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central value 300 GeV.

sents the variation due to Higgs boson mass in the range 60 to IOOO GeV, with

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During the I992 running period of the LEP e+e‘ collider, the DELPHI

Abstract

DELPHI Collaboration

U at the Z Resonance

Sections and Asymmetries

Improved Measurements of Cross% W S 94 0

23 February 1994

CERN-PPE/94-31

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

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M.D.M.De Fez Lasow, C.D€ La Vaissieren, B.De L0tt046, A.De Mir127, L.De Paula", H.Dijkstra7,P.Delpierr€26, N.Dcmaria34, A.De Angclis-K, H.De Boeckz, VV.De Boerls, S.De Brabanderc2, C.Dc Ck-2rcq2,E.Daubi€2, A.Daum15, P.D.Dauncey7, MADavenp0rt7, ].Davies2l, \zV.Da Silvan, C.Def0ix6, G.D€lla Rviccalw,J.Cuevas Macstr033, S.Czcllar13, E.Dah1—Jensen28, J.Dahm52, B.Dalmagne18, M.Dam32, G.Damgaard28,J.L.C0r1treras18, R.C0ntri11, E.C0rtina49, G.C0smel8, F.C0uch0t;18, H.B.Craw1ey1, D.Cre1m€H37, G.Cr0setti11,G.A.ch€1k0v“, L.Chevalicr39, P.Chliapnikov42, v.chOmW1Cz22, J.T.M.Chrin49, v.c1Hdm“, P.Collins3",A.Catta.i7, F.R.Ca.vall05, L.Ccrrit038, V.Chabaud7, A.Chan1, Ph.Charper1ticr7, J.Chauveau22, P.Ch&cchia35,K.Camk0cak`4‘4, F.Ca02, F.Carc11a7, P.Ca1·rilho47, L.Carr0ll21, R.Cascs49, C.Cas0H, M.V.CastiIl0 Gimenez`19,J.A.M.A.Buytaert7, M.Caccia27, M.Ca1vi27, A.J.Camach0 Rozaslu, R.Campi0n21, T.Camp0r€si7, V.Canale38,H.Briand22, C.Bricman2, L.Bril]au1t22, R.C.A.Br0wn7, J—M.Bl`UH€t6, L.Bugge32, T.Burar132, A.Buys7,C.B0urdari0s18, T.J.V.B0wc0ck21, M.B0zz011, S.Braibant2, P.Branchini40, K.D.Brand35, R.A.Brcnner13,P.S.L.B00th2l, G.B0ris0v°2, C.B0si04°, B.B0st,jzmcic43, S.B0sw0rth34, O.BOtI]€T48, B.B0uquet18,D.Bl0ch, J.Bl0cki, S.Blyth4, V.B0cci38, P.N.B0golub0v14, T.B0l0gnesc39, M.B0nesini27, W.B0nivent027,85l3

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'2l"I?1,4’lll)9I`€1<`l1 Physik. University of \\`upp<·rta1. Postfach 100 127. I)-5600 \\iupperta1 1. (Germany OCR Outputllnst. Nuclear Studies and University ot \\`arsaw, Ul. Hoza G9. I’l,—00§i81 \Yarsaw. Poland1llnstitut1`iir llorlienergiophysik. Osterr. Akad. d. \Vissens<il1.. Nikolsilorlergasse 18. .\·l050 Vienna. Austria°IF1(`. Valencia-(`SI(Y. and D.F..·\.M.N., lj. de Valencia, Avda. Dr. 1\1oliner50, E-46100 Burjassot (Valencia), Spain8Dcpartment of Radiation Sciences. University of Uppsala, P.(). Box 535. S-751 21 Uppsala, SwedenIUniv. Federal do Rio de Janeiro. (KP. 68528 (`idade Univ., Ilha do Fundao BR-21945-970 Rio de Janeiro, Braziland lslituto di Fisica. Universita di Udine, 1-33100 Udine.Ila1v°Dipartimento di Fisica, Universita di '1`ri<—st.:— and INFN, Via A. Valerio 2. I-34127 Trieste, Italy‘i’Dipartimento di Fisira Sperimentalv, Universita di Torino and INFN, Via P. Giuria l, I-10125 Turin, Italy`1Fysikum. Stockholm University. Box 6730. S-113 85 Stockholm, Swedenhl. Stefan Institute and Department of Pliysirs, University of Ljubljana, Jamova 39, Sl-61000 Ljubljana, Slovenia2Inst. for High Energy Physics. Serpukov P.O. Box 35, Protvino, (\1oscow Region}. Russian FederationlC.E.A.F.1\’I., C.S.I.C. — Univ. (`antabria. Avda. los Castros. S/N-39006 Santander, Spain0 Istituto Superiore di Sanita, Ist. Naw. di Fisira Nucl. (INFN). Viale Regina Elena 299. I-00161 Rome, ItalygCentre d’Etude de Savlay, 1')S1\1/1)APN1.~\. F-91191 Gif—sur-Yvette (`cdex, FranceSDipartimento di Fisica. Universita di Roma II and INFN, Tor Vergata. I-00173 Rome, Italy’Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK(1 Depto. de Fisica, Pontificia Univ, Catolica, (KP. 38071 RJ-22-153 Rio de Janeiro, Brazil1’Dipartimento di Fisica, Universita di Padova and INFN, Via Marzolo 8. I-35131 Padua, Italy4 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK5 Dpto. Fisica, Univ. Oviedo, C/P.Jimenez Casas, S/N-33006 Oviedo, Spain2Physics Department, University of Oslo, Blindern, N—1000 Oslo 3, Norway1Nationa1 Technical University, Physics Department, Zografou Campus, GR-15773 Athens, GreeceUNIKHEF-H, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands9NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, CS-180 00, Praha 8, Czechoslovakia8Nie1s Bohr Institute, Blegdamsvej 17, Dl{—2100 Copenhagen 0, Denmark'Dipartimento di Fisica, Universita di Milano and INFN, Via Celoria 16, I-20133 Milan, ItalyBUniv. d’Aix - Marseille I1- CPP, IN2P3-CNRS, F-13288 Marseille Cedex 09, France’Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain4 Université Claude Bernard de Lyon. IPNL, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France3Department of Physics, University of Lund, Solvegatan 14, S-22363 Lund, SwedenZLPNHE, IN2P3—CNRS, Universités Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75252 Paris Cedex 05, France1Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UKOLIP, IST, FCUL - Av. Elias Garcia, 14-10, P—1000 Lisboa Codex, PortugalSchool of Physics and Materials, University of Lancaster, Lancaster LA1 4YB, UK

