Measurement of Branching Fractions and CP-Violating Charge Asymmetries in B+ -- rho+ pi0 an
a r X i v :h e p -e x /0307087v 1 30 J u l 2003B A B A R -CONF-03/14
SLAC-PUB-10078
July 2003
Measurement of Branching Fractions and C P -Violating Charge Asymmetries in B +→ρ+π0and B +→ρ0π+decays,and Search for B 0→ρ0π0The B A B A R Collaboration February 7,2008Abstract We present preliminary measurements of branching fractions and CP -violating charge asymmetries in B -meson decays to ρπ.The data sample comprises 89million Υ(4S )→B
Work supported in part by U.S.Department of Energy contract DE-AC03-76SF00515.
The B A B A R Collaboration,
B.Aubert,R.Barate,D.Boutigny,J.-M.Gaillard,A.Hicheur,Y.Karyotakis,J.P.Lees,P.Robbe,
V.Tisserand,A.Zghiche
Laboratoire de Physique des Particules,F-74941Annecy-le-Vieux,France
A.Palano,A.Pompili
Universit`a di Bari,Dipartimento di Fisica and INFN,I-70126Bari,Italy
J.C.Chen,N.D.Qi,G.Rong,P.Wang,Y.S.Zhu
Institute of High Energy Physics,Beijing100039,China
G.Eigen,I.Ofte,B.Stugu
University of Bergen,Inst.of Physics,N-5007Bergen,Norway
G.S.Abrams,A.W.Borgland,A.B.Breon,D.N.Brown,J.Button-Shafer,R.N.Cahn,E.Charles, C.T.Day,M.S.Gill,A.V.Gritsan,Y.Groysman,R.G.Jacobsen,R.W.Kadel,J.Kadyk,L.T.Kerth, Yu.G.Kolomensky,J.F.Kral,G.Kukartsev,C.LeClerc,M.E.Levi,G.Lynch,L.M.Mir,P.J.Oddone, T.J.Orimoto,M.Pripstein,N.A.Roe,A.Romosan,M.T.Ronan,V.G.Shelkov,A.V.Telnov,
W.A.Wenzel
Lawrence Berkeley National Laboratory and University of California,Berkeley,CA94720,USA K.Ford,T.J.Harrison,C.M.Hawkes,D.J.Knowles,S.E.Morgan,R.C.Penny,A.T.Watson,
N.K.Watson
University of Birmingham,Birmingham,B152TT,United Kingdom T.Deppermann,K.Goetzen,H.Koch,B.Lewandowski,M.Pelizaeus,K.Peters,H.Schmuecker,
M.Steinke
Ruhr Universit¨a t Bochum,Institut f¨u r Experimentalphysik1,D-44780Bochum,Germany N.R.Barlow,J.T.Boyd,N.Chevalier,W.N.Cottingham,M.P.Kelly,https://www.wendangku.net/doc/8e15238193.html,tham,C.Mackay,
F.F.Wilson
University of Bristol,Bristol BS81TL,United Kingdom
K.Abe,T.Cuhadar-Donszelmann,C.Hearty,T.S.Mattison,J.A.McKenna,D.Thiessen
University of British Columbia,Vancouver,BC,Canada V6T1Z1
P.Kyberd,A.K.McKemey
Brunel University,Uxbridge,Middlesex UB83PH,United Kingdom V.E.Blinov,A.D.Bukin,V.B.Golubev,V.N.Ivanchenko,E.A.Kravchenko,A.P.Onuchin,
S.I.Serednyakov,Yu.I.Skovpen,E.P.Solodov,A.N.Yushkov
Budker Institute of Nuclear Physics,Novosibirsk630090,Russia
D.Best,M.Bruinsma,M.Chao,D.Kirkby,https://www.wendangku.net/doc/8e15238193.html,nkford,M.Mandelkern,R.K.Mommsen,W.Roethel,
D.P.Stoker
University of California at Irvine,Irvine,CA92697,USA
C.Buchanan,B.L.Hart?el
University of California at Los Angeles,Los Angeles,CA90024,USA
B.C.Shen
University of California at Riverside,Riverside,CA92521,USA
D.del Re,H.K.Hadavand,
E.J.Hill,D.B.MacFarlane,H.P.Paar,Sh.Rahatlou,U.Schwanke,
V.Sharma
University of California at San Diego,La Jolla,CA92093,USA
J.W.Berryhill,C.Campagnari,B.Dahmes,N.Kuznetsova,S.L.Levy,O.Long,A.Lu,M.A.Mazur,
J.D.Richman,W.Verkerke
University of California at Santa Barbara,Santa Barbara,CA93106,USA T.W.Beck,J.Beringer,A.M.Eisner,C.A.Heusch,W.S.Lockman,T.Schalk,R.E.Schmitz,
B.A.Schumm,A.Seiden,M.Turri,W.Walkowiak,D.
