Measurement of Time-Dependent
CP
Asymmetries and the
CP
-Odd Fraction
in the Decay
B
0
!
D
D
B. Aubert,
1
R. Barate,
1
D. Boutigny,
1
J.- M. Ga i l la rd ,
1
A. Hicheur,
1
Y. Karyotakis,
1
J. P. Lees,
1
P. Robbe,
1
V. Tisserand,
1
A. Zghiche,
1
A. Palano,
2
A. Pompili,
2
J. C. Chen,
3
N. D. Qi,
3
G. Rong,
3
P. Wang,
3
Y. S. Zhu,
3
G. Eigen,
4
I. Ofte,
4
B. Stugu,
4
G. S. Abrams,
5
A. W. Borgland,
5
A. B. Breon,
5
D. N. Brow n ,
5
J. Button-Shafer,
5
R. N. Cahn,
5
E. Charles,
5
C. T. Day,
5
M. S. Gill,
5
A.V. Gritsan,
5
Y. Groysman,
5
R. G. Jacobsen,
5
R. W. Kadel,
5
J. Kadyk,
5
L. T. Ker t h ,
5
Yu. G. Kolomensky,
5
J. F. K ra l ,
5
G. Kukartsev,
5
C. LeClerc,
5
M. E. L ev i ,
5
G. Lynch,
5
L. M. Mi r,
5
P. J. Oddone,
5
T. J. Orimoto,
5
M. Pripstein,
5
N. A. Ro e ,
5
A. Romosan,
5
M. T. Ronan,
5
V. G. Shelkov,
5
A. V. Tel nov,
5
W. A . We n z e l ,
5
K. Ford,
6
T. J. Harrison,
6
C. M. Hawkes,
6
D. J. Knowles,
6
S. E. Morgan,
6
R. C. Pen ny,
6
A. T. Watson,
6
N. K. Wat son ,
6
T. Deppermann,
7
K. Goetzen,
7
H. Koch,
7
B. Lewandowski,
7
M. Pelizaeus,
7
K. Peters,
7
H. Schmuecker,
7
M. Steinke,
7
N. R. Barlow,
8
J. T. Boyd,
8
N. Chevalier,
8
W. N. Cottingham,
8
M. P. Kel ly,
8
T. E . L a t h a m ,
8
C. Mackay,
8
F. F. Wilson,
8
K. Abe,
9
T. Cuhadar-Donszelmann,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
D. Thiessen,
9
P. Kyberd,
10
A. K. McKemey,
10
V. E. Blinov,
11
A. D. Bu k i n ,
11
V. B. Golubev,
11
V. N. Ivanchenko,
11
E. A. Kravchenko,
11
A. P. Onuchin,
11
S. I. Serednyakov,
11
Yu.I.Skovpen,
11
E. P. Solodov,
11
A. N. Yushkov,
11
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12
M. Chao,
12
D. Kirkby,
12
A. J. Lankford,
12
M. Mandelkern,
12
S. McMahon,
12
R. K. Mommsen,
12
W. Roethel,
12
D. P. Stoker,
12
C. Buchanan,
13
D. del Re,
14
H. K. Hadavand,
14
E. J. Hill,
14
D. B. MacFarlane,
14
H. P. Paa r,
14
Sh. Rahatlou,
14
U. Schwanke,
14
V. Sharma,
14
J.W. Berryhill,
15
C. Campagnari,
15
B. Dahmes,
15
N. Kuznetsova,
15
S. L. L ev y,
15
O. Long,
15
A. Lu,
15
M. A. Ma z u r,
15
J. D. Richman,
15
W. Verkerke,
15
T. W. Beck,
16
J. Beringer,
16
A. M. Eisner,
16
C. A. Heusch,
16
W. S. Lockman,
16
T. Schalk,
16
R. E. Schmitz,
16
B. A. Schumm,
16
A. Seiden,
16
M. Tu r r i ,
16
W. Wa l k o w i a k ,
16
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16
M. G. Wilson,
16
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17
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17
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17
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17
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U. Nauenberg,
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20
D. Altenburg,
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T. Brandt,
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J. Brose,
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T. Colberg,
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M. Dickopp,
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R. S. Dubitzky,
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A. Hauke,
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H. M. Lacker,
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E. Maly,
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R. Mu
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F. Muheim,
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V. Azzolini,
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D. Bettoni,
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C. Bozzi,
24
R. Calabrese,
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G. Cibinetto,
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E. Luppi,
24
M. Neg r i n i ,
24
L. Piemontese,
24
A. Sa r t i ,
24
E. Treadwell,
25
F. Anulli,
26,
*
R. Baldini-Ferroli,
26
A. Calcaterra,
26
R. de Sangro,
26
D. Falciai,
26
G. Finocchiaro,
26
P. Patteri,
26
I. M. Peruzzi,
26,
*
M. Piccolo,
26
A. Z a l lo ,
26
A. Buzzo,
27
R. Contri,
27
G. Crosetti,
27
M. Lo Vetere,
27
M. Macri,
27
M. R. Monge,
27
S. Passaggio,
27
F. C. Pastore,
27
C. Patrignani,
27
E. Robutti,
27
A. Santroni,
27
S. Tosi,
27
S. Bailey,
28
M. Morii,
28
W. Bhimji,
29
D. A. Bowerman,
29
P. D. Dauncey,
29
U. Egede,
29
I. Eschrich,
29
J. R. Gaillard,
29
G.W. Morton,
29