8Université de Paris-Sud, Lab. de l’Accélérateur Linéaire, IN2P3—CNRS, Bat 200, F-91405 Orsay, FranceCentro Brasileiro de Pesquisas Fisicas, rua Xavier Sigaud 150, RJ-22290 Rio de Janeiro, Brazil

°High Energy Physics Laboratory, Institute of Nuclear Physics, Ul. Kawiory 26a, PL-30055 Krakow 30, PolandFlnstitut fiir Experimentelle Kernphysik, Universitat Karlsruhe, Postfach 6980, D-76128 Karlsruhe, GermanyJoint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russian FederationResearch Institute for High Energy Physics, SEFT, P.O. Box 9, FIN—00014 University of Helsinki, Finland

Zlnstitut des Sciences Nucléaires, IN2P3-CNRS, Université de Grenoble 1, F-38026 Grenoble, FrancelDipartimento di Fisica, Universita di Genova and INFN, Via Dodecaneso 33, I—161-16 Genova, ItalyOFZU, Inst. of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, CS-180 40, Praha 8, Czechoslovakia9Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR—15310 Athens, Greece3'Centre de Recherche Nucléaire, IN2P3 — CNRS/ULP - BP20, F-67037 Strasbourg Cedex, FranceICERN, CH—1211 Geneva 23, Switzerland60011:-sge de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, F—75231 Paris Cedex 05, France5Dipartimento di Fisica, Universita di Bologna and INFN, Via Irnerio 45, I-40126 Bologna, ItalyDepartment of Physics, University of Bergen, Allégaten 55, N-5007 Bergen, NorwayPhysics Laboratory, University of Athens, Solonos Str. 104, GR—10680 Athens, Greeceand Faculté des Sciences, Univ. de 1’Etat l\¢lons, Av. Maistriau 19, B-7000 Mons, Belgiumand IIHE, ULB-VUB, Pleinlaan 2, B—1050 Brussels, BelgiumPhysics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, BelgiumAmes Laboratory and Department of Physics, Iowa State University, Ames IA 50011, USA

394334A.Zalewska16, D.Zavrtanik43, E.Zevgolatakos9, N.l.ZiminM, M.Zito, D.Zontar, R.Zuberi, G.ZumerleG.R.Wilkinson°°, VV.S.C.Willia1ns“ , M.\1Vinter, M.Witek, G.Wormserm, K.\rVoschnagg°”, A.Zaitsev“,87

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784G.Stavrop0ulos9, F.Stichelbaut7, A.Stocchi18, J.Strauss50, J.Straver, R.Strub, B.Stugu, M.Szczekowski51,D.Souza—Santos$°, T.SpassovzU, E.Spiriti4°, S.Squa1·ciaU , H.Staeckb’, C.Stanescu4°, S.Stapnes`”,A.N.Sisakian", G.Skjevling“, G.Smadja2°, N.Smirnov", O.SmirnovaH, G.R.Smith°', R.S0sr1owski°l,A.Seitz, R.Sekulin, R.Seufert", R.C.Shel1ard, I.Siccama, P.Siegrist, S.SimonettiH, F.Sim0netto°°,363°39l537

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progra.1n DELSlM which incorporates the resolution. granularity and efficiency ofthe OCR OutputThe response of the detector to physics processes was modelled using the simulation

tracking chambers and from the calorimeters.the detector is triggered by redundant combinations of signals from scintillators. from thescattering events at small angle and is used to measure the luminosity. The readout of(MUB) and forward (MUF) regions. A lead—scintillat.or calorimeter detects Bhabhacalorimeter (HCAL) and drift chambers for muon identification surround both the barrelin the forward regions. The return yoke of the solenoid is instrumented as a. hadronDensity Projection (lhamber (HP(i`) i11 the barrel and by lead glass detectors (1•`EM(l)drift chambers A and B (FCA and PCB). Electromagnetic energy is measured by the HighOuter Detector (OD). ln the forward region tra.ck reconstruction is complemented by theDetector (VD). the lnner Detector (ID). the Time Projection Chamber (TPC) and themeasured using, (in order of increasing distance from the beams) the silicon Microvertexbarrel region the trajectories of charged particles in the 1.2 T solenoidal magnetic field are

A detailed description of the DELPHI detector can be found in reference ln the

2 The DELPHI Detector

a summary of the results.the results are interpreted within the framework of the Standard Model. Section 8 givesthe combined 1990, 1991 and 1992 data of the DELPH1 collaboration, and in Section 7T+T‘, as well as the results of an inclusive lepton selection. Section 6 reports on Hts totion and forward—backward asymmetry determinations in the channels e+e_, ,u+n' anddetermination. Section 5 contains a description of the event selections, and cross sec

measurement is described and in Section 4 the hadronic event selection and cross section

ponents of the DELPH1 detector relevant for this analysis. In Section 3 the luminosityThis paper is organised as follows. Section 2 contains a brief description of the com

of approximately 24 pb‘cross sections reported here. The data analysed correspond to an integrated luminosityenergies of 51 :|; 5 MeV Small corrections for this effect have been applied to all theThe energy spread of partic.les in the beams leads to an rms spread of centre—of—mass

Em, : 91.280 zi; 0.018 GeV.

the resonant depolarisation measurements was applied The result is a value ofby the integrated luminosity of each fill, was then calculated and an offset derived frommeasured magnetic field in a reference magnet. An average of these energies, weightedof mass energy was used for the 1992 data. Each fill was assigned an energy based on the

