of 13
Measurements of time-dependent
CP
asymmetries in
B
0
!
D
ðÞþ
D
ðÞ
decays
B. Aubert,
1
M. Bona,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
X. Prudent,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
L. Lopez,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
G. S. Abrams,
5
M. Battaglia,
5
D. N. Brown,
5
R. N. Cahn,
5
R. G. Jacobsen,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
5
M. T. Ronan,
5
K. Tackmann,
5
T. Tanabe,
5
C. M. Hawkes,
6
N. Soni,
6
A. T. Watson,
6
H. Koch,
7
T. Schroeder,
7
D. Walker,
8
D. J. Asgeirsson,
9
B. G. Fulsom,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
M. Barrett,
10
A. Khan,
10
V. E. Blinov,
11
A. D. Bukin,
11
A. R. Buzykaev,
11
V. P. Druzhinin,
11
V. B. Golubev,
11
A. P. Onuchin,
11
S. I. Serednyakov,
11
Yu. I. Skovpen,
11
E. P. Solodov,
11
K. Yu. Todyshev,
11
M. Bondioli,
12
S. Curry,
12
I. Eschrich,
12
D. Kirkby,
12
A. J. Lankford,
12
P. Lund,
12
M. Mandelkern,
12
E. C. Martin,
12
D. P. Stoker,
12
S. Abachi,
13
C. Buchanan,
13
J. W. Gary,
14
F. Liu,
14
O. Long,
14
B. C. Shen,
14,
*
G. M. Vitug,
14
Z. Yasin,
14
L. Zhang,
14
V. Sharma,
15
C. Campagnari,
16
T. M. Hong,
16
D. Kovalskyi,
16
M. A. Mazur,
16
J. D. Richman,
16
T. W. Beck,
17
A. M. Eisner,
17
C. J. Flacco,
17
C. A. Heusch,
17
J. Kroseberg,
17
W. S. Lockman,
17
A. J. Martinez,
17
T. Schalk,
17
B. A. Schumm,
17
A. Seiden,
17
M. G. Wilson,
17
L. O. Winstrom,
17
C. H. Cheng,
18
D. A. Doll,
18
B. Echenard,
18
F. Fang,
18
D. G. Hitlin,
18
I. Narsky,
18
T. Piatenko,
18
F. C. Porter,
18
R. Andreassen,
19
G. Mancinelli,
19
B. T. Meadows,
19
K. Mishra,
19
M. D. Sokoloff,
19
P. C. Bloom,
20
W. T. Ford,
20
A. Gaz,
20
J. F. Hirschauer,
20
M. Nagel,
20
U. Nauenberg,
20
J. G. Smith,
20
K. A. Ulmer,
20
S. R. Wagner,
20
R. Ayad,
21,
A. Soffer,
21,
W. H. Toki,
21
R. J. Wilson,
21
D. D. Altenburg,
22
E. Feltresi,
22
A. Hauke,
22
H. Jasper,
22
M. Karbach,
22
J. Merkel,
22
A. Petzold,
22
B. Spaan,
22
K. Wacker,
22
M. J. Kobel,
23
W. F. Mader,
23
R. Nogowski,
23
K. R. Schubert,
23
R. Schwierz,
23
A. Volk,
23
D. Bernard,
24
G. R. Bonneaud,
24
E. Latour,
24
M. Verderi,
24
P. J. Clark,
25
S. Playfer,
25
J. E. Watson,
25
M. Andreotti,
26a,26b
D. Bettoni,
26a
C. Bozzi,
26a
R. Calabrese,
26a,26b
A. Cecchi,
26a,26b
G. Cibinetto,
26a,26b
P. Franchini,
26a,26b
E. Luppi,
26a,26b
M. Negrini,
26a,26b
A. Petrella,
26a,26b
L. Piemontese,
26a
V. Santoro,
26a,26b
R. Baldini-Ferroli,
27
A. Calcaterra,
27
R. de Sangro,
27
G. Finocchiaro,
27
S. Pacetti,
27
P. Patteri,
27
I. M. Peruzzi,
27,
x
M. Piccolo,
27
M. Rama,
27
A. Zallo,
27
A. Buzzo,
28a
R. Contri,
28a,28b
M. Lo Vetere,
28a,28b
M. M. Macri,
28a
M. R. Monge,
28a,28b
S. Passaggio,
28a
C. Patrignani,
28a,28b
E. Robutti,
28a
A. Santroni,
28a,28b
S. Tosi,
28a,28b
K. S. Chaisanguanthum,
29
M. Morii,
29
A. Adametz,
30
J. Marks,
30
S. Schenk,
30
U. Uwer,
30
V. Klose,
31
H. M. Lacker,
31
D. J. Bard,
32
P. D. Dauncey,
32
J. A. Nash,
32
M. Tibbetts,
32
P. K. Behera,
33
X. Chai,
33
M. J. Charles,
33
U. Mallik,
33
J. Cochran,
34
H. B. Crawley,
34
L. Dong,
34
W. T. Meyer,
34
S. Prell,
34
E. I. Rosenberg,
34
A. E. Rubin,
34
Y. Y. Gao,
35
A. V. Gritsan,
35
Z. J. Guo,
35
C. K. Lae,
35
N. Arnaud,
26
J. Be
́
quilleux,
26
A. D’Orazio,
26
M. Davier,
26
J. Firmino da Costa,
26
G. Grosdidier,
26
A. Ho
̈
cker,
26
V. Lepeltier,
26
F. Le Diberder,
26
A. M. Lutz,
26
S. Pruvot,
26
P. Roudeau,
26
M. H. Schune,
26
J. Serrano,
26
V. Sordini,
26,
k
A. Stocchi,
26
G. Wormser,
26
D. J. Lange,
37
D. M. Wright,
37
I. Bingham,
38
J. P. Burke,
38
C. A. Chavez,
38
J. R. Fry,
38
E. Gabathuler,
38
R. Gamet,
38
D. E. Hutchcroft,
38
D. J. Payne,
38
C. Touramanis,
38
A. J. Bevan,
39
C. K. Clarke,
39
K. A. George,
39
F. Di Lodovico,
39
R. Sacco,
39
M. Sigamani,
39
G. Cowan,
40
H. U. Flaecher,
40
D. A. Hopkins,
40
S. Paramesvaran,
40
F. Salvatore,
40
A. C. Wren,
40
D. N. Brown,
41
C. L. Davis,
41
A. G. Denig,
42
M. Fritsch,
42
W. Gradl,
42
G. Schott,
42
K. E. Alwyn,
43
D. Bailey,
43
R. J. Barlow,
43
Y. M. Chia,
43
C. L. Edgar,
43
G. Jackson,
43
G. D. Lafferty,
43
T. J. West,
43
J. I. Yi,
43
J. Anderson,
44
C. Chen,
44
A. Jawahery,
44
D. A. Roberts,
44
G. Simi,
44
J. M. Tuggle,
44
C. Dallapiccola,
45
X. Li,
45
E. Salvati,
45
S. Saremi,
45
R. Cowan,
46
D. Dujmic,
46
P. H. Fisher,
46
G. Sciolla,
46
M. Spitznagel,
46
F. Taylor,
46
R. K. Yamamoto,
46
M. Zhao,
46
P. M. Patel,
47
S. H. Robertson,
47
A. Lazzaro,
48a,48b
V. Lombardo,
48a
F. Palombo,
48a,48b
J. M. Bauer,
49
L. Cremaldi,
49
R. Godang,
49,
{
R. Kroeger,
49
D. A. Sanders,
49
D. J. Summers,
49
H. W. Zhao,
49
M. Simard,
50
P. Taras,
50
F. B. Viaud,
50
H. Nicholson,
51
G. De Nardo,
52a,52b
L. Lista,
52a
D. Monorchio,
52a,52b
G. Onorato,
52a,52b
C. Sciacca,
52a,52b
G. Raven,
53
H. L. Snoek,
53
C. P. Jessop,
54