C.Williams,M.G.Wilson
University of California at Santa Cruz,Institute for Particle Physics,Santa Cruz,CA95064,USA J.Albert,E.Chen,G.P.Dubois-Felsmann,A.Dvoretskii,D.G.Hitlin,I.Narsky,F.C.Porter,A.Ryd,
A.Samuel,S.Yang
California Institute of Technology,Pasadena,CA91125,USA
S.Jayatilleke,G.Mancinelli,B.T.Meadows,M.D.Sokolo?
University of Cincinnati,Cincinnati,OH45221,USA
T.Abe,F.Blanc,P.Bloom,S.Chen,P.J.Clark,W.T.Ford,U.Nauenberg,A.Olivas,P.Rankin,J.Roy,
J.G.Smith,W.C.van Hoek,L.Zhang
University of Colorado,Boulder,CO80309,USA
J.L.Harton,T.Hu,A.So?er,W.H.Toki,R.J.Wilson,J.Zhang
Colorado State University,Fort Collins,CO80523,USA
D.Altenburg,T.Brandt,J.Brose,T.Colberg,M.Dickopp,R.S.Dubitzky,A.Hauke,https://www.wendangku.net/doc/8e15238193.html,cker,
E.Maly,R.M¨u ller-Pfe?erkorn,R.Nogowski,S.Otto,J.Schubert,K.R.Schubert,R.Schwierz,B.Spaan,
L.Wilden
Technische Universit¨a t Dresden,Institut f¨u r Kern-und Teilchenphysik,D-01062Dresden,Germany D.Bernard,G.R.Bonneaud,F.Brochard,J.Cohen-Tanugi,P.Grenier,Ch.Thiebaux,G.Vasileiadis,
M.Verderi
Ecole Polytechnique,LLR,F-91128Palaiseau,France
A.Khan,https://www.wendangku.net/doc/8e15238193.html,vin,F.Muheim,S.Playfer,J.E.Swain,J.Tinslay
University of Edinburgh,Edinburgh EH93JZ,United Kingdom M.Andreotti,V.Azzolini,D.Bettoni,C.Bozzi,R.Calabrese,G.Cibinetto,E.Luppi,M.Negrini,
L.Piemontese,A.Sarti
Universit`a di Ferrara,Dipartimento di Fisica and INFN,I-44100Ferrara,Italy
E.Treadwell
Florida A&M University,Tallahassee,FL32307,USA
F.Anulli,1R.Baldini-Ferroli,M.Biasini,1A.Calcaterra,R.de Sangro,D.Falciai,
G.Finocchiaro,
P.Patteri,I.M.Peruzzi,1M.Piccolo,M.Pioppi,1A.Zallo
Laboratori Nazionali di Frascati dell’INFN,I-00044Frascati,Italy
A.Buzzo,R.Capra,R.Contri,G.Crosetti,M.Lo Vetere,M.Macri,M.R.Monge,S.Passaggio,
C.Patrignani,E.Robutti,A.Santroni,S.Tosi
Universit`a di Genova,Dipartimento di Fisica and INFN,I-16146Genova,Italy
S.Bailey,M.Morii,E.Won
Harvard University,Cambridge,MA02138,USA
W.Bhimji,D.A.Bowerman,P.D.Dauncey,U.Egede,I.Eschrich,J.R.Gaillard,G.W.Morton,
J.A.Nash,P.Sanders,G.P.Taylor
Imperial College London,London,SW72BW,United Kingdom
G.J.Grenier,S.-J.Lee,U.Mallik
University of Iowa,Iowa City,IA52242,USA
J.Cochran,H.B.Crawley,https://www.wendangku.net/doc/8e15238193.html,msa,W.T.Meyer,S.Prell,E.I.Rosenberg,J.Yi
Iowa State University,Ames,IA50011-3160,USA
M.Davier,G.Grosdidier,A.H¨o cker,https://www.wendangku.net/doc/8e15238193.html,place,F.Le Diberder,V.Lepeltier,A.M.Lutz,T.C.Petersen, S.Plaszczynski,M.H.Schune,L.Tantot,G.Wormser
Laboratoire de l’Acc′e l′e rateur Lin′e aire,F-91898Orsay,France
V.Brigljevi′c,C.H.Cheng,https://www.wendangku.net/doc/8e15238193.html,nge,D.M.Wright
Lawrence Livermore National Laboratory,Livermore,CA94550,USA
A.J.Bevan,J.P.Coleman,J.R.Fry,E.Gabathuler,R.Gamet,M.Kay,R.J.Parry,D.J.Payne,
R.J.Sloane,C.Touramanis
University of Liverpool,Liverpool L693BX,United Kingdom
J.J.Back,P.F.Harrison,H.W.Shorthouse,P.Strother,P.B.Vidal
Queen Mary,University of London,E14NS,United Kingdom
C.L.Brown,G.Cowan,R.L.Flack,H.U.Flaecher,S.George,M.G.Green,A.Kurup,C.E.Marker,
T.R.McMahon,S.Ricciardi,F.Salvatore,G.Vaitsas,M.A.Winter University of London,Royal Holloway and Bedford New College,Egham,Surrey TW200EX,United
Kingdom
D.Brown,C.L.Davis
University of Louisville,Louisville,KY40292,USA
J.Allison,R.J.Barlow,A.C.Forti,P.A.Hart,F.Jackson,https://www.wendangku.net/doc/8e15238193.html,?erty,A.J.Lyon,J.H.Weatherall,