Following the recommendation of the Working Group on LEP Energy [3] a single centreleptonic forward—backward asymmetries at the peak.systematic errors allow significantly improved determinations of the cross sections andof the resonance. However, the large increase in statistics and the reduction of someclose to the Z0 peak and therefore add little to the determination of the mass and width

The analysis of the 1992 data is reported here. All the data were taken at an energyterminations of the Z0 resonance parameterssurements of the LEP energy [1], the DELPH1 collaboration has published accurate deperformed at LEP. These data have been carefully analysed and, using the precise mea

During 1990 and 1991 energy scans around the position of the Z0 resonance were

b`}[,,.,,, + l;`§,,_.,_. < 0.9 E;,E.,,,,. OCR Output

the c:+c` channel. For events with i\~”,.;,, less than ll, it was required thatthe forward region, an additional selection was necessary to reduce the background fromof the centreeofemass energy. However, because of more efficient track reconstruction inNd,. was required to be greater than 4 and the charged energy, Em, greater tha.n 12%a polar angle between 200 and l60°. For an event to be accepted, the charged multiplicity.particle tracks only. These were required to have at momentum greater than 0.4 GeV and

As in our previous analysis the hadronic event selection was based on charged

4 Hadronic Event Selection and Cross Section

precise.

the luminosity measurement, since the determination of the absolute acceptance was lessmrad. was used in the on—line monitoring and for consistency checks. It was not used in

The Very Small Angle Tagger (VSAT), which covers the polar angle region 5 to 7containing a component of $0.40% in common with that of 1991 and of 1990.experimental and theoretical uncertainty on the luminosity is estimated to be $0.46%,the event generator BHLUMI [6] and the uncertainty was taken to be 0.25%. The total

The theoretical cross section was calculated on the basis of detailed simulations using$0.31% in common with it, and with that of 1990.is lower than the $0.5% uncertainty of the 1991 luminosity and contains a component ofsystematic uncertainty on the accepted cross section was estimated to be $0.38%. Thisthe acceptance borders of the unmasked calorimeter to be more precisely defined. Theenergy deposits were eliminated. ln addition, the use of the silicon tracker [2] alloweddefinition of the masks was more precisely known and the events with spurious high

Several sources of systematic error were reduced in the 1992 data. The geometrical

vertical axis.

in each calorimeter and azimuthal angle of the shower centroid greater than 8° from theAs in our previous analysis the selected events had energy greater than 0.65 EbmmStudies with a single arm trigger showed that the trigger efficiency was essentially 100%.energy depositions of more than 12 GeV coplanar within $20° in each of the calorimeters.deposits seen previously [2] were eliminated. The luminosity trigger was a coincidence ofentering the unma.sked ca.lorimeter at small angles, and so the spurious high energyvertical junction of the calorimeter half-barrels. A lead cylinder prevented electronsunder the ring mask. An additional lead mask covers the $15° in azimuth around themask extended to smaller radii, thus preventing electrons from entering the calorimeterone of tungsten, which could be machined to tighter tolerances. ln addition the newthe calorimeters. The original lea.d mask was replaced for part of the 1992 running bymrad. The acceptance was defined by an accurately machined mask in front of one ofThis calorimeter detected Bhabha scattering events in the polar angle range 43 to 135

The luminosity measurement in 1992 was based on the Small Angle Tagger (SAT).

3 The Luminosity Measurement

analysis chains as the real data.detector components. Simulated data were passed through the same reconstruction and

llu this paper, hemispheres are clefiuecl by 21 plane perpe11<li<:ul11r to the thrust axis. OCR Output

each method. both the electron and the positron were required to be within the range

the overall efficiency and to allow a better de1.ermination of systematic uncertainties. ln

As in Ref. two different methods of event selection were used in order to increase

5.1 The e+e` Channel

out in the following Sections.were similar to those used i11 our previous analysis [2], but any differences are pointedc+e_, ,u+,u” and T+r_ as well as in the inclusive lepton channel. ln general the techniques

Cross sections and forwardebackward asvmrnetries were determined in the channels

Forward—Backward Charge Asymmetries

5 Leptonic Event Selections, Cross Sections and

asymmetries.

the same quantities for the leptonic cross sections, and the leptonic forwardebackwardthe hadronic cross section of the 1992 data are summarized in Table 1 together with

The event samples, acceptances, efficiencies, backgrounds and systematic errors inresults[2], and compared with the 5eparameter fit described in Section 6.surement. This result is shown in Figure 1 together with previously published DELPHIThe systematic uncertainty does not include the contribution from the luminosity mea

0;, : 30.440 ;l: 0.053 (stat.) :1: 0.040 (Syst.) nb.

The resulting cross section over 4rr solid angle is:which 0.08% are common to the uncertainties of the 1990 and 1991 analyses23.955 pb`1. The overall uncertainty of the hadronic selection amounts to 0.13%, of

A total of 696,543 events was selected, corresponding to an integrated luminosity ofor beam—wall interactions and cosmic showers were negligible (less than 0.5 >< l0”4).vector dominance contributions [10]. Other backgrounds such as p+;f events, beam—gasbe 13 i 4 pb based on simulation using a generator including quark-parton, QCD andBABAMC generator [9] to be (0.06 :1: 0.02%). The two-photon background was found to[8]. The background from e+e` final states was estimated from simulation using theT+¢‘ background was found to be (0.58 :1; 0.05)% using the event generator KORALZless than 9) to the corresponding ones from simulation of qq, TTT- and e+e` events. Theenergy, invariant masses per hemispherel) of the selected data for low multiplicities (Nd,T background was estimated by comparing various distributions (e.g. thrust, charged

The significant backgrounds are from e+e‘—> T+T`, e+e` and two-photon events. Thebe greater than 99.99%.determined from the data by comparing sets of independent triggers and was found toshower generator [7] with different sets of tuning parameters. The trigger efficiency wastainty was reduced compared to our previous analysis [2] by using the JETSET 7.3 parton

