Study of the e + e −→ Zγγ→ q q ̄ γγ process at LEP

26 April 2001

Physics Letters B 505 (2001) 47–58www.elsevier.nl/locate/npe

Study of the e+e− → Zγ γ → qq̄γ γ process at LEP

L3 Collaboration

M. Acciarri z, P. Achardt, O. Adrianiq, M. Aguilar-Benitezy, J. Alcarazy,G. Alemanniv, J. Allabyr, A. Aloisio ab, M.G. Alviggi ab, G. Ambrosit, H. Anderhubav,V.P. Andreevg,ag, T. Angelescum, F. Anselmoj, A. Arefievaa, T. Azemoond, T. Azizk,

P. Bagnaiaal, A. Bajoy, L. Baksayaq, A. Balandrase, S.V. Baldewc, S. Banerjeek,Sw. Banerjeee, A. Barczykav,at, R. Barillèrer, P. Bartaliniv, M. Basilej, N. Batalovaas,

R. Battistonaf, A. Bayv, F. Becattiniq, U. Beckero, F. Behnerav, L. Bellucciq,R. Berbecod, J. Berdugoy, P. Bergeso, B. Bertucciaf, B.L. Betevav, S. Bhattacharyak,M. Biasiniaf, M. Biglietti ab, A. Bilandav, J.J. Blaisinge, S.C. Blythah, G.J. Bobbinkc,A. Böhma,b, L. Boldizsarn, B. Borgiaal, D. Bourilkovav, M. Bourquint, S. Braccinit,

J.G. Bransonan, F. Brochue, A. Buffini q, A. Buijsar, J.D. Burgero, W.J. Burgeraf,X.D. Caio, M. Capello, G. Cara Romeoj, G. Carlinoab, A.M. Cartacciq, J. Casausy,G. Castelliniq, F. Cavallarial, N. Cavalloai, C. Cecchiaf, M. Cerraday, F. Cesaroniw,

M. Chamizot, Y.H. Changax, U.K. Chaturvedis, M. Chemarinx, A. Chenax, G. Chenh,G.M. Chenh, H.F. Chenu, H.S. Chenh, G. Chiefariab, L. Cifarelli am, F. Cindoloj,

C. Civinini q, I. Clareo, R. Clareak, G. Coignete, N. Colinoy, S. Costantinif ,F. Cotorobaim, B. de la Cruzy, A. Csillingn, S. Cucciarelliaf, T.S. Daio,

J.A. van Dalenad, R. D’Alessandroq, R. de Asmundisab, P. Déglont, A. Degrée,K. Deitersat, D. della Volpeab, E. Delmeiret, P. Denesaj, F. DeNotaristefanial,

A. De Salvoav, M. Diemozal, M. Dierckxsensc, D. van Dierendonckc, C. Dionisial,M. Dittmarav, A. Dominguezan, A. Doriaab, M.T. Dovas,5, D. Duchesneaue,

D. Dufournaude, P. Duinkerc, H. El Mamounix, A. Englerah, F.J. Epplingo, F.C. Ernéc,A. Ewersa,b, P. Extermannt, M. Fabreat, M.A. Falagany, S. Falcianoal,r, A. Favarar,

J. Fayx, O. Fedinag, M. Felciniav, T. Fergusonah, H. Fesefeldta,b, E. Fiandriniaf,J.H. Fieldt, F. Filthautr, P.H. Fishero, I. Fiskan, G. Forconio, K. Freudenreichav,C. Furettaz, Yu. Galaktionovaa,o, S.N. Gangulik, P. Garcia-Abiaf, M. Gataullinae,S.S. Gaul, S. Gentileal,r, N. Gheordanescum, S. Giagual, Z.F. Gongu, G. Grenierx,

O. Grimmav, M.W. Gruenewaldi, M. Guidaam, R. van Gulikc, V.K. Guptaaj, A. Gurtuk,L.J. Gutayas, D. Haasf, A. Hasanac, D. Hatzifotiadouj, T. Hebbekeri, A. Hervér,

