Measurement of trilinear gauge couplings in e+e− collisions at 161 GeV and 172 GeV

19 March 1998

Physics Letters B 423 Ž1998. 194–206

Measurement of trilinear gauge couplings in eqey collisions at 161 GeV and 172 GeV DELPHI Collaboration P. Abreu u , W. Adam aw, T. Adye aj, P. Adzic k , G.D. Alekseev p, R. Alemany av, P.P. Allport v, S. Almehed x , U. Amaldi i , S. Amato at , P. Andersson aq , aq ˚ A. Andreazza i , P. Antilogus y, W-D. Apel q , Y. Arnoud n , B. Asman , y i i s u J-E. Augustin , A. Augustinus , P. Baillon , P. Bambade , F. Barao , R. Barbier y, D.Y. Bardin p, G. Barker i , A. Baroncelli am , O. Barring x , M.J. Bates aj, M. Battaglia o , M. Baubillier w, K-H. Becks ay, M. Begalli f , P. Beilliere h , Yu. Belokopytov i,1, A.C. Benvenuti e, C. Berat n , M. Berggren y, D. Bertini y, D. Bertrand b, M. Besancon al , F. Bianchi ar, M. Bigi ar, M.S. Bilenky p, P. Billoir w, M-A. Bizouard s , D. Bloch j, M. Bonesini aa , W. Bonivento aa , M. Boonekamp al , P.S.L. Booth v, A.W. Borgland d , G. Borisov al , C. Bosio am , O. Botner au , E. Boudinov ad , B. Bouquet s , C. Bourdarios s , T.J.V. Bowcock v, I. Bozovic k , M. Bozzo m , P. Branchini am , K.D. Brand ai , T. Brenke ay, R.A. Brenner au , R. Brown i , P. Bruckman ai , J-M. Brunet h , L. Bugge af , T. Buran af , T. Burgsmueller ay, P. Buschmann ay, S. Cabrera av, M. Caccia aa , M. Calvi aa , A.J. Camacho Rozas an , T. Camporesi i , V. Canale ak , M. Canepa m , F. Carena i , L. Carroll v, C. Caso m , M.V. Castillo Gimenez av, A. Cattai i , F.R. Cavallo e, Ch. Cerruti j, V. Chabaud i , M. Chapkin ao , Ph. Charpentier i , L. Chaussard y, P. Checchia ai , G.A. Chelkov p, M. Chen b, R. Chierici ar, P. Chliapnikov ao , P. Chochula g , V. Chorowicz y, J. Chudoba ac , P. Collins i , M. Colomer av, R. Contri m , E. Cortina av, G. Cosme s , F. Cossutti i , J-H. Cowell v, H.B. Crawley a , D. Crennell aj, G. Crosetti m , J. Cuevas Maestro ag , S. Czellar o , B. Dalmagne s , G. Damgaard ab, P.D. Dauncey aj, M. Davenport i , W. Da Silva w, A. Deghorain b, G. Della Ricca as , P. Delpierre z , N. Demaria i , A. De Angelis i , W. De Boer q , S. De Brabandere b, C. De Clercq b, C. De La Vaissiere w, B. De Lotto as ,

1

On leave of absence from IHEP Serpukhov.

0370-2693r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 0 - 2 6 9 3 Ž 9 8 . 0 0 0 8 0 - X

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A. De Min ai , L. De Paula at , H. Dijkstra i , L. Di Ciaccio ak , A. Di Diodato ak , A. Djannati h , J. Dolbeau h , K. Doroba ax , M. Dracos j, J. Drees ay, K.-A. Drees ay, M. Dris ae, A. Duperrin y, J-D. Durand y,i , D. Edsall a , R. Ehret q , G. Eigen d , T. Ekelof au , G. Ekspong aq , M. Ellert au , M. Elsing i , J-P. Engel j, B. Erzen ap, M. Espirito Santo u , E. Falk x , G. Fanourakis k , D. Fassouliotis as , J. Fayot w, M. Feindt q , P. Ferrari aa , A. Ferrer av, S. Fichet w, A. Firestone a , P.-A. Fischer i , U. Flagmeyer ay, H. Foeth i , E. Fokitis ae, F. Fontanelli m , F. Formenti i , B. Franek aj, A.G. Frodesen d , R. Fruhwirth aw, F. Fulda-Quenzer s , J. Fuster av, A. Galloni v, D. Gamba ar, M. Gandelman at , C. Garcia av, J. Garcia an , C. Gaspar i , M. Gaspar at , U. Gasparini ai , Ph. Gavillet i , E.N. Gazis ae, D. Gele j, J-P. Gerber j, L. Gerdyukov ao , N. Ghodbane y, F. Glege ay, R. Gokieli ax , B. Golob ap, P. Goncalves u , I. Gonzalez Caballero an , G. Gopal aj, L. Gorn a,2 , M. Gorski ax , Yu. Gouz ao , V. Gracco m , J. Grahl a , E. Graziani am , C. Green v, A. Grefrath ay, P. Gris al , G. Grosdidier s , K. Grzelak ax , M. Gunther au , J. Guy aj, F. Hahn i , S. Hahn ay, S. Haider i , Z. Hajduk r, A. Hallgren au , K. Hamacher ay, F.J. Harris ah , V. Hedberg x , S. Heising q , R. Henriques u , J.J. Hernandez av, P. Herquet b, H. Herr i , T.L. Hessing ah , J.-M. Heuser ay, E. Higon av, S-O. Holmgren aq , P.J. Holt ah , D. Holthuizen ad , S. Hoorelbeke b, M. Houlden v, J. Hrubec aw, K. Huet b, K. Hultqvist aq , J.N. Jackson v, R. Jacobsson aq , P. Jalocha i , R. Janik g , Ch. Jarlskog x , G. Jarlskog x , P. Jarry al , B. Jean-Marie s , E.K. Johansson aq , L. Jonsson x , P. Jonsson x , C. Joram i , P. Juillot j, F. Kapusta w, K. Karafasoulis k , S. Katsanevas y, E.C. Katsoufis ae, R. Keranen d , B.A. Khomenko p, N.N. Khovanski p, B. King v, N.J. Kjaer ad , O. Klapp ay, H. Klein i , P. Kluit ad , D. Knoblauch q , P. Kokkinias k , M. Koratzinos i , K. Korcyl r, V. Kostioukhine ao , C. Kourkoumelis c , O. Kouznetsov p, M. Krammer aw, C. Kreuter i , I. Kronkvist x , Z. Krumstein p, P. Kubinec g , W. Kucewicz r, K. Kurvinen o , C. Lacasta i , J.W. Lamsa a , L. Lanceri as , D.W. Lane a , P. Langefeld ay, V. Lapin ao , J-P. Laugier al , R. Lauhakangas o , G. Leder aw, F. Ledroit n , V. Lefebure b, C.K. Legan a , A. Leisos k , R. Leitner ac , J. Lemonne b, G. Lenzen ay, V. Lepeltier s , T. Lesiak r, M. Lethuillier al , J. Libby ah , D. Liko i , A. Lipniacka aq , I. Lippi ai , B. Loerstad x , J.G. Loken ah , J.H. Lopes at , J.M. Lopez an , D. Loukas k , P. Lutz al , L. Lyons ah , J. MacNaughton aw, J.R. Mahon f , A. Maio u , A. Malek ay, T.G.M. Malmgren aq , V. Malychev p, F. Mandl aw, J. Marco an , R. Marco an , B. Marechal at ,

