Measurement of the Decay Amplitudes of B0
CLARK, Allan Geoffrey (Collab.), et al.
An angular analysis of B0→J/ψK*0 and B0s→J/ψφ has been used to determine the decay amplitudes with parity-even longitudinal ( A0) and transverse ( A∥) polarization and parity-odd transverse ( A⊥) polarization. The measurements are based on 190 B0 and 40 B0s candidates obtained from 89pb−1 of p¯p collisions at the Fermilab Tevatron. The longitudinal decay amplitude dominates with |A0|2=0.59±0.06±0.01 for B0 and |A0|2=0.61±0.14±0.02 for B0s decays. The parity-odd amplitude is found to be small with |A⊥|2=0.13+0.12−0.09±0.06 for B0 and |A⊥|2=0.23±0.19±0.04 for B0s decays.
CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of the Decay
Amplitudes of B0
→J/ψφ Decays. Physical Review Letters , 2000, vol. 85, no.
22, p. 4668-4673
DOI : 10.1103/PhysRevLett.85.4668
Disclaimer: layout of this document may differ from the published version.
1 / 1
Measurement of the Decay Amplitudes of B0
! J 兾兾兾 c Kⴱⴱⴱ0
! J 兾兾兾 cf Decays
T. Affolder,21H. Akimoto,43A. Akopian,36M. G. Albrow,10 P. Amaral,7S. R. Amendolia,32D. Amidei,24K. Anikeev,22 J. Antos,1G. Apollinari,10T. Arisawa,43 T. Asakawa,41 W. Ashmanskas,7M. Atac,10 F. Azfar,29 P. Azzi-Bacchetta,30
N. Bacchetta,30 M. W. Bailey,26 S. Bailey,14P. de Barbaro,35 A. Barbaro-Galtieri,21 V. E. Barnes,34 B. A. Barnett,17 M. Barone,12 G. Bauer,22 F. Bedeschi,32 S. Belforte,40 G. Bellettini,32J. Bellinger,44 D. Benjamin,9 J. Bensinger,4
A. Beretvas,10 J. P. Berge,10 J. Berryhill,7 B. Bevensee,31 A. Bhatti,36 M. Binkley,10 D. Bisello,30 R. E. Blair,2 C. Blocker,4 K. Bloom,24 B. Blumenfeld,17 S. R. Blusk,35 A. Bocci,32 A. Bodek,35 W. Bokhari,31 G. Bolla,34 Y. Bonushkin,5D. Bortoletto,34 J. Boudreau,33 A. Brandl,26 S. van den Brink,17 C. Bromberg,25 M. Brozovic,9
N. Bruner,26 E. Buckley-Geer,10 J. Budagov,8 H. S. Budd,35 K. Burkett,14 G. Busetto,30 A. Byon-Wagner,10 K. L. Byrum,2P. Calafiura,21 M. Campbell,24 W. Carithers,21 J. Carlson,24 D. Carlsmith,44 J. Cassada,35 A. Castro,30 D. Cauz,40 A. Cerri,32 A. W. Chan,1P. S. Chang,1 P. T. Chang,1J. Chapman,24 C. Chen,31Y. C. Chen,1M.-T. Cheng,1
M. Chertok,38 G. Chiarelli,32 I. Chirikov-Zorin,8 G. Chlachidze,8F. Chlebana,10 L. Christofek,16 M. L. Chu,1 Y. S. Chung,35 C. I. Ciobanu,27A. G. Clark,13 A. Connolly,21 J. Conway,37J. Cooper,10M. Cordelli,12 J. Cranshaw,39 D. Cronin-Hennessy,9R. Cropp,23R. Culbertson,7 D. Dagenhart,42 F. DeJongh,10S. Dell’Agnello,12M. Dell’Orso,32 R. Demina,10 L. Demortier,36 M. Deninno,3P. F. Derwent,10 T. Devlin,37 J. R. Dittmann,10S. Donati,32 J. Done,38
T. Dorigo,14 N. Eddy,16 K. Einsweiler,21 J. E. Elias,10 E. Engels, Jr.,33 W. Erdmann,10 D. Errede,16 S. Errede,16 Q. Fan,35 R. G. Feild,45 C. Ferretti,32 R. D. Field,11 I. Fiori,3 B. Flaugher,10 G. W. Foster,10 M. Franklin,14 J. Freeman,10J. Friedman,22Y. Fukui,20 S. Galeotti,32 M. Gallinaro,36T. Gao,31M. Garcia-Sciveres,21A. F. Garfinkel,34
P. Gatti,30C. Gay,45 S. Geer,10 D. W. Gerdes,24 P. Giannetti,32P. Giromini,12 V. Glagolev,8M. Gold,26 J. Goldstein,10 A. Gordon,14 A. T. Goshaw,9Y. Gotra,33 K. Goulianos,36 C. Green,34 L. Groer,37 C. Grosso-Pilcher,7M. Guenther,34 G. Guillian,24 J. Guimaraes da Costa,14 R. S. Guo,1R. M. Haas,11 C. Haber,21 E. Hafen,22 S. R. Hahn,10 C. Hall,14