K. J. Knoepfel,
54
J. M. LoSecco,
54
W. F. Wang,
54
G. Benelli,
55
L. A. Corwin,
55
K. Honscheid,
55
H. Kagan,
55
R. Kass,
55
J. P. Morris,
55
A. M. Rahimi,
55
J. J. Regensburger,
55
S. J. Sekula,
55
Q. K. Wong,
55
N. L. Blount,
56
J. Brau,
56
R. Frey,
56
O. Igonkina,
56
J. A. Kolb,
56
M. Lu,
56
R. Rahmat,
56
N. B. Sinev,
56
D. Strom,
56
J. Strube,
56
E. Torrence,
56
G. Castelli,
57a,57b
N. Gagliardi,
57a,57b
M. Margoni,
57a,57b
M. Morandin,
57a
M. Posocco,
57a
M. Rotondo,
57a
F. Simonetto,
57a,57b
R. Stroili,
57a,57b
C. Voci,
57a,57b
P. del Amo Sanchez,
58
E. Ben-Haim,
58
H. Briand,
58
G. Calderini,
58
J. Chauveau,
58
P. David,
58
L. Del Buono,
58
O. Hamon,
58
Ph. Leruste,
58
J. Ocariz,
58
A. Perez,
58
J. Prendki,
58
S. Sitt,
58
L. Gladney,
59
M. Biasini,
60a,60b
R. Covarelli,
60a,60b
E. Manoni,
60a,60b
C. Angelini,
61a,61b
G. Batignani,
61a,61b
S. Bettarini,
61a,61b
M. Carpinelli,
61a,61b,
**
A. Cervelli,
61a,61b
F. Forti,
61a,61b
M. A. Giorgi,
61a,61b
A. Lusiani,
61a,61c
G. Marchiori,
61a,61b
M. Morganti,
61a,61b
N. Neri,
61a,61b
E. Paoloni,
61a,61b
G. Rizzo,
61a,61b
J. J. Walsh,
61a
D. Lopes Pegna,
62
C. Lu,
62
J. Olsen,
62
A. J. S. Smith,
62
A. V. Telnov,
62
F. Anulli,
63a
E. Baracchini,
63a,63b
G. Cavoto,
63a
D. del Re,
63a,63b
E. Di Marco,
63a,63b
R. Faccini,
63a,63b
F. Ferrarotto,
63a
F. Ferroni,
63a,63b
M. Gaspero,
63a,63b
P. D. Jackson,
63a
L. Li Gioi,
63a
M. A. Mazzoni,
63a
S. Morganti,
63a
PHYSICAL REVIEW D
79,
032002 (2009)
1550-7998
=
2009
=
79(3)
=
032002(13)
032002-1
Ó
2009 The American Physical Society
G. Piredda,
63a
F. Polci,
63a,63b
F. Renga,
63a,63b
C. Voena,
63a
M. Ebert,
64
T. Hartmann,
64
H. Schro
̈
der,
64
R. Waldi,
64
T. Adye,
65
B. Franek,
65
E. O. Olaiya,
65
F. F. Wilson,
65
S. Emery,
66
M. Escalier,
66
L. Esteve,
66
S. F. Ganzhur,
66
G. Hamel de Monchenault,
66
W. Kozanecki,
66
G. Vasseur,
66
Ch. Ye
`
che,
66
M. Zito,
66
X. R. Chen,
67
H. Liu,
67
W. Park,
67
M. V. Purohit,
67
R. M. White,
67
J. R. Wilson,
67
M. T. Allen,
68
D. Aston,
68
R. Bartoldus,
68
P. Bechtle,
68
J. F. Benitez,
68
R. Cenci,
68
J. P. Coleman,
68
M. R. Convery,
68
J. C. Dingfelder,
68
J. Dorfan,
68
G. P. Dubois-Felsmann,
68
W. Dunwoodie,
68
R. C. Field,
68
A. M. Gabareen,
68
S. J. Gowdy,
68
M. T. Graham,
68
P. Grenier,
68
C. Hast,
68
W. R. Innes,
68
J. Kaminski,
68
M. H. Kelsey,
68
H. Kim,
68
P. Kim,
68
M. L. Kocian,
68
D. W. G. S. Leith,
68
S. Li,
68
B. Lindquist,
68
S. Luitz,
68
V. Luth,
68
H. L. Lynch,
68
D. B. MacFarlane,
68
H. Marsiske,
68
R. Messner,
68
D. R. Muller,
68
H. Neal,
68
S. Nelson,
68
C. P. O’Grady,
68
I. Ofte,
68
A. Perazzo,
68
M. Perl,
68
B. N. Ratcliff,
68
A. Roodman,
68
A. A. Salnikov,
68
R. H. Schindler,
68
J. Schwiening,
68
A. Snyder,
68
D. Su,
68
M. K. Sullivan,
68
K. Suzuki,
68
S. K. Swain,
68
J. M. Thompson,
68
J. Va’vra,
68
A. P. Wagner,
68
M. Weaver,
68
C. A. West,
68
W. J. Wisniewski,
68
M. Wittgen,
68
D. H. Wright,
68
H. W. Wulsin,
68
A. K. Yarritu,
68
K. Yi,
68
C. C. Young,
68
V. Ziegler,
68
P. R. Burchat,
69
A. J. Edwards,
69
S. A. Majewski,
69
T. S. Miyashita,
69
B. A. Petersen,
69
L. Wilden,
69
S. Ahmed,
70
M. S. Alam,
70
J. A. Ernst,
70
B. Pan,
70
M. A. Saeed,
70
S. B. Zain,
70
S. M. Spanier,
71
B. J. Wogsland,
71
R. Eckmann,
72
J. L. Ritchie,
72
A. M. Ruland,
72
C. J. Schilling,
72
R. F. Schwitters,
72
B. W. Drummond,
73
J. M. Izen,
73
X. C. Lou,
73
F. Bianchi,
74a,74b
D. Gamba,
74a,74b
M. Pelliccioni,
74a,74b
M. Bomben,
75a,75b
L. Bosisio,
75a,75b
C. Cartaro,
75a,75b
G. Della Ricca,
75a,75b
L. Lanceri,
75a,75b
L. Vitale,
75a,75b
V. Azzolini,
76
N. Lopez-March,
76
F. Martinez-Vidal,
76
D. A. Milanes,
76
A. Oyanguren,
76
J. Albert,
77
Sw. Banerjee,
77
B. Bhuyan,
77
H. H. F. Choi,
77
K. Hamano,
77
R. Kowalewski,
77
M. J. Lewczuk,
77
I. M. Nugent,
77
J. M. Roney,
77
R. J. Sobie,
77
T. J. Gershon,
78
P. F. Harrison,
78
J. Ilic,
78
T. E. Latham,
78
G. B. Mohanty,
78
H. R. Band,
79
X. Chen,
79
S. Dasu,
79
K. T. Flood,
79
Y. Pan,
79
M. Pierini,
79
R. Prepost,
79
C. O. Vuosalo,
79
and S. L. Wu
79
(
B
A
B
AR
Collaboration)
1
Laboratoire de Physique des Particules, IN2P3/CNRS et Universite
́
de Savoie, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy;
3b
Dipartmento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
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, British Columbia, 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 Riverside, Riverside, California 92521, USA
15
University of California at San Diego, La Jolla, California 92093, USA
16
University of California at Santa Barbara, Santa Barbara, California 93106, USA
17
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
18
California Institute of Technology, Pasadena, California 91125, USA
19
University of Cincinnati, Cincinnati, Ohio 45221, USA
20