2

Now at University of Florida.

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M. Margoni ai , J-C. Marin i , C. Mariotti i , A. Markou k , C. Martinez-Rivero ag , F. Martinez-Vidal av, S. Marti i Garcia v, F. Matorras an , C. Matteuzzi aa , G. Matthiae ak , F. Mazzucato ai , M. Mazzucato ai , M. Mc Cubbin v, R. Mc Kay a , R. Mc Nulty i , G. Mc Pherson v, J. Medbo au , C. Meroni aa , W.T. Meyer a , M. Michelotto ai , E. Migliore ar, L. Mirabito y, W.A. Mitaroff aw, U. Mjoernmark x , T. Moa aq , R. Moeller ab, K. Moenig i , M.R. Monge m , X. Moreau w, P. Morettini m , K. Muenich ay, M. Mulders ad , L.M. Mundim f , W.J. Murray aj, B. Muryn n,r, G. Myatt ah , T. Myklebust af , F. Naraghi n , F.L. Navarria e, S. Navas av, K. Nawrocki ax , P. Negri aa , S. Nemecek l , N. Neufeld i , W. Neumann ay, N. Neumeister aw, R. Nicolaidou n , B.S. Nielsen ab, M. Nieuwenhuizen ad , V. Nikolaenko j, M. Nikolenko j,p, P. Niss aq , A. Nomerotski ai , A. Normand v, A. Nygren x , W. Oberschulte-Beckmann q , V. Obraztsov ao , A.G. Olshevski p, A. Onofre u , R. Orava o , G. Orazi j, K. Osterberg o , A. Ouraou al , P. Paganini s , M. Paganoni aa , S. Paiano e, R. Pain w, R. Paiva u , H. Palka r, Th.D. Papadopoulou ae, K. Papageorgiou k , L. Pape i , C. Parkes ah , F. Parodi m , U. Parzefall v, A. Passeri am , M. Pegoraro ai , H. Pernegger aw, M. Pernicka aw, A. Perrotta e, C. Petridou as , A. Petrolini m , H.T. Phillips aj, G. Piana m , F. Pierre al , M. Pimenta u , E. Piotto ai , T. Podobnik ah , O. Podobrin i , M.E. Pol f , G. Polok r, P. Poropat as , V. Pozdniakov p, P. Privitera ak , N. Pukhaeva p, A. Pullia aa , D. Radojicic ah , S. Ragazzi aa , H. Rahmani ae, J. Rames l , P.N. Ratoff t , A.L. Read af , P. Rebecchi i , N.G. Redaelli aa , M. Regler aw, D. Reid i , R. Reinhardt ay, P.B. Renton ah , L.K. Resvanis c , F. Richard s , J. Ridky l , G. Rinaudo ar, O. Rohne af , A. Romero ar, P. Ronchese ai , E.I. Rosenberg a , P. Rosinsky g , P. Roudeau s , T. Rovelli e, V. Ruhlmann-Kleider al , A. Ruiz an , H. Saarikko o , Y. Sacquin al , A. Sadovsky p, G. Sajot n , J. Salt av, D. Sampsonidis k , M. Sannino m , H. Schneider q , U. Schwickerath q , M.A.E. Schyns ay, F. Scuri as , P. Seager t , Y. Sedykh p, A.M. Segar ah , R. Sekulin aj, V. Senko ao , R.C. Shellard f , A. Sheridan v, R. Silvestre al , F. Simonetto ai , A.N. Sisakian p, T.B. Skaali af , G. Smadja y, N. Smirnov ao , O. Smirnova x , G.R. Smith aj, O. Solovianov ao , A. Sopczak q , R. Sosnowski ax , D. Souza-Santos f , T. Spassov u , E. Spiriti am , P. Sponholz ay, S. Squarcia m , D. Stampfer i , C. Stanescu am , S. Stanic ap, S. Stapnes af , I. Stavitski ai , K. Stevenson ah , A. Stocchi s , J. Strauss aw, R. Strub j, B. Stugu d , M. Szczekowski ax , M. Szeptycka ax , T. Tabarelli aa , O. Tchikilev ao , F. Tegenfeldt au , F. Terranova aa , J. Thomas ah , A. Tilquin z , J. Timmermans ad , L.G. Tkatchev p, T. Todorov j, S. Todorova j, D.Z. Toet ad , A. Tomaradze b, B. Tome u , A. Tonazzo aa , L. Tortora am , G. Transtromer x , D. Treille i , G. Tristram h , A. Trombini s , C. Troncon aa , A. Tsirou i , M-L. Turluer al ,

