Article
Reference
Measurement of the Lifetime Difference between B
sMass Eigenstates
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
We present measurements of the lifetimes and polarization amplitudes for B0s→J/ψϕ and B0d→J/ψK*0 decays. Lifetimes of the heavy and light mass eigenstates in the B0s system are separately measured for the first time by determining the relative contributions of amplitudes with definite CP as a function of the decay time. Using 203±15 B0s decays we obtain τL=(1.05+0.16−0.13±0.02) ps and τH=(2.07+0.58−0.46±0.03) ps. Expressed in terms of the difference ΔΓs and average Γs, of the decay rates of the two eigenstates, the results are ΔΓs/Γs=(65+25−33±1)% and ΔΓs=(0.47+0.19−0.24±0.01) ps−1
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the Lifetime
Difference between B
sMass Eigenstates. Physical Review Letters , 2005, vol. 94, no. 10, p.
101803
DOI : 10.1103/PhysRevLett.94.101803
Available at:
http://archive-ouverte.unige.ch/unige:38098
Disclaimer: layout of this document may differ from the published version.
1 / 1
Measurement of the Lifetime Difference between B
sMass Eigenstates
D. Acosta,16J. Adelman,12T. Affolder,9T. Akimoto,54M. G. Albrow,15D. Ambrose,43S. Amerio,42D. Amidei,33 A. Anastassov,50K. Anikeev,15A. Annovi,44J. Antos,1M. Aoki,54G. Apollinari,15T. Arisawa,56J-F. Arguin,32 A. Artikov,13W. Ashmanskas,15A. Attal,7F. Azfar,41P. Azzi-Bacchetta,42N. Bacchetta,42H. Bachacou,28W. Badgett,15 A. Barbaro-Galtieri,28G. J. Barker,25V. E. Barnes,46B. A. Barnett,24S. Baroiant,6M. Barone,17G. Bauer,31F. Bedeschi,44
S. Behari,24S. Belforte,53G. Bellettini,44J. Bellinger,58E. Ben-Haim,15D. Benjamin,14A. Beretvas,15A. Bhatti,48 M. Binkley,15D. Bisello,42M. Bishai,15R. E. Blair,2C. Blocker,5K. Bloom,33B. Blumenfeld,24A. Bocci,48A. Bodek,47
G. Bolla,46A. Bolshov,31P. S. L. Booth,29D. Bortoletto,46J. Boudreau,45S. Bourov,15B. Brau,9C. Bromberg,34 E. Brubaker,12J. Budagov,13H. S. Budd,47K. Burkett,15G. Busetto,42P. Bussey,19K. L. Byrum,2S. Cabrera,14 M. Campanelli,18M. Campbell,33A. Canepa,46M. Casarsa,53D. Carlsmith,58S. Carron,14R. Carosi,44M. Cavalli-Sforza,3
A. Castro,4P. Catastini,44D. Cauz,53A. Cerri,28L. Cerrito,23J. Chapman,33C. Chen,43Y. C. Chen,1M. Chertok,6 G. Chiarelli,44G. Chlachidze,13F. Chlebana,15I. Cho,27K. Cho,27D. Chokheli,13J. P. Chou,20M. L. Chu,1S. Chuang,58
J. Y. Chung,38W-H. Chung,58Y. S. Chung,47C. I. Ciobanu,23M. A. Ciocci,44A. G. Clark,18D. Clark,5M. Coca,47 A. Connolly,28M. Convery,48J. Conway,6B. Cooper,30M. Cordelli,17G. Cortiana,42J. Cranshaw,52J. Cuevas,10 R. Culbertson,15C. Currat,28D. Cyr,58D. Dagenhart,5S. Da Ronco,42S. D’Auria,19P. de Barbaro,47S. De Cecco,49
G. De Lentdecker,47S. Dell’Agnello,17M. Dell’Orso,44S. Demers,47L. Demortier,48M. Deninno,4D. De Pedis,49 P. F. Derwent,15C. Dionisi,49J. R. Dittmann,15C. Do¨rr,25P. Doksus,23A. Dominguez,28S. Donati,44M. Donega,18 J. Donini,42M. D’Onofrio,18T. Dorigo,42V. Drollinger,36K. Ebina,56N. Eddy,23J. Ehlers,18R. Ely,28R. Erbacher,6
M. Erdmann,25D. Errede,23S. Errede,23R. Eusebi,47H-C. Fang,28S. Farrington,29I. Fedorko,44W. T. Fedorko,12 R. G. Feild,59M. Feindt,25J. P. Fernandez,46C. Ferretti,33R. D. Field,16G. Flanagan,34B. Flaugher,15
L. R. Flores-Castillo,45A. Foland,20S. Forrester,6G. W. Foster,15M. Franklin,20J. C. Freeman,28Y. Fujii,26I. Furic,12 A. Gajjar,29A. Gallas,37J. Galyardt,11M. Gallinaro,48M. Garcia-Sciveres,28A. F. Garfinkel,46C. Gay,59H. Gerberich,14