P. Hidasn, J. Hirschfelderah, H. Hoferav, G. Holznerav, H. Hooraniah, S.R. Houax,Y. Hu ad, I. Iashvili au, B.N. Jinh, L.W. Jonesd, P. de Jongc, I. Josa-Mutuberríay,

0370-2693/01/$ – see front matter 2001 Published by Elsevier Science B.V.PII: S0370-2693(01)00308-2

48 L3 Collaboration / Physics Letters B 505 (2001) 47–58

R.A. Khans, D. Käfera,b, M. Kaurs,6, M.N. Kienzle-Focaccit, D. Kim al, J.K. Kimap,J. Kirkbyr, D. Kissn, W. Kittel ad, A. Klimentovo,aa, A.C. Königad, M. Kopalas,

A. Koppau, V. Koutsenkoo,aa, M. Kräberav, R.W. Kraemerah, W. Krenza,b, A. Krügerau,A. Kunin o,aa, P. Ladron de Guevaray, I. Laktinehx, G. Landiq, M. Lebeaur,

A. Lebedevo, P. Lebrunx, P. Lecomteav, P. Lecoqr, P. Le Coultreav, H.J. Leei,J.M. Le Goffr, R. Leisteau, P. Levtchenkoag, C. Li u, S. Likhodedau, C.H. Linax,

W.T. Lin ax, F.L. Lindec, L. Listaab, Z.A. Liu h, W. Lohmannau, E. Longoal, Y.S. Luh,K. Lübelsmeyera,b, C. Lucir,al, D. Luckeyo, L. Lugnierx, L. Luminarial,

W. Lustermannav, W.G. Mau, M. Maity k, L. Malgerit, A. Malinin r, C. Mañay,D. Mangeolad, J. Mansaj, G. Marianp, J.P. Martinx, F. Marzanoal, K. Mazumdark,

R.R. McNeilg, S. Meler, L. Merolaab, M. Meschiniq, W.J. Metzgerad,M. von der Meya,b, A. Mihul m, H. Milcentr, G. Mirabellial, J. Mnicha,b,

G.B. Mohantyk, T. Moulik k, G.S. Muanzax, A.J.M. Muijsc, B. Musicaran, M. Musyal,M. Napolitanoab, F. Nessi-Tedaldiav, H. Newmanae, T. Niessena,b, A. Nisatial,H. Nowakau, R. Ofierzynskiav, G. Organtinial, A. Oulianovaa, C. Palomaresy,

D. Pandoulasa,b, S. Paolettial,r, P. Paolucciab, R. Paramattial, H.K. Parkah, I.H. Parkap,G. Passalevar, S. Patricelliab, T. Paull, M. Pauluzziaf, C. Pausr, F. Paussav, M. Pedaceal,

S. Pensottiz, D. Perret-Gallixe, B. Petersenad, D. Piccoloab, F. Pierellaj, M. Pieriq,P.A. Pirouéaj, E. Pistolesiz, V. Plyaskinaa, M. Pohlt, V. Pojidaevaa,q, H. Postemao,J. Pothierr, D.O. Prokofievas, D. Prokofievag, J. Quartieriam, G. Rahal-Callotav,r,M.A. Rahamank, P. Raicsp, N. Rajak, R. Ramelliav, P.G. Rancoitaz, R. Ranieriq,A. Rasperezaau, G. Ravenan, P. Razisac, D. Renav, M. Rescignoal, S. Reucroftl,

S. Riemannau, K. Rilesd, J. Rodinaq, B.P. Roed, L. Romeroy, A. Roscai,S. Rosier-Leese, S. Rotha,b, C. Rosenblecka,b, B. Rouxad, J.A. Rubior, G. Ruggieroq,H. Rykaczewskiav, S. Saremig, S. Sarkaral, J. Salicior, E. Sanchezr, M.P. Sandersad,C. Schäferr, V. Schegelskyag, S. Schmidt-Kaersta,b, D. Schmitza,b, H. Schopperaw,

