Study of CP-violating asymmetries in B^0 -- pi^+pi^-, K^+pi^- decays

StudyofCP-violatingasymmetriesinB0→π+π−,K+π−decays

B.Aubert,1D.Boutigny,1J.-M.Gaillard,1A.Hicheur,1Y.Karyotakis,1J.P.Lees,1P.Robbe,1V.Tisserand,1A.Palano,2A.Pompili,2G.P.Chen,3J.C.Chen,3N.D.Qi,3G.Rong,3P.Wang,3Y.S.Zhu,3G.Eigen,4B.Stugu,4G.S.Abrams,5A.W.Borgland,5A.B.Breon,5D.N.Brown,5J.Button-Shafer,5R.N.Cahn,5

A.R.Clark,5M.S.Gill,5A.V.Gritsan,5Y.Groysman,5R.G.Jacobsen,5R.W.Kadel,5J.Kadyk,5L.T.Kerth,5Yu.G.Kolomensky,5J.F.Kral,5C.LeClerc,5M.E.Levi,5G.Lynch,5P.J.Oddone,5A.Perazzo,5M.Pripstein,5N.A.Roe,5A.Romosan,5M.T.Ronan,5V.G.Shelkov,5A.V.Telnov,5W.A.Wenzel,5P.G.Bright-Thomas,6T.J.Harrison,6C.M.Hawkes,6D.J.Knowles,6S.W.O’Neale,6R.C.Penny,6A.T.Watson,6N.K.Watson,6T.Deppermann,7K.Goetzen,7H.Koch,7M.Kunze,7B.Lewandowski,7K.Peters,7H.Schmuecker,7M.Steinke,7J.C.Andress,8N.R.Barlow,8W.Bhimji,8N.Chevalier,8P.J.Clark,8W.N.Cottingham,8N.Dyce,8B.Foster,8C.Mackay,8D.Wallom,8F.F.Wilson,8K.Abe,9C.Hearty,9T.S.Mattison,9J.A.McKenna,9D.Thiessen,9S.Jolly,10A.K.McKemey,10V.E.Blinov,11A.D.Bukin,11D.A.Bukin,11A.R.Buzykaev,11V.B.Golubev,11V.N.Ivanchenko,11A.A.Korol,11E.A.Kravchenko,11A.P.Onuchin,11A.A.Salnikov,11S.I.Serednyakov,11Yu.I.Skovpen,11V.I.Telnov,11A.N.Yushkov,11D.Best,12M.Chao,12A.J.Lankford,12M.Mandelkern,12

S.McMahon,12D.P.Stoker,12K.Arisaka,13C.Buchanan,13S.Chun,13D.B.MacFarlane,14S.Prell,14Sh.Rahatlou,14G.Raven,14V.Sharma,14C.Campagnari,15B.Dahmes,15P.A.Hart,15N.Kuznetsova,15S.L.Levy,15O.Long,15A.Lu,15J.D.Richman,15W.Verkerke,15M.Witherell,15S.Yellin,15J.Beringer,16D.E.Dorfan,16A.M.Eisner,16A.A.Grillo,16M.Grothe,16C.A.Heusch,16R.P.Johnson,16W.S.Lockman,16

T.Pulliam,16H.Sadrozinski,16T.Schalk,16R.E.Schmitz,16B.A.Schumm,16A.Seiden,16M.Turri,16W.Walkowiak,16D.C.Williams,16M.G.Wilson,16E.Chen,17G.P.Dubois-Felsmann,17A.Dvoretskii,17D.G.Hitlin,17S.Metzler,17J.Oyang,17F.C.Porter,17A.Ryd,17A.Samuel,17M.Weaver,17S.Yang,17R.Y.Zhu,17S.Devmal,18T.L.Geld,18S.Jayatilleke,18G.Mancinelli,18B.T.Meadows,18M.D.Sokoloff,18T.Barillari,19P.Bloom,19M.O.Dima,19S.Fahey,19W.T.Ford,19D.R.Johnson,19U.Nauenberg,19A.Olivas,19P.Rankin,19J.Roy,19S.Sen,19J.G.Smith,19W.C.vanHoek,19D.L.Wagner,19J.Blouw,20J.L.Harton,20M.Krishnamurthy,20A.Soffer,20W.H.Toki,20R.J.Wilson,20J.Zhang,20R.Aleksan,21A.deLesquen,21S.Emery,21A.Gaidot,21S.F.Ganzhur,21P.-F.Giraud,21G.HameldeMonchenault,21W.Kozanecki,21M.Langer,21G.W.London,21B.Mayer,21B.Serfass,21G.Vasseur,21Ch.Y`eche,21M.Zito,21T.Brandt,22J.Brose,22T.Colberg,22M.Dickopp,22R.S.Dubitzky,22A.Hauke,22E.Maly,22R.M¨uller-Pfefferkorn,22S.Otto,22K.R.Schubert,22R.Schwierz,22B.Spaan,22L.Wilden,22D.Bernard,23G.R.Bonneaud,23