The selection efficiency determined from simulation was (95.00 i 0.11)%. The uncerwould be rejected. The uncertainty due to this selection is estimated to be ;k0.02%.selected events were rejected, whereas simulation indicates that only 0.04% of e+e“—> qc]sections of the FEMC electromagnetic calorimeter. With this condition about 0.3% of thewhere E fom and Ebac), are respectively the energies recorded in the forward and backward

AQB (s+t) : 0.1177 :1: 0.0069 (stu!.) B; 0.0025 (.sy.st.). OCR Output

440 < H < 1360 was found to be

inition and was estimated to be j:0.0011. The e¤;+c‘ asymmetry in the angular rangecontribution to the systematic error on the asymmetry was due to the acceptance defcharge assigmnents on the asymmetry result were evaluated as being j:0.0022. Anothertracks different from two in the TP( `) could be resolved. and the effects of possible wrongambiguous events (i.e. those having two tracks with the same sign or having a. number oftrack and the most energetic 11P(` cluster in the same hemisphere. WVith this method theto determine the particle charge. based on the difference in azimuth between the VDmine the forward ebackward asymmetry. In this analysis a new method has been used

The sample of events used for the cross section measurements was also used to deterponent of 0.0038 nb common to the data of 1990 and 1991.The systematic error does not include the error due to the luminosity and it has a com

0. (s—only) : 0.9182 i 0.0072 (stat.) i 0.0054 (syst.) nb.

section in the angular range 44°< 9 < 136° was found to beprograms AL1BABA[11] and TOPAZ0 [12]. After these corrections the s-channel crossbe defined by the electron only. Corrections for both effects were computed using theexchange and its interference must be subtracted, and the accepted polar angle must

ln order to allow fitting of the results by the ZFITTER [13] package, the t—channel

as (s-1~t) : 1.0436 :1: 0.0072 (stat.) :1: 0.0036 (syst.) nb.

section in the angular range 44°< (9 < 136° and with an acollinearity less than 10° ofA total of 21,351 e+e` events were used in the method 2 analysis. This yielded a cross

two was used.

and efficiencies the two methods gave consistent results and the arithmetic mean of the(1.23 i 0.04)% for method 1 and method 2 respectively. After correction for backgroundsestimated by simulation using the KORALZ [8] generator. lt was (1.55 :h 0.05)% and

The only significant background in each selection came from T+T` events and wastriggers and was found to be greater than 99.99%.

The trigger efficiency was determined from the data by comparing sets of independentindependent programs ALlBABA[11] and TOPAZ0the 4° polar angle region around 90° which amounted to 4.4%, as computed using twothe 9 acceptance region. Both efficiencies do not include the loss due to the exclusion oftwo could be determined from the data, the latter being found to be (97.26 :1: 0.35)% incorrection for background, the efficiency of each selection and of the logical OR of theincluding ionization information from the TPC and the hit patterns in the OD. AfterHPC and the second using information from the tracking detectors (other than VD),

In method 2, two independent selections were used, one relying on the VD and theazimuthal angle where the HPC has gaps between modules.in the 0 acceptance region. This loss is mainly due to the fiducial cuts of the regions inevents produced using the BABAMC [9] generator and was found to be (89.42 :1: 0.38)%hemisphere. The efficiency of this selection was determined from a sample of simulatedhits in the VD consistent with a final state containing at least one charged particle perEvents from the reaction e+e" ——> 77 were completely eliminated by the requirement ofcalorimeter (HPC) and low charged multiplicity as indicated by the tracking detectors.

ln method 1, the selection relied on large energy deposits in the barrel electromagneticthe electron beam, and the acollinearity was required to be smaller than 10°44°< 0 < 136°, where 0 is the polar angle of the particle with respect to the direction of

common to the data of 1990 and 1991. The asymmetry. corrected to the full angular OCR Outputwere found to give an overall systematic error of zh0.00l0. which can be considered aspossible angle-edependent momentum acceptances, were determined from the data andarising from asymmetries in the detector, from the measurement of polar angle and fromthis source. but with a. negligible effect on the asymmetry. Significant systematic errorsfor the cross section showed that the sample contained (0.14zh 0.05)% background fromhowever these do not bias the asymmetry. A cosmic rav study similar to the one usedestimated that the sample contained a background of (2.00 dz 0.20)% of T+T” events,acollinearity as for the cross section. 32.382 events were selected. Bv simulat.ion it wassince an absolute normalization was not required. \Vith the same cuts on momenta a.nd

For the asymmetry measurement, the angular range was extended to 1l°< 0 < 169°

data of 1990 and 1991.

The systematic error does not include that due to the luminosity and is common to the

0,, : 1.3450 zh 0.0076 (stat.) zh 0.0054 (syst.) nb.

the cuts on momenta and acollinearity given above was found to bethe events in which the negative muon was in the angular range 20°< 9 < 160° and with

After subtraction of backgrounds and correction for inefficiencies, the cross section forbut outside the limits allowed for selected events, and was found to be (0.15 zh 0.05)%.ground was determined by studying events which originated close to the interaction point,ground. lt was found to be (2.00 zh 0.20)% in the selected sample. The cosmic ray backgenerator, and also by studying variables in the data which are sensitive to this backT+*r` background was determined from Monte Carlo simulation using the KORALZ [8]

The significant backgrounds were from the T+T` final state and from cosmic rays. The(99.87 dz 0.08)%.efficiency was computed by comparing sets of independent triggers and was found to beevent selection and identification probability was found to be (94.63dz0.30)%. The triggerThe muon identification efficiency was determined directly from the data. The overallby the study of a sample of simulated events produced using the DYMU3 [14] generator.selection due to the tracking detectors was estimated from the data itself, supplementedparticle. A total of 31,044 events passed these selections. The inefficiency of the eventthe electromagnetic calorimeters HPC or FEMC, consistent with a minimum ionizingchambers MUB or l\/[UF, or by energy depositions in the hadron calorimeter HCAL, oridentified as a muon. Identification was achieved by requiring associated hits in the muon15 GeV, and with acollinearity less than 20°. lt was required that each of the particles bel60°. Events were required to have two charged particles each of momentum greater thanin Ref. The polar angle range for the determination of the cross section was 20°< 9 <

The selection procedure for the e+e‘—> ,n+n` candidates was similar to that described

5.2 The ,u+n` Channel

and contains a component of 0.0024 in common with the data of 1990 and 1991.The systematic error includes effects due to the LEP energy and the t-channel subtraction,

A§B (s-only) : 0.0206 i 0.0079 (stat.) 1 0.0030 (syst.).

