A summary of some recent studies in jet physics is given. Topics include
leading particle production in light flavor events in e+e- annihilations, an
analytical treatment of gluon and quark jets at the
next-to-next-to-next-to-leading order (3NLO), and various studies performed at
LEP and HERA involving separated gluon and quark jets.Comment: 7 pages including 8 figure

Gary, J. William

English

arXiv

A summary of some recent studies in jet physics is given. Topics include leading particle production in light flavor events in e+e- annihilations, an analytical treatment of gluon and quark jets at the next-to-next-to-next-to-leading order (3NLO), and various studies performed at LEP and HERA involving separated gluon and quark jets.A summary of some recent studies in jet physics is given. Topics include leading particle production in light flavor events in e+e- annihilations, an analytical treatment of gluon and quark jets at the next-to-next-to-next-to-leading order (3NLO), and various studies performed at LEP and HERA involving separated gluon and quark jets.A summary of some recent studies in jet physics is given. Topics include leading particle production in light flavor events in e+e- annihilations, an analytical treatment of gluon and quark jets at the next-to-next-to-next-to-leading order (3NLO), and various studies performed at LEP and HERA involving separated gluon and quark jets

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v1.0 - 7th December 1998.Ω00 <00UCRHEP-E288AUGUST 21, 2000JET STRUCTURE STUDIES AT LEP AND HERAyJ. WILLIAM GARYDepartment of Physics, University of California, Riverside CA 92521, USAE-mail: bill.gary@ucr.eduA summary of some recent studies in jet physics is given. Topics include leading particle production inlight flavor events in e+e− annihilations, an analytical treatment of gluon and quark jets at the next-to-next-to-next-to-leading order (3NLO), and various studies performed at LEP and HERA involvingseparated gluon and quark jets.1 Leading particle production inseparated light quark eventsSeparated charm (c) and bottom (b) quarkevents have been well studied in e+e− annihi-lations. c and b quarks are mostly producedat the electro-weak vertex in e+e− ! qq !hadrons events, in which the primary quarkq is c or b, and are relatively easy to iden-tify. In contrast, separated up (u), down (d)and strange (s) events have not been muchstudied. u, d and s quarks are copiously pro-duced during jet development, making eventsin which they are produced as primary quarksmore dicult to identify.A recent study1 by the OPAL Collabora-tion at LEP identies e+e− ! qq ! hadronsevents with q=u, d or s. The probabilitiesiq(xmin.p ) are determined for the quark q=u,d, s (or charge conjugate) to appear in anidentied hadron hi(xmin.p ), where hi=+,K+, K0S, p=proton, or  (or charge conju-gate) is the leading particle in the jet, i.e. ithas the largest momentum, with a scaled mo-mentum xp=2p=ps larger than a minimumxp > xmin.p , whereps=91 GeV. The iq prob-abilities provide unique, detailed informationon the hadronization process and a more di-yTalk presented at the XXXth International Confer-ence on High Energy Physics, July 27 - August 2,2000, Osaka, Japan.rect determination of basic hadronization pa-rameters such as the strange quark suppres-sion factor γs Prob.(s)/Prob.(u or d) thanin most previous studies.The method for the measurement is pre-sented in ref.2. Briefly, e+e− ! hadronsevents are divided into hemispheres us-ing the plane perpendicular to the thrustaxis. Thus an inclusive denition of jetsis used, i.e. a jet is an event hemi-sphere. The single and double tag ratesin the jets are measured, Ni(xmin.p )=Nhad.and Nij(xmin.p )=Nhad., where Ni(xmin.p ) is thenumber of jets in which the highest momen-tum particle has xp > xmin.p and is identiedas +, K+, K0S, p or , and Nij(xmin.p ) isthe analogous quantity for events in which ahadron hi is identied in one hemisphere andhadron a hj is identied in the other.The system of equationsNi(xmin.p )Nhad.= 2∑q=u,d,s,c,biq(xmin.p )RqNij(xmin.p )Nhad.