A measurement of the b¯b forward-backward asymmetry using the semileptonic decay into muons

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•,

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J!i ^l ·:i'\~

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~ t UROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-PPE/91-213

3 December 1991

A Measureme11.t of the bb Forward Backward As:ymmetry Using the

Semileptonic Decay into Muons

DEI.PHI Collaboration

Abstract

The forward backward asymmetry of bottom quarks is measured with statistics of approximately 80 000 h;~dronic Zº-decays produced in e+ e--collisions at a centre of mass energy of y8 ::::: Mz. The tagging of b-quark events has beer;i performed using the semileptonic decay channel b ^--> X

+

^µ. Be·

cause the asymmetry depends on the weak coupling, this leads to a precise measurement of the electrowealk m.ixing angle sin ²9w. The experimental result is

A}

₈ = 0.115 ± 0.043 (stat) ± 0.013 (syst). After correcting the value for the Bº Bº-m.ixing this becomes 1l}₈ = 0.161 ± 0.060 (stat) ± 0.021 (syst) corre- sponding to sin²9~⁵= 0.221 ± 0.011(stat)±0.004 (syst).

(Subnútted to Phys. Lett. B)

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P.Abreu¹⁸1 W.Adam.⁴³^, F.Adami³⁴^, T.Adye³²1 T.Akesson²¹^, G.D.Alekseev¹³^, P.Allen⁴²^, S.Almehed²¹^, S.J.Alvsvaag⁴^, U.Amaldi¹^, E.Anassontzis³^, P.Antilogus²²^, W-D.Apel¹⁴1 R.J.Apsim.on³²^, B.Ásman³⁸^, J-E.Augustin¹⁶, A.Augustinus²⁷1 P.Baillon¹' 1 P.Bambade¹⁶₁ F.Barao¹⁸₁ R.Barate¹¹, G.Barbiellini⁴

º,

D.Y.Bardin¹³, A.Baroncelli³⁵, O.Barring²¹, W.Bartl⁴³, M.J.Bates³⁰, M.Battaglia²⁵, M.Baubillier²º ₁

K-H.Becks't.s, C.J.Beeston³⁰1 M.Begalli.¹⁰^, P.Beilliere⁶^, Yu.Belokopytov³⁷1 P.Beltran⁹^, D.Benedic^{8 ,} J.M.Benlloch⁴²^, M.Berggren¹⁶^, D.Bertrand²^, F .Bianchi³⁹^, M.S.Bilenky¹³^, P.Billoir²º, J.Bjame21 , D.Bloch8 ,

S.Blyth³⁰^, V .Bocci.³³^, P.N .Bogolubov¹³^, T .. Bolognese³⁴^, M.Bonapart²⁷^, M.Bonesini²⁵^, W .Bonivent025 ,

P.S.L.Booth¹⁹^, P.Borgeaud³⁴^, G.Borisov³⁷^, H.Borner⁷^, C.Bosio³⁵^, B.Bostjancic⁷^, O.Botner"l, B.BouquetL6, C.Bourdarios¹⁶^,M.Bo11olº, S.Braibant²^,P.Branchini³⁵^,K.D.Brand³i, R.A.Brenner¹²^,H.Briand²º, C.Bricman2 ,

R.C.A.Brown ⁷^, N .Brummer²⁷^, J-M.Brunet⁶^, L.Bugge²⁹^, T .Buran.²⁹^, H.Burmeister⁷^, J .A.M.A.Buytaert ⁷^, M.Caccia⁷^,M.Calvi²⁵^, A.J.Camacho Rozas³⁶^, A.Campion¹⁹^, T.Camporesi7 , V.Canale³³^, F.Cao^{2 ,} F.Carena^{7 ,} L.Carroll¹⁹^, C.Caso¹⁰^, E.Castelli⁴⁰^, M.V.Castiillo Gim.ene1°'²^, A.Cattai⁷^, F.R.Cavallo⁵^, L.Cerrito³³^, A.Chanl, M.Chapkin³⁷^, P.Charpentier⁷^, L.Chaussard¹⁶^, J.Chauveau²⁰^, P.Checchia³¹^, G.A.Chelkov¹³^, L.Chevalier³⁴^, P.Chliapnikov³⁷^,V.Chorowicm²⁰^,R.Cirio³⁹^,M.P.Clara³⁹^,P.Collim³⁰^,J.L.Contreras²³^,R. Contri lo, G.Cosmel⁶^, F .Couchot¹⁶^, H.B.Crawleyi, D.Crennell³²^, G.Crosetti¹⁰1 M.Cro1on⁶^, J.Cuevas Maestro³⁶, S.Czellarl²,