J. A. Nash,
29
P. Sanders,
29
G. P. Taylor,
29
G. J. Grenier,
30
S.-J. Lee,
30
U. Mallik,
30
J. Cochran,
30
H. B. Crawley,
31
J. L a m sa ,
31
W. T. Meyer,
31
S. Prell,
31
E. I. Rosenberg,
31
J. Yi ,
31
M. Davier,
32
G. Grosdidier,
32
A. Ho
̈
cker,
32
S. Laplace,
32
F. Le Diberder,
32
V. Lepeltier,
32
A. M. Lutz,
32
T. C. Petersen,
32
S. Plaszczynski,
32
M. H. Schune,
32
L. Tantot,
32
G. Wormser,
32
V. Brigljevic
́
,
33
C. H. Cheng,
33
D. J. Lange,
33
D. M. Wright,
33
A. J. Beva n ,
34
J. P. Coleman,
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J. R. F r y,
34
E. Gabathuler,
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M. Kay,
34
R. J. Parry,
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P. Strother,
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G. D. Lafferty,
38
A. J. Lyon,
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38
A. Farbin,
39
A. Jawahery,
39
D. Kovalskyi,
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C. K. L ae ,
39
V. L i l l a r d ,
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D. A. Roberts,
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40
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R. Kofler,
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47,†
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47,†
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C. Sciacca,
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M. A. Baak,
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51
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52
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52
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52
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A. Dorigo,
53
F. Galeazzi,
53
M. Margoni,
53
M. Morandin,
53
M. Posocco,
53
M. Rotondo,
53
PHYSICAL REVIEW LETTERS
week ending
26 SEPTEMBER 2003
V
OLUME
91, N
UMBER
13
131801-1
0031-9007
=
03
=
91(13)
=
131801(7)$20.00
2003 The American Physical Society
131801-1
F. Simonetto,
53
R. Stroili,
53
G. Tiozzo,
53
C. Voci,
53
M. Benayoun,
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`
re,
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54
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54
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54
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55
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55
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56
J. Panetta,
56
C. Angelini,
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G. Batignani,
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S. Bettarini,
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M. Bondioli,
57
F. Bucci,
57
G. Calderini,
57
M. Carpinelli,
57
F. F o r t i ,
57
M. A. Giorgi,
57
A. Lusiani,
57
G. Marchiori,
57
F. Martinez-Vidal,
57,‡
M. Morganti,
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N. Neri,
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70
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75
S. Dasu,
75
M. Datta,
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A. M. Eichenbaum,
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H. Hu,
75
J. R. Johnson,
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P. E. Kutter,
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75
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75
F. Di Lodovico,
75
A. Mihalyi,
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A. K. Mohapatra,
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75
S. J. Sekula,
75
J. H. von Wimmersperg-Toeller,
75
J. Wu,
75
S. L. Wu,
75
Z. Yu,
75
and H. Neal
76
(
BA BAR
Collaboration)
1
Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France
2
Universita
`
di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
3
Institute of High Energy Physics, Beijing 100039, China
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
University of Birmingham, Birmingham B15 2TT, United Kingdom
7
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
8
University of Bristol, Bristol BS8 1TL, United Kingdom
9
University of British Columbia, Vancouver, BC, Canada V6T 1Z1
10
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
12
University of California at Irvine, Irvine, California 92697, USA
13
