arXiv:0810.0037v1 [hep-ex] 30 Sep 2008
Measurement of the angular and lifetime parameters of the decays
B
0d
→
J/ψK
∗0and
B
0
s
→
J/ψφ
V.M. Abazov36, B. Abbott75, M. Abolins65, B.S. Acharya29, M. Adams51, T. Adams49, E. Aguilo6, M. Ahsan59,
G.D. Alexeev36, G. Alkhazov40, A. Alton64,a, G. Alverson63, G.A. Alves2, M. Anastasoaie35, L.S. Ancu35,
T. Andeen53, B. Andrieu17, M.S. Anzelc53, M. Aoki50, Y. Arnoud14, M. Arov60, M. Arthaud18, A. Askew49,
B. ˚Asman41, A.C.S. Assis Jesus3, O. Atramentov49, C. Avila8, F. Badaud13, L. Bagby50, B. Baldin50,
D.V. Bandurin59, P. Banerjee29, S. Banerjee29, E. Barberis63, A.-F. Barfuss15, P. Bargassa80, P. Baringer58,
J. Barreto2, J.F. Bartlett50, U. Bassler18, D. Bauer43, S. Beale6, A. Bean58, M. Begalli3, M. Begel73,
C. Belanger-Champagne41, L. Bellantoni50, A. Bellavance50, J.A. Benitez65, S.B. Beri27, G. Bernardi17,
R. Bernhard23, I. Bertram42, M. Besan¸con18, R. Beuselinck43, V.A. Bezzubov39, P.C. Bhat50, V. Bhatnagar27,
C. Biscarat20, G. Blazey52, F. Blekman43, S. Blessing49, K. Bloom67, A. Boehnlein50, D. Boline62, T.A. Bolton59,
E.E. Boos38, G. Borissov42, T. Bose77, A. Brandt78, R. Brock65, G. Brooijmans70, A. Bross50, D. Brown81,
X.B. Bu7, N.J. Buchanan49, D. Buchholz53, M. Buehler81, V. Buescher22, V. Bunichev38, S. Burdin42,b,
T.H. Burnett82, C.P. Buszello43, J.M. Butler62, P. Calfayan25, S. Calvet16, J. Cammin71, M.A. Carrasco-Lizarraga33,
E. Carrera49, W. Carvalho3, B.C.K. Casey50, H. Castilla-Valdez33, S. Chakrabarti18, D. Chakraborty52,
K.M. Chan55, A. Chandra48, E. Cheu45, F. Chevallier14, D.K. Cho62, S. Choi32, B. Choudhary28, L. Christofek77,
T. Christoudias43, S. Cihangir50, D. Claes67, J. Clutter58, M. Cooke50, W.E. Cooper50, M. Corcoran80,
F. Couderc18, M.-C. Cousinou15, S. Cr´ep´e-Renaudin14, V. Cuplov59, D. Cutts77, M. ´Cwiok30, H. da Motta2,
A. Das45, G. Davies43, K. De78, S.J. de Jong35, E. De La Cruz-Burelo33, C. De Oliveira Martins3, K. DeVaughan67,
F. D´eliot18, M. Demarteau50, R. Demina71, D. Denisov50, S.P. Denisov39, S. Desai50, H.T. Diehl50, M. Diesburg50,
A. Dominguez67, T. Dorland82, A. Dubey28, L.V. Dudko38, L. Duflot16, S.R. Dugad29, D. Duggan49, A. Duperrin15,
J. Dyer65, A. Dyshkant52, M. Eads67, D. Edmunds65, J. Ellison48, V.D. Elvira50, Y. Enari77, S. Eno61,
P. Ermolov38,‡, H. Evans54, A. Evdokimov73, V.N. Evdokimov39, A.V. Ferapontov59, T. Ferbel71, F. Fiedler24,
F. Filthaut35, W. Fisher50, H.E. Fisk50, M. Fortner52, H. Fox42, S. Fu50, S. Fuess50, T. Gadfort70, C.F. Galea35,
C. Garcia71, A. Garcia-Bellido71, G.A. Garcia-Guerra33, V. Gavrilov37, P. Gay13, W. Geist19, W. Geng15,65,
C.E. Gerber51, Y. Gershtein49,c, D. Gillberg6, G. Ginther71, B. G´omez8, A. Goussiou82, P.D. Grannis72,
H. Greenlee50, Z.D. Greenwood60, E.M. Gregores4, G. Grenier20, Ph. Gris13, J.-F. Grivaz16, A. Grohsjean25, S. Gr¨unendahl50, M.W. Gr¨unewald30, F. Guo72, J. Guo72, G. Gutierrez50, P. Gutierrez75, A. Haas70, N.J. Hadley61,
P. Haefner25, S. Hagopian49, J. Haley68, I. Hall65, R.E. Hall47, L. Han7, K. Harder44, A. Harel71, J.M. Hauptman57,
J. Hays43, T. Hebbeker21, D. Hedin52, J.G. Hegeman34, A.P. Heinson48, U. Heintz62, C. Hensel22,d,
