Vitale, L

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Laboratori Nazionali di Frascati OCR OutputSIS - Pubblicaxiouiand q/g Jets at LepScaling Violations, Fragmentation FunctionsLorenzo Vitale>u/1) QCO9 Ottobre 1996 ui1NFN/AE-96/31 npSezione di TriesteISTITUTO NAZIONALE DI FISICA NUCLEAREQa,(Q) the running coupling constant of QCD. short distance regime is perturbatively calculable OCR Outputincreasing energy and the energy dependence of tance regime of the hadronization process. Theergy Q due to the increasing phase space with hard gluons can be radiated and the long disdepends logarithmically on the centre of mass en regimes: the short distance regime, in whichtum ChromoDynami<:s (QCD). Gluon radiation The cross section can be factorized into twothe field theory of the strong interactions, Quan energy squared.pairs which can radiate gluons, the quanta of annihilation Q2 equals s, the total centre of massinates from the production of quark-antiquark mentum Pbmm carried by the hadron h. In e+eHadron production in e+e‘ annihilation orig z : Ph/Pbwm is the fraction of the beam motransferred from the leptons to the hadrons andhilation is defined as the square of the four-momentum1 cx, from Scaling Violation in e'*'e‘ Anni by two kinematic variables, Q2 and x, where Q2in the reaction e+e" —-> h + X can be describedThe inclusive production of charged hadronsmeasured by OPAL with a new techniquegram by Nason and Webbertio between gluon and quark jets at 39 GeV asSection 3 describes the mean multiplicity ra DGLAP evolution equationss employing the prousing a numerical integration of the second ordertified gluon jets 2 is presented in section 2.data on gluon and heavy quark fragmentation andA first observation of scaling violation in idenanalysis extends the previous by including newfunctions (scaling violation).relatively small number of free parameters. Thisenergy dependence of the hadronic fragmentationand string or independent fragmentation, with athe strong coupling constant is extracted from thebased on the exact second order matrix-elementIn the first 1, described in section 1, a value forDELPHl’s previous analysis of this type4 wasthe third by OPAL.violations can be used to determine oi,.decays. The first two are performed by DELPHI,momenta are scaled to that energy. These scalingtification of quark and gluon jets in Z hadronicfunction of the centre of mass energy, even if theThree analysis are presented, all based on the idenmomentum spectra of the produced hadrons as aIntroduction These effects lead to logarithmic variations of ther = 1.552 :l: 0.D41(stat) ;h 0.060(syst) and is only weakly dependent of a jet definition.identified b quark jets and it is applied to a sample of data collected by the OPAL detector. The result isThis technique is based on rare hadronic Z decays in which a high energetic gluon jet recoils against the twousing a new technique to define the jet multiplicity; which is closer to the one used in the theoretical calculations.QCD analytical predictions for the mean multiplicity ratio between gluon and quark jets have been tested byjet at large hadron energy has been found to be 2.8 ;l; 0.8(stat), consistent with the colour factor ratio CA /Cp.within the same detector. The ratio of the energy dependence of the fragmentation functions in gluon to quarkScaling violation has also been observed for the Hrst time in identined gluon jets measured at diHerent energies¤,(MZ) = 0.124fg;gg$ (exp) :i: U.009(the0ry), where the theory error is mainly due to the scale dependence.constant, by means of a numerical integration of the second order DGLAP evolution equations. The result isenergies down to 14 GeV. The large scaling violation observed has been used to extract the strong couplingDELPHI detector at Z energy and have been compared with the fragmentation functions measured at lowerThe hadronic fragmentation functions of the various quark flavors and gluons have been measured with theprecise measurements and quantitative tests of the