D. W. Gerdes,33E. Gerchtein,11S. Giagu,49P. Giannetti,44A. Gibson,28K. Gibson,11C. Ginsburg,58K. Giolo,46 M. Giordani,53M. Giunta,44G. Giurgiu,11V. Glagolev,13D. Glenzinski,15M. Gold,36N. Goldschmidt,33D. Goldstein,7
J. Goldstein,41G. Gomez,10G. Gomez-Ceballos,10M. Goncharov,51O. Gonza´lez,46I. Gorelov,36A. T. Goshaw,14 Y. Gotra,45K. Goulianos,48A. Gresele,4M. Griffiths,29C. Grosso-Pilcher,12U. Grundler,23M. Guenther,46 J. Guimaraes da Costa,20C. Haber,28K. Hahn,43S. R. Hahn,15E. Halkiadakis,47A. Hamilton,32B-Y. Han,47R. Handler,58 F. Happacher,17K. Hara,54M. Hare,55R. F. Harr,57R. M. Harris,15F. Hartmann,25K. Hatakeyama,48J. Hauser,7C. Hays,14 H. Hayward,29E. Heider,55B. Heinemann,29J. Heinrich,43M. Hennecke,25M. Herndon,24C. Hill,9D. Hirschbuehl,25 A. Hocker,47K. D. Hoffman,12A. Holloway,20S. Hou,1M. A. Houlden,29B. T. Huffman,41Y. Huang,14R. E. Hughes,38
J. Huston,34K. Ikado,56J. Incandela,9G. Introzzi,44M. Iori,49Y. Ishizawa,54C. Issever,9A. Ivanov,47Y. Iwata,22 B. Iyutin,31E. James,15D. Jang,50J. Jarrell,36D. Jeans,49H. Jensen,15E. J. Jeon,27M. Jones,46K. K. Joo,27S. Y. Jun,11 T. Junk,23T. Kamon,51J. Kang,33M. Karagoz Unel,37P. E. Karchin,57S. Kartal,15Y. Kato,40Y. Kemp,25R. Kephart,15
U. Kerzel,25V. Khotilovich,51B. Kilminster,38D. H. Kim,27H. S. Kim,23J. E. Kim,27M. J. Kim,11M. S. Kim,27 S. B. Kim,27S. H. Kim,54T. H. Kim,31Y. K. Kim,12B. T. King,29M. Kirby,14L. Kirsch,5S. Klimenko,16B. Knuteson,31 B. R. Ko,14H. Kobayashi,54P. Koehn,38D. J. Kong,27K. Kondo,56J. Konigsberg,16K. Kordas,32A. Korn,31A. Korytov,16
K. Kotelnikov,35A. V. Kotwal,14A. Kovalev,43J. Kraus,23I. Kravchenko,31A. Kreymer,15J. Kroll,43M. Kruse,14 V. Krutelyov,51S. E. Kuhlmann,2S. Kwang,12A. T. Laasanen,46S. Lai,32S. Lami,48S. Lammel,15J. Lancaster,14 M. Lancaster,30R. Lander,6K. Lannon,38A. Lath,50G. Latino,36R. Lauhakangas,21I. Lazzizzera,42Y. Le,24C. Lecci,25 T. LeCompte,2J. Lee,27J. Lee,47S. W. Lee,51R. Lefe`vre,3N. Leonardo,31S. Leone,44S. Levy,12J. D. Lewis,15K. Li,59 C. Lin,59C. S. Lin,15M. Lindgren,15T. M. Liss,23A. Lister,18D. O. Litvintsev,15T. Liu,15Y. Liu,18N. S. Lockyer,43 A. Loginov,35M. Loreti,42P. Loverre,49R-S. Lu,1D. Lucchesi,42P. Lujan,28P. Lukens,15G. Lungu,16L. Lyons,41J. Lys,28 R. Lysak,1D. MacQueen,32R. Madrak,15K. Maeshima,15P. Maksimovic,24L. Malferrari,4G. Manca,29R. Marginean,38
C. Marino,23A. Martin,59M. Martin,24V. Martin,37M. Martı´nez,3T. Maruyama,54H. Matsunaga,54M. Mattson,57 P. Mazzanti,4K. S. McFarland,47D. McGivern,30P. M. McIntyre,51P. McNamara,50R. NcNulty,29A. Mehta,29 S. Menzemer,31A. Menzione,44P. Merkel,15C. Mesropian,48A. Messina,49T. Miao,15N. Miladinovic,5L. Miller,20 R. Miller,34J. S. Miller,33R. Miquel,28S. Miscetti,17G. Mitselmakher,16A. Miyamoto,26Y. Miyazaki,40N. Moggi,4
B. Mohr,7R. Moore,15M. Morello,44P. A. Movilla Fernandez,28A. Mukherjee,15M. Mulhearn,31T. Muller,25 R. Mumford,24A. Munar,43P. Murat,15J. Nachtman,15S. Nahn,59I. Nakamura,43I. Nakano,39A. Napier,55R. Napora,24
0031-9007=05=94(10)=101803(7)$23.00 101803-1 2005 The American Physical Society
D. Naumov, V. Necula, F. Niell, J. Nielsen, C. Nelson, T. Nelson, C. Neu, M. S. Neubauer,
C. Newman-Holmes,15T. Nigmanov,45L. Nodulman,2O. Norniella,3K. Oesterberg,21T. Ogawa,56S. H. Oh,14Y. D. Oh,27 T. Ohsugi,22T. Okusawa,40R. Oldeman,49R. Orava,21W. Orejudos,28C. Pagliarone,44E. Palencia,10R. Paoletti,44 V. Papadimitriou,15S. Pashapour,32J. Patrick,15G. Pauletta,53M. Paulini,11T. Pauly,41C. Paus,31D. Pellett,6A. Penzo,53 T. J. Phillips,14G. Piacentino,44J. Piedra,10K. T. Pitts,23C. Plager,7A. Pomposˇ,46L. Pondrom,58G. Pope,45X. Portell,3