F.Brochard,23J.Cohen-Tanugi,23S.Ferrag,23E.Roussot,23S.T’Jampens,23Ch.Thiebaux,23G.Vasileiadis,23M.Verderi,23A.Anjomshoaa,24R.Bernet,24A.Khan,24D.Lavin,24F.Muheim,24S.Playfer,24J.E.Swain,24J.Tinslay,24M.Falbo,25C.Borean,26C.Bozzi,26S.Dittongo,26L.Piemontese,26E.Treadwell,27F.Anulli,28,∗R.Baldini-Ferroli,28A.Calcaterra,28R.deSangro,28D.Falciai,28G.Finocchiaro,28P.Patteri,28I.M.Peruzzi,28,∗

M.Piccolo,28Y.Xie,28A.Zallo,28S.Bagnasco,29A.Buzzo,29R.Contri,29G.Crosetti,29M.LoVetere,29M.Macri,29M.R.Monge,29S.Passaggio,29F.C.Pastore,29C.Patrignani,29M.G.Pia,29E.Robutti,29

A.Santroni,29S.Tosi,29M.Morii,30R.Bartoldus,31R.Hamilton,31U.Mallik,31J.Cochran,32H.B.Crawley,32

P.-A.Fischer,32J.Lamsa,32W.T.Meyer,32E.I.Rosenberg,32G.Grosdidier,33C.Hast,33A.H¨ocker,33

H.M.Lacker,33S.Laplace,33V.Lepeltier,33A.M.Lutz,33S.Plaszczynski,33M.H.Schune,33S.Trincaz-Duvoid,33

G.Wormser,33R.M.Bionta,34V.Brigljevi´c,34D.J.Lange,34M.Mugge,34K.vanBibber,34D.M.Wright,34M.Carroll,35J.R.Fry,35E.Gabathuler,35R.Gamet,35M.George,35M.Kay,35D.J.Payne,35R.J.Sloane,35

C.Touramanis,35M.L.Aspinwall,36D.A.Bowerman,36P.D.Dauncey,36U.Egede,36I.Eschrich,36

N.J.W.Gunawardane,36J.A.Nash,36P.Sanders,36D.Smith,36D.E.Azzopardi,37J.J.Back,37P.Dixon,37P.F.Harrison,37R.J.L.Potter,37H.W.Shorthouse,37P.Strother,37P.B.Vidal,37M.I.Williams,37G.Cowan,38

S.George,38M.G.Green,38A.Kurup,38C.E.Marker,38P.McGrath,38T.R.McMahon,38S.Ricciardi,38F.Salvatore,38I.Scott,38G.Vaitsas,38D.Brown,39C.L.Davis,39J.Allison,40R.J.Barlow,40J.T.Boyd,40A.C.Forti,40J.Fullwood,40F.Jackson,40G.D.Lafferty,40N.Savvas,40E.T.Simopoulos,40J.H.Weatherall,40

arXiv:hep-ex/0110062v1 25 Oct 20012

A.Farbin,41A.Jawahery,41V.Lillard,41J.Olsen,41D.A.Roberts,41J.R.Schieck,41G.Blaylock,42

C.Dallapiccola,42K.T.Flood,42S.S.Hertzbach,42R.Kofler,42V.G.Koptchev,42T.B.Moore,42H.Staengle,42S.Willocq,42B.Brau,43R.Cowan,43G.Sciolla,43F.Taylor,43R.K.Yamamoto,43M.Milek,44P.M.Patel,44F.Palombo,45J.M.Bauer,46L.Cremaldi,46V.Eschenburg,46R.Kroeger,46J.Reidy,46D.A.Sanders,46D.J.Summers,46J.P.Martin,47J.Y.Nief,47R.Seitz,47P.Taras,47V.Zacek,47H.Nicholson,48C.S.Sutton,48C.Cartaro,49N.Cavallo,49,†G.DeNardo,49F.Fabozzi,49C.Gatto,49L.Lista,49P.Paolucci,49D.Piccolo,49

