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Neutral-current four-fermion production in e

+

e

interactions at 130 GeV ≤ √s ≤ 172 GeV

L3 Collaboration

AMBROSI, Giovanni (Collab.), et al.

Abstract

A study of neutral-current four-fermion processes is performed, using data collected by the L3 detector at LEP during high-energy runs at centre-of-mass energies 130–136, 161 and 170–172 GeV, with integrated luminosities of 4.9, 10.7 and 10.1 pb⁻¹, respectively. The total cross sections for the final states ℓℓℓ′ℓ′ and ℓℓqq (ℓ, ℓ′ = e, μ or τ) are measured and found to be in agreement with the Standard Model prediction.

L3 Collaboration, AMBROSI, Giovanni (Collab.), et al . Neutral-current four-fermion production in e

+

e

interactions at 130 GeV ≤ √s ≤ 172 GeV. Physics Letters. B , 1997, vol. 413, p. 191-200

DOI : 10.1016/S0370-2693(97)01092-7

Available at:

http://archive-ouverte.unige.ch/unige:113182

Disclaimer: layout of this document may differ from the published version.

1 / 1

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6 November 1997

PHYSICS LETTERS B ELSEVIER Physics Letters B 413 (1997) 191-200

Neutral-current four-fermion production in e+e- interactions at 130GeV &I 172GeV

L3 Collaboration

M. Acciarri ac, 0. Adriani r, M. Aguilar-Benitez ab, S. Ahlen I, J. Alcaraz ab, G. Alemanni ‘, J. Allaby ‘, A. Aloisio ae, G. Alverson m, M.G. Alviggi ae, G. Ambrosi “, H. Anderhub ay, V.P. Andreev g,an, T. Angelescu n, F. Anselmo j, A. Arefiev ad, T. Azemoon ‘, T. Aziz k, P. Bagnaia am, L. Baksay at, S. Banerjee k,

SW. Banerjee k, K. Banicz av, A. Barczyk ay7aw, R. Bar-ill&e ‘, L. Barone am, P. Bartalini aj, A. Baschirotto ac, M. Basile j, R. Battiston aj, A. Bay ‘, F. Becattini ‘,

U. Becker q, F. Behner ay, J. Berdugo ab, P. Berges q, B. Bertucci aj, B.L. Betev ay, S. Bhattacharya k, M. Biasini ‘, A. Biland ay, G.M. Bilei aj, J.J. Blaising d, SC. Blyth *, G.J. Bobbink b, R. Bock a, A. Bijhm a, L. Boldizsar O, B. Borgia am,

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P. Denes ‘, F. DeNotaristefani am, D. DiBitonto at, M. Diemoz am, D. van Dierendonck b, F. Di Lodovico ay, C. Dionisi *, M. Dittmar ay, A. Dominguez ap, A. Doria ae, M.T. Dova t71, D. Duchesneau d, P. Duinker b, I. Duran aq, S. Dutta k, S. Easo aj, Yu. Efremenko A, H. El Mamouni aa, A. Engler A,

F.J. Eppling q, F.C. Em6 b, J.P. Ernenwein aa, P. Extermann “, M. Fabre aw, R. Faccini am, S. Falciano am, A. Favara r, J. Fay =, 0. Fedin an, M. Felcini ay,

0370-2693/97/$17X)0 0 1997 Elsevier Science B.V. All rights reserved.