K. Herner72, G. Hesketh63, M.D. Hildreth55, R. Hirosky81, J.D. Hobbs72, B. Hoeneisen12, M. Hohlfeld22,
S. Hossain75, P. Houben34, Y. Hu72, Z. Hubacek10, V. Hynek9, I. Iashvili69, R. Illingworth50, A.S. Ito50,
S. Jabeen62, M. Jaffr´e16, S. Jain75, K. Jakobs23, C. Jarvis61, R. Jesik43, K. Johns45, C. Johnson70, M. Johnson50,
D. Johnston67, A. Jonckheere50, P. Jonsson43, A. Juste50, E. Kajfasz15, D. Karmanov38, P.A. Kasper50,
I. Katsanos70, D. Kau49, V. Kaushik78, R. Kehoe79, S. Kermiche15, N. Khalatyan50, A. Khanov76,
A. Kharchilava69, Y.M. Kharzheev36, D. Khatidze70, T.J. Kim31, M.H. Kirby53, M. Kirsch21, B. Klima50,
J.M. Kohli27, E.V. Komissarov36,‡, J.-P. Konrath23, A.V. Kozelov39, J. Kraus65, T. Kuhl24, A. Kumar69,
A. Kupco11, T. Kurˇca20, V.A. Kuzmin38, J. Kvita9, F. Lacroix13, D. Lam55, S. Lammers70, G. Landsberg77,
P. Lebrun20, W.M. Lee50, A. Leflat38, J. Lellouch17, J. Li78,‡, L. Li48, Q.Z. Li50, S.M. Lietti5, J.K. Lim31,
J.G.R. Lima52, D. Lincoln50, J. Linnemann65, V.V. Lipaev39, R. Lipton50, Y. Liu7, Z. Liu6, A. Lobodenko40,
M. Lokajicek11, P. Love42, H.J. Lubatti82, R. Luna-Garcia33,e, A.L. Lyon50, A.K.A. Maciel2, D. Mackin80, R.J. Madaras46, P. M¨attig26, C. Magass21, A. Magerkurth64, P.K. Mal82, H.B. Malbouisson3, S. Malik67,
V.L. Malyshev36, Y. Maravin59, B. Martin14, R. McCarthy72, M.M. Meijer35, A. Melnitchouk66, L. Mendoza8,
P.G. Mercadante5, M. Merkin38, K.W. Merritt50, A. Meyer21, J. Meyer22,d, J. Mitrevski70, R.K. Mommsen44,
N.K. Mondal29, R.W. Moore6, T. Moulik58, G.S. Muanza15, M. Mulhearn70, O. Mundal22, L. Mundim3,
E. Nagy15, M. Naimuddin50, M. Narain77, N.A. Naumann35, H.A. Neal64, J.P. Negret8, P. Neustroev40, H. Nilsen23, H. Nogima3, S.F. Novaes5, T. Nunnemann25, V. O’Dell50, D.C. O’Neil6, G. Obrant40, C. Ochando16,
D. Onoprienko59, N. Oshima50, N. Osman43, J. Osta55, R. Otec10, G.J. Otero y Garz´on50, M. Owen44, P. Padley80,
G. Pawloski80, B. Penning23, M. Perfilov38, K. Peters44, Y. Peters26, P. P´etroff16, M. Petteni43, R. Piegaia1,
J. Piper65, M.-A. Pleier22, P.L.M. Podesta-Lerma33,f, V.M. Podstavkov50, Y. Pogorelov55, M.-E. Pol2, P. Polozov37,
B.G. Pope65, A.V. Popov39, C. Potter6, W.L. Prado da Silva3, H.B. Prosper49, S. Protopopescu73, J. Qian64,
A. Quadt22,d, B. Quinn66, A. Rakitine42, M.S. Rangel2, K. Ranjan28, P.N. Ratoff42, P. Renkel79, P. Rich44,
M. Rijssenbeek72, I. Ripp-Baudot19, F. Rizatdinova76, S. Robinson43, R.F. Rodrigues3, M. Rominsky75, C. Royon18,
P. Rubinov50, R. Ruchti55, G. Safronov37, G. Sajot14, A. S´anchez-Hern´andez33, M.P. Sanders17, B. Sanghi50,
G. Savage50, L. Sawyer60, T. Scanlon43, D. Schaile25, R.D. Schamberger72, Y. Scheglov40, H. Schellman53,
T. Schliephake26, S. Schlobohm82, C. Schwanenberger44, A. Schwartzman68, R. Schwienhorst65, J. Sekaric49,
H. Severini75, E. Shabalina51, M. Shamim59, V. Shary18, A.A. Shchukin39, R.K. Shivpuri28, V. Siccardi19,
V. Simak10, V. Sirotenko50, P. Skubic75, P. Slattery71, D. Smirnov55, G.R. Snow67, J. Snow74, S. Snyder73,
S. S¨oldner-Rembold44, L. Sonnenschein17, A. Sopczak42, M. Sosebee78, K. Soustruznik9, B. Spurlock78, J. Stark14,
V. Stolin37, D.A. Stoyanova39, J. Strandberg64, S. Strandberg41, M.A. Strang69, E. Strauss72, M. Strauss75, R. Str¨ohmer25, D. Strom53, L. Stutte50, S. Sumowidagdo49, P. Svoisky35, A. Sznajder3, A. Tanasijczuk1,