C.Sciacca,49J.M.LoSecco,50J.R.G.Alsmiller,51T.A.Gabriel,51T.Handler,51J.Brau,52R.Frey,52

M.Iwasaki,52N.B.Sinev,52D.Strom,52F.Colecchia,53F.DalCorso,53A.Dorigo,53F.Galeazzi,53M.Margoni,53

G.Michelon,53M.Morandin,53M.Posocco,53M.Rotondo,53F.Simonetto,53R.Stroili,53E.Torassa,53C.Voci,53M.Benayoun,54H.Briand,54J.Chauveau,54P.David,54Ch.delaVaissi`ere,54L.DelBuono,54O.Hamon,54F.LeDiberder,54Ph.Leruste,54J.Ocariz,54L.Roos,54J.Stark,54S.Versill´e,54P.F.Manfredi,55V.Re,55V.Speziali,55E.D.Frank,56L.Gladney,56Q.H.Guo,56J.Panetta,56C.Angelini,57G.Batignani,57S.Bettarini,57M.Bondioli,57M.Carpinelli,57F.Forti,57M.A.Giorgi,57A.Lusiani,57F.Martinez-Vidal,57M.Morganti,57N.Neri,57E.Paoloni,57M.Rama,57G.Rizzo,57F.Sandrelli,57G.Simi,57G.Triggiani,57

J.Walsh,57M.Haire,58D.Judd,58K.Paick,58L.Turnbull,58D.E.Wagoner,58J.Albert,59P.Elmer,59C.Lu,59K.T.McDonald,59V.Miftakov,59S.F.Schaffner,59A.J.S.Smith,59A.Tumanov,59E.W.Varnes,59G.Cavoto,60

D.delRe,60R.Faccini,14,60F.Ferrarotto,60F.Ferroni,60E.Lamanna,60E.Leonardi,60M.A.Mazzoni,60

S.Morganti,60G.Piredda,60F.SafaiTehrani,60M.Serra,60C.Voena,60S.Christ,61R.Waldi,61T.Adye,62N.DeGroot,8,62B.Franek,62N.I.Geddes,62G.P.Gopal,62S.M.Xella,62N.Copty,63M.V.Purohit,63H.Singh,63F.X.Yumiceva,63I.Adam,P.L.Anthony,D.Aston,K.Baird,N.Berger,E.Bloom,A.M.Boyarski,

F.Bulos,G.Calderini,M.R.Convery,D.P.Coupal,D.H.Coward,J.Dorfan,W.Dunwoodie,R.C.Field,T.Glanzman,G.L.Godfrey,S.J.Gowdy,P.Grosso,T.Haas,T.Himel,T.Hryn’ova,

M.E.Huffer,W.R.Innes,C.P.Jessop,M.H.Kelsey,P.Kim,M.L.Kocian,U.Langenegger,

D.W.G.S.Leith,S.Luitz,V.Luth,H.L.Lynch,H.Marsiske,S.Menke,R.Messner,K.C.Moffeit,

R.Mount,D.R.Muller,C.P.O’Grady,V.E.Ozcan,M.Perl,S.Petrak,H.Quinn,

B.N.Ratcliff,S.H.Robertson,L.S.Rochester,A.Roodman,T.Schietinger,R.H.Schindler,J.Schwiening,V.V.Serbo,A.Snyder,A.Soha,S.M.Spanier,J.Stelzer,D.Su,M.K.Sullivan,

H.A.Tanaka,J.Va’vra,S.R.Wagner,A.J.R.Weinstein,W.J.Wisniewski,D.H.Wright,C.C.Young,P.R.Burchat,65C.H.Cheng,65D.Kirkby,65T.I.Meyer,65C.Roat,65R.Henderson,66

W.Bugg,67H.Cohn,67A.W.Weidemann,67J.M.Izen,68I.Kitayama,68X.C.Lou,68F.Bianchi,69M.Bona,69D.Gamba,69A.Smol,69L.Bosisio,70G.DellaRicca,70L.Lanceri,70P.Poropat,70G.Vuagnin,70R.S.Panvini,71

C.M.Brown,72P.D.Jackson,72R.Kowalewski,72J.M.Roney,72H.R.Band,73E.Charles,73S.Dasu,73