PII SO370-2693(97)01092-7

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192 M. Acciarri et al. /Physics Letters B 413 (1997) I91 -200

B. Fenyi at, T. Ferguson &, F. Ferroni am, H. Fesefeldt a, E. Fiandrini aJ, J.H. Field “, F. Filthaut *, P.H. Fisher q, I. Fisk ap, G. Forconi 9, L. Fredj “,

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V Koutsenko q7ad, R.W. Kraemer ak, W. Krenz a, A. Kunin q,ad,

P. Ladron de’Guevara ab, I. Laktineh aa, G. Landi r, C. Lapoint q, K. Lassila-Perini ay, P. Laurikainen w, M. Lebeau ‘, A. Lebedev q, P. Lebrun aa, P. Lecomte ay, P. Lecoq ‘,

P. Le Coultre ay, H.J. Lee i, J.M. Le Goff ‘, R. Leiste a, E. Leonardi am, P. Levtchenko an, C. Li “, C.H. Lin ba, W.T. Lin ba, F.L. Linde b,s, L. Lista ae, Z.A. Liu h, W. Lohmann ax, E. Longo am, W. Lu ai, Y.S. Lu h, K. Liibelsmeyer a, C. Luci am, D. Luckey q, L. Luminari am, W. Lustermann aw, W.G. Ma “, M. Maity k, G. Majumder k, L. Malgeri am, A. Malinin ad, C. Maiia ab, D. Mange01 ag, S. Mangla k,

P. Marchesini ay, A. Marin I, J.P. Martin aa, F. Marzano am, G.G.G. Massaro b, D. McNally ‘, R.R. McNeil g, S. Mele ae, L. Merola ae, M. Meschini r, W.J. Metzger ag, M. von der Mey a, Y. Mi ‘, A. Mihul “, A. J.W. van Mil ag, H. Milcent ‘, G. Mirabelli am, J. Mnich ‘, P. Molnar ‘, B. Monteleoni r, R. Moore ‘, S. Morganti am, T. Moulik k, R. Mount ‘, S. Miiller a, F. Muheim “, A.J.M. Muijs b,

S. Nahn 9, M. Napolitano ae, F. Nessi-Tedaldi ay, H. Newman ‘, T. Niessen a, A. Nippe a, A. Nisati am, H. Nowak ax, Y.D. Oh as, H. Opitz a, G. Organtini am,

R. Ostonen w, C. Palomares ab, D. Pandoulas a, S. Paoletti am, P. Paolucci ae, H.K. Park *, I.H. Park as, G. Pascale am, G. Passaleva ‘, S. Patricelli ae, T. Paul m,

M. Pauluzzi aj, C. Paus ‘, F. Pauss ay, D. Peach ‘, Y.J. Pei a, S. Pensotti ac, D. Perret-Gallix d, B. Petersen ag, S. Petrak i, A. Pevsner e, D. Piccolo ae, M. Pieri r, P.A. PirouC ‘, E. Pistolesi ac, V. Plyaskin ad, M. Pohl ay, V. Pojidaev ad.r,

H. Postema q, N. Produit ‘, D. Prokofiev an, G. Rahal-Callot ay, N. Raja k, P.G. Rancoita ac, M. Rattaggi ac, G. Raven ap, P. Razis &, K. Read ah, D. Ren ay,

M. Rescigno am, S. Reucroft m, T. van Rhee au, S. Riemann a, K. Riles ‘, A. Robohm aY, J. Rodin q, B.P. Roe ‘, L. Romero ab, S. Rosier-Lees d, Ph. Rosselet ‘,

W. van Rossum a”, S. Roth a, J.A. Rubio ‘, D. Ruschmeier i, H. Rykaczewski ay,

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M. Acciarri et al/Physics Letters B 413 (19971 191-200 193

J. Salicio ‘, E. Sanchez ab, M.P. Sanders ag, M.E. Sarakinos w, S. Sarkar k, M. Sassowsky a, C. Schafer a, V. Schegelsky an, S. Schmidt-Kaerst a, D. Schmitz a,

P. Schmitz a, N. Scholz ay, H. Schopper =, D.J. Schotanus ag, J. Schwenke a, G. Schwering a, C. Sciacca ae, D. Sciarrino “, L. Servoli aj, S. Shevchenko ai,

N. Shivarov ar, V. Shoutko ad, J. Shukla ‘, E. Shumilov ad, A. Shvorob ‘, T. Siedenburg a, D. Son as, A. Sopczak a, B. Smith q, P. Spillantini r, M. Steuer q,

