DELPHI Collaboration DELPHI 2001- 065 CONF 4936 June 2001QCD Results from the DELPHI Measurements ofEvent Shape and Inclusive Particle Distributions atthe highest LEP energiesO. Passon1, J.Drees1, U.Flagmeyer1, K.Hamacher1, R.Reinhardt1 andD.Wicke21 Fachbereich Physik, Bergische Universit�at-GH WuppertalGau�stra�e 20, 42097 Wuppertal, Germany2 CERN, CH{1211 Geneva 23, Switzerland

AbstractInclusive spectra and infrared and collinear safe event shape distributions are de-termined from the data taken in 2000 at centre of mass energies between 200GeVand 208GeV . From the event shapes, the strong coupling �s is extracted in O(�2s)and in NLLA. Comparing these measurements to those obtained at and aroundMZand other LEP2 data, the energy dependency (running) of �s is accessible.Conference contribution for EPS HEP, 12{18 July 2001, Budapest, Hungaryand Lepton Photon 01 23{28 July, Rome, Italy

1 IntroductionIn 2000 LEP operated at centre of mass energies between 200 and 209GeV. This notepresents preliminary results on the measurements of event shape distributions and inclu-sive particle spectra at these energies. From the hadronic event shapes �s is extracted.Together with the results from previous measurements[1, 2] at other LEP2 energies andLEP1 data a test of energy dependencies as predicted by QCD, namely the running of �sand the energy evolution of ��, the maximum of the �p = log 1xp distribution , is performed.In section 2 the selection of hadronic events, the determination of the centre of massenergy, the correction procedures applied to the data, and for energies above the WWthreshold the suppression of W+W� events are brie y discussed. Section 3 contains themeasurement of the inclusive hadronic spectra. The energy dependence of �� is discussed.Section 4 presents event shapes and the comparison of the data with predictions from q�q-based hadronic generators. Measurements of �s using various techniques and the runningof �s, as determined using di�erent methods, are presented in section 4.2 Selection and correction of hadronic dataThe analysis is based on data taken with the DELPHI detector in the year 2000 at centreof mass energies between 200GeV and 209 GeV. The data can be reasonably split intotwo di�erent energy regimes, corresponding to a mean energy of 204.9 and 206.8GeVrespectively. In the following these data sets are denoted as 205 and 207GeV.The integrated luminosities and cross sections are given in table Table 1.DELPHI is a hermetic detector with a solenoidal magnetic �eld of 1.2T. The trackingdetectors, situated in front of the electro-magnetic calorimeters are a silicon micro-vertexdetector VD, a combined jet/proportional chamber inner detector ID, a time projectionchamber TPC as the major tracking device, and the streamer tube detector OD in thebarrel region. The forward region is covered by silicon mini-strip and pixel detectors(VFT) and by the drift chamber detectors FCA and FCB.The electromagnetic calorimeters are the high density projection chamber HPC in thebarrel, and the lead-glass calorimeter FEMC in the forward region. Detailed informationabout the design and performance of DELPHI can be found in [3, 4].In order to select well measured charged particle tracks, the cuts given in the upperEcm 205GeV 207GeVL 75:24 pb�1 131:50 pb�1�q�q 81:04 pb 79:49 pb�q�q (ps0>0:9ps) 17:40 pb 17:07 pb�WW 18:89 pb 18:93 pbNumber of events 1003 1699Table 1: Total cross sections �q�q and �WW as used in the simulation, high energy crosssections �q�q (ps0>0:9ps) as derived from the MC, integrated luminosities L, and �nallyselected (non-radiative) hadronic QCD events for the two energies.1