QCD predictions.The recent progress in the identiHcati0n of quark and gluon jets in Z hadronic decays has allowed a. new set ofemail: vitale@t1·ieste.infn.itINFN, Area di Ricerca, Padricmno 99, 34012 Trieste, ItalyDELPHI speaker, for DELPHI and OPALLorenzo VITALEOCR OutputSCALING VIOLATIONS, FRAGMENTATION FUNCTIONS AND q/g JETS AT LEPcan be fitted to experimental data using equation scribed in detail in 1* and the results have been OCR Outputthe fragmentation functions at a given energy QU has been measured. This technique has been demj = Ph/Pjet of the charged particles in the jetto—leading order in perturbation theory 7. Thusthese gluon jets the fraction of the jet momentumparent parton j. The Pgj (z) are known to nextjets have been identified with a purity of 94%. Forwith momentum fraction z after splitting from itsvariable exceeded 0.1. A total of 6791 gluonHj (z) are the probabilities for finding parton itiquarks and the gluon. The splitting functions taken as a gluon jet if the value of its probabilityby requiring < 0.01 and the remaining jet wasThe indices i and j run over all active quarks, an3-jet events. Both bottom quark jets were taggedmined from tagged gluon jets in b—quark induced2 (W) a$”<z.a>+0<¤?>. (3) The gluon fragmentation function was deterHj(z.¤i(1;n).%) = ·'%»¥K(¤)+;i(l $°) events.charm events, 18% light and 32% bottom-quarkwith the splitting functionsquarks. The resulting sample consists of 50%parts of the D-mesons originating from bottomI ZJ; €i·Pu(Z»¤¤(#R)· %%) D¢(5»Q2)quiring 0.005 < P < 0.015, which suppresses(2)d ln Q2dD1·!1:,Q2! __ richment in charm quarks was achieved by recandidates have been selected. An additional enwritten as:were reconstructed as described in 10. 2580 D*differential evolution equations 5, which can betermined by the following method: D*+-mesonsfunction is described by the coupled integroThe c-quark fragmentation function was deThe scaling violation in the fragmentationand 7% bottom quark events.been taken to be the same.of 357,000 events containing 79% light, 14% charmization scale pp; for simplicity, the two scales havethe interaction point which resulted in a samplein (1) could be chosen differently from the factorprobability that all charged particles come fromprinciple the renormalization scale pg used for 0,light quark sample, using a cut of P > 0.5 for theried out to all orders in perturbation theory. InThe same method has been used to obtain aon up would cancel if the calculation could be carused is described in detail ingthat the dependence of the physical cross sectionwith a purity of 83% is obtained. The techniquean arbitrary factorization scale pp, in such a wayBy requiring P < 0.01 a sample of 217,000 eventscoefficient and fragmentation functions depend oncome from the primary interaction point is small.to the primary quark pair production. Both theputed probability P for all the decay products toresents the next—to-leading order QCD correctionsand their large mass and momentum, the comtroweak theory and the a, dependence of C; rephadrons. Due to the long lifetime of B—hadronsgiven _by the flavour specific weights of the elecimpact parameter for the decay products of Bmentum fraction rc / z. In leading order the C; aretation were selected with the help of the largethis parton fragments into the hadron h with moHadrons coming from bottom quark fragmention function D; represents the probability that3-jet events.fraction z : Pp,,t0,,/Pbmm, while the fragmentacles from gluon fragmentation was obtained fromation of a parton with Havour i and momentumscaled momentum distribution for charged partiwhere C; are the c0eiHcient functions for the creeach quark flavour separately. In addition, thedetermine the scaled momentum distributions fortom, charm and light (uds) quarks were used toci<z,¤,<»R>, Q%> vi<§,~%> uiy *‘U 1 % = Z) €§ 1993 have been used. Samples enriched in botsion for the cross section with the DELPHI detector 8 in the years 1991 toIn the analysis presented here data collectedfactorization