D.J. Schotanusad, G. Schweringa,b, C. Sciaccaab, A. Segantij , L. Servoliaf,S. Shevchenkoae, N. Shivarovao, V. Shoutkoaa, E. Shumilovaa, A. Shvorobae,

T. Siedenburga,b, D. Sonap, B. Smithah, P. Spillantiniq, M. Steuero, D.P. Sticklandaj,A. Stoneg, B. Stoyanovao, A. Straessnerr, K. Sudhakark, G. Sultanovs, L.Z. Sunu,S. Sushkovi, H. Suterav, J.D. Swains, Z. Szillasiaq,3, T. Sztaricskaiaq,3, X.W. Tangh,

L. Tauscherf, L. Taylorl, B. Tellili x, D. Teyssierx, C. Timmermansad,Samuel C.C. Tingo, S.M. Tingo, S.C. Tonwark, J. Tóthn, C. Tully r, K.L. Tungh,

Y. Uchidao, J. Ulbrichtav, E. Valenteal, G. Vesztergombin, I. Vetlitskyaa,D. Vicinanzaam, G. Viertelav, S. Villaak, M. Vivargente, S. Vlachosf, I. Vodopianovag,H. Vogelah, H. Vogtau, I. Vorobievah, A.A. Vorobyovag, A. Vorvolakosac, M. Wadhwaf,

W. Wallraff a,b, M. Wango, X.L. Wangu, Z.M. Wangu, A. Webera,b, M. Webera,b,P. Wienemanna,b, H. Wilkensad, S.X. Wuo, S. Wynhoffr, L. Xia ae, Z.Z. Xuu,

L3 Collaboration / Physics Letters B 505 (2001) 47–58 49

J. Yamamotod, B.Z. Yangu, C.G. Yangh, H.J. Yangh, M. Yangh, J.B. Yeu, S.C. Yehay,An. Zaliteag, Yu. Zaliteag, Z.P. Zhangu, G.Y. Zhuh, R.Y. Zhuae, A. Zichichi j,r,s,

G. Zilizi aq,3, B. Zimmermannav, M. Zöller a,b

a I. Physikalisches Institut, RWTH, D-52056 Aachen, Germany1

b III. Physikalisches Institut, RWTH, D-52056 Aachen, Germany1

c National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam, The Netherlandsd University of Michigan, Ann Arbor, MI 48109, USA

e Laboratoire d’Annecy-le-Vieux de Physique des Particules, LAPP, IN2P3-CNRS, BP 110, F-74941 Annecy-le-Vieux CEDEX, Francef Institute of Physics, University of Basel, CH-4056 Basel, Switzerland

g Louisiana State University, Baton Rouge, LA 70803, USAh Institute of High Energy Physics, IHEP, 100039 Beijing, China7

i Humboldt University, D-10099 Berlin, Germany1

j University of Bologna and INFN-Sezione di Bologna, I-40126 Bologna, Italyk Tata Institute of Fundamental Research, Bombay 400 005, India

l Northeastern University, Boston, MA 02115, USAm Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania

n Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary2

o Massachusetts Institute of Technology, Cambridge, MA 02139, USAp KLTE-ATOMKI, H-4010 Debrecen, Hungary3

q INFN Sezione di Firenze and University of Florence, I-50125 Florence, Italyr European Laboratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerland

s World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerlandt University of Geneva, CH-1211 Geneva 4, Switzerland

u Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, PR China7

v University of Lausanne, CH-1015 Lausanne, Switzerlandw INFN-Sezione di Lecce and Università Degli Studi di Lecce, I-73100 Lecce, Italy