W. Taylor6, B. Tiller25, F. Tissandier13, M. Titov18, V.V. Tokmenin36, I. Torchiani23, D. Tsybychev72,
B. Tuchming18, C. Tully68, P.M. Tuts70, R. Unalan65, L. Uvarov40, S. Uvarov40, S. Uzunyan52, B. Vachon6,
P.J. van den Berg34, R. Van Kooten54, W.M. van Leeuwen34, N. Varelas51, E.W. Varnes45, I.A. Vasilyev39,
P. Verdier20, L.S. Vertogradov36, M. Verzocchi50, D. Vilanova18, F. Villeneuve-Seguier43, P. Vint43,
P. Vokac10, M. Voutilainen67,g, R. Wagner68, H.D. Wahl49, M.H.L.S. Wang50, J. Warchol55, G. Watts82,
M. Wayne55, G. Weber24, M. Weber50,h, L. Welty-Rieger54, A. Wenger23,i, N. Wermes22, M. Wetstein61,
A. White78, D. Wicke26, M. Williams42, G.W. Wilson58, S.J. Wimpenny48, M. Wobisch60, D.R. Wood63,
T.R. Wyatt44, Y. Xie77, C. Xu64, S. Yacoob53, R. Yamada50, W.-C. Yang44, T. Yasuda50, Y.A. Yatsunenko36,
H. Yin7, K. Yip73, H.D. Yoo77, S.W. Youn53, J. Yu78, C. Zeitnitz26, S. Zelitch81, T. Zhao82, B. Zhou64,
J. Zhu72, M. Zielinski71, D. Zieminska54, A. Zieminski54,‡, L. Zivkovic70, V. Zutshi52, and E.G. Zverev38
(The DØ Collaboration)
1Universidad de Buenos Aires, Buenos Aires, Argentina
2
LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil
3
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
4Universidade Federal do ABC, Santo Andr´e, Brazil
5
Instituto de F´ısica Te´orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil
6
University of Alberta, Edmonton, Alberta, Canada, Simon Fraser University, Burnaby, British Columbia, Canada, York University, Toronto, Ontario, Canada, and McGill University, Montreal, Quebec, Canada
7
University of Science and Technology of China, Hefei, People’s Republic of China
8Universidad de los Andes, Bogot´a, Colombia
9
Center for Particle Physics, Charles University, Prague, Czech Republic
10
Czech Technical University, Prague, Czech Republic
11Center for Particle Physics, Institute of Physics,
Academy of Sciences of the Czech Republic, Prague, Czech Republic
12
Universidad San Francisco de Quito, Quito, Ecuador
13LPC, Universit´e Blaise Pascal, CNRS/IN2P3, Clermont, France
14
LPSC, Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France
15CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France
16
LAL, Universit´e Paris-Sud, IN2P3/CNRS, Orsay, France
17
LPNHE, IN2P3/CNRS, Universit´es Paris VI and VII, Paris, France
18
CEA, Irfu, SPP, Saclay, France
19IPHC, Universit´e Louis Pasteur, CNRS/IN2P3, Strasbourg, France
20
IPNL, Universit´e Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universit´e de Lyon, Lyon, France
21
III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
22Physikalisches Institut, Universit¨at Bonn, Bonn, Germany
23
Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany
24
Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany
25Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany
26
Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
27
Panjab University, Chandigarh, India
29
Tata Institute of Fundamental Research, Mumbai, India
30
University College Dublin, Dublin, Ireland
31Korea Detector Laboratory, Korea University, Seoul, Korea
32