University of Colorado, Boulder, Colorado 80309, USA
21
Colorado State University, Fort Collins, Colorado 80523, USA
22
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
23
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
24
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
25
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
26a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy;
26b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy;
27
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
28a
INFN Sezione di Genova, I-16146 Genova, Italy;
28b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
29
Harvard University, Cambridge, Massachusetts 02138, USA
30
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
032002 (2009)
032002-2
31
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
32
Imperial College London, London, SW7 2AZ, United Kingdom
33
University of Iowa, Iowa City, Iowa 52242, USA
34
Iowa State University, Ames, Iowa 50011-3160, USA
35
Johns Hopkins University, Baltimore, Maryland 21218, USA
26
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Universite
́
Paris-Sud 11, Centre Scientifique d’Orsay, B. P. 34,
F-91898 Orsay Cedex, France
37
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
38
University of Liverpool, Liverpool L69 7ZE, United Kingdom
39
Queen Mary, University of London, London, E1 4NS, United Kingdom
40
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
41
University of Louisville, Louisville, Kentucky 40292, USA
42
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
43
University of Manchester, Manchester M13 9PL, United Kingdom
44
University of Maryland, College Park, Maryland 20742, USA
45
University of Massachusetts, Amherst, Massachusetts 01003, USA
46
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
47
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
48a
INFN Sezione di Milano, I-20133 Milano, Italy
48b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
49
University of Mississippi, University, Mississippi 38677, USA
50
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
51
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
52a
INFN Sezione di Napoli, I-80126 Napoli, Italy;
52b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
53
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
54
University of Notre Dame, Notre Dame, Indiana 46556, USA
55
Ohio State University, Columbus, Ohio 43210, USA
56
University of Oregon, Eugene, Oregon 97403, USA
57a
INFN Sezione di Padova, I-35131 Padova, Italy;
57b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
58
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
59
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
60a
INFN Sezione di Perugia, I-06100 Perugia, Italy;
60b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
61a
INFN Sezione di Pisa, I-56127 Pisa, Italy;
61b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy;
61c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
62
Princeton University, Princeton, New Jersey 08544, USA
63a
INFN Sezione di Roma, I-00185 Roma, Italy
63b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
64
Universita
̈
t Rostock, D-18051 Rostock, Germany
65
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
66
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
67
University of South Carolina, Columbia, South Carolina 29208, USA
68
Stanford Linear Accelerator Center, Stanford, California 94309, USA
69
Stanford University, Stanford, California 94305-4060, USA
70
State University of New York, Albany, New York 12222, USA
71
University of Tennessee, Knoxville, Tennessee 37996, USA
72
University of Texas at Austin, Austin, Texas 78712, USA
**
Also with Universita
`
di Sassari, Sassari, Italy.
{
Now at University of South Alabama, Mobile, Alabama 36688, USA.
k
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy.
x
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
Now at Tel Aviv University, Tel Aviv, 69978, Israel.
Now at Temple University, Philadelphia, Pennsylvania 19122, USA.
*
Deceased.
MEASUREMENTS OF TIME-DEPENDENT
CP
...
PHYSICAL REVIEW D
79,
032002 (2009)
032002-3
73
University of Texas at Dallas, Richardson, Texas 75083, USA
74a
INFN Sezione di Torino, I-10125 Torino, Italy
74b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
75a
INFN Sezione di Trieste, I-34127 Trieste, Italy
75b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
76
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
77
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
78
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
79
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 14 August 2008; published 9 February 2009)
We present new measurements of time-dependent
CP
asymmetries for
B
0
!
D
ðÞþ
D
ðÞ
decays using
ð
467