O. Poukhov,13F. Prakoshyn,13T. Pratt,29A. Pronko,16J. Proudfoot,2F. Ptohos,17G. Punzi,44J. Rademacker,41 M. A. Rahaman,45A. Rakitine,31S. Rappoccio,20F. Ratnikov,50H. Ray,33B. Reisert,15V. Rekovic,36P. Renton,41
M. Rescigno,49F. Rimondi,4K. Rinnert,25L. Ristori,44W. J. Robertson,14A. Robson,41T. Rodrigo,10S. Rolli,55 L. Rosenson,31R. Roser,15R. Rossin,42C. Rott,46J. Russ,11V. Rusu,12A. Ruiz,10D. Ryan,55H. Saarikko,21S. Sabik,32
A. Safonov,6R. St. Denis,19W. K. Sakumoto,47G. Salamanna,49D. Saltzberg,7C. Sanchez,3A. Sansoni,17L. Santi,53 S. Sarkar,49K. Sato,54P. Savard,32A. Savoy-Navarro,15P. Schlabach,15E. E. Schmidt,15M. P. Schmidt,59M. Schmitt,37
L. Scodellaro,10A. Scribano,44F. Scuri,44A. Sedov,46S. Seidel,36Y. Seiya,40F. Semeria,4L. Sexton-Kennedy,15 I. Sfiligoi,17M. D. Shapiro,28T. Shears,29P. F. Shepard,45D. Sherman,20M. Shimojima,54M. Shochet,12Y. Shon,58 I. Shreyber,35A. Sidoti,44J. Siegrist,28M. Siket,1A. Sill,52P. Sinervo,32A. Sisakyan,13A. Skiba,25A. J. Slaughter,15
K. Sliwa,55D. Smirnov,36J. R. Smith,6F. D. Snider,15R. Snihur,32A. Soha,6S. V. Somalwar,50J. Spalding,15 M. Spezziga,52L. Spiegel,15F. Spinella,44M. Spiropulu,9P. Squillacioti,44H. Stadie,25B. Stelzer,32O. Stelzer-Chilton,32 J. Strologas,36D. Stuart,9A. Sukhanov,16K. Sumorok,31H. Sun,55T. Suzuki,54A. Taffard,23R. Tafirout,32S. F. Takach,57 H. Takano,54R. Takashima,22Y. Takeuchi,54K. Takikawa,54M. Tanaka,2R. Tanaka,39N. Tanimoto,39S. Tapprogge,21
M. Tecchio,33P. K. Teng,1K. Terashi,48R. J. Tesarek,15S. Tether,31J. Thom,15A. S. Thompson,19E. Thomson,43 P. Tipton,47V. Tiwari,11S. Tkaczyk,15D. Toback,51K. Tollefson,34T. Tomura,54D. Tonelli,44M. To¨nnesmann,34 S. Torre,44D. Torretta,15S. Tourneur,15W. Trischuk,32J. Tseng,41R. Tsuchiya,56S. Tsuno,39D. Tsybychev,16N. Turini,44
M. Turner,29F. Ukegawa,54T. Unverhau,19S. Uozumi,54D. Usynin,43L. Vacavant,28A. Vaiciulis,47A. Varganov,33 E. Vataga,44S. Vejcik III,15G. Velev,15V. Veszpremi,46G. Veramendi,23T. Vickey,23R. Vidal,15I. Vila,10R. Vilar,10 I. Vollrath,32I. Volobouev,28M. von der Mey,7P. Wagner,51R. G. Wagner,2R. L. Wagner,15W. Wagner,25R. Wallny,7
T. Walter,25T. Yamashita,39K. Yamamoto,40Z. Wan,50M. J. Wang,1S. M. Wang,16A. Warburton,32B. Ward,19 S. Waschke,19D. Waters,30T. Watts,50M. Weber,28W. C. Wester III,15B. Whitehouse,55A. B. Wicklund,2E. Wicklund,15
H. H. Williams,43P. Wilson,15B. L. Winer,38P. Wittich,43S. Wolbers,15C. Wolfe,12M. Wolter,55M. Worcester,7 S. Worm,50T. Wright,33X. Wu,18F. Wu¨rthwein,8A. Wyatt,30A. Yagil,15C. Yang,59U. K. Yang,12W. Yao,28G. P. Yeh,15 K. Yi,24J. Yoh,15P. Yoon,47K. Yorita,56T. Yoshida,40I. Yu,27S. Yu,43Z. Yu,59J. C. Yun,15L. Zanello,49A. Zanetti,53
I. Zaw,20F. Zetti,44J. Zhou,50A. Zsenei,18and S. Zucchelli4 (CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439, USA
3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
4Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
5Brandeis University, Waltham, Massachusetts 02254, USA
6University of California at Davis, Davis, California 95616, USA
7University of California at Los Angeles, Los Angeles, California 90024, USA
8University of California at San Diego, La Jolla, California 92093, USA
9University of California at Santa Barbara, Santa Barbara, California 93106, USA
10Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
11Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
12Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
14Duke University, Durham, North Carolina 27708, USA
15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
16University of Florida, Gainesville, Florida 32611, USA
17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
18University of Geneva, CH-1211 Geneva 4, Switzerland
19Glasgow University, Glasgow G12 8QQ, United Kingdom
20Harvard University, Cambridge, Massachusetts 02138, USA
21The Helsinki Group: Helsinki Institute of Physics and Division of High Energy Physics, Department of Physical Sciences, University of Helsinki, FIN-00044, Helsinki, Finland
22Hiroshima University, Higashi-Hiroshima 724, Japan 101803-2
23University of Illinois, Urbana, Illinois 61801, USA
24The Johns Hopkins University, Baltimore, Maryland 21218, USA
25Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
26High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
27Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea;
Seoul National University, Seoul 151-742, Korea;
and SungKyunKwan University, Suwon 440-746, Korea
28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
29University of Liverpool, Liverpool L69 7ZE, United Kingdom
30University College London, London WC1E 6BT, United Kingdom
31Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
32Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7
33University of Michigan, Ann Arbor, Michigan 48109, USA
34Michigan State University, East Lansing, Michigan 48824, USA
35Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
36University of New Mexico, Albuquerque, New Mexico 87131, USA
37Northwestern University, Evanston, Illinois 60208, USA
38The Ohio State University, Columbus, Ohio 43210, USA
39Okayama University, Okayama 700-8530, Japan
40Osaka City University, Osaka 588, Japan
41University of Oxford, Oxford OX1 3RH, United Kingdom
42University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
44Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pisa, Italy
45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
46Purdue University, West Lafayette, Indiana 47907, USA
47University of Rochester, Rochester, New York 14627, USA
48The Rockefeller University, New York, New York 10021, USA
49Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University di Roma ‘‘La Sapienza,’’ I-00185 Roma, Italy
50Rutgers University, Piscataway, New Jersey 08855, USA
51Texas A&M University, College Station, Texas 77843, USA
52Texas Tech University, Lubbock, Texas 79409, USA
53Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy
54University of Tsukuba, Tsukuba, Ibaraki 305, Japan
55Tufts University, Medford, Massachusetts 02155, USA
56Waseda University, Tokyo 169, Japan
57Wayne State University, Detroit, Michigan 48201, USA
58University of Wisconsin, Madison, Wisconsin 53706, USA
59Yale University, New Haven, Connecticut 06520, USA (Received 20 December 2004; published 16 March 2005)
We present measurements of the lifetimes and polarization amplitudes for B0s!J= andB0d! J= K0 decays. Lifetimes of the heavy and light mass eigenstates in the B0s system are separately measured for the first time by determining the relative contributions of amplitudes with definiteCPas a function of the decay time. Using20315B0s decays we obtainL 1:050:160:130:02psandH 2:070:580:460:03ps. Expressed in terms of the differencesand averages, of the decay rates of the two eigenstates, the results ares=s 6525331%ands 0:470:190:240:01ps1.