theorem yields the following expresCombining the two regimes according to the different centre-of-mass energies.ous fit of these calculated spectra to the data atfunctions.constant can then be extracted from a simultaneparametrized by phenomenological fragmentationthe non-calculable long distance regime has to be the evolution equations The strong couplingin terms ofthe so-called c0efHcient functions, while (1) and then evolved to a different energy usingb-quarks and gluons; Qu is the “starting energy" expects a scale dependence of at most O(o1,3). The OCR Outputa resummation of the leading logs. Therefore oneto take different values for light (uds) quarks, c-,where the coemcients Nba; and bg were assumed ing violation is only known up to order 01,2 withand the factorization scale 11 F. However, the scalLia dx z“i(1-:)*5 exp(—·cln°z) dependence of cx, on the renormalization scale pg0 ¤:°ig1—::l°i expg—c1n°a:l (4) If all higher orders are known one expects no¢D¢(¢1Q0l Zsection for various 17 bins and results of the fit.12 was used: Figure 2: Q2 dependence of the inclusive momentum crossIn our analysis the parametrization from Ref.pendent on cx,.10" 1D` QZ(g>c;]Z)mentum spectra at different energies are only deenergies, so that the differences between the moand these parameters have to be the same at allx=0.5-0.7needed at one energy where the evolution starts ii;parametrization of the fragmentation functions isl`°`*1 x=0.4—0.5lution (equation is known. Therefore ax=D.3—0.4rived in perturbative QCD. Only the energy evoThe fragmentation functions cannot be dex=0.2—0.3CELLO 35 GeV4, MARK H 29 GeV 1AMY 54 sev 14, TAsso 44, 35, 22, 14 Gev 15,x =0.l - 0.2ments; DELPH1 91 Gev4, ALEPH 91 sev lm,mixed—fia.vou1· spectra from the following experiTo extract the scaling violation, we used allS A AMY ae Maximg I * Auzru I CELLOFigure 1: Corrected xp distributions and results of the fit.g [ • 1>1zu>1-n v rasso 14223544Q10¤¤,,=r·m..../1>0 0.1 0,2 0.a 0.4 0.s 0.6 0.1 0.s 0.0 1shown in fig.2.dom of the fit was 174.5/175 and the fit results areof the data listed above. The X2 per degree of freeincluding 1% were fitted to the 13 distributions142 < Q2 < 91.22 GeV2 a total of 14 parameterssurements. In the range 0.10 < z < 0.80 andthe N by N covariance matrix between N meaio`1(2) by numerical integration 6. The matrix V iswhich can be computed from equations (1) andin a given Z bin and the theoretical predictionuals between the inclusive momentum spectrumU gluons Here A is a column vector containing the residA b—evems (5)X2 = AT1/-1n._3; k 5 I0 °<5 ‘ O uds-events .l¤E|.1=·H| the following X2 function:Q10N; , b, and c defined in (4) was made by minimizingcorrected :1: distributions are plotted in fig.1. scale 11% and the fragmentation parameters ai,the following way. A simultaneous fit of the QCDtailed Monte Carlo simulation ofthe detector. TheThe strong coupling constant was extracted infactors for each bin of the distributions from a. deApproximation (MLLA).cuts have been corrected by computing correctiontial term is inspired by the Modified Leading-LogDetector effects and the effects of selectionwhich was taken to be 91.2 GeV. The exponenfunctions at the two jet energies are showed for OCR Output(the technique is described in detail in 11).3 millions hadronic Z decays collected by DELPHI In fig.6b the ratios Sig of the fragmentationusing Y and Mercedes events (fig.4) in a sample ofof about 23 and 30 GeV have been measured by Figure 5; Sq_g ratioshadrons for quark and gluon jets at jet energiesScaled momentum distributions of charged¤ su 1:.2 M °* °5 M Q7 0 1Figure 4: Y and Mercedes events topologies.Yevcnm MemedeseveuxsmzJet2 F •1>•¤ sr l ° S/S. I — yuan D E l,I‘H!