Track 0:2GeV � p � 100GeVselection �p=p � 1:0measured track length � 30 cmdistance to I.P in r� plane � 4 cmdistance to I.P. in z � 10 cmEvent Ncharged � 7selection 25� � �Thrust � 155�Etot � 0:50EcmISR rejection ps0rec � 90%EcmWW rejection Ncharged > 500Bmin + 1:5Ncharged � 42Table 2: Selection of tracks and events. p is the momentum, �p its error, r the radialdistance to the beam-axis, z the distance to the beam interaction point (I.P.) along thebeam-axis, � the azimuthal angle, Ncharged the number of charged particles, �Thrust thepolar angle of the thrust axis with respect to the beam, Etot the total energy carried bycharged and neutral particles, ps0rec the reconstructed centre of mass energy, Ecm = psthe nominal centre of mass energy, and Bmin is the minimal jet broadening. The �rst twocuts apply to charged and neutral particles, while the other track selection cuts applyonly to charged particles.part of Table 2 have been applied. The cuts in the lower part of the table are used toselect e+e� ! Z= ! q�q events and to suppress background processes such as two-photoninteractions, beam-gas and beam-wall interactions, leptonic �nal states and initial stateradiation (ISR) and WW pair production.At energies above 91.2GeV, the high cross section of the Z resonance peak raises thepossibility of hard ISR allowing the creation of a nearly on-shell Z boson. These \radiativereturn events" constitute a large fraction of all hadronic events. The initial state photonsare typically aligned along the beam direction and are rarely identi�ed inside the detector.In order to evaluate the e�ective hadronic centre of mass energy of an event, consideringISR, an algorithm called Sprime+ is used [5]. Sprime+ is based on a �t imposingfour-momentum conservation to measured jet four-momenta (including estimates of theirerrors). Several assumptions about the event topology are tested. The decision is takenaccording to the �2 obtained from the constrained �ts with di�erent topologies.Figure 1(left) shows the spectra of the calculated energies for simulated and measuredevents at 205GeV. The agreement between data and simulation is very good for the highenergies relevant to this analysis, while the peak around MZ appears to be slightly shiftedin the simulation. A cut on the reconstructed centre of mass energy ps0rec � 90%Ecmis applied to discard radiative return events (see Table 2). Simulation shows that thiscut keeps more than 96% of the events without ISR (ps � ps0 < 0:1GeV), giving acontamination with events having ps�ps0 > 10GeV of less than 15%.Two photon events are strongly suppressed by the cuts. Leptonic background wasfound to be negligible in this analysis. 2

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Figure 1: Left: Reconstructed centre of mass energy ECM = ps0. Right: Simulation offour fermion background and QCD events in the Ncharged{Bmin plane. The lines indicatethe cut values chosen.Since the topological signatures of QCD four jet events and hadronic WW events (andother four fermion (4F) backgrounds) are similar, no highly e�cient separation of the twoclasses of events is possible. Furthermore any WW rejection implies a severe bias to theshape distributions of QCD events, which needs to be corrected by MC simulation. Byapplying a cut on an observable calculated from the narrow event hemisphere only, thebias to event shape observables mainly sensitive to the wide event hemisphere is reduced.Having used this kinematic information there is essentially only one observable left, whichcan help to reduce the 4F background further. This is the charged multiplcity. The twodimensional cut in the Ncharged{Bmin plane exploits the di�erent correlation between thisobservable in QCD and four fermion events, as shown in Figure 1 (right). Especially somefurther discriminative power against semileptonic decaying 4F events is gained. The linesindicate the cut values chosen. By this cut almost 90% of the four fermion background canbe suppressed. The remaining WW contribution is estimated by Monte Carlo generatorsand subtracted from the measurement. The simulations are normalised using the crosssections given in Table 1.The remaining detector and cut e�ects are unfolded using simulations. The in uenceof detector e�ects was studied by passing generated events (Jetset/Pythia [6] usingthe DELPHI tuning described in [7]) through a full detector simulation (Delsim [3]).These Monte Carlo events are processed with the reconstruction program and selectioncuts as are the real data. In order to correct for cuts, detector, and ISR e�ects a bin bybin acceptance correction C, obtained from e+e� ! Z= ! q�q simulation, is applied tothe data: Ci = h(fi)gen;noISRh(fi)acc (1)3