DOI: 10.1103/PhysRevLett.94.101803 PACS numbers: 13.25.Hw, 11.30.Er, 14.40.Nd
Particle-antiparticle oscillation occurs for both B0d and B0s mesons and gives rise, in each system, to two eigen- states with definite masses (heavy,mH, and light,mL) and widths (H and L). In the standard model (SM), this oscillation is due to second-order contributions from the weak interaction and depends on the Cabibbo-Kobayashi- Maskawa (CKM) quark mixing matrix. Oscillation has been observed in theB0d system, and the mass difference (m mHmL) ismd 0:5070:007ps1 [1]. In theB0s system, direct observation of the oscillation signal has been a challenge: the 95% C.L. limit for the mass
difference isms>14:4 ps1 [1]. The ratio of the decay width difference LH to the average decay width LH=2 is expected to be small (0.2% – 0.3%) for theB0dsystem [2], but sizable for theB0ssystem [3]. Reference [4] predicts s=s 126%, and Ref. [5] gives the ratio of the decay width difference to the mass difference. If ms is too large to be directly measured, a measurement of s could serve instead, along with md, in tests of the unitarity of the CKM matrix. In the SM, the mass eigenstates in the B0s system are expected to be nearly CP eigenstates. The light mass
eigenstate is expected to beCPeven and to have a larger decay width, and thus a shorter lifetime, than the heavy mass eigenstate [6]. By exploiting decays with knownCP content, it is possible to measure the two decay widths separately.
The decays B0s!J= and B0d!J= K0892 are pseudoscalar to vector-vector transitions and are charac- terized by three amplitudes. These amplitudes correspond to transitions in which the J= and (or K0) have a relative orbital angular momentum Lof 0, 1, or 2. In the transversity basis [6], the decay amplitudes correspond to linear polarization states of the vector mesons. TheL1 decays take place via the decay amplitude A? and corre- spond to a parity-odd (perpendicular) correlation between the transverse linear polarization states of the vector me- sons. The other two decay amplitudesA0 and Aklead to decays corresponding to linear combinations of the parity- even L0andL2 decays. In this analysis, the fully reconstructed decays B0s!J= (with J= ! and!KK) andB0d!J= K0 (withJ= ! andK0!K) and their charge conjugates are used to measure the polarization amplitudes. The observed final state particles for the B0s and B0s decays (KK) have a definite CP, which depends on L, and a definite angular distribution. We determine the decay widths for the heavy and light B0s mass eigenstates by measuring the relative contribution of the CP-odd and CP-even decays to the observed angular distribution as a function of the decay time. The B0d decays provide a valuable control sample since they are expected to occur via similar (parity-odd and parity-even) decay amplitudes [6].
The analysis uses a portion of the data from run II at the Fermilab Tevatron ppcollider, corresponding to an inte- grated luminosity of about 260 pb1. The data were col- lected with the upgraded Collider Detector at Fermilab (CDF) [7], the most relevant components of which are described below. A five-layer double-sided silicon micro- strip detector, SVX, provides track measurements at radii between 2.5 and 10.6 cm and allows for precise vertex reconstruction. A cylindrical drift chamber, COT, with eight alternating axial and stereo superlayers (each super- layer containing 12 sense wires) provides track measure- ments for charged particles between radii of 40 and 137 cm. The COT symmetry axis is the main axis of the cylindrical coordinate system used at CDF. Both tracking devices are immersed in a uniform axial 1.4 T magnetic field, allowing precision measurement of the momenta of charged particles in the radial direction pT. Planar drift chambers located outside of calorimeters and additional steel absorbers are used to identify muons. Muons and charged hadrons are reconstructed in the central pseudo- rapidity regionjj<1.
The three-level trigger system of CDF is used to select events of interest by requiring two oppositely charged particle tracks, each with pT>1:5 GeV=c and matched to hits in the muon detector. About 2:0106 J= !
signal candidates were selected by requiring a reconstructed mass within 80:0 MeV=c2 of theJ= mass [1]. AB0s (B0d) meson candidate is reconstructed by asso- ciating a J= candidate with a pair of tracks, each with pT>0:4 GeV=c, consistent with a !KK (K0! K) decay. TheKK(K) mass is required to be within 6:5 MeV=c2 (50:0 MeV=c2) of the (K0) pole mass [1]. When both K andK particle assign- ments are kinematically viable in the K0 reconstruction (no particle identification is used), the one giving the mass closest to the pole K0 mass is chosen. This reduces the contribution from candidates with swapped particle assign- ment down to about 10% of the total signal. Background is suppressed by requiring pTB0s;d>6:0 GeV=c,pT>
2:0 GeV=c, and pTK0>2:6 GeV=c. The more restric- tive cut on pTK0 is determined by an optimization procedure, and is a consequence of the larger combinato- rial background underneath theK0 peak.