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I.A. Tyapkin p, M. Tyndel aj, S. Tzamarias k , B. Ueberschaer ay, O. Ullaland i , V. Uvarov ao , G. Valenti e, E. Vallazza as , G.W. Van Apeldoorn ad , P. Van Dam ad , W.K. Van Doninck b, J. Van Eldik ad , A. Van Lysebetten b, I. Van Vulpen ad , N. Vassilopoulos ah , G. Vegni aa , L. Ventura ai , W. Venus aj, F. Verbeure b, M. Verlato ai , L.S. Vertogradov p, V. Verzi ak , D. Vilanova al , P. Vincent w, N. Vishnevsky ao , L. Vitale as , E. Vlasov ao , A.S. Vodopyanov p, V. Vrba l , H. Wahlen ay, C. Walck aq , F. Waldner as , C. Weiser q , A.M. Wetherell i , D. Wicke ay, J.H. Wickens b, G.R. Wilkinson i , W.S.C. Williams ah , M. Winter j, M. Witek r, T. Wlodek s , G. Wolf i , J. Yi a , O. Yushchenko ao , A. Zalewska r, P. Zalewski ax , D. Zavrtanik ap, E. Zevgolatakos k , N.I. Zimin p, G.C. Zucchelli aq , G. Zumerle ai a

Department of Physics and Astronomy, Iowa State UniÕersity, Ames, IA 50011-3160, USA Physics Department, UniÕ. Instelling Antwerpen, UniÕersiteitsplein 1, BE-2610 Wilrijk, Belgium and IIHE, ULB-VUB, Pleinlaan 2, BE-1050 Brussels, Belgium and Faculte´ des Sciences, UniÕ. de l’Etat Mons, AÕ. Maistriau 19, BE-7000 Mons, Belgium c Physics Laboratory, UniÕersity of Athens, Solonos Str. 104, GR-10680 Athens, Greece d Department of Physics, UniÕersity of Bergen, Allegaten 55, NO-5007 Bergen, Norway ´ e Dipartimento di Fisica, UniÕersita` di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy f Centro Brasileiro de Pesquisas Fısicas, rua XaÕier Sigaud 150, BR-22290 Rio de Janeiro, Brazil ´ and Depto. de Fısica, Pont. UniÕ. Catolica, C.P. 38071, BR-22453 Rio de Janeiro, Brazil ´ ´ and Inst. de Fısica, UniÕ. Estadual do Rio de Janeiro, rua Sao ´ ˜ Francisco XaÕier 524, Rio de Janeiro, Brazil g Comenius UniÕersity, Faculty of Mathematics and Physics, Mlynska Dolina, SK-84215 BratislaÕa, SloÕakia h College ` de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris Cedex 05, France i CERN, CH-1211 GeneÕa 23, Switzerland j Institut de Recherches Subatomiques, IN2P3 - CNRSr ULP - BP20, FR-67037 Strasbourg Cedex, France k Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece l FZU, Inst. of Phys. of the C.A.S. High Energy Physics DiÕision, Na SloÕance 2, CZ-180 40, Praha 8, Czech Republic m Dipartimento di Fisica, UniÕersita` di GenoÕa and INFN, Via Dodecaneso 33, IT-16146 GenoÕa, Italy n Institut des Sciences Nucleaires, IN2P3-CNRS, UniÕersite´ de Grenoble 1, FR-38026 Grenoble Cedex, France ´ o Helsinki Institute of Physics, HIP, P.O. Box 9, FI-00014 Helsinki, Finland p Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, RU-101 000 Moscow, Russian Federation q Institut fur ¨ Experimentelle Kernphysik, UniÕersitat ¨ Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany r Institute of Nuclear Physics and UniÕersity of Mining and Metalurgy, Ul. Kawiory 26a, PL-30055 Krakow, Poland s UniÕersite´ de Paris-Sud, Lab. de l’Accelerateur Lineaire, IN2P3-CNRS, Bat. ´´ ´ ˆ 200, FR-91405 Orsay Cedex, France t School of Physics and Chemistry, UniÕersity of Lancaster, Lancaster LA1 4YB, UK u LIP, IST, FCUL - AÕ. Elias Garcia, 14-1(o), PT-1000 Lisboa Codex, Portugal v Department of Physics, UniÕersity of LiÕerpool, P.O. Box 147, LiÕerpool L69 3BX, UK w LPNHE, IN2P3-CNRS, UniÕ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris Cedex 05, France x Department of Physics, UniÕersity of Lund, SolÕegatan 14, SE-223 63 Lund, Sweden ¨ y UniÕersite´ Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne Cedex, France z UniÕ. d’Aix - Marseille II - CPP, IN2P3-CNRS, FR-13288 Marseille Cedex 09, France aa Dipartimento di Fisica, UniÕersita` di Milano and INFN, Via Celoria 16, IT-20133 Milan, Italy ab Niels Bohr Institute, BlegdamsÕej 17, DK-2100 Copenhagen Ø, Denmark ac NC, Nuclear Centre of MFF, Charles UniÕersity, Areal MFF, V HolesoÕickach 2, CZ-180 00 Praha 8, Czech Republic ad NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands ae National Technical UniÕersity, Physics Department, Zografou Campus, GR-15773 Athens, Greece af Physics Department, UniÕersity of Oslo, Blindern, NO-1000 Oslo 3, Norway ag Dpto. Fisica, UniÕ. OÕiedo, AÕda. CalÕo Sotelo s r n, ES-33007 OÕiedo, Spain 3 b

3

CICYT-AEN96-1681.