5
Þ
10
6
B

B
pairs collected with the
BABAR
detector located at the PEP-II
B
Factory at the
Stanford Linear Accelerator Center. We determine the
CP
-odd fraction of the
B
0
!
D
D

decays to be
R
?
¼
0
:
158

0
:
028

0
:
006
and find
CP
asymmetry parameters
S
þ
¼
0
:
76

0
:
16

0
:
04
and
C
þ
¼
þ
0
:
00

0
:
12

0
:
02
for the
CP
-even component of this decay and
S
?
¼
1
:
80

0
:
70

0
:
16
and
C
?
¼þ
0
:
41

0
:
49

0
:
08
for the
CP
-odd component. We measure
S
¼
0
:
63

0
:
36

0
:
05
and
C
¼

0
:
07

0
:
23

0
:
03
for
B
0
!
D
þ
D

,
S
¼
0
:
62

0
:
21

0
:
03
and
C
¼þ
0
:
08

0
:
17

0
:
04
for
B
0
!
D
D

, and
S
¼
0
:
73

0
:
23

0
:
05
and
C
¼þ
0
:
00

0
:
17

0
:
03
for
B
0
!
D
þ
D

.For
the
B
0
!
D

D

decays, we also determine the
CP
-violating asymmetry
A
¼þ
0
:
008

0
:
048

0
:
013
. In each case, the first uncertainty is statistical and the second is systematic. The measured values
for the asymmetries are all consistent with the standard model.
DOI:
10.1103/PhysRevD.79.032002
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh
I. INTRODUCTION
In the standard model (SM),
CP
violation is described
by the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing
matrix,
V
[
1
,
2
]. In particular, an irreducible complex phase
in the
3

3
mixing matrix is the source of all SM
CP
violation. Both the
BABAR
[
3
] and Belle [
4
] collaborations
have measured the
CP
parameter
sin2

, where


arg
½
V
cd
V

cb
=V
td
V

tb

,in
b
c

c
Þ
s
processes.
The leading-order diagrams contributing to
B
0
!
D
ðÞþ
D
ðÞ
decays are shown in Fig.
1
, where the color-
favored tree-diagram of Fig.
1(a)
dominates. When ne-
glecting the penguin (loop) amplitude in Fig.
1(b)
, the
mixing-induced
CP
asymmetry of
B
0
!
D
ðÞþ
D
ðÞ
, de-
noted
S
, is also determined by
sin2

[
5
]. The effect of
neglecting the penguin amplitude has been estimated in
models based on factorization and heavy quark symmetry,
and the corrections are expected to be a few percent [
6
,
7
].
Large deviations of
S
in
B
0
!
D
ðÞþ
D
ðÞ
decays with
respect to
sin2

determined from
b
c

c
Þ
s
transitions
could indicate physics beyond the SM [
8
10
].
The
CP
asymmetries of
B
0
!
D
ðÞþ
D
ðÞ
decays have
been studied by both the
BABAR
[
11
,
12
] and Belle [
13
15
]
collaborations. In the SM, the direct
CP
asymmetry
C
,
defined in Sec.
IV
, for the
B
0
!
D
ðÞþ
D
ðÞ
decays is
expected to be near zero. The Belle Collaboration has
observed a 3.2 sigma deviation of
C
from zero in the
B
0
!
D
þ
D

channel [
15
]. This has not been observed by
BABAR
nor has it been seen in other
B
0
!
D
ðÞþ
D
ðÞ
decay modes, which involve the same quark-level dia-
grams. As was pointed out in [
9
], understanding any pos-
sible asymmetries in these decays is important to
constraining theoretical models.
In this article, we update the previous measurements of
CP
asymmetry parameters in
B
0
!
D
ðÞþ
D
ðÞ
decays
[
11
,
12
], including the
CP
-odd fraction for
B
0
!
D
D