D.P. Stickland ‘, A. Stone g, H. Stone ‘, B. Stoyanov ar, A. Straessner a, K. Strauch p, K. Sudhakar k, G. Sultanov t, L.Z. Sun “, G.F. Susinno “, H. Suter ay,

J.D. Swain t, X.W. Tang h, L. Tauscher f, L. Taylor m, Samuel C.C. Ting q, S.M. Ting q, M. Tonutti a, S.C. Tonwar k, J. T&h O, C. Tully ai, H. Tuchscherer at,

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J. Xu I, Z.Z. Xu “, B.Z. Yang “, C.G. Yang h, X.Y. Yao h, J.B. Ye “, S.C. Yeh ba, J.M. You *, An. Zalite an, Yu. Zalite ““, P. Zemp ay, Y. Zeng a, Z. Zhang h, Z.P. Zhang “, B. Zhou ‘, G.Y. Zhu h, R.Y. Zhu ai, A. Zichichi jvs,t, F. Ziegler ax

a I. Physikalisches lnstitut, RWTH, D-52056 Aachen, FRG ’ III. Physikalisches Institut, RWTH, D-52056 Aachen, FRG ’

b National Institute for High Energy Physics, NlKHEF, and University of Amsterdam, NL-1009 DB Amsterdam. The Netherlands

’ University of Michigan, Ann Arbor, MI 48109, USA

’ Laboratoire d’Annecy-le-Vieux de Physique des Particules, LAPP,IN2P3-CNRS, BP 110, F-74941 Annecy-le-Views CEDEX, France e Johns Hopkins University, Baltimore, MD 21218, USA

Institute of Physics, University of Basel, CH-4056 Basel, Switzerland g Louisiana State Vniuersity, Baton Rouge, LA 70803, USA h Institute of High Energy Physics, IHEP, 100039 Beijing, China 4

i Humboldt University, D-10099 Berlin, FRG 3

VnivF’ty of Bologna and INFN-Sezione di Bologna, I-40126 Bologna, Italy Tata Institute of Fundamental Research, Bombay 400 005, India

Boston University, Boston, MA 02215, USA m Northeastern University, Boston, MA 02115, USA

n Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania

’ Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary s

’ Harvard University, Cambridge, MA 02139, USA

’ Massachusetts Institute of Technology, Cambridge, MA 02139, USA r INFN Sezione di Firenze and University of Florence, I-50125 Florence, Italy

European Laboratory for Particle Physics, CERN, CH-IZII Geneva 23, Switzerland

World Laboratory, FBLJA Project, CH-I211 Geneva 23, Switzerland

’ University of Geneva, CH-1211 Geneva 4, Switzerland

’ Chinese University of Science and Technology, VSTC, Hefei, Anhui 230 029, China 4 w SEFT, Research Institute for High Energy Physics, P.O. Box 9, SF-00014 Helsinki, Finland

’ University of Lausanne, CH-1015 Lausanne, Switzerland

’ INFN-Sezione di Lecce and Vniversitri Degli Studi di Lecce, l-73100 Lecce, Italy

’ Los Ahmos National Laboratory, Los Alamos, NM 87544, USA

aa lnstitut de Physique Nucleaire de Lyon, IN2P3-CNRS,Vniversite’ Claude Bernard, F-69622 Villeurbanne, France ab Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas, CIEMAT, E-28040 Madrid, Spain 6

a’ INFN-Sezione di Milano, I-20133 Milan, Italy

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194 M. Acciarri et al./ Physics Letters B 413 (1997) 191-200 ad Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russia

ae INFN-Sezione di Napoli and University of Naples, I-80125 Naples, Italy af Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus ag University of Nijmegen and NIKHEF, NL-6525 ED Nijmegen, The Netherlands

ah Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA sI California Institute of Technology, Pasadena, CA 91125, USA