SungKyunKwan University, Suwon, Korea
33
CINVESTAV, Mexico City, Mexico
34FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands
35
Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands
36
Joint Institute for Nuclear Research, Dubna, Russia
37Institute for Theoretical and Experimental Physics, Moscow, Russia
38Moscow State University, Moscow, Russia
39
Institute for High Energy Physics, Protvino, Russia
40
Petersburg Nuclear Physics Institute, St. Petersburg, Russia
41Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University,
Stockholm, Sweden, and Uppsala University, Uppsala, Sweden
42
Lancaster University, Lancaster, United Kingdom
43Imperial College, London, United Kingdom
44
University of Manchester, Manchester, United Kingdom
45
University of Arizona, Tucson, Arizona 85721, USA
46Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
47
California State University, Fresno, California 93740, USA
48
University of California, Riverside, California 92521, USA
49
Florida State University, Tallahassee, Florida 32306, USA
50
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
51
University of Illinois at Chicago, Chicago, Illinois 60607, USA
52
Northern Illinois University, DeKalb, Illinois 60115, USA
53Northwestern University, Evanston, Illinois 60208, USA
54
Indiana University, Bloomington, Indiana 47405, USA
55
University of Notre Dame, Notre Dame, Indiana 46556, USA
56Purdue University Calumet, Hammond, Indiana 46323, USA
57
Iowa State University, Ames, Iowa 50011, USA
58
University of Kansas, Lawrence, Kansas 66045, USA
59Kansas State University, Manhattan, Kansas 66506, USA
60
Louisiana Tech University, Ruston, Louisiana 71272, USA
61
University of Maryland, College Park, Maryland 20742, USA
62Boston University, Boston, Massachusetts 02215, USA
63
Northeastern University, Boston, Massachusetts 02115, USA
64
University of Michigan, Ann Arbor, Michigan 48109, USA
65Michigan State University, East Lansing, Michigan 48824, USA
66University of Mississippi, University, Mississippi 38677, USA
67
University of Nebraska, Lincoln, Nebraska 68588, USA
68
Princeton University, Princeton, New Jersey 08544, USA
69State University of New York, Buffalo, New York 14260, USA
70
Columbia University, New York, New York 10027, USA
71
University of Rochester, Rochester, New York 14627, USA
72State University of New York, Stony Brook, New York 11794, USA
73
Brookhaven National Laboratory, Upton, New York 11973, USA
74
Langston University, Langston, Oklahoma 73050, USA
75University of Oklahoma, Norman, Oklahoma 73019, USA
76Oklahoma State University, Stillwater, Oklahoma 74078, USA
77
Brown University, Providence, Rhode Island 02912, USA
78
University of Texas, Arlington, Texas 76019, USA
79Southern Methodist University, Dallas, Texas 75275, USA
80
Rice University, Houston, Texas 77005, USA
81
University of Virginia, Charlottesville, Virginia 22901, USA and
82University of Washington, Seattle, Washington 98195, USA
(Dated: September 30, 2008)
We present measurements of the linear polarization amplitudes and the strong relative phases
that describe the flavor-untagged decays B0
d→ J/ψK
∗0 and B0
s → J/ψφ in the transversity basis.