University of California at Los Angeles, Los Angeles, California 90024, USA
14
University of California at San Diego, La Jolla, California 92093, USA
15
University of California at Santa Barbara, Santa Barbara, California 93106, USA
16
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
17
California Institute of Technology, Pasadena, California 91125, USA
18
University of Cincinnati, Cincinnati, Ohio 45221, USA
19
University of Colorado, Boulder, Colorado 80309, USA
20
Colorado State University, Fort Collins, Colorado 80523, USA
21
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
22
Ecole Polytechnique, LLR, F-91128 Palaiseau, France
23
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
24
Universita
`
di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
25
Florida A&M University, Tallahassee, Florida 32307, USA
26
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
PHYSICAL REVIEW LETTERS
week ending
26 SEPTEMBER 2003
V
OLUME
91, N
UMBER
13
131801-2
131801-2
27
Universita
`
di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
28
Harvard University, Cambridge, Massachusetts 02138, USA
29
Imperial College London, London SW7 2BW, United Kingdom
30
University of Iowa, Iowa City, Iowa 52242, USA
31
Iowa State University, Ames, Iowa 50011-3160, USA
32
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, F-91898 Orsay, France
33
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
34
University of Liverpool, Liverpool L69 3BX, United Kingdom
35
Queen Mary, University of London, E1 4NS, United Kingdom
36
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
37
University of Louisville, Louisville, Kentucky 40292, USA
38
University of Manchester, Manchester M13 9PL, United Kingdom
39
University of Maryland, College Park, Maryland 20742, USA
40
University of Massachusetts, Amherst, Massachusetts 01003, USA
41
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
42
McGill University, Montre
́
al, QC, Canada H3A 2T8
43
Universita
`
di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
44
University of Mississippi, University, Mississippi 38677, USA
45
Universite
́
de Montre
́
al, Laboratoire Rene
́
J. A. L e
́
vesque, Montre
́
al, QC, Canada H3C 3J7
46
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
47
Universita
`
di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
48
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
49
University of Notre Dame, Notre Dame, Indiana 46556, USA
50
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
51
The Ohio State University, Columbus, Ohio 43210, USA
52
University of Oregon, Eugene, Oregon 97403, USA
53
Universita
`
di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
54
Universite
́
s Paris VI et VII, Lab de Physique Nucle
́
aire H. E., F-75252 Paris, France
55
Universita
`
di Pavia, Dipartimento di Elettronica and INFN, I-27100 Pavia, Italy
56
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
57
Universita
`
di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
58
Prairie View A&M University, Prairie View, Texas 77446, USA
59
Princeton University, Princeton, New Jersey 08544, USA
60
Universita
`
di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
61
Universita
̈
t Rostock, D-18051 Rostock, Germany
62
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
63
DSM/ Dapnia, CEA /Saclay, F-91191 Gif-sur-Yvette, France
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Stanford Linear Accelerator Center, Stanford, California 94309, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
University of Tennessee, Knoxville, Tennessee 37996, USA
69
University of Texas at Austin, Austin, Texas 78712, USA
70
University of Texas at Dallas, Richardson, Texas 75083, USA
71
Universita
`
di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
72
Universita
`
di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
73
Vanderbilt University, Nashville, Tennessee 37235, USA
74
University of Victoria, Victoria, BC, Canada V8W 3P6
75
University of Wisconsin, Madison, Wisconsin 53706, USA
76
Yale University, New Haven, Connecticut 06511, USA
(Received 21 June 2003; published 26 September 2003)
We present a measurement of time-dependent
CP
asymmetries and an updated determination of the
CP
-odd fraction in the decay
B
0
!