, using the final
BABAR
data sample. Charge con-
jugate decays are included implicitly in expressions
throughout this article unless otherwise indicated.
II. DETECTOR, DATA SAMPLE, AND
RECONSTRUCTION
A. The
BABAR
detector
The data used in this analysis were collected with the
BABAR
detector [
16
] operating at the PEP-II
B
Factory
located at the Stanford Linear Accelerator Center (SLAC).
The
BABAR
dataset comprises
ð
467

5
Þ
10
6
B

B
pairs
collected from 1999 to 2007 at the center-of-mass (CM)
energy
ffiffiffi
s
p
¼
10
:
58 GeV
, corresponding to the

ð
4
S
Þ
reso-
nance. We use GEANT4-based [
17
] Monte Carlo (MC)
d
c
W
d
d
b
c
(a) Tree
d
c
g
b
W
t,c,u
d
d
c
(b) Penguin
FIG. 1. Leading-order Feynman graphs for the

B
0
!
D
ðÞþ
D
ðÞ
decays.
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
032002 (2009)
032002-4
simulation to study backgrounds and to validate the analy-
sis procedures.
The asymmetric energies of the PEP-II beams provide
an ideal environment to study time-dependent
CP
phe-
nomena in the
B
0


B
0
system by boosting the

ð
4
S
Þ
in
the laboratory frame, thus making possible precise deter-
mination of the decay vertices of the two
B
meson daugh-
ters.
BABAR
employs a five-layer silicon vertex tracker
(SVT) close to the interaction region to provide precise
vertex measurements and to track low momentum charged
particles. A drift chamber (DCH) provides excellent mo-
mentum measurement of charged particles. Particle iden-
tification of kaons and pions is primarily derived from
ionization losses in the SVT and DCH and from measure-
ments of photons produced in the fused silica bars of a
ring-imaging Cherenkov light detector (DIRC). A CsI(Tl)
crystal-based electromagnetic calorimeter enables recon-
struction of photons and identification of electrons. All of
these systems operate within a 1.5 T superconducting
solenoid, whose iron flux return is instrumented to detect
muons.
B. Candidate reconstruction and selection
The candidates used in this analysis are formed from
oppositely charged
D
ðÞ
mesons where we include the
D
decay modes
D
!
D
0

þ
and
D
!
D
þ

0
and
D
decay modes
D
0
!
K


þ
,
D
0
!
K


þ

0
,
D
0
!
K


þ



þ
,
D
0
!
K
0
S

þ


, and
D
þ
!
K


þ

þ
.In
the
B
0
!
D
D

mode, we reject
B
0
candidates where
both
D

mesons decay to
D
0
because of its smaller
branching fraction and larger backgrounds. Ref-
erence [
18
] contains the details of the reconstruction pro-
cedure, outlined here, used to select signal candidates.
Charged kaon candidates must be identified as such using
a likelihood technique based on the opening angle of the
Cherenkov light measured in the DIRC and the ionization
energy loss measured in the SVT and DCH [
16
]. We
reconstruct
K
0
S
candidates from two oppositely charged
tracks, geometrically constrained to a common vertex
and with an invariant mass within 20 MeV of the nominal
value [
19
]. We also require that the

2
probability of the
vertex fit of the
K
0
S
be greater than 0.1%. We form

0
candidates from a pair of photons detected in the calorime-
ter, each with energy greater than 40 MeV. The invariant
mass of the two photons must be less than
30 MeV
=c
2
from the nominal

0
mass, and their summed energy must
be greater than 200 MeV. In addition, we apply a mass
constraint to the

0
candidates. We require the recon-
structed
D
meson candidate mass to be within
20 MeV
=c
2
of the nominal value, except for the
D
0
!
K


þ

0
decays where we use a looser requirement of
40 MeV
=c
2
. The daughters of each
D
candidate are fit to a
common vertex with their combined mass constrained to
that of the
D
meson. We use
D
candidates combined with a
pion track with momentum less than
450 MeV
=c
in the
CM frame to form
D
candidates. We fit the
B
0
decay
with a vertex constraint.
Since the time of our previous publications [
11
,
12
,
18
],
the
BABAR
reconstruction routines have been extensively
revised, leading to significant improvements in localizing
and reconstructing tracks, particularly for low momentum
charged particles. These improvements have increased the
reconstruction efficiency for final states with multiple slow
particles, such as the
B
0
!
D
D

channel which has a
better than 20% improvement. As a result, the statistical
sensitivity of the measurements in this paper has increased
more than would be expected by just the increment in
luminosity.
To suppress
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
, and
c
) continuum
background, we exploit the spherical shape of
B

B
events
by requiring the ratio of second to zeroth order Fox-
Wolfram moments [
20
] to be less than 0.6. We select the
B
0
candidates based on four variables:

E

E

B

ffiffiffi
s
p
=
2
,
where
E

B
is the energy of the
B
meson in the CM frame,
the
D
candidate flight length significance, defined as the
sum of the two
D
candidate flight lengths divided by the
error on the sum, a Fisher discriminant [
21
], and a mass
likelihood of the
D
ðÞ
mesons. The Fisher discriminant is a
linear combination of 11 variables: the momentum flow in
nine concentric cones around the thrust axis of the
B
0
candidate, the angle between the thrust axis and the beam
axis, and the angle between the line-of-flight of the
B
0
candidate and the beam axis. The mass likelihood is
formed from Gaussian functions,
L
mass
¼
G
ð
m
D
;
m
D
PDG
;
m
D
Þ
G
ð
m

