with the data fromthe symmetric event analysis down to an opening angle of θ1 ’ 30◦. Thelower curve in gure 3 shows the parametrisation Nqq¯(ps) of the data. Theupper curve is Ngg derived from Nqq¯, the corresponding data points from theDelphi symmetric event analysis are calculated from three jet event mul-tiplicities by subtracting Nqq¯. The Ngg data point at 10GeV from Cleohas been used to x the prediction while the point at 40GeV is taken fromOpal’s hemisphere analysis8. The lowest three points from the Cleo analysisare without systematic errors1. The overall agreement between data and pre-diction is good. The result for CA/CF gained by the symmetric event analysisis CA/CF = 2.246 0.062 0.080 0.095theo where an ansatz has been usedwhich takes care of non-perturbative eects by an added oset2. Numericresults from a t with equation 2 are to be expected soon.While the multiplicity is dominated by soft particles, the study of scalingviolation in quark and gluon jets oers the possibility to obtain information10-410-310-210-111010 210κH [GeV]1/NJetdNch/dx E 0.03 ... 0.080.08 ... 0.150.15 ... 0.230.23 ... 0.330.33 ... 0.450.45 ... 0.600.60 ... 0.750.75 ... 0.90All eventsDELPHIxEintervalGluon1st order DGLAP-evolutionOpal Hemisphere EventsFigure 4. The fragmentation function of thegluon as a function of κH .-1.2-1-0.8-0.6-0.4-0.200.20.40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1xEdlog DH(x E,κ) / dlog κQuarkGluonTasso (Quark)DGLAP evolution in 1st orderDELPHIFigure 5. Strength of the scaling viola-tion in quark and gluon jets as a functionof xE .9911018: submitted to World Scientific on November 16, 1999 4from the other end of the spectrum. The energy dependence of the fragmenta-tion functions is described by the DGLAP-equations. As the splitting kernelsoccur in this set of integro-dierential equations, again the colour factor ratioCA/CF is expected to be found in the comparison of gluon to quark jets. Inthe jet analysis the fragmentation functions of quarks and gluons have beeninvestigated5. Figure 4 shows the fragmentation function of the gluon as afunction of κH and xE as a parameter. κH is used as the dynamical scaleas we are dealing with single jets. The curves are the result of an evolutionof the DGLAP-equations to rst order. The description of the data is verygood and extrapolates well to the data taken from the hemisphere analysis atthe rightmost8. Fitting a power-law ansatz through the measured fragmenta-tion functions yields the result shown in gure 5 where the double logarith-mic slopes found in gluon and quark jets are plotted. Obviously the scaledependence is more pronounced in gluon than in quark jets. Again the linesrepresent the results of the evolution of the DGLAP equations. A t with thisevolution yields for the colour factor ratio CA/CF = 2.25 0.09 0.06 0.11where the last error reflects the dependence on the jet nding algorithm andchoice of scale. This is in excellent agreement with the QCD prediction.Also identied particles in[width=]pic6.epsFigure 6. Position of the maximum of the ξpdistribution. The values for ξ are obtained byusing the decimal logarithm.quark and gluon jets have beenstudied, especially pi±, K±, pp, pi0and η as well as the resonancesK∗(892) and φ(1020)4,9. Theseanalyses both have dealt with singlejets similar to the jet analysis described above. The investigation of themultiplicity of these particles in quark in gluon jets is of interest especiallyfor the η and φ(1020), as these mesons are isospin singletts as the gluonsare. Despite this community, no overproduction of these two particles hasbeen found in gluon jets. The multiplicity of η particles has been studied atthree dierent values for κH between 7GeV and 25GeV . The multiplicityfound in quark and in gluon jets as well as the ratio of both always agreedwith the expectations from charged particles9. For the resonances K∗(892)and φ(1020) the normalised ratio RX = [ng(X)/nq(X)]/[ng(ch)/nq(ch)] withnq,g(X) being the multiplicity of particle X in quark or gluon jets and chdenoting all charged particles has been investigated. The results obtainedare RK∗ = 1.7  0.5 and Rφ = 0.7  0.3 revealing especially no excess ofφ in gluon jets4. While also pion and kaon production have been found inagreement with the results for all charged particles, a signicant excess ofprotons in gluon jets has been found with Rp = 1.205  0.041  0.024. Alsothe momentum spectra and ξp distributions9911018: submitted to World Scientific on November 16, 1999 5of these particles have been studied showing a good agreement with the pre-dictions of Jetset and Ariadne and more pronounced deviations from Her-wig predictions. The position of the maximum of the ξp distributions, ξ∗p , isshown in gure 6 for protons, pions and kaons. The data points denotedwith Y and MERC are taken from a jet analysis in which only two symmetricevent topologies where used4. The behaviour of the quark ξ∗p values fromthis jet analysis extrapolates well to the measurements from events at higherenergies. For pions and protons the ξ∗p values found in quark and gluon jetsare in good agreement, while for kaons the ξ∗p values found in gluon jets aresignicantly higher than in quark jets. This observation does not agree withthe assumptions of LPHD.4 AcknowledgementsI would like to thank J.Drees to whom I owe the opportunity to work inthis fascinating eld and K.Hamacher, O.Klapp and P.Langefeld for the verypleasant time working on this subject. I also would like to express my grati-tude to the organising committee for their eort in making the ISMD’99 thedelightful experience it has been.References1. Cleo Collaboration, Phys.Rev. D46 (1992) 4822, Phys.Rev. D56 (1997) 172. Delphi Collaboration, Phys. Lett. B449 (1999) 3833. Delphi Collaboration, DELPHI 99-115 CONF 3024. Delphi Collaboration, DELPHI 99-116 CONF 3035. Delphi Collaboration, CERN-EP/99-1446. P.Eden, G.Gustafson, JHEP 9809:015(1998) hep-ph/98052287. V.A.Khoze, S.Lupia, W.Ochs, Phys.Let. B394 (1997), 1798. Opal Collaboration, CERN-EP/99-0289. Opal Collaboration, OPAL Physics Note, PN4079911018: submitted to World Scientific on November 16, 1999 6

Quark and gluon jet properties at LEP

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Quark and gluon jet properties at LEP

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