x Institut de Physique Nucléaire de Lyon, IN2P3-CNRS,Université Claude Bernard, F-69622 Villeurbanne, Francey Centro de Investigaciones Energéticas, Medioambientales y Tecnologícas, CIEMAT, E-28040 Madrid, Spain4

z INFN-Sezione di Milano, I-20133 Milan, Italyaa Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russiaab INFN-Sezione di Napoli and University of Naples, I-80125 Naples, Italyac Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus

ad University of Nijmegen and NIKHEF, NL-6525 ED Nijmegen, The NetherlandsaeCalifornia Institute of Technology, Pasadena, CA 91125, USA

af INFN-Sezione di Perugia and Università Degli Studi di Perugia, I-06100 Perugia, Italyag Nuclear Physics Institute, St. Petersburg, Russia

ah Carnegie Mellon University, Pittsburgh, PA 15213, USAai INFN-Sezione di Napoli and University of Potenza, I-85100 Potenza, Italy

aj Princeton University, Princeton, NJ 08544, USAak University of Californa, Riverside, CA 92521, USA

al INFN-Sezione di Roma and University of Rome, La Sapienza, I-00185 Rome, Italyam University and INFN, Salerno, I-84100 Salerno, Italyan University of California, San Diego, CA 92093, USA

ao Bulgarian Academy of Sciences, Central Lab. of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgariaap Laboratory of High Energy Physics, Kyungpook National University, 702-701 Taegu, South Korea

aq University of Alabama, Tuscaloosa, AL 35486, USAar Utrecht University and NIKHEF, NL-3584 CB Utrecht, The Netherlands

asPurdue University, West Lafayette, IN 47907, USAat Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland

au DESY, D-15738 Zeuthen, Germanyav Eidgenössische Technische Hochschule, ETH Zürich, CH-8093 Zürich, Switzerland

aw University of Hamburg, D-22761 Hamburg, Germanyax National Central University, Chung-Li, Taiwan, ROC

ay Department of Physics, National Tsing Hua University, Taiwan, ROC

Received 29 January 2001; accepted 15 February 2001


Editor: K. Winter

Abstract

The process e+e− → Zγ γ → qq̄γ γ is studied in 0.5 fb−1 of data collected with the L3 detector at centre-of-mass energiesbetween 130.1 GeV and 201.7 GeV. Cross sections are measured and found to be consistent with the Standard Modelexpectations. The study of the least energetic photon constrains the quartic gauge boson couplings to−0.008 GeV−2 <

a0/Λ2< 0.005 GeV−2 and−0.007 GeV−2< ac/Λ

2< 0.011 GeV−2, at 95% confidence level. 2001 Published by ElsevierScience B.V.

1. Introduction

The LEP data offer new insight into the StandardModel of electroweak interactions [1] by investigat-ing the production of three gauge bosons. Results wererecently reported on studies of the reactions e+e− →Zγ γ [2] and e+e− → W+W−γ [3,4]. This Letter de-scribes the extension of the study of the e+e− → Zγ γprocess to centre-of-mass energies,

√s, between 130

and 202 GeV. Final states with hadrons and isolatedphotons are considered to select Zγ γ → qq̄γ γ events.

In the Standard Model, the e+e− → Zγ γ processoccurs via radiation of photons from the incomingelectron and/or positron. One possible diagram ispresented in Fig. 1(a).

The e+e− → Zγ γ signal is defined by phase-spacerequirements on the energiesEγ and anglesθγ of thetwo photons, and on the propagator mass

√s′:

(1)Eγ > 5 GeV,

(2)|cosθγ |< 0.97,

(3)∣∣√s′ −mZ

∣∣< 2ΓZ,

1 Supported by the German Bundesministerium für Bildung,Wissenschaft, Forschung und Technologie.

2 Supported by the Hungarian OTKA fund under contractnumbers T019181, F023259 and T024011.

3 Also supported by the Hungarian OTKA fund under contractnumbers T22238 and T026178.

4 Supported also by the Comisión Interministerial de Ciencia yTecnología.

5 Also supported by CONICET and Universidad Nacional de LaPlata, CC 67, 1900 La Plata, Argentina.

6 Also supported by Panjab University, Chandigarh-160014,India.

7 Supported by the National Natural Science Foundation ofChina.

wheremZ andΓZ are the Z boson mass and width.In the following, hadronic decays of the Z bosonare considered. Events with hadrons and initial statephotons falling outside the signal definition cuts arereferred to as “non-resonant” background.