” INFN-Sezione di Perugia and Universitci Degli Studi di Perugia, I-06100 Perugia, Italy ak Carnegie Mellon University, Pittsburgh, PA 15213, USA

al Princeton University, Princeton, NJ 08544, USA

am INFN-Sezione di Roma and University of Rome, “La Sapienza”, I-00185 Rome, Italy an Nuclear Physirs Institute, St. Petersburg, Russia

a’ University and INFN> Salerno, 1-84100 Salerno, Italy ap University of California, San Diego, CA 92093, USA

“I Dept. de Fisica de Particulas Elementales, Univ. de Santiago, E-15706 Santiago de Compostela, Spain ar Bulgarian Academy of Sciences, Central Lab. of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgaria as Center for High Energy Physics, Korea Adv. Inst. of Sciences and Technology, 305-701 Taejon, South Korea

at University of Alabama, Tuscaloosa, AL 35486, USA a’ Utrecht University and NIKHEF, NL-3584 CB Vtrecht, The Netherlands

” Purdue University, West Lafayette, IN 47907, USA aw Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland ax DESY-Institutfir Hochenergiephysik, D-15738 Zeuthen, FRG

ay Eidgeniissische Technische Hochschule, ETH Ziirich, CH-8093 Ziirich, Switzerland a University of Hamburg, D-22761 Hamburg, FRG

ba High Energy Physics Group, Taiwan, ROC Received 6 August 1997

Editor: K. Winter

Abstract

A study of neutral-current four-fermion processes is performed, using data collected by the L3 detector at LEP during high-energy runs at centre-of-mass energies 130-136, 161 and 170-172 GeV, with integrated luminosities of 4.9, 10.7 and 10.1 pb-‘, respectively. The total cross sections for the final states e/f’/ and k’/qq (/, /’ = e, p or 7) are measured and found to be in agreement with the Standard Model prediction. 0 1997 Elsevier Science B.V.

1. Introduction

An observation of four-fermion events [l] from e+e- interactions above the expectations from the Standard Model would signal the existence of new physics. The four-fermion final states can arise from several production mechanisms, each giving a contri-

bution to the cross section in a specific configuration of the final-particle phase space. In Fig. 1, all possi- ble classes of neutral-current four-fermion produc- tion diagrams are shown. We will concentrate on the case where the outgoing fermions make at least a 5”

angle with respect to the beam axis, in this way reducing the contribution from the multiperipheral

Also supported by CONICET and Universidad National de 4 Supported by the National Natural Science Foundation of

La Plata. CC 67, 1900 La Plats, Argentina. China.

’ Also supported by Panjab University, Chandigarh-160014, ’ Supported by the Hungarian OTKA fund under contract num-

India. bers T14459 and T24011.

3 Supported by the German Bundesministerium filr Bildung, 6 Supported also by the Comisidn Interministerial de Ciencia y

Wissenschaft, Forschung und Technologie. Technologia.

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M. Acciarri et al. /Physics Letters B 413 (1997) 191-200 195

diagrams. In this latter case, two quasi-real photons are exchanged in the t-channel giving rise to forward electrons/positrons plus a fermion pair with a non- resonant structure (the so-called “two-photon” pro- cess). This class of processes does not contribute to final states via Z exchange, where the main contribu- tions come from the bremsstrahlung, conversion and annihilation diagrams. If an e+e- pair is present in the final state, the bremsstrahlung diagram is domi- nant, otherwise the conversion diagram contributes the most, mainly with an initial-state radiative pho- ton and a Z boson on mass shell. This is in contrast to the situation at LEPl, where the annihilation mechanism dominates. Important characteristics of the four-fermion events are the energy and angular distributions of the outgoing fermions. If an e+e- pair is present in the final state, due to the multipe- ripheral or bremsstrahlung diagrams, the electrons tend to have nearly the beam energy and to be emitted along the beam direction. The other fermions in the event have preferentially lower energies, but still are predominantly generated in the forward di- rection. If no e+e- pair is present in the final state, the outgoing fermions have a flat energy distribution

Conversion Annihilation

Bremsstrahlung Multiperipheral

e-)fc2’

2

b-f--;

Fig. 1. The lowest-order Feynman diagrams for the process e+ e- --) f,T,f&.

up to the beam energy and a forward angular distri- bution.