J.C.Williams
University of Manchester,Manchester M139PL,United Kingdom
A.Farbin,A.Jawahery,D.Kovalskyi,https://www.wendangku.net/doc/8e15238193.html,e,V.Lillard,D.A.Roberts
University of Maryland,College Park,MD20742,USA
G.Blaylock,C.Dallapiccola,K.T.Flood,S.S.Hertzbach,R.Ko?er,V.B.Koptchev,T.B.Moore,
S.Saremi,H.Staengle,S.Willocq
University of Massachusetts,Amherst,MA01003,USA
R.Cowan,G.Sciolla,F.Taylor,R.K.Yamamoto
Massachusetts Institute of Technology,Laboratory for Nuclear Science,Cambridge,MA02139,USA
D.J.J.Mangeol,https://www.wendangku.net/doc/8e15238193.html,ek,P.M.Patel
McGill University,Montr′e al,QC,Canada H3A2T8
https://www.wendangku.net/doc/8e15238193.html,zzaro,F.Palombo
Universit`a di Milano,Dipartimento di Fisica and INFN,I-20133Milano,Italy
J.M.Bauer,L.Cremaldi,V.Eschenburg,R.Godang,R.Kroeger,J.Reidy,D.A.Sanders,D.J.Summers,
H.W.Zhao
University of Mississippi,University,MS38677,USA
S.Brunet,D.Cote-Ahern,C.Hast,P.Taras
Universit′e de Montr′e al,Laboratoire Ren′e J.A.L′e vesque,Montr′e al,QC,Canada H3C3J7
H.Nicholson
Mount Holyoke College,South Hadley,MA01075,USA
C.Cartaro,N.Cavallo,2G.De Nardo,F.Fabozzi,2C.Gatto,L.Lista,P.Paolucci,
D.Piccolo,C.Sciacca
Universit`a di Napoli Federico II,Dipartimento di Scienze Fisiche and INFN,I-80126,Napoli,Italy
M.A.Baak,G.Raven
NIKHEF,National Institute for Nuclear Physics and High Energy Physics,NL-1009DB Amsterdam,The
Netherlands
J.M.LoSecco
University of Notre Dame,Notre Dame,IN46556,USA
T.A.Gabriel
Oak Ridge National Laboratory,Oak Ridge,TN37831,USA
B.Brau,K.K.Gan,K.Honscheid,D.Hufnagel,H.Kagan,R.Kass,T.Pulliam,Q.K.Wong
Ohio State University,Columbus,OH43210,USA
J.Brau,R.Frey,C.T.Potter,N.B.Sinev,D.Strom,E.Torrence
University of Oregon,Eugene,OR97403,USA
F.Colecchia,A.Dorigo,F.Galeazzi,M.Margoni,M.Morandin,M.Posocco,M.Rotondo,F.Simonetto,
R.Stroili,G.Tiozzo,C.Voci
Universit`a di Padova,Dipartimento di Fisica and INFN,I-35131Padova,Italy M.Benayoun,H.Briand,J.Chauveau,P.David,Ch.de la Vaissi`e re,L.Del Buono,O.Hamon,
M.J.J.John,Ph.Leruste,J.Ocariz,M.Pivk,L.Roos,J.Stark,S.T’Jampens,G.Therin Universit′e s Paris VI et VII,Lab de Physique Nucl′e aire H.E.,F-75252Paris,France
P.F.Manfredi,V.Re
Universit`a di Pavia,Dipartimento di Elettronica and INFN,I-27100Pavia,Italy
P.K.Behera,L.Gladney,Q.H.Guo,J.Panetta
University of Pennsylvania,Philadelphia,PA19104,USA
C.Angelini,G.Batignani,S.Bettarini,M.Bondioli,F.Bucci,G.Calderini,M.Carpinelli,F.Forti, M.A.Giorgi,A.Lusiani,G.Marchiori,F.Martinez-Vidal,3M.Morganti,N.Neri,E.Paoloni,M.Rama,
G.Rizzo,F.Sandrelli,J.Walsh
Universit`a di Pisa,Dipartimento di Fisica,Scuola Normale Superiore and INFN,I-56127Pisa,Italy
M.Haire,D.Judd,K.Paick,D.E.Wagoner
Prairie View A&M University,Prairie View,TX77446,USA
N.Danielson,P.Elmer,C.Lu,V.Miftakov,J.Olsen,A.J.S.Smith,H.A.Tanaka,E.W.Varnes
Princeton University,Princeton,NJ08544,USA
F.Bellini,
G.Cavoto,4R.Faccini,5F.Ferrarotto,F.Ferroni,M.Gaspero,M.A.Mazzoni,S.Morganti,
M.Pierini,G.Piredda,F.Safai Tehrani,C.Voena
Universit`a di Roma La Sapienza,Dipartimento di Fisica and INFN,I-00185Roma,Italy
S.Christ,G.Wagner,R.Waldi
Universit¨a t Rostock,D-18051Rostock,Germany
T.Adye,N.De Groot,B.Franek,N.I.Geddes,G.P.Gopal,E.O.Olaiya,S.M.Xella
Rutherford Appleton Laboratory,Chilton,Didcot,Oxon,OX110QX,United Kingdom