where h(fi)gen;noISR represents bin i of the shape distribution f generated with the tunedgenerator. The subscript noISR indicates that only events without relevant ISR (ps �ps0 < 0:1GeV) enter the distribution. h(fi)acc represents the accepted distribution f asobtained with the full detector simulation.3 Inclusive SpectraInclusive stable hadron spectra are highly sensitive to properties of the hadronizationprocess and to resonance decays as well as to details of the parton shower. Here theydepend on the amount of large angle and collinear gluon radiation as well as on thecoherence of gluon radiation. These measurements therefore provide rigid constraints tothe models of the hadronization process.Direct comparisons of QCD calculations su�er from the dependence of inclusive distri-butions to infrared and collinear divergencies. Studies of the energy evolution of inclusivespectra here provide a new quality because the divergent terms may be factorized outand the energy dependence then can be more directly compared to perturbative QCDpredictions.A comprehensive comparision of inclusive distributions with model expectations ispresented as a function of the particle momentum p, the logarithm of the scaled hadronmomentum �p = ln(1=xp) (with xp = p=pbeam), the rapidity with respect to the Thrustaxis yt = 12 ln E+pkE�pk as well as the transverse momenta (pint , poutt ) with respect to thethrust-axes. p and E are the particle momenta and energies respectively. The energieshave been computed assuming the charged particles to be pions. Systematic errors havebeen estimated similar as in [2].Figure 2 shows the �p, yt, pint and poutt spectra as determined from the 205 GeV data .The data are compared to the JETSET, HERWIG and ARIADNE fragmentation modelsas tuned by DELPHI at Z energy. The shaded areas display the size of the WW and ZZbackground which was subtracted from the data. The upper inset in these plots indicatesthe size of the correction factor applied to the data. The lower inset presents the ratio ofthe high energy data to the corresponding results at the Z. This ratio is again comparedto the model predictions.The models describe all inclusive spectra measured at the highest energies very good,as well as the energy evolution from the Z-peak (see lower inset of Fig. 2). The mostprominent change in the �p distribution (Fig. 2a) is an increase at large �p (i.e. low xp).In the rapidity distribution (Fig. 2b) the expected shift of the edge of the distribution tohigher values can clearly be observed, as well as a slight increase in the plateau. Thischange likewise the strong increase in the transverse momentum distributions at large p?(Fig. 2c and d) is due to stronger gluon radiation in the high energy events.MLLA provides a de�nite prediction for the evolution of the maximum, ��, of the�p distribution with energy. As hadronization and resonance decays are expected to actsimilarly at di�erent centre of mass energies, the energy evolution of �� is expected to beinsensitive to non-perturbative e�ects. A small correction is to be expected, however, dueto varying contribution of heavy quark events. These chain decays are known to shift ��di�erent from ordinary resonance decays. This shift also di�ers for the individual stableparticle species due to the di�erent masses. So far in this note the in uence of heavydecays is neglected. 4

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Figure 3: Energy evolution of the �p peak position. The �e� value has been obtainedfrom a �t of the MLLA/LPHD prediction (2). The phase space prediction is described inthe text.The �� values who enter this analysis were determined by �tting the Fong{Webberparametrisation [8]. The �p range �tted was restricted to the part of the distribution closeto the maximum where the distribution value was bigger than 60% of the maximum. Toavoid systematic di�erences due to di�erent strategies to determine �� the same prodedurehas also been performed for the low energy data [9, 10].One obtains ��(205GeV) = 4.273 � 0.050 and ��(207GeV) = 4.277 � 0.040, wherethe statistical and systematic errors are added in quadrature. The full line in Fig. 3 is a�t of the MLLA expectation�� = 0:5 � Y +pC � pY � C +O(Y � 32 ) (2)to the data.Here Y = ln(Ebeam=�e�) and �e� is an e�ective scale parameter. From this �t �e� =200� 3MeV. The quantity C depends weakly on the number of active avours ( C(Nf =3) = 0:2915, C(Nf = 5) = 0:3513). The results are presented for Nf = 3 since thelight quarks dominate quark-pair production in the cascade. The dashed line in Fig. 3represents the slope of the phase space expectation �� = a + Y . Due to angular orderingof gluon bremsstrahlung the rise in �� is slower in the MLLA prediction than in thisscenario. The data clearly prefer the MLLA prediction, although the �� values above200GeV overshoot the full line. The �2=ndf of 1:3 is still reasonable.6