This letter analyses the final states produced at LEP2 by neutral-gauge-boson exchange, i.e. a y or Z. These final states have already been observed at the Z resonance [2]. They can be classified as either

!!/“/’ or //qq events, where /, /’ = e, I_L or r.

2. Data and Monte Carlo samples

The data were collected by the L3 detector 131 at LEP in 1995 and 1996. The data sample corresponds to integrated luminosities of 4.9 pb-‘, 10.7 pb-’ and 10.1 pb-’ at &= 130.3-136.3 GeV, 161.3GeV and 170.3-172.3 GeV, respectively.

To determine the efficiency of our selection crite- ria, the EXCALIBUR [4] Monte Carlo is used to simulate the four-fermion events. These events are generated requiring a minimum momentum for the outgoing fermions of 1 GeV, a minimum invariant mass for each combination of two fermions of 1 GeV and an angle of at least 5” for the outgoing fermions with respect to the beam axis, in this way reducing the contribution from the multiperipheral diagrams.

Possible background comes from fermion-pair pro- duction and charged-current four-fermion events. For the fermion-pair production, radiative Bhabha events are generated using BHAGENE 3 [5] and radiative di-muon and di-tau samples using KORALZ 4.02 [6]. The hadronic background events are generated with PYTHIA 5.72 [7]. For the background coming from the charged-current four-fermion processes, i.e.

where the W boson takes part in the process, KO- RALW 1.21 [8] and PYTHIA 5.718 [7] are used to simulate the reactions e+e- -+ WW and efe- + Wev, respectively.

The L3 detector response is simulated using the GEANT 3.15 program [9], which takes into account the effects of energy loss, multiple scattering and showering in the detector. The GHEISHA program [lo] is used to simulate hadronic interactions in the detector.

3. Four-fermion event selection

Two different event selections are developed, one

for the low-multiplicity (/‘J@‘/‘/‘) and another for

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196 M. Acciarri et al./ Physics Letters B 413 (1997) 191-200 the high-multiplicity (//qq> topologies. The se-

lected criteria for each are described below.

3.1. Lepton identification 3. I. 1. Electrons

Electrons are identified as energy depositions in the electromagnetic calorimeter which are consistent with electromagnetic showers. If the calorimetric cluster is within lcos8) < 0.95, a charged track from the central tracking chamber is required to be associ- ated with it. The track must have a momentum greater than 0.5 GeV and a distance of closest ap- proach to the interaction vertex in the plane perpen- dicular to the beam direction of less than 10 mm.

The same track requirements are also used for the identification of the other leptons. The cluster is selected requiring E, > 1 GeV, where E, is the energy deposited in the electromagnetic calorimeter.

The corresponding deposition in the hadron calorimeter has to be consistent with the tail of an electromagnetic shower (i.e. E,/E, < 0.2 and E,

< 5 GeV, where E, is the energy in the hadronic calorimeter). Finally, the ratio of the energy in a 3 X 3 crystal matrix corrected for lateral leakage to the energy in a 5 X 5 crystal matrix centred around the center of gravity of the electromagnetic shower (Z9/225) is required to be greater than 0.93.

If the identified electrons are in hadronic events, as happens for the /‘/qq final states, the quality cuts are tightened and isolation cuts are applied to reject the background from hadronic semileptonic decays.

We require that x,‘, < 4.5, where the ,Y,,, is an estimator of the consistency of the shower being electromagnetic, and 29/X25 must be larger than 0.975. Moreover, the difference in the azimuthal angle between the electromagnetic cluster and the charged track must be less than 10 mrad, and there must not be more than one track in a cone with a 20”

half-opening-angle around the electron.