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ah Department of Physics, UniÕersity of Oxford, Keble Road, Oxford OX1 3RH, UK Dipartimento di Fisica, UniÕersita` di PadoÕa and INFN, Via Marzolo 8, IT-35131 Padua, Italy aj Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK ak Dipartimento di Fisica, UniÕersita` di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy al DAPNIAr SerÕice de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-YÕette Cedex, France am Istituto Superiore di Sanita, ` Ist. Naz. di Fisica Nucl. (INFN), Viale Regina Elena 299, IT-00161 Rome, Italy an Instituto de Fisica de Cantabria (CSIC-UC), AÕda. los Castros s r n, ES-39006 Santander, Spain 3 ao Inst. for High Energy Physics, SerpukoÕ P.O. Box 35, ProtÕino (Moscow Region), Russian Federation ap J. Stefan Institute, JamoÕa 39, SI-1000 Ljubljana, SloÕenia and Department of Astroparticle Physics, School of EnÕironmental Sciences, KostanjeÕiska 16a, SI-5000 NoÕa Gorica, SloÕenia and Department of Physics, UniÕersity of Ljubljana, SI-1000 Ljubljana, SloÕenia aq Fysikum, Stockholm UniÕersity, Box 6730, SE-113 85 Stockholm, Sweden ar Dipartimento di Fisica Sperimentale, UniÕersita` di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy as Dipartimento di Fisica, UniÕersita` di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy and Istituto di Fisica, UniÕersita` di Udine, IT-33100 Udine, Italy at UniÕ. Federal do Rio de Janeiro, C.P. 68528 Cidade UniÕ., Ilha do Fundao ˜ BR-21945-970 Rio de Janeiro, Brazil au Department of Radiation Sciences, UniÕersity of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Sweden av IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, AÕda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain aw ¨ Institut fur Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austria ¨ Hochenergiephysik, Osterr. ax Inst. Nuclear Studies and UniÕersity of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland ay Fachbereich Physik, UniÕersity of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany ai

Received 14 January 1998 Editor: L. Montanet

Abstract Trilinear gauge boson couplings are measured using data taken by DELPHI at 161 GeV and 172 GeV. Values for WWV couplings Ž V s Z,g . are determined from a study of the reactions eqey™ WqWy and eqey™ Wen , using differential distributions from the WW final state in which one W decays hadronically and the other leptonically, and total cross-section data from other channels. Limits are also derived on neutral ZVg couplings from an analysis of the reaction eqey™ g q invisible particles. q 1998 Elsevier Science B.V.

1. Introduction One of the most important consequences of the SUŽ2. = UŽ1. symmetry of the Standard Model is the existence of non-Abelian self-couplings of the gauge bosons g , W and Z 0 . Using data taken in the DELPHI detector at LEP in 1996 at centre-of-mass energies of 161 and 172 GeV, events from the reactions eqey™ WqWy and eqey™ Wen have been used to study WWV couplings, where V ' Z,g . The reaction eqey™ g q invisible particles has been used to study couplings at the ZVg vertex. The WWV coupling arises in WW production through the diagrams involving s-channel exchange of Z 0 or g . In single W production, the dominant amplitude involving a trilinear gauge coupling ŽTGC. is that arising from radiation of a virtual photon from the incident electron or positron. The Standard Model

predicts a charge coupling, described by a parameter g 1V in an effective WWV Lagrangian L W W V , and a dipole coupling k V , with g 1V s k V s 1 w1x. In a general Lorentz-invariant description of the WWV interaction, other couplings, both CP-conserving and CP-violating, are possible, but their contributions are predicted to be zero in the Standard Model. In searching for the presence of new physics, contributions from gauge-invariant operators of lowest dimension ŽF 6. have been considered, taking only those which have not been excluded by previous measurements. This leads to possible contributions a Wf , a Bf and a W from CP-conserving operators and a˜ BW and a˜ W from CP-violating operators. The CP-conserving parameters are related to the charge and dipole couplings defined above and to the quadrupole couplings lV in L W W V by: D g 1Z

P. Abreu et al.r Physics Letters B 423 (1998) 194–206

a Wf

sw2 c w2

, Dkg s a Wf q a Bf , Dk Z s a Wf y Ž . a Bf c w2 and lg s lZ s a W , where sw and c w are the sine and cosine of the electroweak mixing angle and D g 1Z , Dkg and Dk Z represent deviations from Standard Model values w1x. Similarly, the CP-violating parameters are related to the relevant terms in L W W V sw2 by: k˜g s a˜ BW , k˜ Z s Ž 2 . a˜ BW and l˜g s l˜ Z s a˜ W cw w2x. The process eqey™ g q invisible particles is described within the Standard Model by the radiative production of neutrino-antineutrino pairs, eqey™ nng . A W fusion diagram, containing a WWg coupling, also contributes to nng production, but its amplitude is very small at LEP2 energies, and its relative contribution is negligible w3x. Possible new physics contributions to single photon production could come from new families of neutrinos, from the radiative production of any other neutral weakly interacting particle, or from the s-channel exchange of g or Z leading to Zg production via a triple vector boson coupling. In this paper the latter possibility is examined. The ZVg vertex has been described by Baur and Berger w4x in terms of a vertex function involving four independent terms hV1..4 ; in the Standard Model all of these are zero at tree level. The parameters are normally described by a form factor representation, hVi Ž s . s hVi0rŽ1 q srL2 . n , with an energy L representing the scale at which a novel interaction would become manifest, and with a sufficiently large power n to ensure unitarity conservation at high energy. Conventionally, n s 3 is used for hV1,3 and n s 4 for hV2,4 . The terms in h1 and h 2 are CP-violating, and those in h 3 and h 4 CP-conserving. However, the minimum dimensionality of gauge-invariant operators contributing to LZ Vg is 8 w5x, so the observation of deviations from Standard Model predictions is a priori less likely in this channel than in those involving WWV couplings. Results on WWV couplings have previously been reported in pp experiments w6–8x, and in first reports of results at LEP2 w9,10x. Limits on ZVg couplings have been determined in pp experiments w6,8,11,12x and from LEP data taken at the Z 0 w13x and at 130–136 GeV w14x. The next section of this paper describes the selection of events from the data and the simulation of the s