D
D
using a data sample of
88
10
6
B
B
B
pairs collected by the
BA BAR
detector at the PEP-II
B
Factory at SLAC. We determine the
CP
-odd fraction to be
0
:
063
0
:
055
stat
0
:
009
syst
. The time-dependent
CP
asymmetry parameters
Im
and
j
j
are deter-
minedtobe
0
:
05
0
:
29
stat
0
:
10
syst
and
0
:
75
0
:
19
stat
0
:
02
syst
, respectively. The standard
model predicts these parameters to be
sin2
and 1, respectively, in the absence of penguin diagram
contributions.
DOI: 10.1103/PhysRevLett.91.131801
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh
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131801-3
The symmetry for combined charge conjugation (
C
)
and parity (
P
) transformations is violated in
B
decays.
Measurements of
CP
asymmetries by the
BA BAR
[1] and
BELLE [2] Collaborations established this effect and are
compatible with the standard model expectation based
on the current knowledge of the Cabibbo-Kobayashi-
Maskawa [3] quark-mixing matrix. As a result of the
interference between direct
B
decay and decay after
flavor change, a
CP
-violating asymmetry is expected in
the time evolution of the decays
B
0
!
D
D
[4] within
the framework of the standard model [5]. This
CP
asym-
metry is related to
sin2
when corrections due to theo-
retically uncertain penguin diagram contributions are
neglected [6,7]. Penguin-induced corrections are pre-
dicted to be small in models based on the factorization
approximation and heavy-quark symmetry; an effect of
about 2% is predicted by Ref. [8]. A comparison of
measurements of
sin2
from
b
!
c
c
cs
modes such as
B
0
!
J= K
0
S
[9] with that obtained in
B
0
!
D
D
is
an important test of these models and the standard model.
The
B
0
!
D
D
mode is a pseudoscalar decay to a
vector-vector final state, with contributions from three
partial waves with different
CP
parities: even for the
S
and
D
waves, odd for the
P
wave. The
CP
-odd contribu-
tion is predicted to be about 6% in Refs. [10,11]. We
present an updated [12] determination of the
CP
-odd
fraction,
R
?
, based on a one-dimensional time-integrated
angular analysis. We also present a measurement of the
time-dependent
CP
asymmetry, obtained from a com-
bined analysis of the time dependence of flavor-tagged
decays and the one-dimensional angular distribution of
the decay products. The data used in this analysis were
collected with the
BA BAR
detector at the PEP-II stor-
age ring. The
BA BAR
detector is described in detail else-
where [13]. The data sample corresponds to about
88
10
6
e
e
!
4
S
!
B
B
B
events.
B
0
mesons are exclusively reconstructed by com-
bining two charged
D
candidates reconstructed in
the modes
D
!
D
0
and
D
!
D
0
.Wein-
clude the
D
D
combinations
D
0
;
D
0
and
D
0
;D
0
, but not
D
0
;D
0
due to the smaller
branching fraction and larger backgrounds. Prior to form-
ing a
B
0
,the
D
candidates are subjected to a mass-
constrained fit and vertex fit that includes the position
of the beam spot.
The reconstructed
D
0
and
D
modes are
D
0
!
K
,
K
0
,
K
,
K
0
S
,and
D
!