T. Handa,15 R. Handler,44 W. Hao,39 F. Happacher,12 K. Hara,41 A. D. Hardman,34R. M. Harris,10 F. Hartmann,18 K. Hatakeyama,36J. Hauser,5J. Heinrich,31 A. Heiss,18 M. Herndon,17 K. D. Hoffman,34 C. Holck,31 R. Hollebeek,31
L. Holloway,16 R. Hughes,27 J. Huston,25 J. Huth,14 H. Ikeda,41 J. Incandela,10 G. Introzzi,32 J. Iwai,43 Y. Iwata,15 E. James,24 H. Jensen,10 M. Jones,31 U. Joshi,10 H. Kambara,13 T. Kamon,38 T. Kaneko,41 K. Karr,42 H. Kasha,45 Y. Kato,28 T. A. Keaffaber,34 K. Kelley,22 M. Kelly,24 R. D. Kennedy,10 R. Kephart,10 D. Khazins,9 T. Kikuchi,41 B. Kilminster,35 M. Kirby,9M. Kirk,4B. J. Kim,19 D. H. Kim,19 H. S. Kim,16 M. J. Kim,19 S. H. Kim,41
Y. K. Kim,21 L. Kirsch,4S. Klimenko,11 P. Koehn,27 A. Köngeter,18 K. Kondo,43 J. Konigsberg,11 K. Kordas,23 A. Korn,22 A. Korytov,11 E. Kovacs,2 J. Kroll,31 M. Kruse,35 S. E. Kuhlmann,2K. Kurino,15 T. Kuwabara,41 A. T. Laasanen,34 N. Lai,7S. Lami,36 S. Lammel,10 J. I. Lamoureux,4M. Lancaster,21 G. Latino,32 T. LeCompte,2 A. M. Lee IV,9K. Lee,39S. Leone,32 J. D. Lewis,10 M. Lindgren,5T. M. Liss,16 J. B. Liu,35 Y. C. Liu,1N. Lockyer,31
J. Loken,29 M. Loreti,30 D. Lucchesi,30 P. Lukens,10 S. Lusin,44 L. Lyons,29 J. Lys,21 R. Madrak,14K. Maeshima,10 P. Maksimovic,14 L. Malferrari,3M. Mangano,32 M. Mariotti,30 G. Martignon,30 A. Martin,45 J. A. J. Matthews,26
J. Mayer,23 P. Mazzanti,3 K. S. McFarland,35 P. McIntyre,38 E. McKigney,31 M. Menguzzato,30 A. Menzione,32 C. Mesropian,36 A. Meyer,7 T. Miao,10 R. Miller,25 J. S. Miller,24 H. Minato,41 S. Miscetti,12 M. Mishina,20 G. Mitselmakher,11 N. Moggi,3E. Moore,26 R. Moore,24 Y. Morita,20 M. Mulhearn,22 A. Mukherjee,10 T. Muller,18
A. Munar,32 P. Murat,10 S. Murgia,25 M. Musy,40J. Nachtman,5S. Nahn,45 H. Nakada,41 T. Nakaya,7I. Nakano,15 C. Nelson,10 D. Neuberger,18 C. Newman-Holmes,10 C.-Y. P. Ngan,22 P. Nicolaidi,40 H. Niu,4L. Nodulman,2 A. Nomerotski,11 S. H. Oh,9 T. Ohmoto,15 T. Ohsugi,15 R. Oishi,41 T. Okusawa,28 J. Olsen,44 W. Orejudos,21 C. Pagliarone,32F. Palmonari,32 R. Paoletti,32V. Papadimitriou,39S. P. Pappas,45 D. Partos,4J. Patrick,10G. Pauletta,40
M. Paulini,21 C. Paus,22 L. Pescara,30 T. J. Phillips,9 G. Piacentino,32 K. T. Pitts,16 R. Plunkett,10 A. Pompos,34 L. Pondrom,44 G. Pope,33M. Popovic,23 F. Prokoshin,8J. Proudfoot,2F. Ptohos,12O. Pukhov,8G. Punzi,32 K. Ragan,23
A. Rakitine,22 D. Reher,21 A. Reichold,29 W. Riegler,14 A. Ribon,30 F. Rimondi,3 L. Ristori,32 M. Riveline,23 W. J. Robertson,9 A. Robinson,23 T. Rodrigo,6 S. Rolli,42 L. Rosenson,22 R. Roser,10 R. Rossin,30 A. Safonov,36 W. K. Sakumoto,35 D. Saltzberg,5A. Sansoni,12 L. Santi,40H. Sato,41 P. Savard,23 P. Schlabach,10 E. E. Schmidt,10
M. P. Schmidt,45 M. Schmitt,14 L. Scodellaro,30 A. Scott,5 A. Scribano,32 S. Segler,10 S. Seidel,26 Y. Seiya,41 A. Semenov,8F. Semeria,3T. Shah,22 M. D. Shapiro,21P. F. Shepard,33 T. Shibayama,41M. Shimojima,41 M. Shochet,7 J. Siegrist,21 G. Signorelli,32A. Sill,39P. Sinervo,23 P. Singh,16A. J. Slaughter,45 K. Sliwa,42 C. Smith,17 F. D. Snider,10
A. Solodsky,36 J. Spalding,10 T. Speer,13 P. Sphicas,22 F. Spinella,32 M. Spiropulu,14 L. Spiegel,10 J. Steele,44