44°< 9 < 136° was deduced to bethe electron be in the acceptance, the s—channel e+e` asymmetry in the angular rangeCorrecting for the t-channel and interference effects, and for the requirement that only

the selection efficiencv. defined as the number of events selected divided bv the total OCR Output

TPC and a small smearing of the Monte (tarlo momentum and HPC energy distributions.imperfect modelling of the loss of charged particles in the azimuthal dead regions of theproduced using the KORALZ [Sl generator. After applying a small correction for the

The tau pair selection efficiency was determined from Monte Carlo simulated data

asvmmetrv measurement.

average interaction point. A total of 16,919 events were selected for the cross section andevents were removed with tight cuts on the impact parameters of tracks relative to thedecays, two—plioton events, ,u+,u‘ and c+< ` events. Cosmic ray, beam—gas and beam»wall

These cuts efficiently removed most of the potentia.l backgrounds from hadronic Z0c+c“—-> c+e_ events from the tau pair sample.data because the radial momentum selection was no longer effective in eliminating thebe less than 0.6. This requirement was more severe than in the analysis of the 1991boundary then the radial energy was required to be less than 0.9, otherwise it had toextrapolated trajectories of both these particles was more than 1.5° from the nearestwhere a substantial fraction of the deposited energy was lost. If the entry point of theto the boundaries between adjacent HPC modules (at intervals of 15° in azimuthal angle),selection depended on the proximity of the highest momentum particle in each hemispherethe momentum spectrum of high energy electrons in the detector. The radial energyof the background from e+e` ——> e+e` events due to the difficulty in precisely simulatingdescribed in the Section 5.2 above. This removes a systematic bias in the determinationat least one of the hemispheres satisfied very similar muon identihcation criteria to thosewas consistent with being a muon pair by requiring that the highest momentum particle inmomentum had only to be less than unity (as in the analysis of the 1991 data) if the eventmaximum allowed value which depended on several other features of the event. The radialdirection of the thrust axis in each hemisphere) were both required to be less than somedeposited in the electromagnetic calorimeters inside a 30° half—angle cone around theradial energy Emd (defined as Emd : + Eg/Ebeam where E1 and E2 are the energies

P2 the momenta of the highest momentum charged particle in each hemisphere) and theThe radial momentum variable Pwd (defined as Pmd : \/P? + P3/Pbeam, with P1 and

the conversion pair tracks were replaced with a photon of the appropriate energy.pairs which satisfied the charged particle multiplicity and jet isolation requirements after

which converted before the TPC. The effect of this was to increase the number of tau

detector simulation. A new feature of this analysis was the reconstruction of photons88°< 9 < 92°, where the track reconstruction efficiency is not well modelled by themomentum particle in both hemispheres were reconstructed in the polar angle intervalat least one of the event hemispheres. Furthermore, events were rejected if the highestlie in the polar angle interval 43°< 9 < 137° as did the highest momentum particle inisolated jets. The thrust axis, computed using both charged and neutral energy, had tobelow. The events were required to be of low multiplicity and to consist of two wellsample described in reference [2) but with several important changes which are described

The selection of tau pair candidates followed quite closely the analysis of the 1991 data

5.3 The r+r‘ Channel

A§B = 0.0056 i 0.0053 (stat.) i 0.0010 (syst).

likelihood fit to the lowest order form of the angular distribution, and was found to berange, but not for the momenta and acollinearity cuts was determined by a maximum

the systematic error is common to the published 1990 and 1991 data. OCR OutputQED radiative corrections to the fitted angular distribution. A component of 0.0010 ofmined from the number of like—sign tau pairs and the estimate of the effect of neglectinge+c` subtraction, the contribution from the charge misidentification probability detercorresponding to 4rr solid angle. The systematic error includes the uncertainty on the

ALB : 0.0092 ;b 0.0088 (stat.) i 0.0017 (syst).

was found to be

the angular distribution. taking into account the angular distribution of the background,asymmetry, calculated by the maximum likelihood method using the lowest order form ofrefer to the number of charged particles in each hemisphere). The forward—backwardcharge determination in these cases was not reliable (the numbers defining the topologiesnot belong to the 1eN (N:1,2,3.4,5) or 343 topologies were rejected since the hemispherethese were discarded from the asymmetry measurement. Finally, 369 events which did(228) events in which the charge sum in both hernispheres was positive (negative) andof the thrust axis and the charge sum of particles in each hemisphere. There were 231section. The forward or backward scattered events were defined using the polar angle

The asymmetry analysis was carried out in the same polar angle range as the cross

nent of 0.007 nb common to the data of 1990 and 1991.

The systematic error does not includes that due to the luminosity and includes a compo

0, : 1.491 i 0.012 (stat.) ;l; 0.009 (Syst.) nb.

section in 4rr solid angle was found to beAfter subtraction of the backgrounds and correction for selection efficiency, the cross

systematic error on the cross section was 0.63%.ror on the cross section due to the background subtraction was 0.26% and the overallThe residual cosmic ray background was estimated to be (0.11 i 0.05)%. The total erwith the dominant contributions coming from e+e` —> e+e"e+e` and e+e` —> e+e`,a+,a`tau pair sample. The non-resonant 2—photon background was estimated to be 3.3;t0.9 pb,observed to be (1.14j;0.15)%, (0.46;b0.07)% and (0.84:1:015)% respectively ofthe selectedsimulated data the resonant backgrounds from e+e‘, ,a+,a‘ and hadronic iinal states wereof ref [10] for the two—photon processes. By applying the tau pair selection cuts to the[9] (e+e‘), DYMU3 [14] (a+a‘), JETSET 7.3 Parton Shower [7] (qq) and the generatoraccount in these computations. The background samples were generated with BABAMCrections and smearings to the Monte Carlo samples described above were taken into