R.Aleksan,S.Emery,A.Gaidot,S.F.Ganzhur,P.-F.Giraud,G.Hamel de Monchenault,W.Kozanecki, https://www.wendangku.net/doc/8e15238193.html,nger,M.Legendre,G.W.London,B.Mayer,G.Schott,G.Vasseur,Ch.Yeche,M.Zito
DSM/Dapnia,CEA/Saclay,F-91191Gif-sur-Yvette,France
M.V.Purohit,A.W.Weidemann,F.X.Yumiceva
University of South Carolina,Columbia,SC29208,USA
D.Aston,R.Bartoldus,N.Berger,A.M.Boyarski,O.L.Buchmueller,M.R.Convery,D.P.Coupal, D.Dong,J.Dorfan,D.Dujmic,W.Dunwoodie,R.C.Field,T.Glanzman,S.J.Gowdy,
E.Grauges-Pous,
T.Hadig,V.Halyo,T.Hryn’ova,W.R.Innes,C.P.Jessop,M.H.Kelsey,P.Kim,M.L.Kocian, https://www.wendangku.net/doc/8e15238193.html,ngenegger,D.W.G.S.Leith,S.Luitz,V.Luth,H.L.Lynch,H.Marsiske,R.Messner,D.R.Muller, C.P.O’Grady,V.E.Ozcan,A.Perazzo,M.Perl,S.Petrak,B.N.Ratcli?,S.H.Robertson,A.Roodman,
A.A.Salnikov,R.H.Schindler,J.Schwiening,G.Simi,A.Snyder,A.Soha,J.Stelzer,D.Su,
M.K.Sullivan,J.Va’vra,S.R.Wagner,M.Weaver,A.J.R.Weinstein,W.J.Wisniewski,D.H.Wright,
C.C.Young
Stanford Linear Accelerator Center,Stanford,CA94309,USA
P.R.Burchat,A.J.Edwards,T.I.Meyer,B.A.Petersen,C.Roat
Stanford University,Stanford,CA94305-4060,USA
S.Ahmed,M.S.Alam,J.A.Ernst,M.Saleem,F.R.Wappler
State Univ.of New York,Albany,NY12222,USA
W.Bugg,M.Krishnamurthy,S.M.Spanier
University of Tennessee,Knoxville,TN37996,USA
R.Eckmann,H.Kim,J.L.Ritchie,R.F.Schwitters
University of Texas at Austin,Austin,TX78712,USA
J.M.Izen,I.Kitayama,X.C.Lou,S.Ye
University of Texas at Dallas,Richardson,TX75083,USA
F.Bianchi,M.Bona,F.Gallo,D.Gamba
Universit`a di Torino,Dipartimento di Fisica Sperimentale and INFN,I-10125Torino,Italy
C.Borean,L.Bosisio,G.Della Ricca,S.Dittongo,S.Grancagnolo,https://www.wendangku.net/doc/8e15238193.html,nceri,P.Poropat,6L.Vitale,
G.Vuagnin
Universit`a di Trieste,Dipartimento di Fisica and INFN,I-34127Trieste,Italy
R.S.Panvini
Vanderbilt University,Nashville,TN37235,USA
Sw.Banerjee,C.M.Brown,D.Fortin,P.D.Jackson,R.Kowalewski,J.M.Roney
University of Victoria,Victoria,BC,Canada V8W3P6
H.R.Band,S.Dasu,M.Datta,A.M.Eichenbaum,J.R.Johnson,P.E.Kutter,H.Li,R.Liu,
F.Di Lodovico,A.Mihalyi,A.K.Mohapatra,Y.Pan,R.Prepost,S.J.Sekula,J.H.von
Wimmersperg-Toeller,J.Wu,S.L.Wu,Z.Yu
University of Wisconsin,Madison,WI53706,USA
H.Neal
Yale University,New Haven,CT06511,USA
1Introduction
The study of B meson decays into charmless hadronic?nal states plays an important role in the
understanding of the phenomenon of CP violation in the B system.Recently,the B A B A R experiment
has performed a search for CP-violating asymmetries in neutral B decays toρ±π?[1],where the
mixing-induced CP asymmetry is related to the angleα≡arg[?V td V?tb/V ud V?ub]of the Unitarity
Triangle.However,in contrast to the theoretically clean determination of sin2βin the decay to
charmonium such as B0→J/ψK0S[2,3],the extraction ofαfromρ±π?is complicated by the interference of decay amplitudes with di?erent weak phases.Various strategies to overcome this
problem have been proposed in the literature.One such method is an SU(2)isospin analysis of
theρπ?nal states[4].In the limit of isospin symmetry,the?ve decay amplitudes B0→ρ+π?, B0→ρ?π+,B0→ρ0π0,B+→ρ+π0and B+→ρ0π+form a pentagon in the complex plane. Combining measurements of all the decay rates,mixing-induced and direct CP asymmetries in the neutral B modes,as well as charge asymmetries in the charged B modes,allows a determination of the phaseαthat is free of hadronic uncertainties.