A. Stefanini,32 J. Strologas,16 F. Strumia,13 D. Stuart,10 K. Sumorok,22 T. Suzuki,41 T. Takano,28 R. Takashima,15 K. Takikawa,41 P. Tamburello,9 M. Tanaka,41 B. Tannenbaum,5W. Taylor,23M. Tecchio,24 P. K. Teng,1K. Terashi,36 S. Tether,22D. Theriot,10R. Thurman-Keup,2P. Tipton,35 S. Tkaczyk,10 K. Tollefson,35 A. Tollestrup,10H. Toyoda,28
W. Trischuk,23 J. F. de Troconiz,14 J. Tseng,22 N. Turini,32 F. Ukegawa,41T. Vaiciulis,35 J. Valls,37 S. Vejcik III,10 G. Velev,10R. Vidal,10R. Vilar,6I. Volobouev,21D. Vucinic,22R. G. Wagner,2R. L. Wagner,10J. Wahl,7N. B. Wallace,37
A. M. Walsh,37 C. Wang,9C. H. Wang,1M. J. Wang,1T. Watanabe,41D. Waters,29 T. Watts,37 R. Webb,38H. Wenzel,18 W. C. Wester III,10A. B. Wicklund,2E. Wicklund,10H. H. Williams,31P. Wilson,10B. L. Winer,27D. Winn,24S. Wolbers,10 D. Wolinski,24J. Wolinski,25 S. Wolinski,24 S. Worm,26X. Wu,13J. Wyss,32A. Yagil,10 W. Yao,21 G. P. Yeh,10P. Yeh,1
J. Yoh,10 C. Yosef,25T. Yoshida,28 I. Yu,19S. Yu,31 Z. Yu,45 A. Zanetti,40 F. Zetti,21and S. Zucchelli3 (CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439
3Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
4Brandeis University, Waltham, Massachusetts 02254
5University of California at Los Angeles, Los Angeles, California 90024
6Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
7Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637
8Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
9Duke University, Durham, North Carolina 27708
10Fermi National Accelerator Laboratory, Batavia, Illinois 60510
11University of Florida, Gainesville, Florida 32611
12Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
13University of Geneva, CH-1211 Geneva 4, Switzerland
14Harvard University, Cambridge, Massachusetts 02138
15Hiroshima University, Higashi-Hiroshima 724, Japan
16University of Illinois, Urbana, Illinois 61801
17The Johns Hopkins University, Baltimore, Maryland 21218
18Institut für Experimentelle Kernphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany
19Korean Hadron Collider Laboratory: Kyungpook National University, Taegu 702-701 Korea, and Seoul National University, Seoul 151-742 Korea,
and SungKyunKwan University, Suwon 440-746 Korea
20High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
21Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720
22Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
23Institute of Particle Physics: McGill University, Montreal, Canada H3A 2T8, and University of Toronto, Toronto, Canada M5S 1A7
24University of Michigan, Ann Arbor, Michigan 48109
25Michigan State University, East Lansing, Michigan 48824
26University of New Mexico, Albuquerque, New Mexico 87131
27The Ohio State University, Columbus, Ohio 43210
28Osaka City University, Osaka 588, Japan
29University of Oxford, Oxford OX1 3RH, United Kingdom
30Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
31University of Pennsylvania, Philadelphia, Pennsylvania 19104
32Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pisa, Italy
33University of Pittsburgh, Pittsburgh, Pennsylvania 15260
34Purdue University, West Lafayette, Indiana 47907
35University of Rochester, Rochester, New York 14627
36Rockefeller University, New York, New York 10021
37Rutgers University, Piscataway, New Jersey 08855