S.Dagoreti⁶^, E.Dahl-Jensen²⁶^, B.Dalmagne¹⁶^, M.Dam²⁹^, G.Damgaard²⁶^, G.Darbo¹⁰^, E.Daubie²^, P.D.Dauncey³⁰, M.Davenport⁷, P.David²⁰1 W.Da Silva²⁰, C.Defoix⁶, D.Delikaris⁷, S.Delorme⁷^, P.Delpierre⁶₁ N.Demaria³⁹^,A.De Angelis⁴⁰^,M.De Beer³⁴^,H .. De Boed:2, W.De Boer¹⁴^,C.De Clercq²^,M.D.M.De Fez Luo⁴²^, N.De Groot²⁷^, C.De La Vaisaiere²⁰^, B.De Lciitto⁴⁰^, A.De Min²⁵^, H.Dijbtra⁷^, L.Di Ciaccio³³^, F.Djama⁸^, J.Dolbeau⁶^, M.Donszehnann.²⁷^, K.Doroba⁴⁴^, M.Dracos⁷^, J.Drees⁴⁵^, M.Dris²⁸^, Y.Dufour⁶^, W.Dulinski⁸^, R.Dzhelyadin³⁷^, L-0.Eek", P.A.-M.Eerola⁷^, T.Ekelof", G.Ekspong³⁸^, A.Elliot Peisert³¹^, J-P.Engel', D.Fusouliotis²⁸1 M.Feindt ⁷, M.Femande1 Al:oDS0³⁶, A.Ferrerf.², T .A.Filippas²⁸, A.Firestone¹, H.Foeth ⁷,

E.Fokiti!l²⁸^,P.Folegati⁴⁰1 F .Fontanelli¹⁰1 K.A.J'.Forbes¹⁹^,B.Franek³²^,P.Frenkiel⁸^,D.C.Fries¹⁴^,A.G.Frodesen⁴^, R.Fruhwirthf.³^, F.Fulda-Quenzer¹⁶^, K.Furni¹nll¹⁹, H.Furstenau¹⁴^, J.Fuster⁷^, G.Galeu:1i³¹^, D.Gamba³⁹^, C.Garcia⁴²^, J.Garcia³⁶^, C.Gaspar⁷^, U.Gasp11~³¹, P.Gavillet ⁷^, E.N.Guis²⁸^, l-P.Gerber⁸^, P.Giacomelli⁷^, R.Gokieli⁷^, V.M.Golovatyuk¹³^, J.J.Gome11 Y Cadenas⁷^, A.Goobar³⁸^, G.Gopal³²^, M.Gorski⁴⁴^, V.GraccoL⁰^, A.Grant ⁷^, F .Grard²1 E.Graziani³⁵1 G.Grosdidier¹⁸1 E.Gross ⁷^, P.Grosse- Wiesmann ⁷^, B.Grossetete⁷⁰^, S.Gumenyuk³⁷, J .Guy³², F .Halm.⁷1 M.Habi11¹⁴, S.Haider²⁷, Z.Hajduk¹^,j, A.Hakansson²¹, A.Hallgren-1¹,

K.Hamacher⁴⁵^, G.Ham.el De Monchenault³⁴^, F.J.Harris³⁰^, B.W.Heck⁷^, T.Henkes⁷^, J.J .Hernandez⁴²^, P.Herquet², H.Herr⁷, l.Hietanen¹², C.O.Higgim¹⁹, E.Higon⁴², H.J.Hillr.e⁷, S.D.Hodgson³⁰, T.Hofmok1⁴⁴,

R.Holmes¹^, S-O.Holmgren³⁸^, D.Holthuilen::¡~⁷, P.F .Honore⁶^, J .E.Hooper²⁶^, M.Houlden ¹⁹^, J .Hrubec"³^, P.O.Hulth³⁸^, K.Hultqvist³⁸^, D.Husson⁸^, P.Ioannou³^, D.laenhower⁷^, P-S.Iversen⁴^, J.N.Jacbon¹⁹^, P.Jalocha¹⁵^, G.Jarlskog²¹, P.Jarry³⁴, B.Jean-Marie¹⁶, E.K.Joh&DHon³⁸, D.Jolmson¹⁹, M.Jonker⁷, L.Jonsson²¹, P.Juillot⁸,

G.Kalkanis³^, G.Kalmus³²^, F .Kapusta²⁰1 1~.Karlsson ⁷^, S.Katsaneva.s³^, E.C.Katsoufis²⁸^, R.Keranen¹²^, J.Kesteman², B.A.Khomenko¹³, N.N.Khovamki¹³, B.King¹⁹, N.J.Kjaer⁷, H.Klein⁷, W.Klempt⁷, A.Klovning⁴,