4 Event shape distributionsSelected event shape distributions at 205 and 207GeV are shown in Figure 4. The exactde�nitions of the observables used are comprehensively collected in Appendix A of [7].The data in Figures 4 are corrected to be comparable with pure e+e� ! Z= ! q�qsimulation of charged and neutral hadron production. The amount of WW-backgroundthat was subtracted to obtain the �nal data points is given as a histogram line. Theacceptance corrections are plotted in the upper inset. The plots show a fair agreementbetween the data and Monte Carlo models.5 Determination of �sfrom event shapesFrom event shape distributions, �s is determined by �tting an �s dependent QCD predic-tion folded with a hadronisation correction to the data. As QCD predictions O(�2s), pureNLLA, and the combined O(�2s)+NLLA in lnR-scheme are employed [11, 12, 13]. Thehadronisation correction is calculated using the Jetset PS model (Version 7.4 as tunedby DELPHI [7]). The QCD prediction is multiplied in each bin by the hadronisationcorrection Chad(Ecm) = fSim:had (Ecm)fSim:part (Ecm) , (3)where fSim:had (Ecm) (fSim:part (Ecm)) is the model prediction on hadron (parton) level at thecentre of mass energy Ecm. The parton level is de�ned as the �nal state of the partonshower created by the simulation.The �t ranges used for the di�erent QCD predictions are shown in Figure 5. Theupper limit of the range used for O(�2s)+NLLA is reduced with respect to previous pub-lications [14, 15] in order to reduce the systematic uncertainties due to WW background.The lower limit is chosen such that the �2=ndf for the QCD �t was reasonable at LEP2energies, while maintaining the results at the Z-peak stable. The ranges for pure NLLAand O(�2s) �ts are chosen to be distinct, so that the results are statistically uncorrelated.Their limit is taken from [16], where the size of hadronisation correction, the size of theB-coe�cient, and the stability under �t range changes is considered.In [16] it has been shown that �xing the renormalisation scale to �2 = E2cm resultsin a marginal description of the data. Therefore, the experimentally optimised scalesx� = �2=E2cm are determined from the LEP1 data and are used for the O(�2s) �ts to thehigh energy data for both observables individually. In contrast to the NLLA and thecombined NLLA+O(�2s) �ts, � is set equal to Ecm, so that these results can be comparedto other experiments more directly.The scale errors are calculated by varying x� from 0.25 to 4. An error from thein uence of the used hadronisation model is estimated by calculating Chad with Jetsetand Ariadne. The resulting two values of �s are averaged to get the central value, halfof their di�erence is added in quadrature to the systematic error.The �s values evaluated from the distributions are given in Table 4 and plotted inFigure 6. The QCD expectation is in fair agreement with the data7

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Theory used for measurement d��1s =d log(Ecm)O(�2s) 1:07� 0:16� 0:19NLLA 1:55� 0:17� 0:27O(�2s)+NLLA (lnR-scheme) 1:35� 0:12� 0:18QCD expectation 1:27QCD+Gluinos expectation 0:90Table 3: Results for the slope a when �tting the function 1=(a lnps + b) to �s valuesobtained for the di�erent energies. The theoretical expectation is calculated in 2nd order.5.1 The running of �sThe determination of �s at di�erent energies allows to test the predicted scale dependenceof the coupling due to higher order e�ects. The logarithmic energy slope is given by:d��1sd lnps = 2b0(1 + b1�s + � � �) (4)Thus in leading order this quantity is independent of �s and ps, and twice the coe�cientb0 of the QCD � function (2b0 = 1:22). Evaluating this equation in second order givesa slight dependence on �QCD and the energy scale. With ps = 145GeV and �QCD =0:24GeV one yields d��1s /dlnps=1.27. Table 3 gives the slopes when �tting the function1=(a lnps + b) to the �s values. The results are in good agreement with the QCDexpectation.6 SummaryA measurement of inclusive spectra and event shape distributions is presented as obtainedfrom data taken in 2000 at centre of mass energies of 205 and 207GeV. The results arecompared to previous measurements at centre of mass energies between 91 and 200GeV .Fragmentation models describe the energy evolution of the inclusive spectra well. Theenergy evolution of the maximum of the �p distribution, ��, is in fair agreement with theMLLA prediction. This provides evidence, that e�ects of coherent gluon radiation in theparton shower process manifest themself on hadron level.The strong coupling constant �s has been determined from the event shape distribu-tions of 1�T ,M2h=E2vis using O(�2s), NLLA, and combined QCD predictions (see Table 4).0 .03 .09 0.24 0.51� Tz }| {| {z } | {z }NLLA+O(�2s)(lnR-Scheme)NLLA O(�2s) 0 .02 .04 0.20 0.5M2h=E2visz }| {|{z}| {z }NLLA+O(�2s)(lnR-Scheme)NLLA O(�2s)Figure 5: Fit ranges chosen for �tting �s from di�erent QCD predictions of 1 � T andM2h=E2vis distribution. 9