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various channels involved in the analysis. Results on the trilinear gauge coupling parameters describing the WWV and ZVg vertices are reported in Sections 3 and 4, respectively, and a summary is given in Section 5.

2. Event selection and simulation In 1996, DELPHI recorded integrated luminosities of 10.0 pby1 and 9.98 pby1 at centre-of-mass energies of 161 and 172 GeV, respectively. Details of these data samples, including definition of the criteria imposed for track selection and lepton identification, and a description of the luminosity measurements, have been given in w9,15x. A detailed description of the DELPHI detector may be found in w16x, which includes descriptions of the main components of the detector used in this study, namely, the trigger system, the luminosity monitor, the tracking system in the barrel and forward regions, the muon detectors and the electromagnetic calorimeters. 2.1. Selection of eÕents for the study of WWV couplings In the determination of WWV couplings, events were selected from topologies populated by the production and decay of a WW pair, and from those containing the products of single W production. Pair production of W s populates three final state topologies, depending on the decay mode of each W: the topology in which one W decays leptonically and the other hadronically Ž jj l n ., in which two hadronic jets and an isolated lepton are reconstructed, the fully hadronic topology Ž jjjj ., requiring the presence of four hadronic jets, and the topology containing only two identified leptons coming from the interaction point Ž l n l n .. Single W production in the reaction eqey™ Wen contributes significantly in the kinematic region where a final state electron or positron is emitted at small angle to the beam and is thus likely to remain lost in the beam pipe. Depending on the decay mode of the W, this process populates two final state topologies, that with two jets and missing energy Ž jjX . and that containing only a single lepton com-

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ing from the interaction point, but no other track in the detector Ž l X .. While these final states are topologically distinct, they are all represented by the generic eqey interaction producing four final state fermions, eqey™ f 1 f 2 f 3 f 4 . In particular, the topologies jj l n and jjX contain events in two different kinematic regions of the same four-fermion final state, q1 q2 l n . The four-fermion generators EXCALIBUR w17x and GRC4F w18x, which take account of background diagrams and interference effects coherently, were used to produce simulated events. These generators were interfaced to the JETSET hadronization model w19x, tuned to Z 0 data w20x, and to the full DELPHI simulation program w16x. Samples of events were generated with both Standard Model and non-Standard Model values of TGC parameters, and were used both to determine the efficiency of the selection criteria in the topologies studied, and to check the accuracy of the analysis procedures in deriving the value of TGC parameters used in the generation of events. In addition, in the analysis of the jj l n final state, the ERATO generator w21x was used in conjunction with a fast simulation of the DELPHI detector Žwhich included realistic efficiencies and smearing of generated quantities.. Cross-checks were made to ensure that the fast and full simulations agreed in the distributions of the kinematic variables used in the analysis. The study of the backgrounds due to qq Žg . and ZZ production was made using fully simulated events generated with the PYTHIA program w22x. Each topology was selected as described below. jj l n : Events in the jj l n topology are characterized by two hadronic jets, one isolated electron or muon Žcoming either from W decay or from the cascade decay W ™ t ...™ l .... or a low multiplicity jet with only one charged particle, due to t decay, and missing momentum resulting from the neutrino. The major background comes from qq Žg . production and from four-fermion final states containing two quarks and two leptons of the same flavour. The criteria used to select such events from the 161 and 172 GeV data samples have been defined in w9x and w15x for the two energies respectively. At 161 GeV, 12 events were selected with an efficiency, averaged over the three leptonic channels, of Ž60.9 " 3.0.% and an estimated background of 1.9 " 0.2 events; at