3.1.2. Muons

Muons are identified as tracks in the muon cham- bers pointing to the interaction point. The calori- metric clusters and the tracks in the central chambers which are matched within 100 mrad in the azimuthal and polar angles are associated with those muons.

Isolation criteria are applied to the identified muons

if they are in hadronic events: the calorimetric en- ergy in the region between cones of 5” and 10”

half-opening-angles around the muon direction must be less than 5GeV. The number of tracks in the central tracking chamber in a cone of 20” half-open- ing-angle around the muon direction has to be less than two. Finally, at most one calorimetric cluster is allowed in the angular region between 5” and 20”

around the muon direction.

3.1.3. Taus

The hadronically-decaying taus are identified as one, two or three tracks with calorimetric energy greater than 2GeV. Candidates with two tracks asso- ciated to the tau are kept to account for the finite double-track resolution of the central tracking cham- ber. The tau energy is defined as the energy of the clusters within a 10” angle around the tau-jet direc- tion, which is computed as the sum of the momen- tum vectors of the calorimetric clusters. In order to separate the hadronic-tau candidates from other hadronic jets, the following restrictions are made: not more than one track and live calorimetric clusters in the region 10” < cx < 30” are allowed, where (Y is the half-opening-angle of a cone around the tau direc- tion, and the ratio of the energies deposited in 10” <

(Y < 30” and (Y < 10” must be below 0.5. The lepton- ically-decaying taus are identified as either electrons or muons, as previously described.

3.2. The low-~ultiplici~ event selection

To reject high-multiplicity events, we demand fewer than 10 charged tracks and fewer than 15 calorimetric clusters in the event. The visible energy is required to be larger than 0.2 * 6. At least three leptons are required in the event if there is a calori- metric deposition in the low-polar-angle detector, the forward lead-scintillator calorimeter (ALR). Other- wise, at least four leptons are required. Two of the selected leptons must have the same flavour. A minimum energy of 2 GeV for electrons and 3 GeV for muons and taus is required.

In Fig. 2, the comparison after all the cuts be- tween the data and Monte Carlo is shown for the energy of all the leptons (excluding those in the ALR), the invariant mass of the pair of leptons of the

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M. Acciarri et al. / Physics Letters B 413 (1997) 191-200 197

I

?2 $1.5

-1

Mllm=

(GeV)

Fig. 2. Distributions for the low-multiplicity selection (//‘/“/‘) of (a) the lepton energy, (b) the highest lepton-pair invariant mass per event for leptons of the same flavour and (c) the correspond- ing recoil mass. The open histograms are the Monte Carlo pre- dicted four-fermion distributions, the hatched histograms are the Monte Carlo predicted background distributions and the points are the data events.

same flavour with the highest invariant mass and the corresponding recoil mass. The recoil mass is de- fined as the missing mass against the chosen pair of leptons. In the first plot, there are at least three entries per event, depending on the number of se- lected leptons. The characteristics of the data events which survive the selection at the three centre-of- mass energies are listed in Table 1.

3.3.

The high-multiplicity event selection

J

The !/qq events are characterized by hadronic jets and a pair of leptons isolated from the hadronic system. Only the configuration with a pair of isolated electrons or muons is investigated. No dedicated selection of rrqq events is performed, thus the surviving events come from the eeqq and pkqq selections. To select hadronic events, at least five charged tracks and 1.5 calorimetric clusters are re-

Table 1

Candidate events from the low-multiplicity and high-multiplicity selections: the centre-of-mass energy, the observed final state, the lepton-pair invariant mass and the corresponding recoil mass are reported. For the low-multiplicity selection the lepton-pair used in the calculation is the one with the highest invariant mass, exclud- ing leptons tagged by the ALR. This corresponds to the first lepton-pair reported in the second column Negative squared invariant masses are not reported

Selection fi (GeV) Final state M$x(GeV) M,,(GeV) Low-multiplicity 130.3 eet+ 85.7kO.8 39+3