P.Kluit²⁷^, J.H.Koehne¹⁴^, B.Koene²⁷^, P.Kokkliniu⁹1 M.Kopf¹⁴^, M.Korat1inos³⁹^, K.Korcyl¹⁵^, A.V .Korytovl³^, V .Kostiukhin³⁷^,C.Kourkoumelis³^,P.H.Krame:t⁴⁵^,T .Kreuzberger⁴³^,J .Krolikowski.⁴⁴^,I.Kronk.vist²^L,J .Kntic³⁰^, U.Kruener-Marquia⁴⁵^, W.KrupinsJd.¹⁵^, W JCucewics²⁵^, K.Kurvinen¹²^, C.Lacasta⁴²^, C.Lambropoulos⁹^, J.W.LB1D.Sa¹^, L.Lanceri⁴⁰^, V.Lapin³⁷^, J-P.La·o.gier³⁴^, R.Lauhabnga.s¹²^, G.Leder⁴³^, F .Ledroit¹¹^, R.Leitner⁷^, Y.Lemoigne³^4.,J.Lemonne²^,G.Lemen.⁴⁵^,V.Lepeltier¹⁶^,A.Letessier-Selvon²⁰^,E.Lieb⁴⁵^,D.Liko⁴³^,E.Lillethun⁴^, J.Lindgren¹²^, R.Lindnerf,⁵^, A.Lipniac:ka.⁴⁴^, I.:Lippi³¹^, R.Llosa²³^, B.Loerstad.²¹^, M.Lokajicekl³^, J.G.Loken³⁰^, A.Lopes-Femande•¹⁶^,M.A.Lope11 Aguera³⁶^,M:.101²⁷, D.Loulms⁹^,A.Louni1⁸1 J.J.Losanof.²^,P.Lutz⁶^,L.Lyons³⁰^, G.Maehlum ⁷^, J .Maillard⁶^, A.Mal.temos⁹^, F .:Mandlf.³^, J .Marco³⁶^, M.Margoni³¹^, J-C.Marin ⁷^, A.Markou⁹^, T.Maronf.⁵1 S.Marti⁴²^,L.Mathi9¹1 F .Matorras:¹⁶1 C.Matteusri²⁵^,G.Matthiae³³^,M.Matveev³⁷^,M.Mazzucato³L, M.Mc CubbiD.¹⁹, R.Mc Kay¹, R.Mc Nulty¹⁹, E.Menichetti³⁹, G.Meolaio, C.Meroni²⁵, W .T.Meyert, M.Michelotto³¹1 W .A.Mitaroff4'³^, G.V .Mitseb:J11akher¹³1 U .Mjoernmark.²¹^, T .Moa³⁸^, R.Moeller²⁶1 K.Moenig ⁷^, M.R.Monge¹⁰^,P.Morettini¹⁰^,H.Mueller¹⁴^,W.J.Murray³²^,B.Muryn¹⁶^,G.Myattªº, F.Naraghi²⁰^,F .L.NaYB.Irias, P.Negri²⁵₁ B.S.Nielsen²⁶, B.Nijjhar¹⁹, V .Nikolaenko³⁷, V .Obraztsov³⁷, K.Oesterberg¹², A.G.Olshevski ¹³,

R.Orava¹²^, A.Ostankov³⁷^, A.Ouraou³f., M.P'aganoni²⁵^, R.Pain²⁰^, H.Palb²⁷^, T.Papadopoulou²⁸^, L.Pape⁷^, A.Passerl.³⁵^, M.Pegoraro³¹^, J.Pennanen¹²^, V.Perevo1c:hikov³⁷^, M.Pernicka.⁴³^, A.Perrotta⁵^, F .Pierre³⁴^, M.Pim.enta¹⁸₁ O.Pingot², M.E.Pol⁷, G.Polok:¹⁵, P.Poropat"º 1 P.Privitera¹⁴, A.Pullia²⁵, D.Radojicic³⁰,

S.Raga111i", P.N.Ratofr¹⁷^, A.L.Read²⁹^, N.G.Redaelli", M.Regler⁴3, D.Reld¹⁹^, P.B.Renton³⁰^, L.K.Resvani.', F .Richard¹⁶^,M.Richardson¹⁹1 J .Ridky¹³^, G.Rinaudo³⁹^,I.Roditi⁷^,A.Romero³⁹^,I.Roncagliolo¹⁰^, P.Ronchese³¹^, C.Ronnqvist¹²^,E.I.Rosenberg¹1 U.Rossi⁵^,E.R.osso⁷^,P.Roudeau¹⁶^,T.Rovelli⁵^,W.Ruckstuhl²T 1 V.Ruhlmann³⁴^, A.Ruiz³⁶^,K.Rybicld.¹⁵^,H.Saarikko¹²^,Y.Sacquiin³⁴^,G.Sajot¹¹^,J.Salt⁴²^,E.Sanchez⁴²^,J.Sanche1²³^,M.Sannino¹⁰^, M.Schaeft'er⁸^, S.Schael¹⁴^, H.Schneider¹f,, M .. A .. E.Schyns⁴⁶^, F .Scuri⁴⁰^, A.M.Segar³⁰^, R.Sek:ulin³²^, M.Sessa⁴⁰1

G.Sette¹

º,

R.Seufert¹^"-,R.C.Sbellard⁷^,P.Siegrii1t³⁴^,S.Sim.onetti¹º, F.Simonetto³¹^,A.N.Sissakian¹³^,T.B.Skaali.²⁹^, G.Slrjevling²⁹^, G.Smadja³f,•²²^, N .Smirnov³⁷^, G.R.Smith³²1 R.Sosnowsk:i⁴f,, T .S.Spassofl't ¹^, E.Spiriti³⁵^,

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S.Squarcia¹⁰^, H.Staeck⁴¹¹^, C.Stanescu³⁶^,G.Sta·vropoulos⁹^, F .Stichelbaut²^, A.Stocchi¹⁶^, J.Strauss⁴³^,R.Strub⁸^, M.Szczekowski.⁴-4., M.Szeptycka"'-4., P.Szymanski⁴⁴, T.Tabarelli²⁵, S.Tavernier², G.E.Theodosiou⁹, A.Tilquin²⁴,

J.Timmen:nans²⁷^, V.G.Timofeev¹³^, L.G.Tka1tchev¹³^, T.Todorov¹³^, D.Z.Toet²⁷^, O.Toker¹²^, E.Torassa³⁹^, L.Tortora³¹¹, M.T.Trainor³⁰, D.Treille⁷, :U.Tr11!1vÜ!an¹⁰, W.Trischuk⁷, G.Tristram⁶, C.Troncon²⁵, A.Tsilou⁷,

E.N.Tsygauov¹³, M.Turala¹s, R.Turchetta⁸, M-L.Turluer³⁴, T.Tuuva¹², I.A.Tyapkin¹³, M.Tyndel³²,