172 GeV, 40 events were selected Ž17 jj mn , 14 jjen and 9 jjtn ., the average efficiency was Ž67.2 " 1.5.% and a background contamination of 3.6 " 0.4 events was estimated. A 6-constraint kinematic fit was then applied to the 172 GeV data, imposing 4-momentum conservation, requiring both W masses to be equal to 80.35 GeVrc 2 and requiring the x 2 probability of the fit to exceed 0.001. This resulted in a sample of 34 events Ž15 jj mn , 12 jjen and 7 jjtn . with average efficiency of Ž62.6 " 1.5.% and an estimated background contamination of 1.9 " 0.3 events. jjjj: The criteria used to define the sample of events in the jjjj topology at 161 GeV have been given in w9x. In this procedure, events were forced to a four-jet configuration. A variable D was defined mi n as D s EEma u rŽ Emax y Emin ., where Emin and Emax x min are the energies of the jets with minimum and maximum energy and umin is the minimum interjet angle. The dominant background, which arises from the qqg final state, was suppressed by imposing the condition D ) 0.013 GeVy1 . At 172 GeV, the requirement on D was replaced by a condition on the three eigenvalues, P1..3 , of the momentum tensor which, when normalized such that their sum is unity, each have an expectation value of 1r3: the product 27 P P1 P2 P3 was required to exceed 0.025. In addition, at least one of the three 5-constraint kinematic fits which could be made to the event, imposing equality of two di-jet masses, was required to have x 2 - 50. The selected jjjj samples consisted of 15 events at 161 GeV and 52 events at 172 GeV, with estimated background contamination of 5.5 " 0.6 and 15.2 " 1.0 events, respectively. The efficiencies for reconstructing events in the kinematically accepted region were found to be Ž69 " 3.% at 161 GeV and Ž71 " 2.% at 172 GeV. l n l n : Events in the l n l n topology were selected from events with multiplicity less than 5 and which satisfied a 2-jet description, thus allowing decays into t leptons as well as into m and e to be included. Requirements on the minimum polar angle of the jets relative to the beam axis and on the direction of the missing momentum helped to suppress the dominant backgrounds, which are from eq ey™ ZŽg ., Bhabha scattering and two-photon collisions. The criteria used at 161 and 172 GeV are described in w9x and w23x, respectively. They resulted in the selection of 2 events at 161 GeV and 7 events

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at 172 GeV, with estimated efficiencies of Ž48 " 3.% and Ž55 " 1.% and background contamination of 0.6 " 0.4 and 1.9 " 0.5 events at the two energies, respectively. jjX: The selection of events in the single W channel jjX was devised so as to accept events which could be interpreted in terms of two jets and missing momentum, but to reject events from the qq Žg . final state, in which the missing momentum is expected to lie near the beam direction. This reaction constitutes the principal background in the selection of jjX events, but with a cross-section which is falling with increasing centre-of-mass energy. Events were reconstructed with the LUCLUS algorithm w19x with d join s 5.5 GeVrc and those with 2 or 3 jets were forced into a 2-jet configuration. Cuts were then applied on the energy of each jet Ž Ej ) 20 GeV at 161 GeV, Ej ) 10 GeV at 172 GeV., on the jet polar angles relative to the beam axis Ž258 - u jet 1558 at 161 GeV, 158 - u jet - 1658 at 172 GeV., on the di-jet invariant mass Ž m j j ) 45 GeVrc 2 at 161 GeV, m j j ) 50 GeVrc 2 at 172 GeV., on the angle between the direction of the missing momentum and the beam direction Ž
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mentum p - 75 GeVrc, with transverse component pt ) 20 GeVrc. Efficiencies of Ž94 " 2.% and Ž81 " 3.% in the selected kinematic region were estimated at both 161 and 172 GeV for muon and electron events, respectively, and the background was estimated to be negligible. One muon event was selected at each of the two energies while, for Standard Model values of the couplings, 0.7 and 0.8 events were expected at each energy, respectively. 2.2. Selection of eÕents for the study of ZVg couplings The study of ZVg couplings in the reaction eqey ™ nng involved a search for events containing only a single photon of high energy, emitted at large angle u to the beam direction. Such events were selected by requiring the presence of a ‘‘good quality shower’’ Ždefined in w16x. of energy Eg ) 25 GeV in the angular region 458 - u - 1358, covered by the barrel electromagnetic calorimeter. Events with a signal in the forward electromagnetic calorimeter were rejected, and a second shower in the barrel calorimeter was accepted only if it was within 208 of the first one. Events were also rejected if any charged particles were detected in the time projection chamber, the main tracking device of DELPHI, or in the forward tracking chambers. The presence of charged particles not pointing to the nominal beam crossing point also caused events to be rejected; this suppressed background from beam gas interactions and cosmic ray events. In order to reject the background from radiative Bhabha and Compton events, no energy deposit was allowed in the luminosity monitor, situated in the very forward direction. A further rejection of cosmic ray events was achieved by imposing a constraint on the photon direction: the line of flight and the shower direction measured in the calorimeter were required to coincide within 158. Application of these criteria produced samples of 8 events at 161 GeV and 7 events at 172 GeV. In order to estimate the cross-section for the single photon production process, the trigger and identification efficiencies must be known. The former was measured using radiative events Ž mq my g and eq ey g . and Compton events. The identification efficiency was estimated using samples of 2500 fully simulated events at each energy, produced with the

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generator NUNUGPV w24x. The overall efficiency was shown to be dependent on the photon energy in the angular region under consideration, ranging from 58% at Eg s 25 GeV to G 71% for Eg ) 50 GeV. Possible sources of background to the single photon production process include the QED processes eqey ™ g eqey and eqey™ gg , gg collisions, cosmic ray and Compton events, and beam gas interactions. All of these were found to give negligible contributions.

3. Results on WWV couplings From the results of previous studies w1x, it is expected that the data in the jj l n topology at 172 GeV will provide the greatest precision in the determination of WWV couplings. These data were analyzed by studying the joint distribution of two variables which retain all the available information of the 7-dimensional phase space describing the fourparticle final state. These ‘‘Optimal Variables’’ w25x are derived from the formalism of optimal observables w26x which has been applied to TGC determination in w1,27x. Results using this method are compared below with those using distributions of wellmeasured variables, namely the production angle of the Wy with respect to the electron beam, u W , and the polar angle of the lepton in the laboratory frame, u l . In addition, information obtained from the total numbers of events observed in the jjjj and l n l n channels, and data from the single W topologies jjX and l X, were used to obtain overall results from the 172 GeV data. Results from the same topologies at 161 GeV, using information from the distributions of u W and u l in the jj l n final state, were combined