A single initial state radiation photon can alsolower the effective centre-of-mass energy of the e+e−collision tomZ, with the subsequent production of aquark–antiquark pair. This photon can be mistaken forthe most energetic photon of the e+e− → Zγ γ →qq̄γ γ process. Two sources can then mimic the leastenergetic photon: either the direct radiation of photonsfrom the quarks or photons originating from hadronicdecays, misidentified electrons or unresolvedπ0s.These background processes are depicted in Figs. 1(b)and 1(c), respectively.

In order to compare experimental results with e+e−→ qq̄γ γ matrix element calculations, a further re-quirement is applied on the angleθγq between the pho-tons and the nearest quark:

(4)cosθγq< 0.98.

This cut avoids collinear divergences. Its inclusionmakes the signal definition used here different fromthe previous one [2]. Signal cross sections calculatedwith the KK2f Monte Carlo program [5] range from0.9 pb at

√s = 130.1 GeV down to 0.3 pb at

√s =

201.7 GeV.The Zγ γ final state could also originate from the

s-channel exchange of a Z boson, as presented inFig. 1(d). This process is forbidden at tree level inthe Standard Model, but it is expected to occur in thepresence of Quartic Gauge boson Couplings (QGC)beyond the Standard Model.


(a) (b)

(c) (d)

Fig. 1. Diagrams of (a) the Standard Model contribution to e+e− → Zγ γ signal and “non-resonant” background, (b) the background from directradiation of photon from the quarks, (c) the background from photons, misidentified electrons or unresolvedπ0s originating from hadrons and(d) the anomalous QGC diagram.

2. Data and Monte Carlo samples

This measurement uses data collected with theL3 detector [6] at LEP in the years from 1995through 1999, at centre-of-mass energies between√s = 130.1 GeV and

√s = 201.7 GeV, for a total

integrated luminosity of 0.5 fb−1. The centre-of-massenergies and the corresponding integrated luminositiesare listed in Table 1. Given their relatively low lumi-nosities, the

√s = 130.1 GeV and

√s = 136.1 GeV

data sample are combined into a single luminosityaveraged sample at

√s = 133.1 GeV. Similarly the√

s = 161.3 GeV and√s = 172.3 GeV samples are

merged into a single sample at√s = 166.8 GeV.

The KK2f Monte Carlo program is used to gen-erate e+e− → qq̄(γ γ ) events, that are assigned tothe signal or the background according to the cri-teria (1)–(4). The hadronisation process is simulatedwith the JETSET [7] program. Other backgroundprocesses are generated with the Monte Carlo pro-grams PYTHIA [7] (e+e− → Ze+e− and e+e− →ZZ), KORALZ [8] (e+e− → τ+τ−(γ )), PHOJET [9]

Table 1Average centre-of-mass energies and corresponding integrated lu-minosities of the data samples used for this analysis√s (GeV) Integrated luminosity (pb−1)

133.1 12.0

166.8 21.1

182.7 55.3

188.7 176.3

191.6 29.4

195.5 83.7

199.5 82.8

201.7 37.0

(e+e− → e+e− hadrons) and KORALW [10] forW+W− production except for the eνeqq̄′ final states,generated with EXCALIBUR [11].