In this letter,we present preliminary measurements of the branching fractions of the decay
modes7B+→ρ0π+,B+→ρ+π0,and perform a search for the decay B0→ρ0π0.For the charged modes we also present measurements of the CP-violating charge asymmetry A CP,de?ned by
ˉf)
A CP≡Γ(B?→f)?Γ(B+→
B pairs collected at theΥ(4S)resonance(“on-resonance”),while
the B0→ρ0π0search uses a slightly larger sample of88.9×106B
7If not stated otherwise,charge conjugation is implied throughout this document.
light(DIRC).The typical separation between pions and kaons varies from8σat2GeV/c to2.5σat4GeV/c,whereσis the averageθC resolution.Lower momentum kaons are identi?ed with a combination ofθC(for momenta down to0.7GeV/c)and measurements of energy loss,dE/dx,in the DCH and SVT.
3Discriminating Variables
To reject background from continuum e+e?→qˉq(q=u,d,s,c)events and other B decays,we use the following discriminating variables:
?m ES:the beam-energy-substituted mass is de?ned by
m ES=
of energy deposition in the EMC consistent with an electromagnetic shower.The invariant mass m(γγ)of the photon pair must satisfy0.11 Two of the three?nal state pions are used to form a charged or a neutralρcandidate(the third pion is referred to as the bachelor pion hereafter).For the B+→ρ+π0mode,theρ+ candidate is reconstructed from the positively charged track and one of the twoπ0candidates.For the B+→ρ0π+and B0→ρ0π0modes,theρ0candidate is reconstructed from two oppositely-charged tracks.The mass of theρcandidates must satisfy0.4 For the B+→ρ+π0and B0→ρ0π0modes,the invariant mass of either track and theπ0must be less than5.14GeV/c2to reject two-body B background. B candidates are required to satisfy kinematic?t-region cuts.For B+→ρ+π0decays,can-didates must satisfy5.20 For the B+→ρ0π+mode,we remove background from charmed decays B→D0→K+π?orπ+π?,by requiring that all pairs of oppositely-charged tracks have invariant masses either smaller than1.844GeV/c2or greater than1.884GeV/c2,assuming both kaon and pion hypotheses for the positively-charged track. The?nal samples of signal candidates are selected with a cut on the NN outputs for all three decay modes.For example,the NN cut for the B+→ρ0π+decay mode retains85%(11%)of the signal(continuum)events. In each event,?nal state particles other than the three pions that form the signal B meson are assumed to belong to the other B meson.These particles are used to tag the?avor of the other B meson and to inclusively-reconstruct its vertex for decay time determination.In this letter,this other B is referred to as B tag. For the B0→ρ0π0mode,we use the proper decay time as a discriminating variable in the ML?t.The time di?erence?t is obtained from the measured distance between the z positions (along the beam direction)of the Bρ0π0and B tag decay vertices,and the known boost of the e+e?system.The vertex of the B tag is reconstructed from all tracks in the event except those from the Bρ0π0,and an iterative procedure[2]is used to remove tracks with a large contribution to the vertexχ2.An additional constraint is obtained from the three-momentum and vertex position of the Bρ0π0candidate,and the average e+e?interaction point and boost.We require|?t|<20ps andσ(?t)<2.5ps,whereσ(?t)is the error on?t estimated on an event-by-event basis. Approximately33%(7%and8%)of the events from signal Monte Carlo(MC)simulation have more than one candidate satisfying the selection in the B+→ρ+π0(B+→ρ0π+and B0→ρ0π0) decay mode.In this case,we choose the candidate with the reconstructedρinvariant mass closest Table1:Signal e?ciencies(?),fractions of misreconstructed signal events(f scf),and fractions of misreconstructed signal events with wrong B candidate charge(ωQ)in selected MC-simulated events.The last row gives the numbers of selected on-resonance events entering the maximum likelihood?ts. B+→ρ+π0B+→ρ0π+B0→ρ0π0 3and taken as the standard deviations.Tables2,3and 4summarize the dominant B background modes to B+→ρ+π0,B+→ρ0π+and B0→ρ0π0, respectively. 