We also measure the mean lifetime ¯τs of the Bs0 mass eigenstates and the lifetime ratio ¯τs/τd. The
analyses are based on approximately 2.8 fb−1 of data recorded with the D0 detector. From our
measurements of the angular parameters we conclude that there is no evidence for a deviation from flavor SU(3) symmetry for these decays and that the factorization assumption is not valid for the
B0
PACS numbers: 14.20.Mr, 14.40.Nd, 13.30.Eg, 13.25.Hw
B mesons are fertile ground to study CP violation and search for evidence of new physics. There are elements, in addition to CP violation, involved in the theoretical de-scription of B meson decays, such as flavor SU(3) symme-try, factorization and final-state strong interactions. To understand the role CP violation plays in these decays, it is essential to understand and isolate the effect of each of these elements in the B meson decays.
Factorization states that the decay amplitude of B meson decays can be expressed as the product of two single current matrix elements [1] and this implies that the relative strong phases are 0 (mod π) [2]. A different measured value for the strong phases would indicate the presence of final-state strong interactions. The B0
dmeson
can be formed by replacing the s quark with the d quark in the B0
s meson. From flavor SU(3) symmetry applied
to the B0
d-Bs0 system one expects that the theoretical
description is similar; in particular the B0
d → J/ψK∗0
and B0
s → J/ψφ [3] decays, can be described in the
transversity basis [2] by the linear polarization ampli-tudes, A0, Ak, and A⊥, and the relative strong phases δ1
and δ2. Flavor SU(3) symmetry requires that the
ampli-tudes and phases characterizing these decays should have the same values.
Other observables of these decays are the lifetimes of both mesons, which allow us to compare with theoretical predictions of the lifetime ratio. Phenomenological mod-els predict differences of about 1% [4, 5] between the Bd0
and Bs0 lifetimes. Previous B meson lifetime
measure-ments [6] are consistent with these predictions.
In this Letter we report the measurements of the pa-rameters that describe the time-dependent angular dis-tributions of the decays B0
d → J/ψK∗0and Bs0→ J/ψφ
in the transversity basis, where the initial B meson fla-vor is not determined (“untagged”). We study the B0 d
and B0
s mesons to verify the validity of the factorization
assumption [2] and to check if flavor SU(3) symmetry [2] holds for these decays. We also report the lifetime ra-tio ¯τs/τd for these mesons and the width difference ∆Γs
between the light and heavy B0
s mass eigenstates. The
analyses were performed using data collected with the D0 detector [7] in Run II of the Fermilab Tevatron Collider during 2003 − 2007 with an integrated luminosity of ap-proximately 2.8 fb−1 of p¯p collisions at a center-of-mass energy of 1.96 TeV. In contrast with the flavor-tagged analysis reported in Ref. [8], in this Letter we report a simultaneous analysis of both the B0
d and Bs0 meson
de-cays, carried out in such a way that a straightforward comparison between their angular and lifetime parame-ters can be performed.
We use the B0
s → J/ψφ, J/ψ → µ+µ−, φ → K+K−
selection described in Ref. [9]. The decay B0
d→ J/ψK∗0,
J/ψ → µ+µ−, K∗0 → K±π∓ is reconstructed using
similar selection criteria and algorithms as the B0 s
chan-nel because they have the same four-track topology in the final state. The differences are the requirement that the transverse momentum of the pion be greater than 0.7 GeV/c, the invariant mass for the (J/ψ, K∗0(892))
pair be in the range 4.93 − 5.61 GeV/c2, and the
se-lection of the K∗0(892) candidates by demanding the
two-particle invariant mass between 850 MeV/c2 and
930 MeV/c2. Due to lack of charged particle
identifi-cation, we assign the mass of the pion and kaon to the latter two tracks and use the combination with invariant mass closest to the K∗0mass.
The proper decay length (PDL), defined as in Refs. [10, 11], for a given B0
dor Bs0candidate is determined by
mea-suring the distance traveled by each b-hadron candidate in a plane transverse to the beam direction, and then applying a Lorentz boost correction. In the B0
d and B0s
final selection, we require a PDL uncertainty of less than 60 µm. We find 334199 and 41691 candidates that pass the B0
d and Bs0selection criteria, respectively (see Fig. 1).