38Texas A&M University, College Station, Texas 77843
39Texas Tech University, Lubbock, Texas 79409
40Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy
41University of Tsukuba, Tsukuba, Ibaraki 305, Japan
42Tufts University, Medford, Massachusetts 02155
43Waseda University, Tokyo 169, Japan
44University of Wisconsin, Madison, Wisconsin 53706
45Yale University, New Haven, Connecticut 06520 (Received 12 July 2000)
An angular analysis ofB0 !J兾cKⴱ0andB0s !J兾cfhas been used to determine the decay ampli- tudes with parity-even longitudinal (A0) and transverse (Ak) polarization and parity-odd transverse (A⬜) polarization. The measurements are based on 190B0and 40B0scandidates obtained from89pb21ofpp¯ collisions at the Fermilab Tevatron. The longitudinal decay amplitude dominates withjA0j2苷0.596 0.0660.01forB0andjA0j2苷0.6160.1460.02forB0s decays. The parity-odd amplitude is found to be small withjA⬜j2苷0.1310.1220.09 60.06forB0 andjA⬜j2苷0.2360.1960.04forB0s decays.
PACS numbers: 13.25.Hw, 11.30.Er
The decays B0 !J兾cKⴱ0 and B0s ! J兾cf are pseudoscalar to vector-vector decays and, in principle, have three decay amplitudes which can be determined by studying the angular distributions of the final state particles. These decays can have orbital angular momenta between the J兾c andKⴱ (or f) of 0, 1, or 2, and three decay amplitudes govern these transitions. Another con- venient description is given in the transversity basis [1,2]
in which the decay amplitudes are defined in terms of the linear polarization of the vector mesons. In this basis the L苷 1 (P wave) decays are governed by a single decay amplitude, A⬜, corresponding to a parity-odd correlation between transversely polarized vector mesons. The other two decay amplitudes,A0andAk, are combinations of the parity-even L苷0 and L 苷2 (S and D wave) decays.
The longitudinal polarization fraction, as is commonly defined in the helicity basis , is given byGL兾G 苷jA0j2. Determination of the decay amplitudes and phases probes the limitations of the factorization hypothesis .
Factorization assumes that a weak decay matrix element can be described as the product of two independent (hadronic) currents, in this case treating the J兾c and B !Kⴱ (f) as currents. To the extent that factorization holds, final state interactions are negligible. The matrix elements factorize into short and long distance (weak and strong) parts and the polarization decay amplitudes do not interfere and so are expected to be relatively real.
A measurement of the parity-odd amplitude, A⬜, is pertinent to studies of CP invariance. For example, if the decay B0 !J兾cKⴱ0 (with Kⴱ0 !Ks0p0) were to occur mainly through either a parity-odd or even ampli- tude, then this mode could be used [1,5] as readily as theB0 !J兾cKs0decay mode for determining  the CP nonconserving parameter sin共2b兲. The situation holds as well for the decayB0s !J兾cf, which is expected to have a very small CP decay rate asymmetry in the standard Cabibbo-Kobayashi-Maskawa model. In addition the po- larization of the decayB0s ! J兾cf is interesting for its potential to improve the precision of measurements of the lifetime difference between theB0smass eigenstates via an angular analysis [2,7].