All backgrounds were estimated using Monte Carlo simulations. The various cordetermination was 0.58%, which includes the Monte Carlo statistical error.in the event generator. The total error on the cross section from the selection efficiencyof identifying converted photons, and the tau polarisation and branching ratio values usedsources of systematic errors are the choice of the radial impact parameter cuts, the effectthe HPC energy response and the radial momentum and energy cuts. Other smallerefficiency are the TPC track loss correction, the smearing of the Monte Carlo momentum,

The most significant contributions to the systematic error on the tau pair selectionby examining a set of independent trigger components and found to be (99.98 :1; 0.01)%.quoted is solely due to the Monte Carlo statistics. The trigger efficiency was calculatednumber of tau pairs generated in 4rr solid angle, was (48.01 :1; 0.16)%, where the error

AQ.,} : 0.0175 dz 0.0037 (slut.) i 0.0025 (syst.), OCR Output

range, the asymmetry is found to beaccount the fraction of OW ` events in the 1--1 topology. (Yorrecting to the full angulardue to the t-channel contribiition in ¢+e` was estimated as in Section 5.1, taking intocorrections were applied for cosmic ray a.nd two-photon backgrounds. The asymmetry50,356 events was ob1ained. The asyninietry was computed by the counting method and1-1 topology, and having two particle tracks of opposite charge were used. A sample of

l*`or the deterinination of the forward-backward asvnnnetrv, onlv the events of the

data of 1990 and 1991.

The systematic error does not includes that due to the luminosity, and is common to the

al : 1.4938 zh 0.0059 (stat.) dz 0.0045 (syst.) nb.

cross section for one flavour was found to be over 477* solid angle:After subtracting backgrounds and correcting for selection efficiencies, the s—channel

The corresponding uncertainty was estimated to be dz0.05%.that described in Section 5.1, taking account of the fraction of e+e“ events in the sample.

The t-channel contribution in the e+e" channel was subtracted in a similar manner tofrom hadronic decays was estimated to be (0.14 zh 0.02)%.photon processes within the acceptance was found to be 5.8 dz 0.3 pb and the backgroundThe other backgrounds were estimated from simulated samples. The cross section for twodistribution of impact parameters within the data and was found to be (0.52 i 0.03)%.cesses and from hadronic decays. The cosmic ray background was estimated from the

The significant sources of background were from cosmic rays, from tw0—photon proselected sample. lt was found to be (99.95Jjgj?g)%.separated channels, weighting by the estimated number of events of each type in the

The trigger efficiency was taken as the average of those determined for the flavourefficiency of (57.40 dz 0.43)%, corresponding to events over the full solid angle.KORALZ [8] was used to determine the efficiency. The result was an event selection

For the TTT- channel a sample of Monte Carlo events produced using the generator(94.83 dz 0.24)% for [4+,LF events and (94.27 jh 0.24)% for e+e` events.for muons and (0.86i0.20)% for electrons. The overall selection efficiencies were therefore(4.87 i 0.14)%. Within the sensitive region the track loss was found to be (0.30 dz 0.20)%of these types. The dead regions of the TPC were found to give a track inefficiency ofregion. Both of these effects were measured from the data using events identified as beingregions of the TPC, and failure to reconstruct a particle passing through the sensitivedetermined principally by two sources: loss of those particles passing through insensitive

For e+e“ and ,u+,u' within the accepted polar angle range, the selection inefficiency wasrequired to have momentum greater than 3 GeV. A total of 65,200 events was selected.the other hemisphere, was required to be less than 20° and one particle in the event wasdefined by the isolated track and the resultant momentum of the group of particles inone charged particle, and the other between 1 and 5 charged particles. The acollinearity,in the polar angle range 43°< H < 137°. At least one hemisphere was required to contain2 and 6 charged particles with momentum greater than 0.2 GeV, with at least two lyingprocedure was the same as for the 1991 data, that is, events were required to have betweento provide a cross-check on the leptonic analyses described above. The event selection

As in our previous analysis [2] a flavour independent analysis was carried out in order

I13I. Full account was taken of the LFP energy uncertainties and their point-to-point OCR Outputbackward asymmetries of 1990, 1991 and 1992. were made using the program ZFITTER

Fits to the hadronic cross sections a.nd tl1e leptonic cross sections and forwarde

6 ZU Parameters

resultsI2I, and with the results of the 5 ceparameter fit described in Section 6.are shown in Figures 2 and 3 respectively. together with previously published 1)ELPHl

The cross section and forward--backward asymmetry results for the leptonic channels

Ilncludes the uncertainty due to the t-channel subtraction.luminosity is not included in the above numbers.specihcally to analysis method 2. The total systematic uncertainty of dz0.46% in theand the leptonic forward—backward asymmetries for the 1992 data. The e+e“ data refertances, backgrounds and systematic errors in the hadronic and leptonic cross sections,Table 1: Summary of event samples, angular acceptances, efficiencies within the accep

Tot. syst. error i0.0030I I zh0.0010 I zh0.00l7 I dz0.0025

Selected events 21,351 I 32,382 I 16,091 I 50,356H acceptance (°) 44-136 I 11-169 I 43-137 I 43-137Asymmetry AQB

rec. syst. error (%) I $0.13 I 40.601 I 40.37 I 40.63 I 40.30Cosmic ray bkgd. (%) 0.15 zh 0.05 I 0.11 dz 0.05 I 0.52 zh 0.03

3.3 dz 0.9 I 5.8 i 0.6Two—photon bkgd. (pb) I 13 dz 41.60 zh 0.17 I he+e_ -I— ,u+;4“ bkgd. (%)I 0.06 dz 0.020.84 i 0.15 I 0.14 dz 0.02qi] background ((70)

T+T` background (%) I 0.58 i 0.05 I 1.23 zh 0.04 I 2.00 i 0.20

Selection efficiency ((70) 95.00 i 0.11 97.26 i 0.35 94.63 dz 0.30 81.71 i 0.47 92.65 dz 0.27Trigger efficiency (%) I > 99.99 I > 99.99 I99.87 i 0.08I99.98 i 0.01I 99.9518%Selected events I 696,543 I 21,351 I 31,044 I 16,919 I 65,2000 acceptance (3) I 0-180 I 44-136 I 20-160 I 43-137 I 43-137Cross section