D
;
m

D
PDG
;
m

D
Þ
f
core
G
ð

m
D
;
m
D
PDG
;

m
core
Þ
þð
1

f
core
Þ
G
ð

m
D
;
m
D
PDG
;

m
tail
Þ
f
core
G
ð

m
D

;
m
D

PDG
;

m
core
Þ
þð
1

f
core
Þ
G
ð

m
D

;
m
D

PDG
;

m
tail
Þ
;
(1)
where the PDG subscript refers to the nominal value [
22
].
The reconstructed masses and uncertainties

m

D
for the
D
mesons prior to the mass constraint are used in the like-
lihood. The
D

portion of the likelihood is the sum of two
Gaussian functions, a central core and a wider tail. The
value of
f
core
and the widths of the
D

Gaussian functions
are taken from detailed signal MC studies, which show
good agreement between data and MC samples. The se-
lection criteria are optimized for each
D
decay channel to
maximize the total signal significance
S=
ffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
p
for each
B
0
decay mode, where
S
and
B
are the signal and
background yields, respectively. The optimized selections
are specified in [
18
]. We keep candidates with
m
ES

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s=
4

p

2
B
q
>
5
:
23 GeV
=c
2
, where
p

B
is the momentum
of the
B
candidate in the CM frame. On average 1.1–1.8
candidates per event satisfy all of the selection criteria
MEASUREMENTS OF TIME-DEPENDENT
CP
...
PHYSICAL REVIEW D
79,
032002 (2009)
032002-5
depending on the process. When more than one
B
0
candi-
date meets the selection criteria, the one with the best
L
mass
is kept. We find from MC that this procedure retains the
correct candidate more than 95% of the time.
To determine the signal yields of the data sample, we use
unbinned maximum likelihood (ML) fits to the
m
ES
dis-
tributions. The signal is described by a Gaussian function
and the combinatorial background by a threshold function
[
23
]. In detailed MC studies of the background, we find
that there is a background contribution that exceeds the
threshold function in the region
m
ES
>
5
:
27 GeV
=c
2
,
where most of the signal events lie. We describe this
component with a Gaussian function having the same
mean and width as the signal and refer to it as peaking
background because if neglected, it would lead to an over-
estimate of the signal yields. In the
B
0
!
D
D

chan-
nel, the peaking background arises primarily from
misreconstructed
B
þ
!
D

D

0
events where the slow

0
from the

D

0
!

D
0

0
decay is replaced by a


to
form a
D

candidate. For the other three processes, our
studies of the composition of the peaking background show
it to be consistent with that of the combinatorial back-
ground in the region
m
ES
<
5
:
27 GeV
=c
2
. We treat the
peaking background component as an extension of the
combinatorial background. The peaking background yields
relative to the signal are fixed from MC to
ð
1
:
6

1
:
9
Þ
%
,
ð
7
:
1

5
:
9
Þ
%
, and
ð
7
:
4

2
:
9
Þ
%
for the
B
0
!
D
D

,
B
0
!
D
þ
D

, and
B
0
!
D

D

modes, respectively,
where the errors are due primarily to the size of the MC
sample available for background studies. The signal mean
and background shape are free parameters in the fits. We
fix the width of the signal Gaussian shape for
B
0
!
D
þ
D

and
B
0
!
D

D

to 2.46
MeV
=c
2
and
2
:
55 MeV
=c
2
,
respectively, determined from MC, while the width of the
B
0
!
D
D

signal is allowed to float because of its
much higher purity. The signal yields are
934

40
B
0
!
D
D

events,
152

17
B
0
!
D
þ
D

events,
365

26
B
0
!
D
D

events, and
359

26
B
0
!
D
þ
D

events,
where the uncertainty is statistical only. The signal yields
are consistent with previously measured
B
0
!
D
ðÞþ
D
ðÞ
decay branching fractions from
BABAR
[
18
] and Belle
[
15
,
24
]. When compared with past
BABAR
measurements
m (GeV/c )
ES
2
5.23
5.25
5.27
5.29
2
50
150
250
350
(a)
B
DD
5.23
5.25
5.27
5.29
20
60
100
m (GeV/c )
ES
2
2
(b)
B
DD
5.25
5.27
5.29
20
60
100
140
180
5.23
2
m (GeV/c )
ES
2
(c)
B
DD
5.23
5.25
5.27
5.29
20
60
100
140
180
2
m (GeV/c )
ES
2
(d)
B
DD
FIG. 2 (color online). Projections of the
m
ES
fit results. The solid line represents the total fit PDF and the dashed line is the
background contribution.
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
032002 (2009)
032002-6
[
18
,
25
,
26
], the low
B
0
!
D
þ
D

yield in Ref. [
11
]is
consistent with a statistical fluctuation. The fit projections
for each mode onto
m
ES
are shown in Fig.
2
.
III. TIME-INTEGRATED MEASUREMENT OF THE
CP
-ODD FRACTION
The
B
0
!
D
D

process has two vector mesons in
the final state and is an admixture of
CP
-even and
CP
-odd
states depending on the orbital angular momentum of the
decay products. We measure the
CP
-odd fraction
R
?
using
a time-integrated angular analysis [
27
]. We define the three
angles in the transversity basis as depicted in Fig.
3
: the
angle