161.3 t+ee 10.1 tro.2 10812 161.3 i+ee 84.7 + 2.7 35&16

172.3 eeee 161.9* 1.3 -

172.3 eeee 66.8rtO.6 23*7

&(GeV) Final state M//(GeV) M,,(GeV) High-multiplicity 136.3 eeqq 81 f 10 49+5

161.3 eeqq 78.1kO.7 38*4

172.3 eeqq 76.2 + 0.7 39*4 172.3 eeqq 145.1 f 1.2 11 k24

0

a) L3 . Y o I,

8 l-

& 0.5 -L

M,, KW

Fig. 3. Distributions for the high-multiplicity selection (/tqq) of (a) the lepton-pair invariant mass and (b) the their recoil mass.

The open histograms are the Monte Carlo predicted four-fermion distributions, the hatched histograms are the Monte Carlo pre- dicted background distributions and the points are the data events.

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198 M. Acciarri et al. /Physics Letters B 413 (1997) 191-200

quired. The visible energy must be greater than 0.5 . 6 and, finally, a pair of electrons or muons, or an electron and a calorimetric deposition in the ALR is required. The energy of each lepton is required to exceed 3GeV. The selected electrons and muons have to satisfy the isolation cuts and the tighter set of quality cuts since they are in a hadronic environ- ment.

In Fig. 3, the distributions of the invariant mass of the two selected leptons and their recoil mass are shown for the data and Monte Carlo, after the cuts.

All data events which survive the selection contain two identified electrons; no event with two muons is found. The data events which pass the selection at the three centre-of-mass energies are listed in Table 1, where the invariant mass and the recoil mass of the two electrons are presented.

4. Efficiencies and systematic errors

The selection efficiency for signal events is evalu- ated using Monte Carlo simulation. The efficiencies of the low-multiplicity and high-multiplicity event selections are given in Table 2 with the correspond- ing systematic errors from the Monte Carlo statistics only. The efficiencies are calculated for events in which all four-fermions have an angle of at least 5”

with respect to the beam axis. From Table 2, it can be seen that the cross feeding between channels is very small. The main sources of systematic errors are the detector uncertainties and inefficiencies, which include: (a) uncertainty on the energy intercalibration constants; (b) uncertainty on the global energy scale;

(c) uncertainty on the tracking inefficiency; and the Monte Carlo statistics. To estimate effect (a>, each energy calibration constant was varied independently according to a normal distribution with a standard deviation of 5%, as explained in detail in Ref. [ll].

To estimate effect (b), the total energy was shifted by +3% and, finally, to take into account effect cc>, 2%, of the tracks were randomly eliminated in the Monte Carlo events. The net effect of these errors due to the detector systematics on the signal effi- ciency is found to be at most 2%, which is usually less than the Monte Carlo statistical error.

The dominant error on the number of expected

Table 2

Low-multiplicity and high-multiplicity event selection efficiencies for the k’/k”!’ and /k’qq channels, with the corresponding Monte Carlo statistical error, for the three centre-of-mass energies

Selection & /‘F/F Channel f!aa Channel Low- 130-136 GeV (8.1+ 0.31% (0.06 f 0.02)%

multiplicity 161 GeV (6.8 f 0.21% to.05 + O.Ol)%

170-172 GeV (7.7 +o.z)% (0.08 + 0.021%

High- 130-l 36 GeV (0.32 k 0.06)% (8.5 *0.3)%

multiplicity 161 GeV (0.27 + 0.031% (7.1 + 0.21%

170-172 GeV (0.25 +0.03)% (7.7 + 0.2)%

background events is also due to the Monte Carlo statistics, which gives a contribution of at least 10%.

Moreover, an overall normalisation error, estimated to be lo%, due to the finite precision of the event generators is taken into account.

5. Results

The total number of events expected from the signal, the background and the number of events observed in the data after all the cuts are shown in Table 3, where the total error is also reported.