We fit theBcandidates subject to the constraint that the four tracks originate from a common point. In order to improve the mass resolution, the mass is con- strained to the J= mass. To ensure only well measured vertices, a set of track and vertex quality requirements is applied [8]. In particular, all four tracks are required to have measurements in at least three axial layers of the silicon detector. The proper decay time, t, is determined from the radial distance lT from the beam axis to the B meson decay vertex, signed relative to the direction of p~T of theBcandidate:ctc~lTp~TMB=p2T. The position of the beam axis is determined using data taken with an inclusive jet trigger. The radial profile of the beam is approximately Gaussian with a rms of about30m.
In the B0d system, the mass eigenstates are not CP eigenstates, and the observed decays are flavor specific with the charge of the K meson identifying whether the decay is that of aB0d or aB0d. Summing over initially pro- ducedB0dandB0dyields a differential decay rate [9] which is insensitive to first order to a lifetime difference [2]:
d4P; t~
d ~dt / jA0j2f1 jA~ kj2f2~ jA?j2f3~ ImAkA? f4~
ReA0Ak f5~ ImA0A? f6e~ dt:
Here the upper (lower) sign is used forK(K) in the final state andd 1=B0
d. The functionsfi~ depend on the transversity variables ~ fcos"; ’;cos g, all of which are defined in Ref. [9].
In theB0s system, the SM expectation is thatCPviola- tion due to mixing is small, and the mass eigenstates are nearly CPeigenstates. IgnoringCPviolation due to mix- ing, and summing the distributions for initially produced B0s and B0s mesons, the interference terms between the CP-even andCP-odd amplitudes cancel, leaving
101803-4
d4P;t~
d ~dt / jA0j2eLtf1 jA~ kj2eLtf2~
jA?j2eHtf3~ ReA0Ak f5e~ Lt: In theB0s analysis, the observed final states have definite CPwhich depends onL. TheCP-even angular decay terms (A0;k) evolve in time aseLt, while theCP-odd angular decay terms (A?) evolve aseHt.
For bothB0dandB0s decays, the amplitudes are normal- ized so thatjA0j2 jAkj2 jA?j21, and an unobserv- able overall phase is removed by settingargA0 0. The decay amplitudes are assumed to beCPconserving.
An unbinned likelihood fit is performed to mass,ct, and
~
in order to extract the decay amplitudesA0;k;?and decay widths(HandLin the case of theB0s). Inclusion of the mass information in the fit is crucial for separation of the signal from the background. The mass distribution is mod- eled with a Gaussian for the signal peak and a linear shape for the background. The mass-measurement uncertainty is incorporated for each candidate. The probability density function forctincludes positive exponentials for the sig- nal, a $ function for the prompt background (which is about 85% of the total) and a set of exponentials for positive and negative decay lengths which describe a short-lived background component due to mismeasured vertices and a long-lived contribution due to incorrectly reconstructed heavy-flavor decays. Each contribution is convoluted with a Gaussian resolution function, the width of which is proportional to the uncertainty of the candi- date’sct measurement. To allow for a systematic under- estimate of the uncertainties, the mass and the ct uncertainties are multiplied by scale factors determined in the fit. The~ distribution of the signal is parametrized in accordance with the equations above. The background distributions inct and~ are assumed to be uncorrelated.
The latter is described by a shape similar to that of the signal, but with an independent set of amplitudes. The relationship of mass,ct, and~ of the B0d candidates with K misassignment to those of correctly reconstructed candidates is established via Monte Carlo simulation.
Distributions in~ are distorted by the detector accep- tance, the trigger efficiency, and, most importantly, the kinematic selection criteria. We use the method developed for the CDF run I measurement of transversity amplitudes [10,11] to account for this distortion. With as little as six constants extracted from Monte Carlo decays generated uniformly in, this method allows one to avoid the need~ for explicit parametrization of the distortion in the like- lihood. All aspects of the fitting are extensively verified using Monte Carlo simulations.
Data and fit projections in mass andctfor theB0sandB0d are shown in Figs. 1 and 2. Fits in the transversity subspace are illustrated by Fig. 3.
The single largest source of systematic uncertainty in the measurement of the transversity amplitudes ofB0dandB0sis the choice of parametrization of the background distribu-
tion in . The~ B0s transversity amplitudes receive a small contribution to their systematic uncertainty from a 3.5%
contamination from B0d. Two other sources contribute to the uncertainty inB0d amplitudes: the way candidates with incorrect K assignment are handled and the potential contribution of K final states that are not due to B0d!J= K0892 decays, which is estimated to be less than 4% of the total signal. The systematic uncertainty in the lifetimes receives contributions from the choice of the ct parametrization and from the SVX alignment.