= (2−ij)∑q=u,d,s,c,bij(xmin.p )iq(xmin.p )iq(xmin.p )Rqis then solved, where Rq=ΓZ0!qqΓZ0!hadronsis thepartial decay width of the Z0 to the dierentquark flavors, taken from the standard modelfor q=u, d, s and from LEP for q=c, b, andij are hemisphere correlations due mostly10-210-110.1 0.2 0.3 0.4 0.5 0.6 0.7xcutTagging probability - mesonsOPALdata HERWIGd → pions → pions → kaonu → kaond → kaonFigure 1. Tagging probabilities for pions and kaons asa function of the minimum scaled momentum xmin.p ,in comparison to Monte Carlo predictions.to well understood eects such as geometricacceptance and gluon bremsstrahlung. Theij factors are evaluated using QCD MonteCarlo and are the only MC information en-tering the equations. Their values are typi-cally ij1.01-1.10. To solve the above sys-tem of equations, supplementary informationinvolving assumptions of isospin symmetryand the flavor independence of the strong in-teraction are invoked (see refs.1,2).The measured probabilities iq for i=and K are shown in gure 1 as a function ofxmin.p . From this gure, the so-called leadingparticle eect is clearly visible, i.e. primaryquarks appear primarily as valence quarksin the highest momentum hadrons. Thus dand u quarks appear predominantly in pions,and s quarks in kaons, rather than vice versa.The leading particle eect has been observedmany times for b and c quarks. There isonly one previous study of the eect for lightquarks, given in ref.3.Using the probabilities iq, basic hadron-ization parameters such as the strange quarksuppression factor γs can be determinedu ussK+s suuK+Figure 2. Illustration of the determination of thestrangeness suppression factor γs from the ratio ofthe tagging probabilities for K mesons to be pro-duced either from a primary u quark (top) or primarys quark (bottom).rather directly. For example the probabil-ity factors K±u and K±s dier only by ssor uu pair production from the sea, see g-ure 2. Their ratio thus determines γs. Notethat most other measurements of γs eithercompare the yields of hadrons with dierentmasses, such as kaons and pions, or else relyon the tuning of Monte Carlo parameters.They are thus not as direct as the methoddescribed here which employs kaons only.The result for γs is 0:422  0:049 (stat:) 0:059 (syst:), about one standard deviationhigher than the result in ref.3 based on a sim-ilar technique.2 Experimental properties ofgluon and quark jets from apoint sourceThe inclusive (hemisphere) denition of jetsyields unbiased jets whose properties can becompared directly to the predictions of an-alytic calculations. Inclusive production ofhadrons in e+e− annihilations provides a nat-ural source for unbiased quark jets, used { forexample { in the study described in section 1.One can ask if an analogous sample of highenergy unbiased gluon jets can be identied.The answer, as discussed in ref.4, is yes,by selecting rare events in e+e− annihilationsin which two identied quark jets appear inthe same hemisphere of an event. The oppo-site hemisphere, against which the two quarkjets recoil, approximates an unbiased gluonjet with high accuracy4. Such events havebeen labeled e+e− ! qtagqtaggincl. events todierentiate them from \ordinary" qqg three-jet events dened using a jet nder. Thetagged quark jets qtag and qtag are identiedusing b tagging. The recoiling hemisphere\gincl." is the unbiased gluon jet.Experimental analysis of gincl. jets fromZ0 decays has been presented by OPAL5.Starting from their full LEP-1 data sample ofabout 4 million events, a sample of 439 gincl.jets is isolated with a purity of about 82%.The gincl. jet energy is about 40 GeV. Thegincl. jets are compared to a sample of light(u,d and s) quark jets, also from Z0 decays,dened using the hemisphere denition. Thequark jet sample is resticted to light flavors tobetter approximate the massless quark con-dition employed by analytic calculations.Only one aspect of the results will be pre-sented here, namely the ratio of soft particlesat large transverse momentum p? betweenthe unbiased gluon and quark jets. p? is de-ned with respect to the jet axis. As dis-cussed in ref.6, this ratio provides a directmeasurement of the QCD color factor ratioCA=CF.Figure 3 shows the charged particle mul-tiplicity ratio between the unbiased gluon andquark jets, r, as a function of the softnessof the particles. The softness of the par-ticles is dened by the maximum particlemomentum pmax. considered when determin-ing r. The particles are required to have p?