S.T21amarias⁷^, S.Ueberschaer⁴⁵^, O.Ullaland⁷^, V.Uvarov³⁷^, G.Valentf", E.Valluza³⁹^, J.A.VallsFerret⁴²^, C.Vandet Velde², G.W.Van Apeld0orn²⁷, P.Van Dam²⁷, W.K.Van Doninck.2, J.Varela¹⁸, P.Var/, G.Vegni25 ,

L.Ventura³¹, W.Venus³², F.Verbeure², :L.S.Vettogradov¹³1 D.Vilanova³⁴, L.Vitale⁴⁰, E.Vlasov³⁷,

S.Vlassopoulos²⁸^, A.S.Vodopyanov¹³^, M.Volhner⁴⁵^, S.Volponi⁵^, G.Voulgaris³₁ M.Voutilainen¹²^, V.Vrba³⁵^, H.Wahlen4.⁵^, C.Walck:³⁸^, F.Waldner-4.⁰^, M.Wayne¹1 A.Wehr4.⁵^, M.Weierstall⁴⁵^, P.Weilhammer⁷^, J .Wemer⁴⁵^, A.M.Wetherell⁷^, J .H.Wickens²^, J .Wikne²⁹^, G·.R.Wilkinson³⁰^, W.S.C.Williams³⁰^, M.Winter⁸^, D.Wormald²⁹^, G.Wormser¹⁶^, K.Wosclmagg⁴¹^, N.Yamdagni³⁸^, P.Yepes⁷^, A.Zaitsev³⁷^, A.Zalewsb.¹⁵^, P.Zalewski¹⁶^, D.Zavrtanik⁷, E.Zevgolatakos⁹, G.Zhangts, N.I.Zirnin¹³, M.Zito³⁴, R.Zitoun²⁰, R.Zukanovich Funchal⁶,

G.Zumerle³¹, J.Zuniga⁴²

1 Ames Laboratory and Department of Physics, lowa State University, Ames IA 50011, USA

2 Ph.vsics Department, Univ. Instelling Antwerp!=·n, Universiteitsplein 1, B-2610 Wilrijk, Belgium and l!HE, ULB-VUB, Ple;n!aan 2, B-1050 Brussels, Belg;wn

and Service de Phys. des Part. Elém., Faculté eles Scienccs, Ur:üvenité de l'Etat Mons, Av. l'vlaistriau 19, 8-7000 Mons, Belgium

3Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece

4 Department of Physics, University of Bergen, A.llégaten 55, N-5007 Bergen, Norway

5Dipartimento di Fisica, UniversitA di Bologna i!~d INFN, Via Imerio 46, 1-40126 Bologna, Italy

6College de France, Lab. de Physique Corpuscu1aire, 11 pl. M. Berthelot, F-75231 Paris Cedex 05, France

7CERN, CH-1211 Geneva 23, Switzerland

8Division des Hautes Energies, CRN - Groupe D¹ELPHI and LEPSI, B.P.20 CRO, F-67037 Strasbourg Cedex, France

91nstitute o! Nuclear Physics, N.C.S.R. Demo.kritos, P.O. Box 60228, GR-15310 Athens, Greece 1ºDipartimento di Fisica, UrüversitA di Genova ai:id INFN, Via Dodecaneso 33, l-16146 Genova, Italy

11 lnstitut des Sciences Nucléaires, Université de C}renoble 1, F-38026 Grenoble, France

12 Research Institute for High Energy Physie!i, UnJversity of Helsinki, Siltavuorenpenger 20 C, SF-00170 Hclsinki 17, Finland

13 Joint Institute for Nuclear Researeh, Dubna, H•ead Post Office, P.O. Box 79, 101 000 Moscow, USSR.

14 Institut für Experimentelle Kemphysik, Unive~sitit Karlsruhe, Postfach 6980, D-7500 Karlsruhe 1, FRG

15 High Energy Physics Laboratory, lnstitute of N'uclear Physics, Ul. Kawiory 26 a, PL-30055 Krakow 30, Poland

16Université de Paris-Sud, Lab. de l'Accélératew· Linéaire, Bat 200, F-91405 Orsay, France 17School of Phyeics and ~[aterials, University of La.nca.ster- Lancaster LAl 4YB, UK

18LIP, Av. Elias Garcia 14 - le, P-1000 Lisbon Codex, Portugal

19Department of Physics, Ur:üvereity of Liverpool, P.O. Box 147, GB - Liverpool L69 38X, UK

20LPNHE, Ur:üversités París VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75230 Paris Cedex 05, France 2l Department of Phyeics, University o! Lund, SOl:vegatan 14, S-22363 Lund, Sweden

22Université Claude Bernard de Lyon, 43 Bd du ll Novembre 1918, F-69622 Villeurbanne Cedex, France

23Universidad. Complutense, Avda. Complutense s/n, E-28040 l\·ladrid, Spain

2 " Univ. d'Aix - Mancille 11 - Case 907 - 70, rout,e Léon Lachamp, F-13288 Marseille Cedex 09, France

25Dipartimento di Fisica, Universit& di Milano and INFN, Via Celoria 16, 1-20133 Milan, ltaly

26Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O, Derunark

27NIKHEF-H, Postbus 41882, NL-1009 DB Amst,erdam., The Netherlands

28National Tecluúcal Univenity, Physics Departn:i.ent, Zogra.fou Campus, GR-15773 Athens, Greece 29Physics Department, Univenity of Oslo, Blind4!1m, N-1000 Oslo 3, Norway