Due to the lack of statistics, the cross sections U/cel/ and U/Y,, of the processes e+e- +/Yc@‘/’

and e+e- +/‘/qq are determined simultaneously in a one-variable maximum-likelihood fit by fixing the ratio of the two cross sections to the Standard Model value. This corresponds to a determination of the total cross section gtot = ff,,,t/ + a,,,,. The mea- surement of this total cross section is done indepen- dently for the three centre-of-mass energies. The total likelihood is given by the product of the Pois- son probabilities, P(Ni,pi), for the low-multiplicity (i = 1) and high-multiplicity (i = 2) selections, where Ni is the number of selected events and pi the number of expected events:

j=i,2 _ _

Here, eij is the efficiency of selection i to accept events from process j, where j = 1 for the //J”/

channel and j = 2 for the //qq channel. Moreover,

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M. Acciarri et al. / Physics Letters B 413 (19971 191-200 199

Table 3

The number of expected four-fermion and background events, with their total errors, and the number of data events observed at the three centre-of-mass energies

Process fi = 130-136GeV 6 = 161 GeV 6 = 170-172GeV

eeee. 0.50 f 0.02 0.66 f 0.04 0.65 + 0.04

ecpk 0.29 f 0.02 0.38 + 0.06 0.35 + 0.05

ee77 0.10 + 0.01 0.14 * 0.03 0.13 F 0.03

ILPW 0.0250 i 0.0008 0.029 f 0.002 0.024 f 0.002

)*ILTT 0.024 + 0.001 0.029 + 0.003 0.025 f 0.002

7777 0.0034 f 0.0004 0.0051 + 0.0009 0.0034 f 0.0006

eee’e’ 0.95 + 0.03 1.23 + 0.08 1.18 + 0.07

eeqq 0.93 f 0.03 1.16 + 0.06 1.09 + 0.06

PPW 0.210 f 0.004 0.27 + 0.01 0.29 + 0.01

774q 0.012 * 0.001 0.014 i 0.002 0.012 i 0.002

f/W 1.15 f 0.03 1.45 i 0.06 1.40 f 0.06

Total Signal 2.10 + 0.04 2.7 + 0.1 2.56 f 0.09

Background 0.8 f 0.3 0.71 + 0.09 0.8 + 0.2

Data 2 3 4

Nibkgd is the number of expected background events and L, is the integrated luminosity for selection i.

Finally, uj is the cross section for process j. The systematic error on the cross section is estimated as the RMS of the measured cross section obtained with a random variation of the signal efficiency and the number of expected background events, according to their total errors. The measured total cross sections are:

ff tot = 2.9?‘$ (stat) f 0.17 (sys) pb (5.2pb) at& = 133GeV

u 101 = 3.2?::: (stat) at6 = 161GeV cr tot = 4.1:;:; (stat)

at& = 172GeV

+ O.O6(sys) pb (3.4pb)

+O.O8(sys)pb (3.2pb)

The Standard Model values for the cross sections are given in parentheses. Assuming the scaling of the cross sections with energy from the Standard Model, a,,,‘!’ and c//qq at any energy can be taken as

unknown parameters to be measured independently.

For instance at & = 161 GeV:

~j>>~,=2.0?~:~(stat)fO.O4(sys)pb crjyq, = 1.31 h:i (stat) + 0.03 (sys) pb

Finally, assuming both the scaling with energy and the ratio of the cross sections a,,,‘/ and a,,,, from the Standard Model, only one parameter is left free in the fit. Chosing the total cross section at &

= 161 GeV as free parameter, we measure:

a161 = 3.3’;:: IO, (stat) +0.05 (sys) pb

The results agree with the Standard Model predic- tions and there is no indication of any new physics.

Acknowledgements

We wish to express our gratitude to the CERN accelerator divisions for the excellent performance of the LEP machine. We acknowledge the contributions of all the engineers and technicians who have partici-

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200 M. Acciarri et al./Physics Letters B 413 (1997) 191-200 pated in the construction and maintenance of this

experiment.

References

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