[1,-1-[VLHadrons I e+e` T+T_ I l+l‘

of the lepton—identified results.asymmetry was found to be —0.0075 1 0.0055. The good agreement supports the validityinclusive lepton and the mean of the lepton4identified results for the forward—backwarderrors due the incomplete overlap of the different channels. Similarly the difference in thebe 0.9972 zh 0.0052, where the error takes account of the systematic errors, and statisticalsection for e+e‘—> l+l` to the mean of the lepton—identified results was then found tomean of the lepton—identilied results was then computed. The ratio of the measured crossI13I, so that they corresponded to a 4rr detector with no cuts applied. The weightedidentification. To do this the leptoneidentified results were corrected, using ZFITTER

The inclusive lepton results were compared with those of the analyses with leptoncharge misidentification, and is connnon to that of the 1990 and 1991 data.where the systematic error comes mainly from the t-channel subtraction and possible

consistently tlnougliout. OCR Outputllere Rl is defined for the Z0 decay into a. pair of massless charged leptons and is treatedThe correlation coefficients ofthe parameters of the 5—parameter fit are given in Table 3.

\2/DF : 110/108.A§B : 0.0177 i 0.0037

20.62 i 0.10

O' (1 41.23 i 0.20 nb

2.483 j; 0.012 GeV

Z 91.187 A; 0.009 GeV

carried out and yielded the following results:l\lodel. A 5eparameter fit assuming flavour independence of the couplings was thereforeRf for each lepton species are shown, together with some predictions of the Standardof the couplings. This is demonstrated in Figure 4 where the allowed regions of A§Bj and

These fit parameters are in good agreement with the hypothesis of lepton universalitycients for the parameters ofthe 9—para1neter fit are given in Table 2.where gy, and gAf are effective vector and axial—vector couplings. The correlation coeffi

*7 ') 7 (gv. + air.) (yt, + yi,)A;)`Bf I 3 gvggfle

respectively. The parameters A§Bf are defined as:where Thad and l`f are the partial decay widths into hadrons and the lepton species f

7R Z I had

pole cross section. The parameters R f for lepton species f are defined aswhere MZ, FZ and 00 are respectively the mass and width of the Z0 and the hadronic

108/104,X2/DF

0.022 i 0.007Ag;

0.014 i 0.005AEBU

0.025 i 0.009Aiise

20.68 i 0.18

20.54 5; 0.14

20.74 :|; 0.18

41.23 :1; 0.20 nb

2.483 :1; 0.012 GeV

N12 91.187 1 0.009 GeV

for the different lepton species then a 9—parameter fit yields the following parameters :18 lVleV [3], uncorrelated t0 that 0f the other years. lf independent couplings are allowedref. The single centre—0f-mass energy ofthe 1992 data was assigned an uncertainty 0f26 MeV The energies ofthe 1991 data were obtained by the procedures described incomclations The ovcrall energy scale ofthe 1990 data was assigned an uncertainty of

10

unknown parameters. Taking the mass ofthe top quark, nz,. as 180 GeV and the mass OCR Output\’V1l·l1l11 the Minimal Standard Model the ratio 1],/I`; shows little dependence on the

Model

7 Interpretation of the Results within the Standard

Table 3: The correlation coefficients for the parameters of the 5—pa.rameter fit.

0.01Ii,

0.13 -0.01

FZ [ -0.14 0.00 -0.01MZ |-0.01 0.01 0.00 0.16

FZ O`(] R] A;B

Table 2: The correlation coefficients for the parameters of the 9—parameter fit.

0.04A3!

0.03 0.02A3;

0.00 0.00 0.01

0.010.05 0.00 0.00R,.

0.01 0.00 0.000.05 0.04

0.00 0.00 -0.010.07 0.10 0.07

0.000.00 0.00FZ | -0.14 0.00 0.00 0.000.070.00 0.08MZ |-0.01 0.01 0.01 0.01 0.00

rn n rAiig Ai;AiiuFZ G0 R8 RH RT

agreement with those published by the other LEP collaborations [15117].The results ofthe 5—parameter and Qeparameter {its to the DELPHI data are in good

width for Z0 decays into invisible final states.where l`], gw, gA, and l`m,, are defined assuming lepton universality, and l`im, is the partial

1.723 1 0.010 GeV,Fhad

509.4 1 7.0 MeVFinv

9];, 0.2499 1 0.0014

9% (1.50 dz 0.31)><10“

83.56 1 0.45 MeV

83.55 ;k 0.91 MeV

84.15 j; 0.77 MeVFH

83.311 0.54 MeV

parameters:Alternatively the results ofthe preceeding fits can be expressed in terms ofthe following

11

$1112 0Qyj : 0.2:12s 4 0.<10i:s(1.11,11.)i3;3g3},( 11*z_q_q.$) OCR Output

GeV, with central value 300 GeV. This value of 77It corresponds to:where (Higgs) represents the variation due to Higgs boson mass in the range 60 to 1000

J

nz, : 15TJfi3(c.1·p/.)f;3(IIiggs) GeV.

for the top quark mass:os measured by the D1til1PHl collaboration 1181 as a constraint, yields the following value

A Standard l\1lodel fit to all the cross section and asymmetry data using the value of

sin: 0.2306 :h 0.0020.g

then the leptonic vector and axial—vector couplings correspond to

gme/at = (1 — MinGtjrpf)1

If the weak mixing angle is defined by the relation

ds : 0.108 :1: 0.012.

unconstrained, then the fit yielded the value:was obtained. If the number of neutrino species was lixed to be three, but cvs was left

NL, : 3.023 :1: 0.035,

was used as a constraint then the result:

as I 0.123 :h 0.005

ration [18],If the value for the strong coupling constant as as determined by the DELPHI collabo

N, = 3.057 :1: 0.040.