6The Likelihood We use unbinned extended maximum likelihood?ts to extract theρπevent yields,the charge asymmetries,and other parameters used to model signal and background events.The?ts minimize the quantity?2ln L,where L is the total likelihood de?ned over all tagging categories k by L= k e?N′k N k i=1L i,k,(3) and where N′k is the sum of the signal and continuum yields(to be determined by the?t)and the ?xed B-background yields,N k are the numbers of observed events in category k,and L i,k is the likelihood computed for event i.Note that no tagging information is used in the B+→ρ0π+?t.The data sample of each mode is assumed to consist of signal,continuum background and B-background components.The variables m ES,?E and the NN output discriminate signal from background. For B0→ρ0π0,the variable?t is used to obtain additional background discrimination. The likelihood L i,k for event i is the sum of the probability density functions(PDF)of all components,weighted by the expected yields for each component, L i,k=Nρπ?k Pρπi,k+N qˉq k P qˉq i,k+N B j=1 L B ij,k,(4) where ?Nρπis the number of signal events in the entire sample.For theρ+π0andρ0π+modes,the charge asymmetries are introduced by multiplying the signal yields by1 B background’s contribution of the N B B background categories.Correlations between the variables are usually neglected except that for B backgrounds we use two-dimensional PDFs for m ES and?E to model the sizable correlations. The signal PDFs are decomposed into two parts with distinct distributions:signal events that are correctly reconstructed and misreconstructed signal events.Moreover,for the charged B modes we distinguish misreconstructed signal events with right-sign B charge from those with wrong-sign B charge in the likelihood.Their individual fractions are taken from MC simulation and given in Table2:B background modes considered in the B+→ρ+π0maximum likelihood?t.The second column gives the branching fractions used(estimated branching fractions are indicated by an aster-isk),and the third column quotes the expected number of events entering into the sample,scaled to 81.5fb?1(88.5×106Υ(4S)→B B0→π0π01.6±1.64.8±4.8 B+→π+π05.2±0.85.6±0.9 B+→K+π012.7±1.24.9±0.5 B0→ρ±π?22.6±2.844.6±5.6 B0→ρ?K+7.3±1.82.5±0.6 B+→K0S(π0π0)π+4.1±0.45.4±0.5 B0→K?0(K+π?)π08.7±5.03.8±2.2 B0→K?0(K0Sπ0)π07.5±5.03.9±2.6 B+→K?+(K+π0)π04.4±2.56.1±3.5 B+→ρ+γ2.3±2.31.3±1.3 B0→ρ+ρ?long.40.0+50??3564.8+81?57 B0→ρ+ρ?tran.40.0+50??351.6+2.0?1.4 B+→ρ+ρ0long.30.1+8.3?9.917.0+4.3?5.2 B+→a+1π035±35?25.0±25.0 B+→(K(??)Xπ)+40±26?15±9.8 B+→(K(??)Xρ)+20±20?1.2±1.2 B0→(K(??)Xπ)072±54?23±17.3 B0→(K(??)Xρ)020±20?6.0±6.0 B0→X0c–72.0±16.0 B+→X+c–133.0±30.0 Table3:B background modes considered in the B+→ρ0π+maximum likelihood?t.The second column gives the branching fractions used(estimated branching fractions are indicated by an aster-isk),and the third column quotes the expected number of events entering into the sample,scaled to 81.5fb?1(88.5×106Υ(4S)→B B0→ρ±π?22.6±2.829.3±5.2 B0→ρ?K+7.3±1.81.1±0.3 B+→ρ0K+3.9±1.24.9±1.5 B+→f0(980)K+11.7±4.01.1±0.4 B+→K0S(π+π?)π+9.0±0.95.3±0.5 B0→K?+(K+π0)π?8.7±5.01.4±0.8 B+→K?0(K+π?)π+10.3±2.611.1±2.8 B+→π+ω(π+π?)0.14±0.043.6±1.0 B0→ρ+ρ?long.40+50??356.3+7.8?5.5 B0→ρ0ρ0long.3.5±3.5?1.7±1.7 B+→ρ+ρ0long.30.1+8.3?9.97.9+2.2?2.6 B+→η′(ρ0γ)π+3.0±2.0?2.2±1.5 B0→a+1π?35±35?5.3±5.3 B+→(K(??)Xπ)+40±26?2.9±1.9 B0→(K(??)Xπ)072±54?7.4±5.5 B0→X0c-19.2±5.8 B+→X+c-54.1±13.1 Table4:B background modes considered in the B0→ρ0π0maximum likelihood?t.The second column gives the branching fractions used(estimated branching fractions are indicated by an aster-isk),and the third column quotes the expected number of events entering into the sample,scaled to 81.9fb?1(88.9×106Υ(4S)→B B+→π+π0 5.2±0.8 1.4±0.2 B+→K+π012.7±1.20.9±0.1 B0→ρ±π?22.6±2.816.9±1.4 B0→ρ?K+7.3±1.80.7±0.2 B+→ρ+π015.0+15?10*15.8+15.8 ?10.5 B0→K0S(π+π?)π0 3.5±0.5 5.0±0.7 B0→f0(980)π00.0±3.0*0.0+3.1?0.0 B0→π+π?π0(non-res.)0.0±5.0*0.0+4.1?0.0 B0→K?0(K+π?)π08.7±5.0*13.6±7.8 B0→K?0((Kπ)0)γ40.2±2.7 1.7±0.1 B0→ρ+ρ?long.40.0+50?35*10.9+13.6 ?9.5 B+→ρ+ρ0long.30.1+8.3?9.9*15.8+4.4?5.2 B+→a+1((ρπ)+)π035.0±25.0* 5.2±3.7 B0→η′(ρ0γ)π00.0±1.0*0.0+2.0?0.0 B+→(K(??)Xπ)+40±26* 2.3±1.5 B0→(K(??)Xπ)072±54* 3.2±2.4 B0→X0c-23.8±7.1 B+→X+c-35.2±10.6 Continuum background is modeled by a linear function with a slope that is free to vary in the?t. ?NN output.PDFs for correctly reconstructed and for misreconstructed signal events are taken from MC simulation and parameterized using empirical shape-?tting techniques[9]. A small discrepancy between data and MC is observed for the NN output distributions of control samples using fully-reconstructed B0→D?