K
,
K
0
S
,
K
K
. The reconstructed mass of the
D
0
(
D
)
candidates is required to be within
20 MeV
=
c
2
of the
nominal
D
0
(
D
) mass [14], except for
D
0
!
K
0
,
which has a looser requirement of
35 MeV
=
c
2
.The
D
candidates are subjected to a mass-constrained fit prior to
forming
D
candidates.
Charged kaon candidates are required to be inconsis-
tent with the pion hypothesis, as inferred from the
Cherenkov angle measured by the Cherenkov detector
and the specific ionization measured by the charged-
particle tracking system. No particle identification re-
quirements are made for the kaon from the decay
D
0
!
K
. The reconstructed mass of
K
0
S
!
candi-
dates is required to be within
25 MeV
=
c
2
of the nominal
K
0
S
mass. The angle between the flight direction and the
momentum vector of the
K
0
S
is required to be less than
200 mrad, and the transverse flight distance from the
primary event vertex must be greater than 2 mm. A
mass-constrained fit is applied to each
K
0
S
candidate.
Neutral pion candidates are formed from two photons
detected in the electromagnetic calorimeter, each with
energy above 30 MeV; the mass of the pair must be
within
20 MeV
=
c
2
of the nominal
0
mass, and their
summed energy must be greater than 200 MeV. A mass-
constrained fit is applied to these
0
candidates. The mass
of the
0
from
D
!
D
0
, however, is required to be
within
35 MeV
=
c
2
of the nominal
0
mass, and the
momentum in the
4
S
frame in the interval
70
<
j
p
j
<
450 MeV
=
c
, with no requirement on the photon
energy sum.
We construct a mass likelihood
L
Mass
that includes the
mass and mass uncertainty of the
D
and
D
candidates.
The
D
mass resolution is modeled by a Gaussian whose
variance is determined on a candidate-by-candidate basis.
The
D
-
D
mass difference resolution is modeled by a
double-Gaussian distribution whose parameters are deter-
mined from simulated events. The value of
L
Mass
is used
to select
B
0
candidates, with a different requirement used
for each
D
decay mode combination. In an event where
more than one
B
0
candidate is reconstructed, the candi-
date with the largest
L
Mass
value is chosen.
The primary variables used to distinguish signal from
background are the energy-substituted mass,
m
ES
E
2
Beam
p
2
B
q
, and the difference of the
B
candidate en-
ergy from the beam energy,
E
E
B
E
Beam
, where all
variables are evaluated in the
4
S
center-of-mass
frame. The
B
0
candidates are required to have
39
<
E<
31 MeV
and
m
ES
>
5
:
2 GeV
=
c
2
.
To reject backgrounds from the
e
e
!
c
c
continuum
process, events are required to have a ratio of second to
zeroth Fox-Wolfram moments [15] of less than 0.6. We
also require that the cosine of the angle between the
thrust axis of the reconstructed
B
and the thrust axis of
the rest of the event be less than 0.9.
After all selection criteria have been applied, a fit to the
m
ES
distribution using a Gaussian and an ARGUS func-
tion [16] for the signal and background, respectively,
results in a signal yield of
156
14
stat
events. In the
region
m
ES
>
5
:
27 GeV
=
c
2
, the signal purity is 73%.
We perform a one-dimensional angular analysis to
determine the fraction,
R
?
,ofthe
P
wave,
CP
-odd com-
ponent of the
B
0
!
D
D
decay. In the transversity
basis [5], the following three angles are defined: the angle
1
between the momentum of the slow pion from the
D
in the
D
rest frame and the direction of flight of the
D
in the
B
rest frame; the polar angle
tr
between the
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normal to the
D
decay plane and the direction of
flight of the slow pion from the
D
in the
D
rest
frame; and the corresponding azimuthal angle
tr
.The
time-dependent angular distribution of the decay prod-
ucts is given in Ref. [17].