ªºNuclear Physics Laboratory, University of Oxfc1rd, Keble Road, GB - Oxford OXl 3RH, UK

31 Dipartim.ento di Fisica, UrüversitA di Padova am.d INFN, Via Manolo 8, 1·35131 Padua, ltaly 32 Rutherford Appleton Laboratory, Chilton, GB - Didcot OXll OQX, UK

ª³Dipartimento di Fisica, UniversitA di Roma 11 omd INFN, Tor Vergata, 1-00173 Rome, Italy

34CEN·Saclay, DPhPE, F-91191 Gif-sur-Yvette C~edex, France

3?11stituto Superiore di Sanit&, Ist. Naz. di Fisica Nucl. (INFN), Viale Regina Elena 299, 1-00161 Rome, Italy 3SFacultad. de Ciencias, Universidad. de Santander, av. de los Castros, E - 39005 Santander, Spain

37Inst. for High Energy Physics, Serpukow P.O. lBox 35, Protvino, (Moecow Region), USSR.

38 Institute of Physics, University of Stockholm, 'la.nadisvii.gen 9, S.113 46 Stockholm, Sweden

39Dipartimento di Fisica Sperimentale, Universit.a di Torino and INFN, Via P. Giuria 1, I-10125 Turin, ltaly

4ºDipartimenLo di Fisica, Universitil. di Trieste and INFN, Via A. Valerio 2, 1-34127 Trieste, ltaly and lstituLo di Fisica, Universit& di Udine, 1-33100 Udine, ltaly

fil Department of Radiation Sciences, Urüversity <>f Uppsala1 P.O. Box 535, S-751 21 Uppsala, Sweden

42 Inst. de Fisica Corpuscular IFIC, Centro Mixt1:> Univ. de Valencia-CSIC, and Departamento de Física Atomica Molecular y Nuclear, Urüv. de Valencia, Avda. Dr. Moliner 50, E-46100 Burjas80t (Valencia), Spain

4³Institut für Hochenergiephysik, Oesterreich Ak;~. d. Wiesensch., Nikolsdorfergasae 18, A-1050 Vienna, Austria 44 Inst. Nuclear Studies and, Urüversity of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland

fi 5Fachbereich Physik, University of Wuppertal, Postfach 100 127, D-5600 Wuppertal 1, FRG

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•

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1 Introduction

The forward backward asymmetry AFB in e+e---+

Jf

(! = µ, e, r, q) is sensitive to the axial- and vector-coupling of the initial and final state fermions. At .j8 = Mz it is described in lowest order by the relation :

with

A _ 2v¡a¡ 2(1-4jQ¡jsin²8w)

1 -

v] +a} --

1+(1-4IQ1I sin²llw)²

which is valid for light fermions (

~ <

1) and neglecting terms of the order (

-f¡;)

²^for

the ")'-exchange. Results on AFB for ¡1, e and T final states have already be presented by the LEP collaborations [l].

In this paper the asymmetry for bottom quarks

A}

₈ is determined by selecting their semileptonic decay into muons. The angular distribution of the b-quark in the reaction e+e- --+ bb at .j8 = Mz is predicted by the Standard model to be :

de~:

111 ^ex: (1 + cos²ll¡ + 2 cos ll¡A,,A¡) = ( 1 + cos²11¡ +

~

^{cos 8¡A}}8 )

The line of flight of the b-quark is obtained from the direction of the event thrust axis, with orientation determined by the measured muon charge. The charge of the muon follows from the charge of the quark, up to Bº .8°-mixing effects which can change the decay fiavour content of the B-meso~1 and thus fake the opposite direction. The muons produced by b-decay have large transverse momentum with respect to the jet axis. This allows the backgrounds from other d1annels to be reduced. To interpret the measured asymmetry in terms of the b-quark asymmetry, the fiavour origin of muons as well as the hadronic background must be known ..

2 The Detector

The DELPHI detector has been d.escribed in detail elsewhere [2]. Only components relevant to this analysis are summariz1~d here. Charged particle tracks are reconstructed in a 1.23 T magnetic field, generated by ^illarge superconducting solenoid. A time projection chamber is the main tracking device, which is supplemented in the barre! region by the inner detector and the outer detector. Two forward drift chambers complete the tracking system.

The iron return yoke of the magn.et is instrumented with a hadron calorimeter seg- mented along its depth into four towers in both the barre! and the endcaps. The muon identification chambers are situated a.t the periphery of DELPHI after more than 1 m of iron. The barre! muon detector is divided into three layers: an inner, an externa! and a peripheral !ayer covering the dead space between sectors. Each !ayer consists of two active planes of drift chambers parallel to the beam axis measuring the transverse and longitudinal coordinates of the muon track. The forward muon detector consists of two

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layers arranged in quadrants. Each layer contains two planes of drift chambers crossed at right angles, which measure the horizontal and vertical coordinates of the muon.

DELPHI is triggered by a redund1a.nt combination of signals from tracking chambers, electromagnetic calorimeters, muon c:hambers and scintillation hodoscopes in the barre!

and forward region. The trigger efficiency for hadronic events is la.rger than 99 3 for 1cos8,h¡ < 0.93, where 8,h is the polar angle of the thrust axis of the event.