F.DiLodovico,73A.M.Eichenbaum,73H.Hu,73J.R.Johnson,73R.Liu,73Y.Pan,73R.Prepost,73I.J.Scott,73

S.J.Sekula,73J.H.vonWimmersperg-Toeller,73S.L.Wu,73Z.Yu,73T.M.B.Kordich,74andH.Neal74

(TheBABARCollaboration)

LaboratoiredePhysiquedesParticules,F-74941Annecy-le-Vieux,FranceUniversit`adiBari,DipartimentodiFisicaandINFN,I-70126Bari,Italy

3

InstituteofHighEnergyPhysics,Beijing100039,China4

UniversityofBergen,Inst.ofPhysics,N-5007Bergen,Norway

5

LawrenceBerkeleyNationalLaboratoryandUniversityofCalifornia,Berkeley,CA94720,USA

6

UniversityofBirmingham,Birmingham,B152TT,UnitedKingdom

7

RuhrUniversit¨atBochum,Institutf¨urExperimentalphysik1,D-44780Bochum,Germany

8

UniversityofBristol,BristolBS81TL,UnitedKingdom9

UniversityofBritishColumbia,Vancouver,BC,CanadaV6T1Z110

BrunelUniversity,Uxbridge,MiddlesexUB83PH,UnitedKingdom11

BudkerInstituteofNuclearPhysics,Novosibirsk630090,Russia12

UniversityofCaliforniaatIrvine,Irvine,CA92697,USA

13

UniversityofCaliforniaatLosAngeles,LosAngeles,CA90024,USA14

UniversityofCaliforniaatSanDiego,LaJolla,CA92093,USA

15

UniversityofCaliforniaatSantaBarbara,SantaBarbara,CA93106,USA

16

UniversityofCaliforniaatSantaCruz,InstituteforParticlePhysics,SantaCruz,CA950,USA

17

CaliforniaInstituteofTechnology,Pasadena,CA91125,USA18

UniversityofCincinnati,Cincinnati,OH45221,USA19

UniversityofColorado,Boulder,CO80309,USA20

ColoradoStateUniversity,FortCollins,CO80523,USA

21

3

DAPNIA,Commissariat`al’EnergieAtomique/Saclay,F-91191Gif-sur-Yvette,France

TechnischeUniversit¨atDresden,Institutf¨urKern-undTeilchenphysik,D-01062,Dresden,Germany

23

EcolePolytechnique,F-91128Palaiseau,France

24

UniversityofEdinburgh,EdinburghEH93JZ,UnitedKingdom25

ElonUniversity,ElonUniversity,NC27244-2010,USA

26

Universit`adiFerrara,DipartimentodiFisicaandINFN,I-44100Ferrara,Italy

27

FloridaA&MUniversity,Tallahassee,FL32307,USA

28

LaboratoriNazionalidiFrascatidell’INFN,I-00044Frascati,Italy

29

Universit`adiGenova,DipartimentodiFisicaandINFN,I-16146Genova,Italy

30

HarvardUniversity,Cambridge,MA02138,USA31

UniversityofIowa,IowaCity,IA52242,USA32

IowaStateUniversity,Ames,IA50011-3160,USA

33

Laboratoiredel’Acc´el´erateurLin´eaire,F-918Orsay,France34

LawrenceLivermoreNationalLaboratory,Livermore,CA94550,USA35

UniversityofLiverpool,LiverpoolL693BX,UnitedKingdom

36

UniversityofLondon,ImperialCollege,London,SW72BW,UnitedKingdom

37

QueenMary,UniversityofLondon,E14NS,UnitedKingdom

38

UniversityofLondon,RoyalHollowayandBedfordNewCollege,Egham,SurreyTW200EX,UnitedKingdom

39

UniversityofLouisville,Louisville,KY40292,USA

40

UniversityofManchester,ManchesterM139PL,UnitedKingdom41

UniversityofMaryland,CollegePark,MD20742,USA42

UniversityofMassachusetts,Amherst,MA01003,USA

43

MassachusettsInstituteofTechnology,LaboratoryforNuclearScience,Cambridge,MA02139,USA