The L3 detector response is simulated using theGEANT [12] and GHEISHA [13] programs, whichmodel the effects of energy loss, multiple scattering


Table 2Energy dependent criteria for the selection of e+e− → Zγ γ → qq̄γ γ events√s (GeV) 133.1 166.8 182.7 188.7 191.6 195.5 199.6 201.7

βZ < 0.48 0.61 0.64 0.66 0.66 0.67 0.69 0.70

Eγ1 (GeV)< 31.9 55.0 67.6 69.8 72.8 74.2 75.8 76.6

and showering in the detector. Time dependent detec-tor inefficiencies, as monitored during data taking pe-riods, are also simulated.

3. Event selection

The e+e− → Zγ γ → qq̄γ γ selection demands bal-anced hadronic events with two isolated photons andsmall energy deposition at low polar angle. Selec-tion criteria on photon energies and angles follow di-rectly from the signal definition asEγ > 5 GeV and|cosθγ |< 0.97. The invariant massMqq̄ of the recon-structed hadronic system, forced into two jets usingthe DURHAM algorithm [14], is required to be consis-tent with a Z boson decaying into hadrons, 72 GeV<Mqq̄< 116 GeV.

The main background after these requirements isdue to the “non-resonant” production of two photonsand a hadronic system. The relativistic velocityβZ =pZ/EZ of the system recoiling against the photons,calculated assuming its mass to be the nominal Z mass,is larger for part of these background events than forthe signal and an upper cut is used to reject thoseevents. It is optimised for each centre-of-mass energy,as listed in Table 2.

Other classes of background events, shown in Figs.1(b) and 1(c), are rejected by an upper bound onthe energyEγ1 of the most energetic photon. Thisrequirement, presented in Table 2, suppresses theresonant return to the Z, whose photons are harder thanthe signal ones. A lower bound of 17◦ on the angleωbetween the least energetic photon and the closest jetis also imposed. This requirement is more restrictivethan the similar cut on cosθγq included in the signaldefinition. Data and Monte Carlo distributions of theselection variables are presented in Fig. 2 for thedata collected at

√s = 192–202 GeV when selection

criteria on all the other variables are applied. Goodagreement between data and Monte Carlo is observed.

4. Results

The signal efficiencies and the numbers of eventsselected in the data and Monte Carlo samples aresummarised in Table 3. The dominant background ishadronic events with photons. About half of these are“non-resonant” events. In the remaining cases, theyoriginate either from final state radiation or are fakephotons.

A clear signal structure is observed in the spectraof the recoil mass to the two photons, as presented inFig. 3 for the

√s = 192–202 GeV data sample and for

the total one. The e+e− → Zγ γ → qq̄γ γ cross sec-tions,σ , are determined from a fit to the correspondingspectra at each

√s. Background predictions are fixed

in the fit. The results are listed in Table 4 with theirstatistical and systematic uncertainties. The system-atic uncertainties on the cross section measurement areof the order of 10% [2]. The main contributions arisefrom the signal and background Monte Carlo statistics(6%) and a variation of±2% of the energy scale ofthe hadronic calorimeter (6%). A variation of±0.5%of the energy scale of the electromagnetic calorimeterdoes not yield sizable effects. Other sources of sys-tematic uncertainties are the selection procedure (3%)and the background normalisation (3%). The latter isestimated by varying by 10% the normalisation of the“non-resonant” background, as estimated from a com-parison between the KK2f and PYTHIA Monte Carlopredictions for hadronic events with photons, and by20% that of the other backgrounds. Uncertainties onthe determination of the integrated luminosity are neg-ligible.

The measurements are in good agreement withthe theoretical predictionsσSM, as calculated with


Fig. 2. Distributions of (a) the invariant massMqq̄ of the hadronic system, (b) the relativistic velocityβZ of the reconstructed Z boson, (c) theenergyEγ1 of the most energetic photon and (d) the angleω between the least energetic photon and the nearest jet. Data, signal and backgroundMonte Carlo samples are shown for

√s = 192–202 GeV. The arrows show the position of the final selection requirements. In each plot, the

selection criteria on the other variables are applied.