3 Selection of hadronic Zº-events

The data used in this analysis ha.v1e been collected during the year 1990 by DELPHI at the LEP collider. The sample of had1:onic decays of the Zº is obtained with the following requirements :

a) at least 7 reconstructed cha.rgecl particles coming from the interaction region with polar angle 8 between 20º and 160° and momentum above 0.2 Ge V /c

b) the total visible energy of charg4~d and neutral particles has to be greater than 30 3 of the centre of mass energy

c) the visible energy has to be a.t least 3 Ge V in both the forwa.rd and ba.ckward hemispheres with respect to the beain axis

These cuts reduce the background (

zo

leptonic deca.ys, bea.m-gas events, ')"')'-events) to less than 0.3

%.

The efficiency of this selection is determined by Monte Cario simula- tions to be about 93

3

for hadronic Zº-deca.ys. The identification of muons is essentially performed with the muon chambers in connection with the tracking devices in the ba.rrel and in the forward region. In the a1~a.lysis only data are retained taken in runs, where all necessary detectors were working well. In this way 79 271 events are selected with a.

centre of mass energy of .¡8 =

Mz ±:

^0.2GeV.

4 Selection of m111on candidates

The

zo_, ^bb

channel is tagged by the identification of a muon coming from the semileptonic decay of a b- or b-qua.rk. Only pa.rticles with momentum la.rger than 3 Ge V/ e a.re considered, beca.use the muons have to penetrate through the hadron calorimeter iron to the muon chambers.

To accept a track a.s a muon candidate a fit combining the muon chamber hits with the tracking information is performecl. Therefore the tracks are extrapolated to the muon chambers and then associated and fitted to the muon chamber hits. The result of this procedure is a fitted track at the muon chambers and a.

x

²^• In the ba.rrel region the following requirements must be fulfilled:

• There must be at least 2 planes hit in the muon chambers with at least one pla.ne hit in one of the two external fayers .

•

__________

^,,^_^__)

(6)

• The fit should have an acceptable

x

²^,where the

x

²is calculated from the difference in transverse position and azimuthal angle between the extrapolated trajectory and the fitted track.

In the forward region the following re:quirements must be fulfilled:

• There must be at least 2 planes hit in the forward muon chambers with at least one plane hit in the externa! !ayer.

• The fit should have an acceptable

x

²per degree of freedom, where the

x

²is calculated from a) the difference in position between the extrapolated trajectory and fitted track in the horizontal and vertical coordinates and in the azimuthal and polar angle and b) the difference between the fitted track and the hits in the muon chambers.

The values of the the

x

²cut in the barre! and forward region were evaluated from the data and optimised to suppress back¡~ound (punch through, decays etc.) while keeping a high muon identification efficiency.

The analysis is restricted to muons with a polar angle (J" su ch that:

o.o3

<

1cos9,.1 < 0.60 0.11 < 1cos9,.1 < o.93

in order to exclude regions with poor geometrical acceptance. The identification efficiency is determined to be e,. = 78

±

2

%

inside the acceptance of the barre! and forward muon chambers for muons with momenta larger than 3 Ge V/ c . This number is determined by Monte Cario simulation and checked with data from the Zº--+ µ+ µ- channel. More details on muon identification can be found in reference [4].

With these criteria 6564 muon candidates were selected in the momentum range 3GeV/c < p" < 35GeV/c.

5 Analysis method

The experimental muon distributio'n was modeled by generating simulated events with the Lund parton shower program JETSET 7.2 [3] using string fragmentation. For b- and c-quarks the fragmentation is described by the Peterson function [5]

z(l - z)² f(z) = [(z - 1)2

+

ez]2

where z is the fraction of the quark momentum carried by the hadron. The hardness of the fragmention is determined by the parameter e. The mean scaled energy of B- hadrons (zE) = 0.705

±

0.011 as receutly measured by the LEP-collaborations [6] can be translated to e = 0.005

±

0.002 usin:g the Lund parton shower program. This value is chosen for the analysis. The generated events were passed through the full DELPHI chain of simulation and reconstruction.

Knowledge of the composition of the identified muon sample is needed for the determination of the asymmetry. Therefore the Monte Cario sample is divided into four classes:

(7)

1) fb muons from direct b-deca.y ( b -+ µ) 2)

/be

muons from b-cascade (b-+ c(c)-+ µ) 3) fe muons from direct c-decay (e-+µ)

4) fbaek other background ( e.g. pi•nch through hadrons, muo ns from decay ... )

The first class includes a small contribution of the order of a few percent from the process b ^--+^T -+ µ. The composition of the sample predicted by Monte Cario simulation depends strongly on the momentum spectra of the muon candidates. The variables used in the analysis are the longitudinal momentum PL and the transverse momentum PT of the muon with respect to the jet axis, which is determined using the Lund cluster algorithm [3] for charged and neutral particles. The parameter for the cluster distance scale is ch osen to be D join = 2.5 Ge V/ c. For the calculation of the axis of the jet to which the muon belongs, the muon momentum is excluded. The jet axis reproduces the original B-hadron direction with an accuracy of about 2 degrees on Monte Cario simulated events. The relative contributions of the four classes obtained by full detector simulation for different PT-cuts are summarized in Table l.

The charge of the muon in the semileptonic b-decay reflects the charge of the original quark. The direction of quarks in th" centre of mass system is taken to be the thrust axis of charged and neutral particles in hadronic events. The orientation is then calculated by multiplying - cos 8,h with the mu.on charge.