44

McGillUniversity,Montr´eal,QC,CanadaH3A2T8

45

Universit`adiMilano,DipartimentodiFisicaandINFN,I-20133Milano,Italy

46

UniversityofMississippi,University,MS38677,USA

47

Universit´edeMontr´eal,LaboratoireRen´eJ.A.L´evesque,Montr´eal,QC,CanadaH3C3J7

48

MountHolyokeCollege,SouthHadley,MA01075,USA

49

Universit`adiNapoliFedericoII,DipartimentodiScienzeFisicheandINFN,I-80126,Napoli,Italy

50

UniversityofNotreDame,NotreDame,IN46556,USA51

OakRidgeNationalLaboratory,OakRidge,TN37831,USA

52

UniversityofOregon,Eugene,OR97403,USA

53

Universit`adiPadova,DipartimentodiFisicaandINFN,I-35131Padova,Italy54

Universit´esParisVIetVII,LabdePhysiqueNucl´eaireH.E.,F-75252Paris,France55

Universit`adiPavia,DipartimentodiElettronicaandINFN,I-27100Pavia,Italy

56

UniversityofPennsylvania,Philadelphia,PA19104,USA

57

Universit`adiPisa,ScuolaNormaleSuperioreandINFN,I-56010Pisa,Italy

58

PrairieViewA&MUniversity,PrairieView,TX77446,USA

59

PrincetonUniversity,Princeton,NJ08544,USA

60

Universit`adiRomaLaSapienza,DipartimentodiFisicaandINFN,I-00185Roma,Italy

61

Universit¨atRostock,D-18051Rostock,Germany

62

RutherfordAppletonLaboratory,Chilton,Didcot,Oxon,OX110QX,UnitedKingdom

63

UniversityofSouthCarolina,Columbia,SC29208,USA

StanfordLinearAcceleratorCenter,Stanford,CA94309,USA65

StanfordUniversity,Stanford,CA94305-4060,USA66

TRIUMF,Vancouver,BC,CanadaV6T2A367

UniversityofTennessee,Knoxville,TN37996,USA68

UniversityofTexasatDallas,Richardson,TX75083,USA

69

Universit`adiTorino,DipartimentodiFisciaSperimentaleandINFN,I-10125Torino,Italy

70

Universit`adiTrieste,DipartimentodiFisicaandINFN,I-34127Trieste,Italy

71

VanderbiltUniversity,Nashville,TN37235,USA72

UniversityofVictoria,Victoria,BC,CanadaV8W3P673

UniversityofWisconsin,Madison,WI53706,USA74

YaleUniversity,NewHaven,CT06511,USA

(Dated:October25,2001)

22

21

Wepresentameasurementofthetime-dependentCP-violatingasymmetriesinneutralBdecaystotheπ+π−CPeigenstate,andanupdatedmeasurementofthechargeasymmetryinB0→K+π−decays.Inasampleof33millionΥ(4S)→B

IntheStandardModel,allCP-violatingeffectsarisefromasinglecomplexphaseinthethree-generationCabibbo-Kobayashi-Maskawa(CKM)quark-mixingma-trix[1].Oneofthecentralquestionsinparticlephysicsiswhetherthismechanismissufficienttoexplainthepat-ternofCPviolationobservedinnature.Recentmea-surementsoftheparametersin2βbytheBABAR[2]andBELLE[3]CollaborationsestablishthatCPsymmetryisviolatedintheneutralB-mesonsystem.Inadditiontomeasuringsin2βmoreprecisely,oneoftheprimarygoalsoftheB-Factoryexperimentsinthefuturewillbetomeasuretheremainingangles(αandγ)andsidesoftheUnitarityTriangleinordertofurthertestwhethertheStandardModeldescriptionofCPviolationiscorrect.ThestudyofBdecaystocharmlesshadronictwo-bodyfinalstateswillplayanincreasinglyimportantroleinourunderstandingofCPviolation.IntheStandardModel,thetime-dependentCP-violatingasymmetryinthere-actionB0→π+π−isrelatedtotheangleα.Inaddi-tion,observationofasignificantrateasymmetrybetweenB0→K+π−and

Bpairs[4].Inthispaper,usingadatasam-pleofapproximately33millionB

B0pairpro-ducedinΥ(4S)decayevolvesintimeinacoherentP-wavestateuntiloneofthetwomesonsdecays.Were-constructasampleofBmesons(Bhh)decayingtothe

h+h′−finalstate,wherehisapionorkaon,andex-aminetheremainingchargedparticlesineacheventto“tag”theflavoroftheotherBmeson(Btag).Thede-cayratedistributionf+(f−)whenh+h′−=π+π−andBtag=B0(

4τ

[1±Sππsin(∆md∆t)∓Cππcos(∆md∆t)],

(1)

whereτistheB0lifetime,∆mdistheB0

4

2

1+|λ|

2

andC−|λ|

ππ=

1Vud∗

Vub

VtbVtd

∗󰀅󰀄

N.