The comparison of �s as measured at the Z and at higher energies con�rms that theenergy dependence (running) of the strong coupling is consistent with the QCD expecta-tion.

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Ecm Theory QCD-parameter Result � stat � sys � scale205GeV O(�2s) �s(205GeV) 0.1067 � 0.0046 � 0.0031 � 0.0023�s(MZ) 0.1199 � 0.0058 � 0.0033 � 0.0027NLLA �s(205GeV) 0.1093 � 0.0055 � 0.0036 � 0.0047�s(MZ) 0.1232 � 0.0062 � 0.0038 � 0.0059O(�2s)+NLLA �s(205GeV) 0.1083 � 0.0033 � 0.0021 � 0.0034(lnR-scheme) �s(MZ) 0.1219 � 0.0042 � 0.0026 � 0.0043207GeV O(�2s) �s(207GeV) 0.1073 � 0.0035 � 0.0032 � 0.0023�s(MZ) 0.1209 � 0.0044 � 0.0034 � 0.0027NLLA �s(207GeV) 0.1079 � 0.0046 � 0.0036 � 0.0049�s(MZ) 0.1216 � 0.0059 � 0.0038 � 0.0062O(�2s)+NLLA �s(207GeV) 0.1096 � 0.0026 � 0.0036 � 0.0037(lnR-scheme) �s(MZ) 0.1238 � 0.0033 � 0.0038 � 0.0048Table 4: �s as obtained from distributions by averaging the results from the 1 � T andM2h=E2vis.

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References[1] DELPHI Coll., P. Abreu et al. Phys.Lett. B456(1999) 397.[2] DELPHI Coll., P. Abreu et al. Phys.Lett. B459(1999) 397.[3] DELPHI Coll., P. Abreu et al. The DELPHI detector at LEP. Nucl. Instr. Meth.A303(1991) 233.[4] DELPHI Coll., P. Abreu et al. Performance of the DELPHI detector. Nucl. Instr.Meth. A378(1996) 57.[5] DELPHI Coll., P. Abreu et al. Nucl. Instrum. Methods Phys. Res. A 427(1999) .[6] T. Sj�ostrand. Comp. Phys. Comm. 39(1986) 347.[7] DELPHI Coll., P. Abreu et al. Tuning and test of fragmentation models based onidenti�ed particles and precision event shape data. Z. Phys. C73(1996) 11.[8] C. P. Fong and B. R. Webber. Higher order corrections to hadron energy distributionsin jets. Phys. Lett. B229(1989) 289.[9] ALEPH Coll. QCD studies with e+e� annihilatin data from 130 to 172 GeV. Ref.#629 contributed to the EPS HEP conference in Jerusalem, 1997.[10] ALEPH Coll. Phys.Rep. 294(1998) 1.[11] R. K. Ellis, D. A. Ross, and A. E. Terrano. Nucl. Phys B178(1981) 412.[12] S. Catani, G. Turnock, B. R. Webber, and L. Trentadue. Thrust distribution in e+e�annihilation. Phys. Lett. B263(1991) 491.[13] S. Catani, G. Turnock, and B. R. Webber. Heavy jet mass distribution in e+e�annihilation. Phys. Lett. B272(1991) 368.[14] DELPHI Coll., P. Abreu et al. Determination of �s in second order QCD fromhadronic z decays. Z. Phys. C54(1992) 21.[15] DELPHI Coll., P. Abreu et al. Z. Phys. C59(1993) 21.[16] DELPHI Coll., P. Abreu et al. E.Phys.J. C14(2000) 557.

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