1Source1 no PT cut 1PT<0.1) Ge V /e 1PT>0.7GeV /c 1PT>1.2 Ge V /e 1

fb 27.23 4.53 44.23 61.9%

/be

^14.23 ^15.3% ^13.03 ^9.0%

fe 14.4% 19.3% 10.6% 6.8%

fbaek 44.2% 60.93 32.2% 22.33

Table 1: Composition of the sample of muon candidates generated with the full DELPHI simulation, for muon momenta betw1een 3 and 35 Ge V /c.

6 Fitting proced·ures

The determination of the forward backward asymmetry

A}

8 has been performed using three different fitting procedures. The first one is an unbinned maximum likelihood fit to the PL and PT distribution of the muons with respect to the the thrust axis. To check the results of this fit a binned maximum likelihood fit to the same distribution is performed.

As an independent analysis also a dii:ect

x

²-fit to the angular distribution of muons after acceptance correction and background subtraction was done.

6.1 The unbinned maxin1um likelihood fit

A precise determination of the parameter

A}

₈ is achieved by an unbinned maximum likelihood fit to the cos 8,h distribution in the region ¡I' > 3 Ge V/ e and p~ > O. 7 Ge V/ c

(8)

•

using the PL - PT distribution to dete1~mine the different contributions coming from the 4 classes defined in section 5. The number of events selected within these kinematical cuts is 3226. Figures 1,2 and 3 compare tb.e measured distributions of p, PT and -Q,.. cos O,h with the prediction from simulation, split into the different classes. The method has already been used in a similar way by the 13-collaboration [7]. First a distance is defined inside the momentum plane as follow:s :

V1,2 = j(logpL,I - logpL,2 )2

+

^{(e-PT,1 -} ^e-PT,2)2

To calculate the probabilities that an event belongs to the different classes, Monte Cario generated events close to the d;~ta event are used. For each event the NMc Monte Cario events with the smallest distan.ce in the logpL vs. e-PT plane are collected. Data events with a muon in the barre! (forward) muon chambers are compared only with Monte Cario events with a muon in the barre! (forward) chambers respectively. The definition of the distance ensures that the density of simulated events around each data point is approximately constant. From the NMc Monte Cario events the probabilities that the event belongs to one of the four classes quoted in section 5 are calculated. For this analysis NMc = 40 is chosen, wbich is a valm: optimized for the available statistics. It has been checked that for the present analysis the systematic bias of the fit result introduced by the fit procedure is less than one tentlli of the statistical error. The statistical error of the Monte Cario event sample is given in Table 2.

The asymmetry at a fixed polar augle O,h determines the contribution to the log like- lihood according to the different origi.n of muons :

with A₁

-

^Ab,ezp_FB

A2

-

^Abc,ezp^FB

-

^-C1^Ab,ezp^FB

AJ

-

^A~B

-

^-c2^Ab,e:cp^FB

A4

- ^o

where Ak is the integrated asymmetry of class k and the superscript 'ezp' indicates that the experimental measured asymmetry is reduced by Bº B⁰-mixing. The additional factor c₁has been calculated with the JETSET 7.2 Monte Cario program. lt is due to the fact that the b-quark may decay either into a c-quark or into a c-quark. Because of the opposite charge sign of the produced muons, the contributions of these two different processes cancel partly. The correction factor c2 has been calculated using KORAL-Z [8]

(sin²Ow = 0.23) and correcting for Bº Bº-mixing assuming X= 0.143 (see also section 7).

On the Zº-peak these factors are found to be : c1 = 0.77

C2 = 0.88

The asymmetry of the background A₁is calculated with the Monte Cario simulation and is compatible with zero. Due to the cos O,h dependence of the thickness of penetrated iron inside the detector the background fraction depends on the polar angle of the muon. To take tbis into account the Monte Cado ratio of background to true muons was fitted as a polynomial in cos Oth· The background events have been reweighted according to their

(9)

polar angle keeping the total number constant. No cos fJ,h dependence was found for the ratios of the other cla.sses .

Combining all information gives the negative logarithm of the likelihood function, which has to be minimized :

where Pk; is the probability of event j to belong to dass kas determined from the NMc

Monte Cario events around event j.

The fitted asymmetry for the sample is :

A~~?= 0.115

:±:

0.043 (stat)

±

^0.013^(syst)

The statistical uncertainty comes from the lit, while the contributions to the total systematic uncertainty shown are detail•~d in Table 2. These contributions ha ve been studied and evaluated in the ranges given.

1 range

l±llA~~PI

Variation of the Peterson

fragmentation parameter ^E:b 0.003-0.007 0.007 Variation of the b-casc:~de

fraction (0.80-1.20)· fbc 0.001

Variation of the c-quark

fraction (0.89-1.11)·/c 0.001

Variation of the total

background fraction (0.90-1.10)· f&ack 0.002 Variation of the background

fraction in the endcap 1region (0.50-1.50)· f!.":t 0.006 Variation of the factor c1 for

different b-ca.scade con1>ributions 0.5-1.0 0.002 Variation of the factor c2

for the c-quark a.symm•~try 0.6-1.l 0.005 Transverse momentum smearing with respect

to the beam axis by il1' = 0.01 · p² 0.001 Fit method ( definition of the distance,

number of Monte Cario events collected) 0.005 Statistical error of the Monte Cario sample 0.006