>0.8 GeV/c. Particles with p? < 0.8 GeV/care dominated by the eects of hadronizationas is established using MC. The solid curveshows the prediction of the Herwig MonteCarlo.With no explicit cut on pmax. (\All mo-menta") the multiplicity ratio is predicted tobe about 1.8. As softer and softer particlesare selected (pmax. is decreased), the curveapproaches the QCD result CA=CF=2.25 as11.21.41.61.822.22.42.62.830 2 4 6 8 10 12 14 16 18 20CA/CF = 2.25All momentagincl./uds jetsHerwig 5.9Maximum momentum (GeV/c)(Nch.) gluon/(Nch.) quark,  pT>0.8 GeV/cFigure 3. Ratio r of charged particle multiplicitiesbetween unbiased gluon and quark jets for particleswith large transverse momenta to the jet axis denedby p?> 0.8 GeV/c. The results are shown as a func-tion of the softness of the the particles, dened by themaximum particle momentum used to determine r.predicted in ref.6. OPAL results are shownfor pmax.=2 GeV/c and 4 GeV/c. Theresult using pmax.=4 GeV/c is r=2:29 0:017 (stat: + syst:) which provides one ofthe most accurate current experimental de-terminations of CA=CF. Note that unlikeall other methods, this result is not based ona t of a QCD motivated expression { inwhich CA=CF is extracted as a tted param-eter { but is the ratio of directly measuredquantities.3 Analytic description of multipli-city in gluon and quark jetsAn analytic description of multiplicity in un-biased gluon and quark jets has recentlybeen performed at the next-to-next-to-next-to-leading order (3NLO) in perturbationtheory7. Details of the calculation are pre-sented in refs.7,8. Here some comparisons ofthe results with experiment will be discussed.The currently available measurements ofmean multiplicity in unbiased gluon jets, nG,from the CLEO Collaboration at CESR9 atlow energies and from OPAL gincl. jets5 athigh energy, are shown in gure 4. The051015202530350 20 40 60 80 100 120CLEO Υ(1s)CLEO Υ(3s)OPAL3NLO fitHerwig 5.9 gg eventsScale Q (GeV)Gluon jetsnGFigure 4. Measurements of unbiased gluon jetcharged particle multiplicity in comparison to MonteCarlo and the 3NLO analytic predictions.dashed curve is the prediction of Herwig,which describes the data rather well. Thesolid curve is a t of the 3NLO analyticprediction7 using two free parameters: (1) anoverall normalization K and (2) an eec-tive QCD scale parameter . Translatingthe tted result for  into S(MZ) yieldsS(MZ)=0:14  0:01, not too dierent fromthe world average value S(MZ)0.12 foundusing MS.Measurements of mean multiplicity inunbiased quark jets, nF , performed by manyexperiments, are shown in gure 5. AgainHerwig (dashed curve) describes the datarather well. Making a one parameter t of the3NLO expression for quark jet multiplicity7to the data (solid curve), with  as the t-ted parameter and with the normalizationK xed from the t to the gluon jet data,yields S(MZ)=0:1350:002, not very dier-ent from the result presented above for gluonjets. This demonstrates the consistency ofthe analytic approach to the growth of mul-tiplicity with scale. Note that the inclusive(unbiased) denition of jets is crucial to ob-tain this result. If the quark and gluon jetsare dened using a jet nder such as the k?510152025300 50 100 150 200ARGUSJADETASSOHRSAMYLEP-1LEP-1.5LEP-2Fit Λ to n_F, use K from fit to nGHerwig 5.9 qq eventsScale Q = Ec.m.