with those at 172 GeV to give final values for the couplings. The analysis using the method of Optimal Variables exploits the fact that the differential cross-section, d srdV, where V represents the phase space variables, is quadratic in TGC parameters: d s Ž V, a .rdV s c 0 Ž V . q Ý i a i c1i Ž V . q Ý i j a i a j = c 2i j Ž V ., where the sums are over the set a ' a 1... a N of parameters under consideration. In the case of the determination of single parameters a considered in this paper, the right-hand side of the above expression is a simple quadratic expansion in a : d s Ž V, a .rdV s c 0 Ž V . q a c1Ž V . q a 2 c 2 Ž V .. In w25x it is shown that the distribution in the 2-variable space of c1Ž V .rc0 Ž V . and c 2 Ž V .rc0 Ž V . retains the whole information carried by the full distribution d srdV and hence allows the determination of a with maximum precision, equivalent to that of a maximum likelihood fit over all the phase space variables. Furthermore, it is argued and confirmed by tests on simulated events that little loss of precision occurs if the phase space variables V available after reconstruction of events from experimental data are used in place of the true variables V. The sample of 34 jj l n events at 172 GeV was analyzed by performing a binned extended maximum likelihood fit to the two-dimensional distribution of c1Ž V .rc0 Ž V . and c 2 Ž V .rc0 Ž V . for each of the parameters a Wf .. defined in Section 1, keeping the others fixed to their Standard Model values of zero. The expected numbers of events were computed for several values of the couplings using the ERATO four-fermion generator and a full simulation of the DELPHI detector. A reweighting technique was then used to estimate the expected cross-section in each bin as a continuous function of each parameter fitted.

Table 1 Results obtained from fits to CP-conserving WWV coupling parameters at 172 GeV using various analysis procedures and data from various final state topologies. Values shown in the third and fourth columns have been obtained by combining the jj l n results in the first column with data from additional topologies. In each fit, the values of the other TGC parameters were kept at their Standard Model values TGC

Topologies used

parameter

jj l n ŽOptimal Variables.

jj l n Žcos u W , cos u l .

jj l n q jjjj ql n l n

jj l n q jjjj ql n l n q jjX q l X

a Wf aW a Bf

.32 0.38q0 y0.32 q0.57 0.28y0.57 q1.12 1.45y1.47

0.61q0.42 y0.49 q0.59 0.91y0.74 q1.20 1.74y2.67

0.35q0.28 y0.39 q0.50 0.26y0.53 q0.99 1.27y1.39

0.30q0.28 y0.30 q0.45 0.24y0.53 q0.85 0.24y0.93

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Fig. 1. Distributions of pairs of variables used in the fitting of WWV coupling parameters in the jj l n final state at 172 GeV; a. and b. the Optimal Variables c1Ž V .r c 0 Ž V . and c 2 Ž V .r c 0 Ž V . for a Wf ; c. and d. cos u W and cos u l . The points represent the data, and the histograms the expectation for the values of a Wf shown in table 1 with background contributions shaded.

Results on the CP-conserving TGC parameters a Wf , a W and a Bf are shown in the first column of Table 1. Fig. 1a and Fig. 1b show the distributions of c1Ž V .rc0 Ž V . and c 2 Ž V .rc0 Ž V ., respectively, together with the expected distributions for the fitted value of one TGC parameter, a Wf . The validity of the technique was verified by applying it to a large number of samples of fully simulated events corresponding to the same integrated luminosity as the data, generated both with Standard Model and nonStandard Model values of the couplings. The mean values of the precisions in the TGC parameters obtained from these samples were found to be compatible with those from the data, and the pull distributions had means and variances compatible with 0 and 1, respectively. These results may be compared with those obtained from an analysis of the joint distribution in Žcos u W ,cos u l .. These quantities can be directly estimated without serious bias from the sum of the two measured hadronic jet vectors and the direction of the observed lepton. Using the sample of jj l n events obtained before application of a kinematic fit, the

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binned distribution in the Žcos u W ,cos u l . plane was fitted to that predicted using ERATO and a fast simulation of the detector response; the results are shown in the second column of Table 1. They are in agreement with those from the Optimal Variables analysis, though, as expected, with lower precision. The distributions of these variables are shown in Figs. 1c. and d. together with the expected distributions for the fitted value of a Wf . Further analyses of the distributions in these variables using different four-fermion generators w18,28x have given results in agreement with those shown in the table. The third and fourth columns of Table 1 show the increase in precision obtained in the CP-conserving TGC parameters at 172 GeV by addition to the results obtained from the Optimal Variables analysis of the jj l n channel, first, of data from the jjjj and l n l n final states, then from the single W topologies jjX and l X. For the jjjj and l n l n topologies, the observed total numbers of events were compared with those expected as a function of each TGC parameter. In the analysis of the jjX final state, the differential distribution in
161 GeV

172 GeV

161q172 GeV

a Wf aW a Bf a˜ BW a˜ W

.74 y0.27q0 y0.70 q1.40 y0.90y0.98 0.18q0.98 y2.70 0.72q0.77 y2.20 y0.54q1.31 y0.40

0.30q0.28 y0.30 q0.45 0.24y0.53 q0.85 0.24y0.93 0.02q0.80 y0.77 0.19q0.28 y0.38

0.22q0.25 y0.28 "0.06 q0.48 0.11y0.49 "0.09 0.22q0.66 y0.83 "0.24 0.11q0.71 y0.88 "0.09 0.19q0.28 y0.41 "0.11