The dependence of the detector efficiency on the
decay angles can introduce a bias in the measured
value of
R
?
. Including the efficiency explicitly in the
decay rate and then integrating over time and the angles
1
and
tr
results in the one-dimensional differential
decay rate:
1
d
d
cos
tr
9
32
1
R
?
sin
2
tr
1
2
I
0
cos
tr
1
2
I
k
cos
tr
2
R
?
cos
2
tr
I
?
cos
tr
;
(1)
where
R
?
M
2
?
=
M
2
0
M
2
k
M
2
?
,
M
2
0
M
2
k
=
M
2
0
M
2
k
,and
M
0
;M
k
;M
?
are the magnitudes of the
amplitudes in the transversity basis. The three efficiency
moments,
I
k
k
0
;
k
;
?
, are defined as
I
k
cos
tr
Z
d
cos
1
d
tr
g
k
1
;
tr
!
1
;
tr
;
tr
;
(2)
where
g
0
4cos
2
1
cos
2
tr
,
g
jj
2sin
2
1
sin
2
tr
,
g
?
sin
2
1
,and
!
is the detector efficiency. The efficiency
moments are determined using simulated events. The
efficiency moments are fit to second-order even polyno-
mials in
cos
tr
, the parameters of which are fixed in the
subsequent likelihood fit to the
cos
tr
distribution.
The measurement of
R
?
is based on a combined un-
binned maximum likelihood fit of the
cos
tr
and
m
ES
distributions. The probability density function (pdf ) for
the
m
ES
distribution is given by the sum of ARGUS and
Gaussian functions. The background shape is modeled by
an even second-order polynomial in
cos
tr
. The pdf used
for signal events is given by Eq. (1). The experimental
resolution of
tr
is not negligible and is accounted for by
convolving the signal pdf with a double Gaussian. Also,
the resolution of
tr
has significant tails caused by mis-
reconstructed events. The effect of these tails is ac-
counted for by an additional term in the signal pdf. The
parametrization of the
tr
resolution is determined from
simulations.
We categorize our events in three types:
D
D
!
D
0
;
D
0
,
D
0
;D
0
,and
D
0
;
D
0
be-
cause events with a neutral slow pion and events with a
charged slow pion have different background levels, de-
tection efficiencies, and
cos
tr
resolutions. Thus, the pa-
rameters determined in the likelihood fit are three signal
fractions, the
cos
tr
background shape parameter, three
m
ES
parameters (
"
and mean of the Gaussian, and
#
from
the ARGUS function), and
R
?
. The fit to the data set
yields a value of
R
?
0
:
063
0
:
055
stat
0
:
009
syst
:
(3)
Figure 1 shows the distribution of
cos
tr
for events in the
range
m
ES
>
5
:
27 GeV
=
c
2
. The value of
is fixed to zero
in the fit, incurring a (negligible) systematic uncertainty.
The largest systematic uncertainties arise from the para-
metrization of the angular resolution (0.005) and the de-
termination of the efficiency moments (0.005).
In addition to the time-independent measurement of
the
CP
-odd fraction, we perform a combined analysis of
the
cos
tr
distribution and the time dependence in order to
determine the time-dependent
CP
asymmetry, using the
sample of
B
0
!
D
D
events described previously. We
also use information from the other
B
meson in the event
to tag its flavor as either a
B
0
or
B
0
.
Although factorization models predict a small pen-
guin contamination in the weak phase difference in
Im
f
sin2
[8], a sizable penguin contribution
cannot
a priori
be excluded. Thus, the value of
f
%
CP
q=p
A
A
f
=A
f
[17] can be different for the three
transversity amplitudes (
f
?
;
0
;
k
) because of possible
different penguin-to-tree ratios. This possibility is explic-
itly included in the parametrization of the decay rates
described here.