Slightly larger contributions come from the choice of the background parametrization in ~ and, in the case of B0s, fromB0dcontamination. Fors=s the only two sources of systematic uncertainty are from the choice of the back- ground ~ parametrization and from B0d contamination.
Other potential sources of systematic uncertainty, includ- ing those from the method of correcting for distortion of the signal distribution in ~ and potential contribution of B0s!J= f0980 decays, were found to be negligible.
The precision of all of the results of this analysis is statis- tically limited.
Results from the time-dependent angular analysis are given in Table I. TheB0ddecay amplitudes and phases are of comparable precision and in agreement with results from BABAR [12] and Belle [13], and the lifetime is in
2) mass (GeV/c K-
K+
µ-
µ5.3+ 5.4 5.5 2 candidates per 5.0 MeV/c
0 20 40
60 Bs→ J/ψφ
± 15 Yield: 203
a
2) mass (GeV/c K-
K+
µ-
µ5.3+ 5.4 5.5 2 candidates per 5.0 MeV/c
0 20 40 60
2) mass (GeV/c π-
K+
µ-
µ+
5.20 5.25 5.30 5.35
2 candidates per 2.5 MeV/c
0 50 100 150
200 Bd→ J/ψ K*0
± 39 Yield: 1155
b
2) mass (GeV/c π-
K+
µ-
µ+
5.20 5.25 5.30 5.35
2 candidates per 2.5 MeV/c
0 50 100 150 200
FIG. 1. Mass distribution with the fit projection overlaid:
(a)B0s !J= ; (b)B0d!J= K0.
agreement with the world average value [1]. Previous results [11] for theB0s decay amplitudes, obtained from a time-integrated analysis, are in agreement with the results obtained in this analysis. Within uncertainties, the ampli- tudes for the B0s and B0d decays are in agreement, as is
expected in the limit of SU3 flavor symmetry [9].
Explicitly requiring exact SU3symmetry by setting the B0sdecay amplitudes to be equal to those of theB0dgives a consistent result fors=s within uncertainties.
It is predicted [3] that theB0dandB0s total decay widths should be equal to within 1%. This expectation can be used as a constraint in the B0s fit by requiring 1=s B0
s 2HL=HL B0
d 1=d, with cB0
d
460:84:2m, the known value for the B0d lifetime [1]
with an additional 1% uncertainty added in quadrature.
By applying this constraint in the fit, we find s=s 7124281% and s 0:460:170:18 0:01 ps1. Although the uncertainties are still sizable, the fits with and without the sd constraint favor a nonzero value fors=s.
Monte Carlo methods are employed to estimate the probability for an experiment with similar statistical sensi- tivity to yield s=s as large as is observed in this analysis. For the SM expectation, s=s12%, one experiment in 84 (204) would give a result larger than that obtained from the unconstrained (constrained) fit. If no lifetime difference were expected, s=s0, one experiment in 315 (718) would give a result larger than that obtained from the unconstrained (constrained) fit.
A lifetime difference should result in an increase of the fraction ofCP-oddB0s!J= decays obtained in a time- integrated angular fit as a function of a cut onct. The time- integrated CP-odd fraction extracted from fits for four values of the ct cut are shown in the second column of Table II. Using cL and cH obtained from the time- dependent fit and the observation that the time-integrated CP-odd fraction is 20% forct >0, one obtains expected fractions for the otherctcuts, shown in the third column in Table II, which are in agreement with the observations. The B0d!J= K0decays provide an important cross-check of the results obtained for theB0s !J= decays. Fits for the time-integrated fraction of parity-oddB0ddecays show, as
θ
-1 cos0 1
0 0.5
1 B0s→ J/ψφ
φ
0 0.1 0.2 0.3
π
- 0 π
φ ψ
→ J/
0
Bs
ψ
-1 cos0 1
0 0.5
1 B0s→ J/ψφ
θ
-1 cos0 1
0 0.5 1
K*0
ψ
→ J/
0
Bd
φ
0 0.1 0.2 0.3
π
- 0 π
K*0
ψ
→ J/
0
Bd
ψ
-1 cos0 1
0 0.5 1
K*0
ψ
→ J/
0
Bd
FIG. 3. Projections of the fit onto transversity variables for the mass-side- band-subtracted acceptance-corrected signal: B0s!J= (top row); B0d ! J= K0 (bottom row). A ct >0 cut is applied.
ct (cm)
0.0 0.1 0.2 0.3
mµcandidates per 50 1
10 102 103
φ ψ
→ J/
Bs
data fit all
L
fit Bs H
fit Bs
fit bkg.
ct (cm)
0.0 0.1 0.2 0.3
mµcandidates per 50 1
10 102 103
ct (cm)
0.0 0.1 0.2 0.3
mµcandidates per 50
1 10 102 103
104 Bd→ J/ψ K*0
data fit all fit sig.
fit bkg.
b
ct (cm)
0.0 0.1 0.2 0.3
mµcandidates per 50
1 10 102 103 104
FIG. 2. ctdistribution with the fit projection for the signal and background (bkg.) overlaid: (a)B0s!J= ; (b)B0d!J= K0.