( ‘a l iJai / ami / °¤ , ..... r .... g ¤»· "¤v$‘¤"i`¢‘»¢¢ l; JM3 Jme ·as • SG E1: ° s• "DFI PHI__ 452 Scaling Violation in Gluou Jetsi . rg-.1;·¥Y1"l `iii {»i»#+• 0 I; gtions 17 and with a similar analysis of ALEPH 1which is in agreement with other rr, determina ;;>,¤“.g 0* id¤,(MZ) Z 0.124i3·_?,g$(wp) 4; 0.009(¢hw»·y) (6)above.metrizing the dominant theoretical error yields:partonic processes is indeed the hardness definedCombining the errors in quadrature and symthe theoretical presumption that the scale of thebetween 142 and 292 GeV2 tum E'2,3 ·sin 62,3, 0 defined in fig.4), supportingout by changing the lowest Q2- value in the tit ilar hardness (largest possible transverse momenfor non-perturbative corrections has been carriedall events at centre of mass energies 1*15 of simthe range O.5\/E < u < 2X/E. An additional checkare in good agreement with those measured frommated as half the maximum variation for scales in These fragmentation function, showed in fig.5,tion and factorization scale uncertainty was estiThe theoretical error due to the renormalizaresult, which is shown in fig.3 too. Figure 5: Scaled momentum distributions.n uingly, it did not decrease with respect to the OM?)scale dependence of a, is shown in Hg.3. Surpris i I .254.Figure 3: Rcnormalization scale dependence of aa.wavem |. ·:¤v¤um “·m*a**a%·—1¢-ra·*·1··—rJ*s~·rr·r%:···:0.11 "`m1AX¢Bl.R_·lIGV h :i;:£.$._¤UGV·¤J&Vg L ;$I?Tgl E _°¤U_ I>ELPI·llE °°mj_ Bl·ZLl’S·lIY¤¤v·¤¤-»sy M¤=·=¤¤¤v=·\¤s»than 1.5 and the maximum scaled momentum of HERWIG and J ETSET models, and of the analytOCR Outputimpact parameter normalized by its error bigger shown in fig.9 together with the predictions oftagged as uds hemisphere if the are no tracks withrch : 1.552 :|: 0.041(stat) zi: 0060(syst) (10)opposite to identified uds jets. A hemisphere isthe charged particles observed in the hemisphere Finally the ratio obtained is:The uds quark jets are defined inclusively by using 9.43 i 0.06 ;l: 0.22.termined to be 39.2 1 0.3(siat) :h 1.8(syst) GeV. analytical prediction 19, yielding (nd, ),,d, (39.2) :mated purity. The mean gluon jet energy is de been evolved to 39.2 GeV by employing the QCDgluon jets are selected, with (83.0 ;|: 1.7)% esti gluon and uds jet multiplicities, (nc;,)ud, (45.6) hasOPAL from 1991 , to 1994. In total 278 gmc; samples, before forming the ratio rch between theof about 3,044,000 hadronic events collected by To account for the different energies of the twoThe present analysis is based on a sample dashed lines respectively.sphere. and JETSET models are visible as the solid andof all the particles observed in the opposite hemijets compared to predictions of HERWIG and JETSET.taken to be the gluon jet, is defined by the sumFigure 8: Charged particle multiplicity for gluon and udsthe thrust axis of the event. The quantity gmcy,hemisphere defined by the plane perpendicular toidentified b quark jets which appear in the sametype e"”e` —+ qigmd in which the q and Q are(ci r:__-snow_ _Figure 7: Topology of studied events. izgig <(b E__·91.zc.vin has:-:, r_-sucev(<¤_>:: u»••¤'h•¤•, <·.>.....Q®¢V .quarkjetbminus ........ . ........... 9.]gu l' 0*) < na >¤u¤¤ngluon jet hemisphere0 Jam12.quark jeta 4} ner-ws s§ om;.culations. It is based on rare events (fig.?) of the14.inition, similar to that used for the analytical calgluon jets are identified by using an inclusive def(u)<nd` >“d_new method, proposed in Ref. 18. In this methodand gluon jets has been studied by OPAL with aThe diiierence between the multiplicity of quark in fig.8, where also the predictions of HERWIGond the systematical. The results are showedand Gluon Jetwhere the first error is the statistical and the sec3 Multiplicity Difference between Quark(ncp,)ud, (45.6) = 10.05 :h 0.04 zi: 0.23, (9)CA /C;:· = 9/4.which is consistent with the colour factor ratioare obtained:ground the following mean charged multiplicities(7)2.8 ;i; 0.8(stat),response, initial-state photon radiation and backof simulated events. After correcting for detectorwhich averaged for z > 0.2 yieldsand uds selections are estimated from a sampleting probability. Fig.6c shows the ratio Sg/Sq,mated purity of (93.2 ;l; 0.2)%. 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Scaling violations, fragmentation functions and q/g jets at LEP

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