The decay rate
F
F
for a neutral
B
meson tagged as
a
B
0
B
0
is given by
F
t
e
j
t
j
=*
B
0
4
*
B
0
G
1
1
2
D
D
S
sin
m
d
t
C
cos
m
d
t
;
(4)
where
t
t
rec
t
tag
is the difference between the proper
decay time of the reconstructed
B
meson (
B
rec
) and of the
tagging
B
meson (
B
tag
),
*
B
0
is the
B
0
lifetime, and
m
d
is
the mass difference determined from the
B
0
-
B
0
oscilla-
tion frequency. The dilution factor,
D
1
2
!
, where
)
tr
θ
cos(
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Events / ( 0.2 )
0
5
10
15
20
25
30
35
40
45
FIG. 1 (color online).
Measured distribution of
cos
tr
and
fi
t
results. The data points are from the region
m
ES
>
5
:
27 GeV
=
c
2
and the solid line is the projection of the
fi
t result
in the same region. The dotted line represents the background
component.
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!
is the average mistag fraction, describes the effect of incorrect tags, and
D
accounts for possible differences in the
mistag probabilities for
B
0
and
B
0
.The
G
,
C
,and
S
coef
fi
cients are de
fi
ned as
G
3
4
1
R
?
sin
2
tr
2
R
?
cos
2
tr
;C
3
4
1
R
?
1
j
j
2
1
j
j
2
sin
2
tr
2
R
?
1
j
?
j
2
1
j
?
j
2
cos
2
tr
;
S
3
4
1
R
?
2Im
1
j
j
2
sin
2
tr
2
R
?
2Im
?
1
j
?
j
2
cos
2
tr
:
(5)
Because the two
CP
-even transversity amplitudes pro-
duce the same distribution in
cos
tr
, we are sensitive only
to
, the appropriate average of
k
and
0
:
Im
1
j
j
2
Im
k
1
j
k
j
2
M
2
k
Im
0
1
j
0
j
2
M
2
0
M
2
k
M
2
0
;
1
j
j
2
1
j
j
2
1
j
k
j
2
1
j
k
j
2
M
2
k
1
j
0
j
2
1
j
0
j
2
M
2
0
M
2
k
M
2
0
:
(6)
If angular acceptance effects are not taken into account
and the
CP
-odd fraction is allowed to
fl
oat in the
fi
t, then
no bias is seen in the resulting value of
based on
simulations. Hence, a dedicated method to correct for de-
tector ef
fi
ciency is not required. The value of
R
?
obtained
is therefore an effective value, which is not identical to
the acceptance-corrected value from the time-integrated
measurement.
The time interval
t
is calculated from the measured
separation
z
between the decay vertex of the recon-
structed
B
meson and the vertex of the
fl
avor-tagging
B
meson along the collision axis. Events with a
t
un-
certainty
<
2
:
5ps
and a measured
j
t
j
<
20 ps
are ac-
cepted. The mistag fractions and
t
resolution functions
are determined from a sample of neutral
B
decays to
fl
avor eigenstates,
B
flav
,asinthe
sin2
measurement
using charmonium decays [9]. Vertex reconstruction, the
determination of
t
, and the algorithms used for the
determination of the
fl
avor of
B
tag
are described in
Refs. [9,18].
We determine the parameters
Im
and
j
j
with a
simultaneous unbinned maximum likelihood
fi
ttothe
t
distributions of the
B
rec
and
B
flav
tagged samples (Fig. 2).
The
t
distribution of the
B
flav
sample evolves according
to the known frequency for
fl
avor oscillations in neutral
B
mesons. The observed magnitude of the
CP
asymmetry
in the
B
rec
sample and the
fl
avor oscillation in the
B
flav
sample are reduced by the same factor
D
due to
fl
avor
mistags. The
t
distributions for the
B
rec
and
B
flav
samples are both convolved with a common
t
resolution
function. The
tr
angular resolution is accounted for in the
same way as described previously. Events are assigned
signal and background probabilities based on their
m
ES
values. Backgrounds are incorporated with an empirical
description of their
t
distributions, containing prompt
(zero lifetime) and nonprompt components convolved
with a separate resolution function [9].