101803-6
expected, that the fraction remains unchanged with respect to cuts onct(last column of Table II). In addition, a fit of theB0d data can be performed allowing two lifetime com- ponents. The results are consistent with no lifetime differ- ence for the full sample [= 1512%], as well as for independent subsamples having a statistical sensitivity similar to theB0s decay sample. This result is not a mea- surement of a lifetime difference in theB0d system, but is rather a cross-check of the analysis technique.
In conclusion, we have performed the first time- dependent angular analysis of B0s!J= decays and have performed a similar measurement with B0d ! J= K0decays. The measuredB0dpolarization amplitudes are of comparable precision to, and in agreement with,
previously published results. The measured B0s polariza- tion amplitudes are the most precise available. Analysis of the B0s!J= decays indicates a nonzero lifetime dif- ference between the heavy and light mass eigenstates of the B0ssystem. The result obtained, s=s 6525331%, has a central value larger than the SM expectation of 126%.
We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.
This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science, and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Founda- tion; the A. P. Sloan Foundation; the Bundesministerium fuer Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, U.K.; the Russian Foundation for Basic Research; the Comision Interministerial de Ciencia y Tecnologia, Spain; and in part by the European Community’s Human Potential Programme under Contract No. HPRN-CT-20002, Probe for New Physics.
[1] S. Eidelmanet al., Phys. Lett. B592, 1 (2004).
[2] A. Dighe, T. Hurth, C. Kim, and T. Yoshikawa, Nucl.
Phys.B624, 377 (2002).
[3] I. Bigi et al., in B Decays, edited by S. Stone (World Scientific, Singapore, 1994), 2nd ed.
[4] I. Dunietz, R. Fleischer, and U. Nierste, Phys. Rev. D63, 114015 (2001).
[5] M. Benekeet al., Phys. Lett. B459, 631 (1999).
[6] A. S. Dighe, I. Dunietz, H. J. Lipkin, and J. L. Rosner, Phys. Lett. B369, 144 (1996).
[7] CDF Collaboration, Fermilab Report No. FERMILAB- PUB-04-440-E, 2004.
[8] K. Anikeev, Ph.D. thesis, MIT (Institution Report No. FERMILAB-THESIS-2004-12, 2004).
[9] A. Dighe, I. Dunietz, and R. Fleischer, Eur. Phys. J. C6, 647 (1999).
[10] S. Pappas, Ph.D. thesis, Yale University (Institution Report No. FERMILAB-THESIS-1999-48, 1999).
[11] CDF Collaboration, T. Affolderet al., Phys. Rev. Lett.85, 4668 (2000).
[12] BABAR Collaboration, B. Aubertet al., Phys. Rev. Lett.
87, 241801 (2001).
[13] Belle Collaboration, K. Abeet al., Phys. Lett. B538, 11 (2002).
TABLE II. Time-integrated CP-odd B0s and parity-odd B0d fractions (in %) vs a cut on the decay length,ct.
ctcut B0s fitted B0s expected B0d fitted
>0m 209 20 (reference) 224
>150m 2410 24 234
>300m 3013 29 234
>450m 3912 34 245
TABLE I. Summary of the results of the time-dependent an- gular analysis of B0s !J= and B0d!J= K0 decays. A measurement of argA? is not possible for the B0s decays because the final state particles do not distinguish the decay of aB0sfrom that of aB0s. For theB0sdecays, any pair of quantities describing signal lifetimes (B0s 1=s,H, L,s=s, and s) may be used as free parameters in a fit; separate fits using different pairs are performed to obtain directly the results and asymmetric (statistical) uncertainties for each of the quantities.
B0s B0d
Nsig 20315 115539
A0 0:7840:0390:007 0:7500:0170:012 jAkj 0:5100:0820:013 0:4730:0340:006 jA?j 0:3540:0980:003 0:4640:0350:007 argAk 1:940:360:03 2:860:220:07
argA? 0:150:150:04
cB0
d 462156m
cB0s 41945386m cL 31648406m cH 6221751389m s=s 6525331%
s 0:470:190:240:01ps1