(4)

K−π++NK+π−

Thedata1sampleusedinthisanalysisconsistsof33.7fb−collectedwiththeBABARdetectorattheSLACPEP-IIstorageringbetweenOctober1999andJune2001.ThePEP-IIfacilityoperatesnominallyattheΥ(4S)resonance,providingcollisionsof9.0GeVelectronson3.1GeVpositrons.Thedatasetincludes30.4fb−1col-lectedinthisconfiguration(on-resonance)and3.3fb−1collectedbelowtheB

Thefluxreturnforthesolenoidiscomposedofmultiplelayersofironandresistiveplatechambersfortheidenti-ficationofmuonsandlong-livedneutralhadrons.

TracksfromtheBhhdecayareidentifiedaspionsorkaonsbytheCherenkovangleθcmeasuredwithadetec-torofinternallyreflectedCherenkovlight(DIRC).Thetypicalseparationbetweenpionsandkaonsvariesfrom8σat2GeV/cto2.5σat4GeV/c,whereσistheaver-ageresolutiononθc.LowermomentumkaonsusedinBflavortaggingareidentifiedwithacombinationofθc(formomentadownto0.7GeV/c)andmeasurementsofionizationenergylossdE/dxintheDCHandSVT.Hadroniceventsareselectedbasedontrackmultiplic-ityandeventtopology.Werequireatleastthreetracksinthelaboratorypolarangleregion0.41<θlab<2.54satisfyingthefollowingrequirements:transversemomen-tumgreaterthan100MeV/c,atleast12DCHhits,andoriginatingfromtheinteractionpointwithin10cminzand1.5cminr–ϕ[12].Residualtwo-prongeventsfromthereactione+e−→l+l−(l=e,µ,τ)aresuppressedbyrequiringtheratioofFox-WolframmomentsH2/H0[13]tobelessthan0.95andthesphericity[14]oftheeventtobegreaterthan0.01.

CandidateBhhdecaysarereconstructedfrompairsofoppositely-chargedtracksformingagoodqualityvertex,wheretheBhhfour-vectoriscalculatedassumingthepionmassforbothtracks.WerequireeachtracktohaveanassociatedθcmeasurementwithaminimumofsixCherenkovphotonsabovebackground,wheretheaverageisapproximately30forbothpionsandkaons.ProtonsarerejectedbasedonθcandelectronsarerejectedbasedondE/dx,showershapeintheEMC,andtheratioofshowerenergyandtrackmomentum.Backgroundfromthereactione+e−byremovingjet-like→eventsqq¯(qfrom=u,thed,s,sample:c)issuppressedwedefinetheCMangleθSbetweenthesphericityaxesoftheBcandidateandtheremainingtracksandphotonsintheevent,andrequire|cosθSthebackground.Thetotal|󰀂Wedefineabeam-energysubstitutedmassmES=sandE+−

iarethetotalener-giesoftheeesystemintheCMandlaboratoryframes,respectively,andpiandpBarethemomentumvectorsinthelaboratoryframeofthee+e−systemandtheBhhcandidate,respectively.SignaleventsareGaussiandis-tributedinmESwithameanneartheBmassandaresolutionof2.6MeV/c2,dominatedbythebeamenergyspread.Thebackgroundshapeisparameterizedbyathresholdfunction[15]withafixedendpointgivenbytheaveragebeamenergy.

Wedefineasecondkinematicvariable∆Easthedif-ferencebetween√theenergyoftheBhhcandidateintheCMframeand