The longitudinal polarization inB0 !J兾cKⴱ0was first measured by ARGUS  as⬃1.0followed by a CLEO 
measurement of0.860.2and a CDF (Collider Detector at Fermilab) measurement  of0.656 0.11. A full an- gular analysis by CLEO  obtained a longitudinal po- larization fraction of0.52 60.08and a parity-odd fraction of0.16 60.09. The only previous measurement of theB0s
decay mode, by CDF , obtained a longitudinal polar- ization fraction of0.566 0.21, consistent with the results forB0, as expected under SU共3兲-flavor symmetry.
This Letter describes a full angular analysis of both the B0 and B0s decay modes based on 89pb21 of pp¯ collisions at p
s 苷1.8TeV collected with the CDF detector at the Fermilab Tevatron. In this analysis, the B0! J兾cKⴱ0andB0s !J兾cfdecays are reconstructed from the decay modes J兾c !m1m2, Kⴱ0 !K1p2, and f !K1K2. After the selection described below, there are 190 B0 !J兾cKⴱ0 and 40 B0s !J兾cf candi- dates above background. The results presented here are independent of those in Ref. .
CDF is a general purpose detector and has been described in detail elsewhere . For this analysis important elements of the detector are the silicon vertex detector, with track impact parameter resolution of10mm, and the drift chamber, with charged particle momentum resolution of dpT兾pT ⬃0.001pT, wherePT (in GeV兾c) is the component of the momentum transverse to the pp¯ collision axis. Chambers for muon detection provide cov- erage for particles with direction within 40±of the trans- verse direction.
The event sample for this measurement is selected by online trigger and offline reconstruction criteria. The trigger signature is the decay of a J兾c to two muons.
Hits in the muon chambers forming a track segment consistent with a nominal muon transverse momentum PT . 3.0GeV兾c satisfy the first level of the trigger.
Candidate muon track segments must be separated by more than 10± in the plane transverse to the collision axis. The second level requires drift chamber tracks, with PT . 2GeV兾c, which extrapolate to the track segments in the muon chambers. The third level accepts J兾c candidates with a reconstructed mass between 2.8 and 3.4GeV兾c2.
The offline reconstruction first selectsJ兾c candidates.
Two muons of opposite charge satisfying quality require- ments are combined into aJ兾c candidate. A kinematic fit requiring the muons to originate from a common vertex is performed, and the confidence level of the fit is required to be at least 0.01. This results in a sample of about 290 000 candidate J兾c’s.
Of these, candidates within80MeV兾c2of theJ兾cmass (3096.88MeV兾c2)  are then combined with two op- positely charged tracks that form aKⴱ (f) for theB0! J兾cKⴱ0 (B0s !J兾cf) decays. CDF lacks the particle identification capability to distinguish between the two
K-pcharge assignments for aKⴱcandidate. However, the mass distribution for misidentified candidates is broader than the natural width of theKⴱand their contribution is largely suppressed by choosing the assignment yielding a Kⴱ mass closer to, and within 80MeV兾c2 of, the world average (896.1MeV兾c2).
To further improve the signal-to-noise ratio, the B0 candidate is required to havePT .6.0GeV兾c, with the Kⴱ having PT .2.0GeV兾c. All four particles from the B0 decay are required to come from a common
“secondary” vertex, with the confidence level of the fit being greater than 0.001. The proper decay length (c 3proper decay time) for the B0 is required to be at least100mm. The resultingKpm1m2mass distribution is plotted in Fig. 1(a).
For the B0s decay, the f candidate is required to have a mass within 10MeV兾c2 of the nominal f mass (1019.4 MeV兾c2). The narrow natural width of the f provides for better background rejection than the Kⴱ.
In order to compensate for the lower expected yield of B0s events, looser requirements are imposed: transverse momentum cuts of1.5GeV兾cand4.5GeV兾care applied to the f andB0s candidates. The confidence level of the four-track fit is again required to be greater than 0.001, and the proper decay length is required to be at least 50mm. The resulting KKm1m2 mass distribution is plotted in Fig. 1(b).