1 Total 0.013 ¹

Table 2: Contributions to the systematic error of the maximum likelihood lit

•

(10)

,

6.2 The binned maximun11 likelihood fit

A binned maximum likelihood :fit in the 2-dimensional PL·JJT-distribution has been performed to obtain the asymmetry of the b-quark. The method is based on counting the number of events in the forward a:o.d backward hemispheres with respect to the initial electron direction. The asymmetry is then determined from:

N forw _ Nback Ab,erp ·- - - -

FB ·- Nforw

+

^Nback

All muon candidates with PT > O.~r Ge V /c are weighted according to:

Fk '=

2

1 (1

±

Ak )

where the

+/-

sign is used for events iD1 forward and backward hemispheres. The likelihood function is defined as above where the probability Pk; is evaluated in each hin of pi,PT·

In the fit the values for Ak are taken to be the same as above and the b-quark asymmetry is left free. The asymmetry becomes:

A~'!?= 0.108

±

0.048 (stat)

±

0.013 (syst)

which is consistent with the result obtained with the unbinned maximum likelihood fit.

6.3 The x

²

-fit

The unbinned maximum likelihood fit is considered to be the most precise method for the determination of the asymmetry due to the construction of the likelihood function.

On the other hand the understa:o.di:o.g of the acceptance a:o.d the background ca:o. be proved performing a conventional least square fit to the a:o.gular distribution, where the evaluation of the quality of the fit is ¡~ven by the x²value. The distribution of the polar angle of the thrust axis is directly compared with the prediction of the Standard model :

du [ 2 8obs ]

d cos ^9th^<X 1

+

cos ^9th

+ 3

^AFBcos ^9,h

To enrich the sample of b-quark ca.io.didates a more severe cut on the transverse momentum of PT

>

1.2 Ge V /c is performed .. This reduces the number of events with identified muons to 1714. The sample includes contributions from b-cascade, charmed quarks, misidentified hadrons a.io.d decays. fo this kinematical region the latter two amount to a fraction of 22

%.

The background contribution ca.io. be checked with muon candidates whiclo. have PT

<

0.6 Ge V /c. In this region the background is expected to be dominant (see Table 1) and the asymmetry, obt111.ined by counting the backward and forward events, is found to be

A1;í/

⁼0.005

±

0.020.

After hadronic background subt:raction and acceptance correction the expression quoted above has been fitted to the data using a conventional

x

²-fit method with the asymmetry as a free parameter. The a.io.gular domain of the thrust axis is restricted to 1cos9th 1 < 0.90. The result of the fit gives the observed asymmetry :

A/fr.B =

^0.073^±0.039 with

x

²

=

11.0 for 16 degrees of freedom

The a.io.gular distribution a.io.d the result of the fit are shown in figure 4. The observed asymmetry is related to the b-asymmetry as follows :

Aobs _ _{FB -} _Jb^~/A^l>,erp_FB

+

f,'Ac

+

~/ A ^be

e FB Jbc FB

(11)

with

f,' = f;

' Íb

+

Íbc

+

Íc

The asymmetry of the b-cascade and of the c-quark is aga.in assumed to be :

A^be Ab,.,xp d Ac Ab,exp

FB = -C¡ FB a.n ^FB= -c2 FB

using the same values for c1 and c2 as quoted before. Extracting the fractions

f&, f&c

and

f~ from Monte Carlo simulation lead:s to :

A~';;'P = 0.116 :!: 0.062 (stat)

±

0.021 (syst)

This result is consistent with the previous estimates. lt has however larger statistical errors due to the higher p, cut and "to the background and acceptance corrections. The systematic error has been evaluated varying the fractions f; of the different muon sources a.nd the values of _{c 1}a.nd c2 in the :tanges of Table 2. This gives a contribution of the fractions of 0.020 and of the factors of 0.004 a.nd 0.005 respectively.

7 Extraction of the electroweak mixing an- gle

The relation between the quark 8.IILd the measured asymmetry is sensitive to the mixing in the

B3 .83-

and

B2

.82-system. The:tefore the experimentally determined asymmetry has to be corrected by a factor (1 - 2x)-¹, where

x

gives the probability that the neutral B-meson has cha.nged its flavour co1ntent. For the mixing parameter the average value measured at LEP-energies [6] is used

XLEP = 0.143

±

0.023

where the natural mixture of the diffE•rent B-hadrons produced at the Zºare included. The result of the unbinned maximum likdihood fit, which yields the smallest error, increases to a value of

Ab,exp

A~

8

^{= (} ^FB ⁾ ⁼0.161:!:0.060 (stat)

±

0.018 (syst)

±

0.010 (syst) 1-2XLEP

The last contribution of the error is due to the uncerta.inty of the mixing parameter. U sing the program ZFITTER [9], which i1ncludes QED radiative corrections, the electroweak mixing angle in the MS renormalisation scheme is determined to be :

sin²11~⁵= 0.221

±

O.Oll. (stat)

±

0.003 (syst)

±

0.002 (syst)

The result agrees with the values determined from bb-asymmetries by the other LEP collaborations [7,10] a.nd also with those obta.ined from di-lepton asymmetries and Zº- lineshape measurements [11].

Acknowledgements

We are greatly indebted to our technical collaborators a.nd to the funding agencies for their support in building a.nd operating the DELPHI detector, a.nd to the members of the CERN-SL Division for the excellent performance oí the LEP collider.