(GeV)Quark jetsn FFigure 5. Measurements of unbiased quark jetcharged particle multiplicity in comparison to MonteCarlo and the 3NLO analytic predictions.jet nder, such consistency is not observed(see ref.7).One other result will be discussed here,namely the ratio of the slopes of multi-plicity, dened by r(1) =dhnGi=dydhnF i=dy wherey=ln(Q=) with Q the jet energy. The ratioof slopes r(1) has the same asymptotic limitof 2.25 as r, but is predicted7 to have smallerpre-asymptotic corrections. The 3NLO pre-diction for r(1) versus Q is shown in gure 6 incomparison to measurements from OPAL10and the DELPHI11 Collaboration at LEP.The experimental results exhibit some scat-ter because of dierences in the denition ofjets but are in general agreement with theprediction r(1)1.9.4 Substructure dependence ofdijet cross sections inphotoproduction at HERAA recent study from the ZEUS Collabora-tion at HERA concerns the photoproductionof dijets in low Q2 ep scattering12. Speci-cally, the reaction γp! 2 jets + X is stud-ied, where the two-jet system is either qq, gg11.21.41.61.822.22.42.62.830 10 20 30 40 50 60 70 80 90 100DELPHI PLB449 (1999) 383OPAL CERN-EP-2000-070DELPHI prelim. (2000)3NLO predictionRatio of slopes r(1)Scale Q (GeV)Figure 6. The ratio of slopes r(1) between gluon andquark jets in comparison to the 3NLO analytic pre-diction.or qg. Jet shapes (see below) are used to tagsamples enhanced in quark and gluon jets.Measurements are then made of the rapiditydistributions of the jets.Events with at least two jets are se-lected using the longitudinally invariant k?jet nder. Events are retained if they con-tain at least two jets with transverse energyET>14 GeV in the pseudo-rapidity range{1<<2.5, where ={ln(tan(=2)), with the polar angle with respect to the protonbeam direction. The two jets with highestET are analyzed. Specically, the jet prolesand sub-jet multiplicities of these jets are de-termined. The jet prole Ψ(r) is the distribu-tion of the fraction of jet energy inside a coneof half radius r around the jet axis, relativeto a cone with r=1 radians.The mean prole of the selected jets ispresented in gure 7. The data, shown bythe points, are well represented by the MonteCarlo, indicated by the solid line. The indi-vidual contributions of gluon and quark jetsas predicted by the simulation are shown bythe dashed and dash-dotted curves, respec-tively. The proles of the gluon and quarkjets are seen to dier substantially. In par-Figure 7. Jet prole of the two highest energy jets inγp→ 2 jets + X events.ticular, gluon jets are predicted to be muchless collimated around the jet axis than quarkjets, a fact that has been well established ex-perimentally in e+e− collisions13.Choosing a cone size r=0.3 radians,quark and gluon jet dominated samplesare selected by requiring Ψ(r=0.3)>0.8 orΨ(r=0.3)<0.6, respectively. The resultingsamples are denoted \thin" jets and \thick"jets and have quark and gluon jet purities ofabout 85% and 60%, again respectively. Therapidity distributions of \thin" and \thick"jets are shown in gure 8 by the open andsolid points. The curves show the MonteCarlo predictions for quark and gluon jets inγp collisions. Gluon jets are produced mostlythrough resolved processes, in which the pho-ton in the γp collision acts as a source of par-tons. In contrast, quark jets are producedmostly through direct processes in which thephoton couples directly to partons in the pro-ton. This explains the dierent rapidity dis-tributions predicted for gluon and quark jets.The \thick" and \thin" jet measurements areseen to follow the predictions for gluon andquark jets quite well, demonstrating a suc-cessful separation and test of the cross sec-tions for gluon and quark jets individually.Figure 8. Rapidity distribution of \thick" and \thin"jets in comparison to the Monte Carlo predictions forgluon and quark jets in γp collisions.5 0, , K0 and charged particlemultiplicities in quark and gluonjetsLast, I discuss a recent study from OPAL10on dierences in the production rates of iden-tied particles in gluon and quark jets.QCD predicts that rh { the ratio of themean multiplicities of identied hadrons be-tween gluon and quark jets { is the same forall hadrons h. In practice, rh might dier fordierent particles because of the decay prop-erties of hadrons or because of dynamical dif-ferences between the hadronization of gluonsand quarks. For example, the gluon octetmodel of Peterson