The linear polarization of the vector mesons is de- termined from the angular distribution of the final state decay products. The decay angles are defined  as QKⴱ, QT, and FT. In the rest frame of the Kⴱ, QKⴱ is the angle between the K momentum and the direction opposite the B meson (for the f, the K1 defines the angle). The transversity angles, QT andFT, are defined in the J兾c rest frame: QT is the angle between the m1 momentum and the perpendicular to theKⴱ-K plane; FT is the azimuthal angle from theKⴱto the projection of the m1 momentum onto theKⴱ-K plane.
The decay angular distribution is :
dG兾dV ~2cos2QKⴱ共1 2sin2QTcos2FT兲jA0j2 1sin2QKⴱ共12 sin2QTsin2FT兲jAkj21 sin2QKⴱsin2QTjA⬜j2 1 1
p2 sin2QKⴱsin2QTsin2FTRe共Aⴱ0Ak兲7 sin2QKⴱsin2QTsinFTIm共AⴱkA⬜兲
6 1 p
2 sin2QKⴱsin2QTcosFTIm共Aⴱ0A⬜兲. Normalization of the distribution to unity impliesjA0j21 jAkj2 1jA⬜j2 苷1, and an unobservable phase is removed by requiring arg共A0兲 苷0. This leaves four measurable quantities: the polarization fractions, GL兾G 苷jA0j2 and G⬜兾G 苷jA⬜j2, and the phases of the matrix elements, arg共Ak兲 and arg共A⬜兲. CP invariance has been assumed throughout for the decay amplitudes.
The last two terms of the angular distribution have opposite signs for particle and antiparticle decay. TheB0 and B0 decays are flavor tagged by the charge of the K meson. The B0s and B0s are not distinguishable by their final state particles, so forB0s decays the information about the phase ofA⬜ is lost. The angular distribution as given holds initially, that is, att 苷 0, for an untaggedBssample.
The time dependence of the terms will differ if the mass
µµKπ mass GeV/c2
Candidates per 0.005 GeV/c2
(a) B0→ J/ψ K*
Yield: 193 ± 17
0 10 20 30 40 50 60 70
5.15 5.20 5.25 5.30 5.35 5.40
µµKK mass GeV/c2
Candidates per 0.01 GeV/c2
(b) B0s→ J/ψφ Yield: 40.3 ± 9.7
0 5 10 15 20 25 30 35
5.25 5.30 5.35 5.40 5.45 5.50
FIG. 1. Invariant mass distributions, after all selection require- ments, for (a)B0!J兾cKⴱ0and (b)B0s !J兾cfcandidates.
eigenstates have different lifetimes and in this case there can also be a CP violating contribution which is expected to be small (few percent) due to B0s 2 B0s mixing in the standard model . The small statistics of theBs sample is such that the current measurement is not sensitive to a lifetime difference.
cos(ΘK*) (a) B0→ J/ψ K*
0 0.5 1
-1 0 1 0
-1 0 1 0
0.1 0.2 0.3
-π -ππ/2 0 ππ/2 π
cos(ΘK*) (b) B0s→ J/ψφ
0 0.5 1
-1 0 1 0
-1 0 1 0
0.1 0.2 0.3
-π -ππ/2 0 ππ/2 π
FIG. 2. Projections of the results from the full angular fit and the background subtracted data, corrected for acceptance, are shown for each of the decay angles, for (a) the B0!J兾cKⴱ0 mode and (b) the B0s !J兾cf mode.
TABLE I. Fitted decay amplitudes and phases (in radians). The uncertainties are statistical and systematic, respectively.
Quantity B0!J兾cKⴱ0 B0s !J兾cf
A0 0.7760.0460.01 0.7860.0960.01 Ak 0.5360.1160.04 0.4160.2360.05
arg共Ak兲 2.260.560.1 1.161.360.2
A⬜ 0.3660.1660.08 0.4860.2060.04
arg共A⬜兲 20.660.560.1 · · ·
GL兾G 苷jA0j2 0.5960.0660.01 0.6160.1460.02 G⬜兾G 苷jA⬜j2 0.13 1
0.09 60.06 0.2360.1960.04
The matrix elements are extracted by fitting the observed decay angular distribution. The fit is performed over the decay angles and the B candidate mass range covered in Fig. 1. To account for detector acceptance and selection criteria, Monte Carlo events are generated with detector and trigger simulations and processed by the same recon- struction software used on the data. The fit method uses an unbinned log-likelihood with the normalization depending on the parameters in the fit [14,15].