A total of 38 parameters are varied in the
fi
t: the values
of
Im
and
j
j
(2), the effective
CP
-odd fraction (1),
the average mistag fraction
!
and the difference
!
between
B
0
and
B
0
mistags for each tagging category
(8), parameters for the signal
t
resolution (9), and
parameters for the background time dependence (7),
t
resolution (3), and mistag fractions (8). Because the
CP
-odd fraction is small, we have little sensitivity to
the parameters
j
?
j
and
Im
?
. Therefore they are
fi
xed
to 1.0 and
0
:
741
[9], respectively. These are the values
expected if direct
CP
violation and contributions from
penguin diagrams are neglected. The changes in the
fi
tted
values of
Im
and
j
j
for different input values of
Im
?
(varied between
1
:
0
and 1.0) and
j
?
j
(varied
between 0.7 and 1.3) are taken into account as systematic
uncertainties. The results obtained from the
fi
t (Fig. 2) are
Entries / 1 ps
B
0
tags
B
−
0
tags
∆
t (ps)
Raw Asymmetry
0
20
0
20
-1
0
1
-5
0
5
FIG. 2.
From top to bottom: Number
N
B
0
N
B
0
of candidate
events in the region
m
ES
>
5
:
27 GeV
=
c
2
with a
B
0
(
B
0
) tag, and
the raw asymmetry
N
B
0
N
B
0
=
N
B
0
N
B
0
, as functions of
t
. The solid curves represent the result of the combined
fi
tto
the full sample. The shaded regions represent the background
contributions.
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Im
0
:
05
0
:
29
stat
0
:
10
syst
;
(7)
j
j
0
:
75
0
:
19
stat
0
:
02
syst
:
(8)
The dominant sources of systematic uncertainty come
from the variation of the value of
?
[0.056 and 0.008,
respectively, for
Im
and
j
j
], and the level, com-
position, and
CP
asymmetry of the background (0.078
and 0.005).
If the
B
!
D
D
transition proceeds only through
the
b
!
c
c
cd
tree amplitude, we expect that
Im
sin2
and
j
j
1
. To test this hypothesis, we
fi
x
Im
0
:
741
[9] and
j
j
1
and repeat the
fi
t.
The observed change in the likelihood corresponds to
2.5 standard deviations (statistical uncertainty only).
In summary, we have reported a measurement of the
CP
-odd fraction and measurements of time-dependent
CP
asymmetries for the decay
B
0
!
D
D
. The mea-
surement of
R
?
supersedes the previous
BA BAR
result
[12], with a factor of 3 reduction in the statistical uncer-
tainty, and indicates that
B
0
!
D
D
is mostly
CP
even. The time-dependent asymmetries are found to dif-
fer slightly from standard model predictions with pen-
guin amplitudes ignored.
We are grateful for the excellent luminosity and ma-
chine conditions provided by our PEP-II colleagues and
for the substantial dedicated effort from the computing
organizations that support
BA BAR
. The collaborating in-
stitutions wish to thank SLAC for its support and kind
hospitality. This work is supported by the DOE and NSF
(USA), NSERC (Canada), IHEP (China), CEA and
CNRS-IN2P3 (France), BMBF and DFG (Germany),
INFN (Italy), FOM (The Netherlands), NFR (Norway),
MIST
(Russia),
and
PPARC
(United
Kingdom).
Individuals have received support from the A. P. Sloan
Foundation, the Research Corporation, and the Alexander
von Humboldt Foundation.
*Also with Universita
`
di Perugia, Perugia, Italy.
†
Also with Universita
`
della Basilicata, Potenza, Italy.
‡
Also with IFIC, Instituto de F
ı
́
sica Corpuscular, CSIC-
Universidad de Valencia, Valencia, Spain.
x
Deceased.
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PHYSICAL REVIEW LETTERS
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UMBER
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