We denote the set of the angular variables defined in the transversity basis, where the decays B0
d → J/ψK∗0
and B0
s → J/ψφ are studied, as ω = {ϕ, cos θ, cos ψ}.
The description of these decays in this basis gives us ac-cess to the three linear polarization amplitudes at pro-duction time, t = 0, |A0(0)|, |Ak(0)|, and |A⊥(0)|,
satisfy-ing |A0|2+ |Ak|2+ |A⊥|2= 1 [12]; and the CP-conserving
strong phases δ1 ≡ arg[A∗kA⊥], and δ2 ≡ arg[A∗0A⊥].
Since only the relative phases of the amplitudes can enter physics observables, we are free to fix the phase of one of them, and we choose to fix δ0≡ arg(A0) = 0.
According to the standard model, CP-violation effects in the B0
s system are very small [13]. In this analysis,
we assume CP conservation and express the differential decay rate for the untagged decay B0
s→ J/ψφ as [2]:
d4P/ (dω dt) ∝ e−ΓLt|A
0|2f1(ω) + Re(A∗0Ak)f5(ω)
+ |Ak|2f2(ω) + e−ΓHt|A⊥|2f3(ω), (1)
where ΓL(H)≡ 1/τL(H)is the inverse of the lifetime
corre-sponding to the light (heavy) mass eigenstate. The mea-sured parameters, the width difference ∆Γs≡ ΓL− ΓH
and the mean lifetime ¯τs ≡ 1/¯Γ = 2/ (ΓL+ ΓH), are
given in terms of these inverse lifetimes. The angular functions fi(ω) are defined in Ref. [2]. In this decay, we
have access to the phase δk= arg(A∗0Ak), which is related
to δ1 and δ2by δk= δ2− δ1.
In the Bd0system, there is evidence of interference
be-tween the P - and S-wave Kπ amplitudes [14], which is taken into account in this analysis. The differential de-cay rate for the untagged dede-cay B0
d → J/ψK∗0 is given
by [2, 14]:
d4P/ (dω dt) ∝ e−Γdtcos2λ|A
+ |A⊥|2f3(ω) − ζ Im(A∗kA⊥)f4(ω) + Re(A∗0Ak)f5(ω) + ζ Im(A∗0A⊥)f6(ω) + sin2λ · f7(ω) + 1 2sin 2λf8(ω) cos δk− δs |Ak| + f9(ω) sin (δ⊥− δs) |A⊥| + f10(ω) cos δs· |A0|]} , (2)
where Γd ≡ 1/τd is the inverse of the Bd0 lifetime, ζ =
+1(ζ = −1) for K+(K−); λ, δs, and fi(ω) are defined in
Refs. [2, 14]. For the B0
d, ∆Γdis expected to be zero [13].
An unbinned likelihood fit is performed to extract all the B0
d and Bs0 parameters. For the jth B meson
can-didate, the inputs for the fit are the mass mj, PDL
ctj, PDL uncertainty σctj, and the angular variables ωj. The likelihood function L for the untagged decays
B0 d → J/ψK∗0and B0s→ J/ψφ, is defined by L = QN j=1 h fsFsj+ (1 − fs)Fbj i , (3)
where N is the total number of selected events and fs is
the fraction of signal events in the sample, a free param-eter in the fit.
Fsis the product of the signal probability distribution
functions (PDF) of mass, PDL, and transversity angles, and the angular acceptances, which are determined via Monte Carlo simulations. The mass and PDL signal dis-tributions are modeled for both decays in the same way. The mass distribution is modeled by a Gaussian func-tion with free mean and width. The PDL distribufunc-tion is described [10] by the convolution of an exponential, whose decay constant is one of the fit parameters with a resolution function represented by two weighted Gaus-sian functions centered at zero. The widths siσctj of each Gaussian with scale factors si(i = 1, 2) are free
param-eters in the fit to allow for a possible misestimate of the PDL uncertainty. The transversity angular distributions are modeled by the corresponding normalized Eqs. (1) and (2). The contribution where the mass of the K and π are misassigned in our data is estimated by using Monte Carlo studies to be about 13% and is taken into account. Fb is the product of the background PDF of the same
variables and the angular acceptance as in the signal. We separate the background contributions into two types. The prompt background accounts for directly produced J/ψ mesons combined with random tracks. Non-prompt background is due to J/ψ mesons produced by a b hadron decay combined with tracks that come from either a multibody decay of the same b hadron or from hadroniza-tion. The mass distribution for the background is mod-eled by two independent normalized negative-slope ex-ponentials, one for the prompt and one for the non-prompt contributions. The PDL distribution for the prompt background is parameterized by the resolution function described above. The PDL distribution for the
non-prompt background is modeled by a sum of two ex-ponential components for positive ct and one for negative ct that account for a mix of heavy flavor meson decays and their possible misreconstruction. The angular distri-butions for the background components are modeled by a shape similar to that of the signal, but with an inde-pendent set of amplitudes and phases.