and Walsh14 predicts rhto be larger for isoscalar particles than fornon-isoscalars, e.g. an enhancement in rh for mesons compared to charged particles. Sofar, studies at LEP of identied particles ingluon jets have either considered (1) +, K+,p, K0S and  production (or c.c.) in identiedsamples of gluon and quark jets15, leadingto experimental determinations of rh, or else(2) the production of 0, , 0, K0S and  (orc.c.) in the lowest energy jet of e+e− three-jet events in comparison to the correspond-ing result for charged particles or to MonteCarlo predictions16,17,18. The OPAL studydiscussed here is the rst to employ the for-mer strategy for 0 and  mesons, i.e. therst to determine rh for 0 and .Three-jet events are selected using thek?, cone, or LUCLUS jet nders: thedierence in the results denes a system-atic uncertainty related to the jet deni-tion. The jets are ordered such that jet 1has the highest energy and jet 3 the low-est. The jet energy species the gluon jetcontent of the jet. The jets are then ex-amined in terms of the so-called hardnessscale19 Qjet=Ejet sin(min.=2), where min. isthe smaller of the angles with respect tothe two other jets. The hardness scale hasbeen shown11 to be a much more appropriatescale than the jet energy Ejet when compar-ing jets embedded in a three-jet environment,i.e. when comparing biased jets, as opposedto the unbiased jets discussed in sections 1-3.The 0, , K0S and charged particle ratesin jets 2 and 3 are compared in their over-lap region, dened by 7<Qjet<30 GeV. Themultiplicity measurements are unfolded alge-braically using the known quark and gluon jetcontent of jets 2 and 3 to obtain results corre-sponding to pure gluon and quark jets. Theresults for rh for 0,  and K0S are then di-vided by the corresponding result for chargedparticles to obtain:rη=rch. = 1:09 0:12rpi0=rch. = 1:01 0:04rK0s =rch. = 0:95 0:04All three results are consistent with unity, in-dicating no evidence for a dynamical dier-ence in the hadronization of gluon and quarkjets. This conclusion is in agreement with re-cent results from the ALEPH Collaborationat LEP18. The OPAL and ALEPH results for mesons contradict the conclusion of an ear-lier study17 by the L3 Collaboration at LEP,in which evidence for a dynamical enhance-ment of  mesons in gluon jets was reported.References1. OPAL Collab., G. Abbiendi et al.,CERN-EP/99-164.2. J. Letts and P. Ma¨ttig, Z. Phys. C 73,217 (1997).3. SLD Collab., K. Abe et al., Phys. Rev.Lett. 78, 3442 (1997).4. J.W. Gary, Phys. Rev. D 49, 4503(1994).5. OPAL Collab., G. Alexander et al.,Phys. Lett. B 388, 659 (1996); OPALCollab., K. Ackersta et al., Eur. Phys.J. C 1, 479 (1998); OPAL Collab., G.Abbiendi et al., Eur. Phys. J. C 11,217 (1999).6. V. Khoze, S. Lupia and W. Ochs, Eur.Phys. J. C 5, 77 (1998).7. I.M. Dremin and J.W. Gary, Phys. Lett.B B459, 341 (1999); I.M. Dremin andJ.W. Gary, hep-ph/0004215; A. Capellaet al., Phys. Rev. D 61, 074009 (2000).8. I.M. Dremin and J. Tran Thanh Van,hep-ph/0008054.9. CLEO Collab., M.S. Alam et al., Phys.Rev. D 46, 4822 (1992); CLEO Collab.,M.S. Alam et al., Phys. Rev. D 56, 17(1997).10. OPAL Collab., G. Abbiendi et al.,CERN-EP-2000-070.11. DELPHI Collab., P. Abreu et al., Phys.Lett. B 449, 383 (1999); DELPHI Col-lab., CERN-OPEN-2000-134.12. ZEUS Collab., Contribution #906 toICHEP 2000.13. OPAL Collab., P.D. Acton et al., Z.Phys. C 58, 387 (1993).14. C. Peterson and T.F. Walsh, Phys. Lett.B B91, 455 (1980).15. DELPHI Collab., P. Abreu et al., Phys.Lett. B B401, 118 (1997); OPAL Col-lab., K. Ackersta et al., Eur. Phys. J.C 8, 241 (1999); DELPHI Collab., P.Abreu et al., CERN-EP-2000-007.16. L3 Collab., M. Acciarri et al., Phys.Lett. B 407, 389 (1997).17. L3 Collab., M. Acciarri et al., Phys.Lett. B 371, 126 (1996).18. ALEPH Collab., R. Barate et al.,CERN-EP/99-105.19. Yu. Dokshitzer et al., Basics of pertur-bative QCD, Editions Frontieres (1991).

Jet Structure Studies at LEP and HERA

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Jet Structure Studies at LEP and HERA

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