ρ+decays.This is accounted for in the systematic error evaluation. For B+→ρ+π0and B+→ρ0π+(B0→ρ0π0),the PDFs describing the NN output for con-tinuum events are parametrized by a third-order(?fth-order)polynomial with its parameters determined in the?t. ??t is used in the B→ρ0π0?t to improve the discrimination against continuum back-ground.The distributions for correctly reconstructed signal,misreconstructed signal and B background events are treated as decays of neutral or charged B’s,convoluted with a?t resolution function which is the sum of three Gaussians with parameters determined from a ?t to fully reconstructed B decays[2].This treatment does not introduce a bias in the signal yield according to MC studies. The continuum?t distribution is parameterized as the sum of three Gaussian distributions with common mean,two relative fractions,and three distinct widths that scale the?t event-by-event error,yielding six free parameters. The shapes of the B background PDFs are obtained from MC simulation and parameterized using empirical shape-?tting techniques[9]. We perform?ts on large MC samples with the measured proportions of signals and continuum and B backgrounds.Biases observed in these tests are due to imperfections in the likelihood model, e.g.,unaccounted correlations between the discriminating variables of the signal and B background PDFs.The observed signal yields are corrected for these?t biases and the full correction is assigned as a systematic uncertainty. 7Preliminary Results We obtain the event yields170.8±28.7(stat.)forρ+π0,232.5±26.4(stat.)forρ0π+and15.6± 11.7(stat.)forρ0π0.Assuming equal branching fractions forΥ(4S)decays into neutral and charged B mesons,the yields translate into the branching fractions B(B+→ρ+π0)=(11.0±1.9(stat.)±1.9(syst.))×10?6, B(B+→ρ0π+)=(9.3±1.0(stat.)±0.8(syst.))×10?6, B(B0→ρ0π0)<2.5×10?6at90%C.L., where the?rst errors are statistical and the second systematic.We?nd the charge asymmetries: =0.23±0.16(stat.)±0.06(syst.), Aρ+π0 CP Aρ0π+ =?0.17±0.11(stat.)±0.02(syst.). CP Figure1shows distributions of m ES,?E,the NN output and theρmass for B+→ρ0π+,enhanced in signal content by cuts on the signal-to-continuum likelihood ratios of the other discriminating Figure1:Distributions of m ES(upper left),?E(upper right),NN output(lower left)and the ρmass(lower right)for samples enhanced inρ0π+signal content using cuts on the signal-to-continuum likelihood ratio.The solid curves represent projections of the?t result.The dashed curves represent the contribution from continuum events,and the dotted lines indicate the combined contributions from continuum events and B backgrounds.For theρmass distribution,the?t has been repeated withρ-related information removed from the NN. variables.The plots of m ES,?E and NN correspond to the?t reported here,while the plot of the ρmass is obtained from a?t withρ-related information removed from the NN. The statistical signi?cance of the previously unobserved B+→ρ+π0signal amounts to9.4σ, which reduces to6.6σwhen also considering systematic errors.Figure2shows the corresponding signal-enhanced distributions of m ES and?E. For B0→ρ0π0,a90%con?dence-level upper limit of33.2is obtained on the signal yield using a limit setting procedure similar to Ref.[10].To obtain an upper limit for the branching ratio,the upper limit on the signal yield is shifted upwards by one sigma of the systematic error on the yield, and the e?ciency and other scaling factors are shifted downwards by one sigma of their systematic errors.Figure3shows the corresponding signal-enhanced distributions of m ES and?E. All results are given in Tables5and6together with the systematic uncertainties discussed below. Figure2:Distributions of m ES(left)and?E(right)for samples enhanced inρ+π0signal content using cuts on the signal-to-continuum likelihood ratio.The solid curves represent projections of the ?t result.The dashed curves represent the contribution from continuum events,and the dotted lines indicate the combined contributions from continuum events and B backgrounds. Figure3:Distributions of m ES(left)and?E(right)for samples enhanced inρ0π0signal content using cuts on the signal-to-continuum likelihood ratio.The solid curves represent projections of the ?t result.The dashed curves represent the contribution from continuum events,and the dotted lines indicate the combined contributions from continuum events and B backgrounds. 