The results of our measurements are summarized in Table I. Figures 1 and 2 show the mass and the PDL distributions for the B0
d and Bs0candidates, respectively,
with the projected results of the fits. The parameters with the strongest correlations are the linear amplitudes for the B0
d, and the width difference and the mean lifetime
for the B0 s.
TABLE I: Summary of measurements for the decays B0
d →
J/ψK∗0 and B0
s → J/ψφ. The uncertainties are only
statis-tical. Parameter B0 d B 0 s Units |A0|2 0.587 ± 0.011 0.555 ± 0.027 − |Ak|2 0.230 ± 0.013 0.244 ± 0.032 − δ1 −0.38 ± 0.06 − rad δ2 3.21 ± 0.06 − rad δk − 2.72+1.12−0.27 rad τ 1.414 ± 0.018 1.487 ± 0.060 ps ∆Γs − 0.085+0.072−0.078 ps−1 Nsig 11195 ± 167 1926 ± 62 −
Table II summarizes the systematic uncertainties in our measurements for B0
d and Bs0 decays. To study the
systematic uncertainty due to the model for the mass dis-tributions, we vary the shapes of the mass distributions for background by using two normalized first-order poly-nomials instead of the nominal two negative exponentials. We estimate the systematic uncertainty due to the res-olution on the PDL by using one Gaussian function for the resolution model. The fitting code is tested for the presence of biases by generating 1300 pseudo-experiments for B0
d and 1000 for Bs0, each with the same statistics as
our data samples. We generated the events following the PDL, mass, and transversity angular distributions de-scribed above. The differences between the input and output values are quoted as the systematic uncertainty due to the fitting. The systematic uncertainty for δk
re-ported for this source is due to an intrinsic ambiguity for this parameter in Eq. (1). The pseudo-experiments produced also cover the other solution for δk. The
contri-bution from the detector alignment uncertainty is taken from Ref. [11]. Other potential sources of systematic uncertainties have been investigated and found to give negligible variations in the measured parameters. The systematic uncertainties for the ratio ¯τs/τd are obtained
by finding the ratio of the lifetimes for each systematic variation on Table II and taking the difference between this value and the nominal ratio.
TABLE II: Summary of systematic uncertainties in the measurement of angular and lifetime parameters. The total uncertainties are given combining individual uncertainties in quadrature.
B0
d B
0 s
Source |A0|2 |Ak|2 δ1 (rad) δ2 (rad) τd(ps) |A0|2 |Ak|2 δk(rad) ∆Γs (ps−1) τ¯s (ps) ¯τs/τd
Mass background − 0.024 0.09 0.05 0.030 0.004 0.002 0.02 − 0.021 0.009 PDL resolution 0.013 0.008 0.02 0.03 0.013 0.005 0.003 − − 0.016 0.012 Fitting code 0.001 − − − 0.004 0.004 0.014 0.26 0.001 0.008 0.003 Alignment − − − − 0.007 − − − − 0.007 − Total 0.013 0.025 0.09 0.06 0.034 0.006 0.014 0.26 0.001 0.028 0.015 ) 2 Mass (GeV/c 5 5.1 5.2 5.3 5.4 5.5 5.6 2
Events per 9 MeV/c
0 1000 2000 3000 4000 5000 ) 2 Mass (GeV/c 5 5.1 5.2 5.3 5.4 5.5 5.6 2
Events per 9 MeV/c
0 1000 2000 3000 4000 5000 Total fit Prompt background Non prompt background
-1 D0, 2.8 fb (a) ) 2 Mass (GeV/c 5.1 5.2 5.3 5.4 5.5 5.6 5.7 2
Events per 9 MeV/c
0 100 200 300 400 500 600 700 800 ) 2 Mass (GeV/c 5.1 5.2 5.3 5.4 5.5 5.6 5.7 2
Events per 9 MeV/c
0 100 200 300 400 500 600 700 800 -1 D0, 2.8 fb Total Fit Prompt background Non prompt background (b)
FIG. 1: Invariant mass distribution for selected (a) B0
d and
(b) B0
scandidate events. The points with error bars represent
the data, and the curves represent the fit projections for the total and the background components.