5

B0

mixing[16]analyses.Thealgorithmreliesonthecorre-lationbetweentheflavorofthebquarkandthechargeoftheremainingtracksintheeventafterremovaloftheBhhcandidate.Wedefinefivemutuallyexclusivetag-gingcategories:Lepton,Kaon,NT1,NT2,andUntagged.LeptontagsrelyonprimaryelectronsandmuonsfromsemileptonicBdecays,whileKaontagsexploitthecor-relationintheprocessb→c→sbetweenthenetkaonchargeandthechargeofthebquark.TheNT1andNT2categoriesarederivedfromaneuralnetworkthatissen-sitivetochargecorrelationsbetweentheparentBandunidentifiedleptonsandkaons,softpions,orthechargeandmomentumofthetrackwiththehighestCMmo-mentum.TheadditionofUntaggedeventsimprovesthesignalyieldestimatesandprovidesalargersampleforde-terminingbackgroundshapeparametersdirectlyinthemaximumlikelihoodfit.ThequalityoftaggingfectiveefficiencyQ=󰀃isexpressedintermsoftheef-iǫiD2

i,whereǫiisthefractionofeventstaggedincategoryiandthedilutionDi=1−2wiisrelatedtothemistagfractionwi.ThestatisticalrorsonSππandCππareproportionalto1/

√er-TABLEI:Taggingefficiencyǫ,averagedilutionD=1/2(DB0+DB0,andeffectivetaggingefficiencyQforsignaleventsineachtaggingcategory.Category

ǫ(%)

D(%)

∆D(%)

Q(%)

TotalQ26.3±1.2

TABLEII:Taggingefficiencies(%)forbackgroundeventsineachspecies.

Category

ǫ(ππ)

ǫ(Kπ)

ǫ(KK)

6

B0mixing,dependingon

thechargeofthekaonandtheflavorofBtag.Weparam-eterizeB0→K+K−decaysasanexponentialconvolvedwiththeresolutionfunction.

Thereare18freeparametersinthefit.InadditiontotheCP-violatingparametersSππ,Cππ,andAKπ,thefitdeterminessignalandbackgroundyields(sixparam-eters),thebackgroundKπchargeasymmetry,andeightparametersdescribingthebackgroundshapesinmES,∆E,andF.Wefixτand∆mdtotheworld-averagevalues[17].

Inasampleof33millionB

TABLEIII:Centralvaluesand90%C.L.intervalsforSππ,Cππ,andAKπfromthemaximumlikelihoodfit.

Parameter

CentralValue

90%C.L.Interval

B0(∆t))/(NB0(∆t)+N

7

B0.Solidcurvesrepresentprojections

ofthemaximumlikelihoodfit,dashedcurvesrepresentthesumofqq¯andKπbackgroundevents,andtheshadedregionrepresentsthecontributionfromsignalππevents.Figure(c)showsAππ(∆t)fordata(pointswitherrors),aswellasfitprojectionsforsignalandbackgroundevents(solidcurve),andsignaleventsonly(dashedcurve).

inthedatafitareallconsistentwithexpectationsbasedonthesepseudo-experiments,andallfreeparametersareunbiased.WehavecheckedthatconsistentresultsareobtainedwhenseparatingeventsbyBtagflavor.Asa

validationofthe∆tparameterizationindata,wefitthefulldatasettosimultaneouslyextractyields,back-groundparameters,τ,∆md,Sππ,andCππ.Wefindτ=(1.52±0.12)psand∆md=(0.54±0.09)¯hps−1,andallotherparametersareconsistentwiththenominalfit.Insummary,wehavepresentedameasurementoftime-dependentCP-violatingasymmetriesinB0caysandanupdatedmeasurementofthecharge→π+π−de-asym-metryAKπ.ThelatterisconsistentwithourpreviousresultreportedinRef.[4],aswellasresultsfromotherexperiments[21,22].WeobservenoevidencefordirectCPviolationintheKπmodeanddeterminea90%C.L.intervalexcludingasignificantpartoftheallowedregion.AlthoughthecurrentmeasurementsofSππandCππdonotsignificantlyconstraintheUnitarityTriangle,withtheadditionofmoredataandfurtherimprovementsindetectorperformanceandanalysistechniques,futurere-sultswillyieldimportantinformationaboutCPviolationintheB-mesonsystem.

Wearegratefulfortheexcellentluminosityandma-chineconditionsprovidedbyourPEP-IIcolleagues.ThecollaboratinginstitutionswishtothankSLACforitssupportandkindhospitality.ThisworkissupportedbyDOEandNSF(USA),NSERC(Canada),IHEP(China),CEAandCNRS-IN2P3(France),BMBF(Ger-many),INFN(Italy),NFR(Norway),MIST(Russia),andPPARC(UnitedKingdom).Individualshavere-ceivedsupportfromtheSwissNSF,A.P.SloanFoun-dation,ResearchCorporation,andAlexandervonHum-boldtFoundation.

∗

†

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