1
between the slow pion from the
D

and the
direction opposite to the
D
momentum in the
D

rest
frame; the polar angle

tr
and the azimuthal angle

tr
of the
slow pion from the
D
in the
D
rest frame where the
z
axis is normal to the
D

decay plane and the
x
axis is
opposite the
D

momentum. Working in the transversity
basis, the time-dependent angular distribution of the
B
0
decay products is
1

d
4

d
cos

1
d
cos

tr
d
tr
dt
¼
9
16

1
j
A
0
j
2
þj
A
k
j
2
þj
A
?
j
2

2cos
2

1
sin
2

tr
cos
2

tr
j
A
0
j
2
þ
sin
2

1
sin
2

tr
sin
2

tr
j
A
k
j
2
þ
sin
2

1
cos
2

tr
j
A
?
j
2

sin
2

1
sin2

tr
sin

tr
Im
ð
A

k
A
?
Þþ
1
ffiffiffi
2
p
sin2

1
sin
2

tr
sin2

tr
Re
ð
A

0
A
k
Þ

1
ffiffiffi
2
p
sin2

1
sin2

tr
cos

tr
Im
ð
A

0
A
?
Þ

;
(2)
where
A
k
, with
k
¼k
;
0
;
?
, represent time-dependent amplitudes given by
A
k
ð
t
Þ¼
ffiffiffi
2
p
A
k
ð
0
Þ
1
þj

k
j
2
e

imt
e

t=
2

B
0

cos

m
d
t
2
þ
i
k
CP

k
sin

m
d
t
2

:
(3)
Here,
k
CP
is the
CP
eigenvalue,
þ
1
for
A
k
;
0
,

1
for
A
?
;

k
is the
CP
parameter defined in Sec.
IV
;

m
d
is the
B
0
mixing
frequency,
ð
0
:
507

0
:
005
Þ
ps

1
; and

B
0
is the
B
0
lifetime,
ð
1
:
530

0
:
009
Þ
ps
[
19
]. Expressions similar to Eq. (
2
) hold
for

B
0
decays where each
A
k
is replaced by the appropriate

A
k
including
A
?
!

A
?
. Integrating Eq. (
2
)over
t
,

tr
,
cos

1
and averaging over
B
flavor while taking into account detector efficiency yields
1

d

d
cos

tr
¼
9
32

ð
1

R
?
Þ
sin
2

tr

1
þ
2
I
0
ð
cos

tr
Þþ
1

2
I
k
ð
cos

tr
Þ

þ
3
2
R
?
cos
2

tr

I
?
ð
cos

tr
Þ
;
(4)
where we define
R
?
¼
j
A
0
?
j
2
j
A
0
0
j
2
þj
A
0
k
j
2
þj
A
0
?
j
2
¼
j
A
0
0
j
2
j
A
0
k
j
2
j
A
0
0
j
2
þj
A
0
k
j
2
;
and
A
0
k
¼
A
k
ð
0
Þ
. The three efficiency moments
I
k
ð
cos

tr
Þ
are defined as
I
k
ð
cos

tr
Þ¼
Z
d
cos

1
d
tr
g
k
ð

1
;
tr
Þ
"
ð

1
;
tr
;
tr
Þ
;
(5)
where
g
0
¼
4cos
2

1
cos
2

tr
,
g
k
¼
2sin
2

1
sin
2

tr
,
g
?
¼
sin
2

1
, and
"
is the detector efficiency. The moments
I
k
are parameterized as second-order even polynomials in
cos

tr
whose parameters are determined from signal MC
simulation and fixed in the fit. The three
I
k
functions
deviate only slightly from the same constant, making
Eq. (
4
) nearly insensitive to
, which we fix to zero in
the fit.
Because
cos

tr
is defined with respect to the slow pion
from the
D
decay, the measurement resolution smears its
distribution. We convolve the function from Eq. (
4
) with a
resolution function
R
ð


tr
Þ
which is modeled as the sum
of three Gaussian functions. In addition, we include an
uncorrelated Gaussian shape centered at
=
2
and normal-
ized in
0
<
tr
<
to describe decays where the slow pion
is poorly reconstructed leading to a loss of angular infor-
mation. The uncorrelated term represents 3% of the signal
events where both slow pions are charged and around 16%
FIG. 3. Depiction of the
B
0
!
D
D

decay in the trans-
versity basis with the
D

!

D
0


decay plane shown. The
three transversity angles are defined in the text.
MEASUREMENTS OF TIME-DEPENDENT
CP
...
PHYSICAL REVIEW D
79,
032002 (2009)
032002-7
in the modes where one of the slow pions is neutral. We
determine the parameters of the resolution model and of
the uncorrelated term from signal MC simulation and fix
them in the ML fit. Small differences observed in the
angular distributions based on the charge of the slow pions
lead us to divide the efficiency moment and resolution
parameters into three categories,

0


,

þ

0
, and

þ


.
We determine
R
?
in a simultaneous unbinned ML fit to
the
m
ES
and
cos

tr
distributions for the three slow-pion
modes. The
m
ES
probability density function (PDF) was
described in Sec.
II B
. The signal
cos

tr
distribution is
given by Eq. (
4
) convolved with the resolution model.
The background
cos

tr
distribution is modeled as a
second-order even polynomial
f
bg
ð
cos

tr
Þ¼
1
þ
b
2
cos
2

tr
, where
b
2
, common to the three slow-pion
modes, is allowed to float. The yield for each of the three
slow-pion modes is determined by the fit. We validate the
fitting procedure using high-statistics MC samples divided
into data-sized subsets and find no significant bias. Fitting
the data and including systematic uncertainties described
below, we find
R
?
¼
0
:
158

0
:
028
ð
stat
Þ
0
:
006
ð
syst
Þ
:
(6)
Figure
4
shows the projection of the fit result.
To evaluate the systematic uncertainty of
R
?
, we vary
the parameters used to model the efficiency moments
within the uncertainties of the MC simulation used to
extract them. We do the same for the parameters used to
model the experimental resolution. In both cases, we take
into account correlations among the parameters when per-
turbing the values. We fix
to zero in the nominal fit, so we
also set it to

1
and assign the effect on the fitted result as a
systematic uncertainty. We change the
m
ES
and
cos

tr
shapes of the peaking background and assign the corre-
sponding changes in
R
?
as a systematic uncertainty. We
allow the
cos

tr
background to have an additional fourth-
order term to test our assumption of this background shape.
This term is found to be consistent with zero, and we take
the difference in
R
?
with respect to the nominal second-
order background description as the uncertainty with this
model. We include as a systematic uncertainty the statisti-
cal uncertainty associated with the MC validation. A sum-
mary of the systematic uncertainties is found in Table
I
.
The total systematic uncertainty is the sum in quadrature of
the individual contributions.
IV. TIME-DEPENDENT
CP
MEASUREMENT
The decay rate
f
þ
(
f