The background is modeled by a sum of polynomial terms of cosQKⴱ and cosQT, and sines and cosines of FT and2FT. The background angular distribution is de- termined from the events on both sides of the B meson mass peak.
Additional terms are included in the angular distribution to account for the residual probability (⬃6%) of misidenti- fying the final state hadrons in the selectedB0 !J兾cKⴱ0 decays. Events reconstructed under the wrong hypothesis will yield incorrect decay angles having a distribution dif- ferent from, but fully correlated with, the polarized decay distribution. The augmented likelihood function corrects for the effect based on the kinematics as determined from Monte Carlo.
The results from the global fit are illustrated in Fig. 2.
The independent variables are functions of the transversity angles: cosQKⴱ, cosQT, andFT. The points are the back- ground subtracted projection of the data corrected for de- tector and reconstruction efficiencies. The superimposed curves are derived from the results of the global fit.
Sources of systematic uncertainty are, in order of impor- tance, the model of the background shape, Monte CarloB generation parameters, trigger simulation, andB0-B0scross talk. The last two are found to have negligible contribu- tion. The uncertainty of the final result is still dominated by the statistics of the event sample .
The underlying background shape is not known from first principles. To estimate the systematic uncertainty from the background modeling, multiple fits with differ- ent parametrizations of the background decay angles were studied. Different models of the shape are sensitive to dif- ferent inaccuracies of the background shape function, and the spread in the fitted values is used to estimate the sen- sitivity to possibly unaccounted structure.
The input parameters to the Monte Carlo generation of Bmesons are thebquark mass and generation mass scales, the parton distribution functions, and fragmentation pa- rameters. The effect on the measurement is determined by varying the parameters by their nominal uncertainties and refitting for the decay amplitudes. Systematic uncer- tainties due to the modeling of the trigger selection criteria are studied in a similar fashion.
The similarity of the decay kinematics for theB0andB0s decays allows for a possible cross contamination through K-p misidentification. Monte Carlo studies give contami- nation fractions of2.1%(4.4%) in theB0(B0s) sample. The assigned systematic uncertainty is equal to the difference in the B0 and B0s polarization fraction, multiplied by the contamination fraction.
The final results of this analysis are summarized in Table I, and are illustrated in Fig. 3. For the B0!J兾 cKⴱ0 the magnitudes of decay amplitudes are in good agreement with the results from CLEO .
The longitudinal polarization fraction dominates:
GL兾G 苷jA0j2苷 0.596 0.066 0.01and the parity-odd fraction is small: G⬜兾G 苷jA⬜j2 苷0.1310.1220.09 60.06. In contrast to the CLEO result, the CDF measurement for the phase ofAkfavors the presence of strong final state interac- tions, inasmuch as arg共Ak兲is not close to0orp. However, the results from the two experiments are not inconsistent, given their uncertainties. The results for theB0s !J兾cf
Real Axis →
Imaginary Axis →
A⊥ (a) B0 → J/ψ K*
-i 0 i
-1 0 1
Real Axis →
Imaginary Axis →
A⊥ (b) B0s → J/ψ φ
-i 0 i
-1 0 1
FIG. 3. One-standard-deviation contours, including statistical and systematic uncertainties, for the fitted decay amplitudes in the complex plane, for (a) B0!J兾cKⴱ0 and (b) B0s ! J兾cf decays.
are the first available from a full angular analysis. The B0s results also show a dominant longitudinal polar- ization fraction GL兾G 苷jA0j2 苷0.61 60.14 60.02 and a small parity-odd fraction: G⬜兾G 苷 jA⬜j2苷 0.23 60.19 60.04, consistent with the B0 results and SU(3) flavor symmetry.
We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.
This research was supported by the U.S. Department of Energy and the National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Edu- cation, Science and Culture of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss Na- tional Science Foundation; the A. P. Sloan Foundation; and the Bundesministerium für Bildung und Forschung, Ger- many. We thank H. Lipkin for bringing the transversity basis to our attention and acknowledge illuminating corre- spondence and discussions with I. Dunietz and J. Rosner.
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