as : 0.098 :1: 0.014

were:

of neutrino species and the value of the strong coupling constant, cvs, free. The resultsAn alternative procedure is to carry out a Standard Model fit, but leaving the number

N., = 3.060 d: 0.041.

can be derived, and hence the number of light neutrino species can be deduced to be

Fm/I`; : 6.10 :1: 0.08

results given in Section 6 the ratio130 GeV < mt < 230 GeV and 60 GeV < mg < 1000 GeV respectively. From thewhere the uncertainty corresponds t0 variations of mt and my within the ranges

I`.,/I`; : 1.992 :1: 0.002,

of the Higgs boson, mg, as 300 GeV the model predicts

12

their continuing support. OCR Outputthe technical and engineering staffs in our laboratories and to our funding agencies forand for their careful work on the beam energy determinations. We are also grateful to

We thank the SL Division of CERN for the excellent performance of the LEP collider

Acknowledgements

mt : 1571“ig(expt.)i;3(Higgs) GeV.

then the Standard Model fit yieldsby the DELPHI collaboration from a study of hadronic final states is used as a constraint,strong coupling constant ds. We {ind cvs : 0.108 j: 0.012. lf the value of ds determined

Within the context of the Standard Model the data can be used to determine the

2sinGL?} : 0.2306 :1; 0.0020.

angle ofwidths and couplings. The leptonic couplings correspond to a value of the weak mixinggive improved determinations of the resonance parameters, notably the leptonic partialhave been combined with the previous DELPHI results at energies around the 20 peak tobackward asymmetries, all at a mean centre-of~mass energy of 91.280 GeV. These resultshave been analysed to give hadronic and leptonic cross sections and leptonic forward

During 1992, DELPHI accumulated approximately 24 pb`1 at the Z0 peak. These data

DELPHI Collaboration, P. Abreu et al., Z. Phys. C59 (1993) 21. OCR Output[1811171 OPAL Colla.boration, R. Akers et al., Z. Phys. C61 (1994) 19.

preprint CERN-PPE/93-31 (1993).[161 L3 Collaboration, O. Adriani et al., ”Results from the L3 Experiment at LEP",

pair forward—backward asymmetries”, preprint CERN-PPE/ 94-30 (1994).1151 ALEPH Collaboration, D. Buskulic et al., ”Z production cross-sections and lepton1141 J.E. Campagne and R. Zitoun, Z. Phys. C43 (1989) 469.

in e+e" Annihilation”, preprint CERN-TH 6443/92 (1992) and references therein.D. Bardin et al., "ZFITTER: An Analytical Program for Fermion Pair Production113176 (1993) 328.

1121 G. Montagna et al., Nucl. Phys. B401 (1993) 3, and Comput. Phys. Commun.Nucl. Phys. B349 (1991) 323.

[11] \xV..l.P. Beenakker, EA. Berends and S.C. van der Marck,and Nucl. Phys. B253 (1985) 441.EA. Berends, P.H. Daverveldt, R. Kleiss, Comput. Phys. Commun. 40 (1986) 285,photon processes”, DELPHI Note 90-35 (1990), unpublished,S. Nova, A. Olshevski and T. Todorov, “Monte Carlo event generator for two[101

[9] EA. Berends, VV. Hollik and R.Kleiss, Nucl. Phys. B304 (1988) 712.181 S. Jadach, B.F.L. V/ard and Z. V)/as, Comput. Phys. Commun. 66 (1991) 276.

TH 6488/92 (1992).T. Sjostrand, “PYTHlA 5.6 JETSET 7.3 Physics and Manual”, preprint CERNT. Sjostrand and M. Bengtsson, Comput. Phys. Commun. 43 (1987) 367.

[71 T. Sjostrand, Comput. Phys. Commun. 27 (1982) 243, ibid.28 (1983) 229.S. Jadach et al., Comput. Phys. Commun. 70 (1992) 305.161User guide”, DELPHI Note 89-67 (1989), unpublished.DELPHI Collaboration, "DELPHl Event generation and detector simulation[5]

[41 DELPHI Collaboration, P. Aarnio et al., Nucl. Instr. & Meth. A303 (1991) 233.21 (D1) (1993), unpublished.L. Arnaudon et al., “'1`he Energy Calibration of LEP in 1992°°, CERN SL/93Decays”, preprint CERN—PPE/94-08, Nucl. Phys. B to be published.Z0 and Determination of Electroweak Parameters from its Hadronic and Leptonic

[2] DELPHI Collaboration, P. Abreu et al., “Measurements ofthe Lineshape of theB307 (1993) 187.

[1] \V0rking Group 0n LEP Energy and the LEP Collaborations, Phys. Lett.

References

14

shows the ratio of tl1e measurements to tl1e best {it values. OCR Output

are sl1ow11 together with the result of tl1e 5-parameter fit described in Section 6. Plot (b)amounts to 0.6% and that between the 1992 and 1990/91 results 0.30%. In (a) the datastatistical only. The uncorrelated systematic error between the 1990 and 1991 resultsFigure 1: Hadronic cross sections from 1990, 1991 and 1992 data. The errors shown are

x/s (GeV)87 88 89 90 91 92 93 94 95 96

0.95

U (b)E 1.05

\/s (GeV)87 88 89 90 91 92 93 94 95 96

20

¤ 1992

· 1991

O 1990I-IcdronsQ l (c) `“A 40

DELPHI

15

60 GeV to 1000 GeV.

prediction as nz, varies from 100 (1eV to 250 GeV, as from 0.118 to 0.128 and my fromfor my : 180 GeV. as : 0.123 and my : 300 GeV. The arrows show the changes of theis indicated by l and is sliziclecl. The point shows the expectation of the Sta.nclzrr<l Modele, iz. and T, while the region allowed by the 5r])&l`H.I11€‘t€1` fit assuming lepton universalityContours from the 9 eparameter fit, without assuming lepton universality. are inclicated byFigure 4: Allowed contours at the 68% confidence level in the A§Bf — Rf plane. The

20 20.2 20.4 20.6 20.8 21 21.2

0.01

0.02

0.03

OCR OutputOCR Output0.04

18