8Systematic Uncertainties The systematic errors in the branching fractions are obtained by adding in quadrature the sys- tematic uncertainties in the signal yields,the systematic uncertainties in e?ciencies of tracking, particle identi?cation,π0reconstruction and the systematic uncertainties on the selection cuts.The systematic errors on the A CP measurements are introduced by the uncertainties in the treatment of the B background and by possible charge biases of the detector. The basis for evaluating the systematic uncertainties on the cuts that are applied in the selec- tion process is the di?erences in?E,m ES and NN between on-resonance data and Monte Carlo simulation.The di?erences between data and Monte Carlo distributions of?E and m ES are ex- tracted from various fully-reconstructed B control samples for the three decay modes.The number of DIRC photons cut for the bachelor track in B+→ρ0π+decay mode will cause1.0%uncertainty on the signal yield.The corrections and uncertainties on the signal e?ciencies are summarized in Table5for the three decay modes. We evaluate the systematic uncertainties due to the signal m ES,?E and NN PDFs with a large B data control sample.The small di?erences observed in the distribution shapes for Monte Carlo events and the distribution shapes obtained from the data control sample are used to estimate the systematic uncertainty on the signal m ES and?E PDFs.The uncertainties due to the estimated fractions of misreconstructed events are obtained from a control sample of fully-reconstructed B→ D?ρ+decays as in Ref.[1].We perform?ts on the large MC samples with the measured proportions ofρ+π0,ρ0π+andρ0π0signals,and continuum and B background.Fit biases observed in MC?ts are added in quadrature and assigned as a systematic uncertainty of the?t procedure,referred to as“?tting procedure”in Table5. The expected yields from the background modes are varied according to the uncertainties in the measured or estimated branching fractions indicated in Tables2,3and4for the B+→ρ+π0,B+→ρ0π+and B0→ρ0π0decay modes,respectively.Since B background modes may exhibit direct CP violation,the corresponding parameters are varied within their physical ranges.Contributions from non-resonant B+→π+π0π0for theρ+π0mode and B+→π+π?π+for theρ0π+mode are negligible according to our dedicated studies.To check for these types of B backgrounds,a ?t withoutρ0mass andρ0helicity information in its NN training is performed,and the results are compatible with the?t results reported here.The systematic error on theρ0π0yield due to non-resonant B0→π+π?π0is considered as part of the B background one,based on Ref.[11]. For the B+→ρ0π+and B0→ρ0π0decay modes,systematic uncertainties due to possible interference betweenρ0and f0(980)or a broad scalarσ(400?1200)are estimated to be small.The orbital angular momentum forρ0π0(ρ0π+)is one,while for f0(980)π0orσπ0(f0(980)π+orσπ+) it is zero.Therefore the two wave functions are orthogonal.The interference term vanishes when integrated over the whole space.As a cross check,MC samples with interference e?ects are made from non-resonant B+→π+π?π+and B0→π+π?π0Monte-Carlo using a reweighting technique. The full selection is then applied.The relative phase is chosen to maximize interference.Small e?ects are observed,as expected. Table5summarizes the various sources contributing to the systematic errors in the branching fractions.The dominant systematic errors are due to the?t procedure(imperfection in likelihood model)and the uncertainties in the B background model.Table6summarizes the possible sources contributing to the systematic errors in the charge asymmetries. Table5:Results and breakdown of systematic errors for the branching ratios measurements. Signal yields and e?ciencies B+→ρ+π0B+→ρ0π+B0→ρ0π0 Statistical error on signal yield28.726.411.7 Sub-total(absolute)21.09.38.1 B)1.1%1.1%1.1% Total systematic error16.9%8.3%52.5% Branching ratio[×10?6]11.0±1.9±1.99.3±1.0±0.80.9±0.7±0.5