Fig. 3. Recoil mass to the photon pairs in data, Zγ γ and background Monte Carlo for (a)√s = 192–202 GeV and (b) the total sample.

Fig. 4. The cross section of the process e+e− → Zγ γ → qq̄γ γ as a function of the centre-of-mass energy. The signal is defined by thephase-space cuts of Eqs. (1)–(4). The width of the band corresponds to the Monte Carlo statistics and theory uncertainties. Dashed and dottedlines represent anomalous QGC predictions fora0/Λ

2 = 0.015 GeV−2 andac/Λ2 = 0.015 GeV−2, respectively.


Table 3Yields of the e+e− → Zγ γ → qq̄γ γ selection. The signal efficienciesε are given, together with the observed and expected numbers of events.

The right half of the table details the composition of the Monte Carlo samples withNs denoting the signal,Nqq̄b

the q̄q andNOtherb

the otherbackgrounds. The uncertainties are statistical only√s (GeV) ε (%) Data Monte Carlo Ns N

qq̄b

NOtherb

133.1 45 4 5.9±0.5 5.0± 0.5 0.8±0.2 0.08±0.02

166.8 52 4 6.7±0.3 4.9± 0.3 1.4±0.1 0.4±0.1

182.7 51 13 13.6±0.7 10.8± 0.6 2.7±0.2 0.06±0.02

188.7 52 38 40.3±2.0 32.5± 1.7 7.2±1.1 0.6±0.1

191.6 42 2 5.9±0.4 4.1± 0.3 1.8±0.3 0.06±0.02

195.5 46 13 17.5±0.9 12.4± 0.7 4.9±0.5 0.2±0.1

199.6 46 14 15.0±0.8 11.5± 0.6 3.4±0.5 0.13±0.05

201.7 48 9 6.9±0.5 5.2± 0.4 1.7±0.3 0.06±0.02

Table 4Results of the measurements of the e+e− → Zγ γ → qq̄γ γcross section,σ , with statistical and systematic uncertainties. Thepredicted values of cross sections,σSM, are also listed√s (GeV) σ (pb) σSM (pb)

133.1 0.70± 0.40± 0.07 0.923± 0.012

166.8 0.17± 0.13± 0.02 0.475± 0.006

182.7 0.36± 0.13± 0.04 0.379± 0.004

188.7 0.34± 0.06± 0.03 0.350± 0.004

191.6 0.09± 0.09± 0.01 0.326± 0.004

195.5 0.30± 0.11± 0.03 0.321± 0.004

199.6 0.28± 0.11± 0.03 0.304± 0.004

201.7 0.50± 0.18± 0.05 0.296± 0.003

the KK2f Monte Carlo program, listed in Table 4.The error on the predictions (1.5%) is the quadraticsum of the theory uncertainty [5] and the statisticaluncertainty of the Monte Carlo sample generated forthe calculation. These results are presented in Fig. 4together with the expected evolution with

√s of the

Standard Model cross section.The distribution of the recoil mass to the two

photons for the full data sample, presented in Fig. 3(b),is fitted to calculate the ratioRZγ γ between allthe observed data and the signal expectation. Thebackground predictions are fixed in the fit, which

yields:

RZγ γ = σ

σSM = 0.85± 0.11± 0.06,

in agreement with the Standard Model. The first uncer-tainty is statistical while the second is systematic. Thecorrelation of the energy scale and background nor-malisation uncertainties between data samples is takeninto account.

5. Study of quartic gauge boson couplings

The contribution of anomalous QGCs to Zγ γ pro-duction is described by two additional dimension-sixterms in the electroweak Lagrangian [15,16]:

L06 = − πα

4Λ2a0FµνF

µν �Wρ · �Wρ,

Lc6 = − πα4Λ2acFµρF

µσ �Wρ · �Wσ ,whereα is the fine structure constant,Fµν is the fieldstrength tensor of the photon and�Wσ is the weakboson field. The parametersa0 and ac describe thestrength of the QGCs andΛ represents the unknownscale of the New Physics responsible for the anom-alous contributions. In the Standard Model,a0 = ac= 0. A more detailed description of QGCs has recentlyappeared [17]. Indirect limits on QGCs were derivedfrom precision measurements at the Z pole [18].