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W velocity, the sensitivity of the data to TGC parameters at 161 GeV is considerably smaller than at 172 GeV. Nonetheless, differential data Žcos u W , cos u l . from jj l n events, the total numbers of events observed in the jjjj and l n l n final states, the distribution of
Table 3 Estimated systematic uncertainties in the determination of WWV coupling parameters. Details of the common and topology-dependent contributions are shown for 172 GeV data; the total of all non-common contributions is summarized for 161 and 172 GeV data. The entries for the jj l n topology at 172 GeV refer to the analysis based on Optimal Variables, described in the text

a Wf

aW

a Bf

a˜ BW

a˜ W

Common systematics: W mass Ec m Cross-section Luminosity

0.02 0.02 0.03 0.01

0.03 0.02 0.04 0.01

0.08 0.04 0.16 0.05

0.02 0.02 0.03 0.01

0.04 0.02 0.06 0.02

Topology jj l n , 172 GeV: Binning granularity Signal estimation Background estimation

0.02 0.02 0.01

0.03 0.03 0.02

0.04 0.12 0.06

0.03 0.02 0.01

0.03 0.04 0.02

Topologies jjjjq l n l n , 172 GeV: Signal estimation 0.04 0.05 Background estimation 0.03 0.03

0.06 0.04

0.04 0.03

0.04 0.03

Topologies jjX q l X, 172 GeV: Signal estimation 0.03 Background estimation 0.09

0.10 0.21

0.04 0.13

0.00 0.00

0.01 0.02

Combined systematics, 172 GeV: 0.03

0.07

0.12

0.05

0.05

Combined systematics, 161 GeV: 0.07

0.10

0.15

0.15

0.30

Fig. 2. Distributions of log likelihood as a function of WWV coupling parameters; a. a Wf , b. a W , c. a Bf , d. a˜ BW , e. a˜ W . The dotted curves show the functions obtained using data at 161 GeV, the dashed curves are from data at 172 GeV, and the full curves show the results from the two energies combined. In each case, the curves include the effects of statistical and systematic errors.

table contains contributions arising from a conservatively estimated precision of "100 MeVrc 2 in the value of the W mass w29x, from the uncertainty in the LEP beam energy w30x and experimental luminosity, from the theoretical uncertainty in the cross-section evaluation Žtaken to be "2% w1x., from the errors in the estimated signal and background cross-sections due to limited simulated statistics and, in the jj l n final state, from the granularity of the binning used in the fits and from uncertainties in the detector response which could affect the differential distributions, as described in w15x. The systematic error due to the use of a different hadronization algorithm in jet reconstruction was also computed and found to be small compared to those quoted in the table. The combined effect of all contributions to the systematic uncertainty at 161 GeV is also shown. The third column of Table 2 shows the final results for the TGC parameters, obtained by combining the results at 161 and 172 GeV, together with their statistical and systematic errors. The systematic errors were obtained by adding in quadrature the first four contributions in Table 3, considered as common to all topologies and to both energies, and combining the result with the non-common contributions, which

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were each weighted with the statistical precision of the topology concerned. The log likelihood distributions from which the results are derived are shown in Fig. 2. The parameter values determined are all consistent with zero, and hence with the expectations of the Standard Model.

4. Results on ZVg couplings The sample of 15 events selected from the combined data at 161 and 172 GeV yields a cross-section

s Ž eqey™ g q invisible particles. s 1.47 " 0.38 Ž stat. . " 0.30 Ž syst. . pb in the region of phase space with Eg ) 25 GeV and 458 - ug - 1358, corrected for the experimental efficiencies within these selections. The systematic uncertainty comes mainly from the calibration of the calorimeter energy scale and from the errors on the detection and trigger efficiencies. The cross-section given above corresponds to a 95% C.L. limit

s Ž eqey™ g q invisible particles. - 2.5 pb in the same region of phase space, including the effect of systematic uncertainties. This limit is shown in Fig. 3 together with the predicted cross-section as

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a function of the ZVg coupling parameters hg30 and Z h 30 defined in Section 1. Limits at 95% C.L. of < hg30 < - 0.8 and

Z < < h 30 - 1.3

are derived at a scale L s 1 TeV and with n s 3 in the form factor representation of hV3 . The limit obtained for < hg30 < represents a considerable improvement over those reported previously from LEP data w13,14x, and may be compared with the current limit set by the D0 experiment: < hg30 < - 0.37 for L s 750 Z < GeV w12x. The limit obtained for < h 30 exceeds the Z < < unitarity limit, h 30 s 0.99, for the values of L and n used in the form factor, and for current values of 's , the data show little sensitivity to the other CP-conserving vertex factors, hV4 . If the analysis is g applied to measure the CP-violating parameters h10 Z V and h10 , the same limits are obtained as for h 30 .

5. Conclusions Trilinear gauge couplings have been measured in DELPHI using data corresponding to integrated luminosities of 10.0 pby1 at 161 GeV and 9.98 pby1 at 172 GeV. Values of the CP-conserving WWV couplings a Wf , a W and a Bf and of the CP-violating couplings a˜ BW and a˜ W have been derived using data from topologies populated both by WW production, eqey™ WqWy, and by single W production, eqey™ Wen . The results are summarized in Table 2. Limits on the ZVg couplings hg3 , Z have also been determined using data from single photon production, with results given in Section 4. No evidence for deviations from Standard Model predictions is observed in the present data. Further running at LEP2 should yield an improvement of up to an order of magnitude in the precision of the results obtained.

Acknowledgements

Fig. 3. Variation of the predicted cross-section for large angle single photon production in DELPHI at 161 and 172 GeV with the Z ZVg couplings hg30 and h 30 , for energy scale L s1 TeV and ns 3 in the form factor representation of hV3 . The square points on the curves show the unitarity limits for the two couplings corresponding to these values of L and n.

We thank the SL division of CERN for the excellent performance of the LEP collider and their careful work on the beam energy determination. We are also grateful to the technical and engineering staffs in our laboratories and to our funding agencies for their continuing support.

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