In conclusion, we have measured the angular and lifetime parameters for the time-dependent angular un-tagged decays B0
d → J/ψK∗0 and Bs0 → J/ψφ, the
lifetime ratio of both B mesons, and the width differ-ence ∆Γs for the Bs0 meson. From the measured
life-time parameters ¯τs and τd we obtain the ratio ¯τs/τd =
1.052 ± 0.061 (stat) ± 0.015 (syst) which is consistent with the theoretical prediction [5] and previous mea-surements [6]. The measurement of the width difference ∆Γs= 0.085+0.072−0.078(stat) ± 0.006 (syst) ps−1is consistent
with the theoretical prediction [5, 13] and with the value reported in Refs. [6, 16]. D0 also has a measurement of ∆Γsin a flavor-tagged analysis of B0s→ J/ψφ in Ref. [8].
Our measurements for the linear polarization
am-ct (cm) -0.1-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Events per 0.007 cm 1 10 2 10 3 10 4 10 5 10 ct (cm) -0.1-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Events per 0.007 cm 1 10 2 10 3 10 4 10 5 10 -1 D0, 2.8 fb (a) Total fit Signal Background ct (cm) -0.1-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Events per 0.005 cm 1 10 2 10 3 10 4 10 ct (cm) -0.1-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Events per 0.005 cm 1 10 2 10 3 10 4 10 Total fit L τ c H τ c Background -1 D0, 2.8 fb (b)
FIG. 2: PDL distribution for selected (a) B0
d and (b) B
0 s
candidate events. The points with error bars represent the data, and the curves represent the fit projections for the total, signal, and background components.
plitudes for the B0
d, taking into account the
inter-ference between the Kπ S-wave and P -wave, are |A0|2 = 0.587 ± 0.011 (stat) ± 0.013 (syst) and |Ak|2 =
0.230 ± 0.013 (stat) ± 0.025 (syst); and for B0
s: |A0|2 =
0.555 ± 0.027 (stat) ± 0.006 (syst), and |Ak|2 = 0.244 ±
0.032 (stat) ± 0.014 (syst) are consistent and competitive with those reported in the literature [6, 14, 15]. Our mea-surement of the strong phases δ1 and δ2 indicates the
presence of final-state interactions for the decay B0
d →
J/ψK∗0[2] since δ
1= −0.38±0.06 (stat)±0.09 (syst) rad
is 3.5σ away from zero, where σ is the total uncertainty. From the comparison of the measured amplitudes and strong phases [17] for both decays we conclude that they are consistent with being equal for B0
there is no evidence for a deviation from flavor SU(3) symmetry. In our sample we find that the Kπ S-wave intensity, as described in Ref. [14], is (4.0 ± 1.0)%.
We thank the staffs at Fermilab and collaborating institutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); STFC (United Kingdom); MSMT and GACR (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); CAS and CNSF (China); and the Alexander von Humboldt Foundation (Ger-many).
[a] Visitor from Augustana College, Sioux Falls, SD, USA. [b] Visitor from The University of Liverpool, Liverpool, UK.
[c] Visitor from Rutgers University, Piscataway, NJ, USA. [d] Visitor from II. Physikalisches Institut,
Georg-August-University, G¨ottingen, Germany.
[e] Visitor from Centro de Investigacion en Computacion -IPN, Mexico City, Mexico.
[f] Visitor from ECFM, Universidad Autonoma de Sinaloa,
Culiac´an, Mexico.
[g] Visitor from Helsinki Institute of Physics, Helsinki, Fin-land.
[h] Visitor from Universit¨at Bern, Bern, Switzerland.
[i] Visitor from Universit¨at Z¨urich, Z¨urich, Switzerland.
[‡] Deceased.
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[17] Using the relation between these phases we obtain
δk,B0