Fig. 5. Distributions for the least energetic photon: (a) the energyEγ2, (b) the cosine of its polar angle|cosθγ2|, (c) its transverse momentumP tγ2 with respect to the beam axis. Data, signal and background Monte Carlo are displayed for the full data sample together with QGCpredictions.

Anomalous values of QGCs are expected to man-ifest themselves via deviations in the total e+e− →Zγ γ cross section, as presented in Fig. 4. In the Stan-dard Model, Zγ γ production occurs via bremsstrah-lung with the low energy photon preferentially pro-duced close to the beam direction. The QGCs-channelproduction results instead in a harder energy spectrumand a more central angular distribution of the least en-ergetic photon [16]. Distributions for this photon ofthe reconstructed energy, the cosine of the polar angleand the transverse momentum for the full data sampleare compared in Fig. 5 with the predictions from sig-nal and background Monte Carlo. Predictions in thecase of a non zero value ofa0/Λ

2 or ac/Λ2 are alsoshown. They are obtained by reweighting [2] the Stan-

dard Model signal Monte Carlo events with an analyti-cal calculation of the QGC matrix element [16]. MonteCarlo studies indicate the transverse momentum asthe most sensitive distribution to possible anomalousQGC contributions. A fit to this distribution is per-formed for each data sample, leaving one of the twoQGCs free at a time and fixing the other to zero. Ityields the 68% confidence level results:

a0/Λ2 = −0.002+0.003

−0.002 GeV−2 and

ac/Λ2 = −0.001+0.006

−0.004 GeV−2,

in agreement with the expected Standard Model valuesof zero. A simultaneous fit to both the parameters gives


Fig. 6. Two-dimensional contours for the QGC parametersa0/Λ2 andac/Λ2. The fit result is shown together with the Standard Model (SM)

predictions.

the 95% confidence level limits:

−0.008 GeV−2< a0/Λ2< 0.005 GeV−2 and

−0.007 GeV−2< ac/Λ2< 0.011 GeV−2,

as shown in Fig. 6. A correlation coefficient of−57%is observed. The experimental systematic uncertaintiesand those on the Standard Model e+e− → Zγ γ →qq̄γ γ cross section predictions are taken into accountin the fit.

Acknowledgements

We wish to express our gratitude to the CERNaccelerator divisions for the superb performance andthe continuous and successful upgrade of the LEPmachine. We acknowledge the contributions of theengineers and technicians who have participated in theconstruction and maintenance of this experiment.

Appendix A

To allow the combination of our results with thoseof the other LEP experiments, the cross sectionsσ

are also measured in the more restrictive phase spaceobtained by modifying the conditions (2) and (4) into|cosθγ | < 0.95 and cosθγq < 0.9, respectively. Theresults are:

σ(182.7 GeV)= 0.11± 0.11± 0.01 pb

(SM: 0.233± 0.003 pb),

σ (188.7 GeV)= 0.28± 0.07± 0.03 pb

(SM: 0.214± 0.003 pb),

σ (194.5 GeV)= 0.15± 0.07± 0.02 pb

(SM: 0.197± 0.003 pb),

σ (200.2 GeV)= 0.15± 0.07± 0.01 pb

(SM: 0.185± 0.003 pb).

The first uncertainty is statistical, the second sys-tematic and the values in parentheses indicate theStandard Model predictions. The samples at

√s =

192–196 GeV and√s = 200–202 GeV are respec-

tively merged into the√s = 194.5 GeV and

√s =

200.2 GeV ones.

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Study of the e + e −→ Zγγ→ q q ̄ γγ process at LEP

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