) of the neutral
B
meson to a
common final state accompanied by a
B
0
(

B
0
) tag is
f

ð

t
Þ/
e
j

t
j
=
B
0
1


w
Þð
1

2
w
Þ
S
sin
ð

m
d

t
Þ
C
cos
ð

m
d

t
Þg
;
(7)
with
CP
asymmetry parameters
S
¼
2Im
ð

Þ
=
ð
1
þj

j
2
Þ
,
C
¼ð
1
j

j
2
Þ
=
ð
1
þj

j
2
Þ
, and

¼ð
q=p
Þð

A=A
Þ
, where
A
(

A
) is the decay amplitude for
B
0
(

B
0
) and
q=p
is the ratio
of the flavor contributions to the mass eigenstates [
28
]. The
parameter
w
is the average mistag probability, and

w
is
the difference between the mistag probabilities for
B
0
and

B
0
. Here,

t

t
reco

t
tag
is the proper time difference
between the
B
reconstructed as
B
0
!
D
ðÞþ
D
ðÞ
(
B
rec
)
and the
B
used to tag the flavor (
B
tag
). In the case of
B
0
!
D
D

, we obtain an expression similar to Eq. (
7
) from
Eqs. (
2
) and (
3
),
f

ð

t;
cos

tr
Þ/
e
j

t
j
=
B
0
f
F
ð
1


w
Þð
1

2
w
Þ
G
sin
ð

m
d

t
Þ
H
cos
ð

m
d

t
Þg
:
(8)
The
F
,
G
, and
H
coefficients [
29
] are
F
¼ð
1

R
?
Þ
sin
2

tr
þ
2
R
?
cos
2

tr
;
G
¼ð
1

R
?
Þ
S
þ
sin
2

tr

2
R
?
S
?
cos
2

tr
;
H
¼ð
1

R
?
Þ
C
þ
sin
2

tr
þ
2
R
?
C
?
cos
2

tr
:
(9)
The

k
parameters in Eq. (
3
) need not be the same because
cos
θ
tr
-0.6
Events / ( 0.1)
20
40
60
80
100
-1.0
-0.2
0.2
0.6
1.0
FIG. 4 (color online). Projection of the fit result onto
cos

tr
for
events with
m
ES
>
5
:
27GeV
=c
2
. The solid line is the projected
fit result. The dashed line is the background component.
TABLE I. Summary of systematic uncertainties on the mea-
surement of
R
?
.
Angular efficiency moments
0.0024
Angular measurement resolution
0.0036
parameter uncertainty
0.0026
Peaking background
0.0014
cos

tr
background shape
0.0002
Potential fit bias
0.0017
Total
0.0055
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
032002 (2009)
032002-8
of possible differences in the relative contribution of pen-
guin and tree amplitudes, therefore the
S
and
C
parameters
for each of the three
ð
0
;
k
;
amplitudes can also differ.
Note that the minus sign before
S
?
in the expression for
G
absorbs
?
CP
. We then define
S
þ
¼
S
k
A
02
k
þ
S
0
A
02
0
A
02
k
þ
A
02
0
;C
þ
¼
C
k
A
02
k
þ
C
0
A
02
0
A
02
k
þ
A
02
0
;
(10)
where
A
0
k
¼
A
k
ð
0
Þ
from Eq. (
3
).
In the absence of penguin contributions,
S
D
þ
D

¼
S
þ
¼
S
?
¼
sin2

, and
C
D
þ
D

¼
C
þ
¼
C
?
¼
0
. Because
B
0
!
D

D

is not a
CP
eigenstate, the expressions for
S
and
C
are related,
S
D

D

¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1

C
D

D

p
sin
ð
2

eff

Þ
, where
is the strong phase difference between
B
0
!
D
D

and
B
0
!
D
þ
D

decays [
30
]. Neglecting the
penguin contributions,

eff
¼

, and
C
D
D

¼
C
D
þ
D

.
The technique used to measure the time-dependent
CP
asymmetry is discussed in detail in Ref. [
31
]. We calculate

t
between the two
B
decays from the measured separation

z
of their decay vertices along the
z
axis. The
B
rec
decay
vertex is determined from the daughter tracks of the
B
0
!
D
ðÞþ
D
ðÞ
decay. The
B
tag
decay vertex is determined in a
fit of the charged tracks not belonging to
B
rec
to a common
vertex with a constraint on the beam spot location and the
B
rec
momentum. Events that do not satisfy
j

t
j
<
20 ps
and


t
<
2
:
5ps
are considered untagged in the time-
dependent fit.
The flavor of the
B
tag
meson is determined using a
multivariate analysis of its decay products [
31
]. The tag-
ging algorithm classifies the
B
flavor and assigns the
candidate to one of six mutually exclusive tagging catego-
ries based on the output. A seventh untagged category is for
events where the flavor could not be determined. The
performance of the tagging algorithm, its efficiency and
mistag rates, is evaluated using the time-dependent evolu-
tion of a high-statistics data sample of

ð
4
S
Þ!
B
tag
B
flav
,
where the
B
flav
meson decays to a flavor eigenstate
D
ðÞ
h
þ
and
h
þ
may be a

þ
,
þ
,or
a
þ
1
. The tagging
algorithm has an efficiency
"
tag
¼ð
74
:
4

0
:
1
Þ
%
and an
effective tagging power
Q

"
tag
ð
1

w
Þ
2
¼ð
31
:
2

0
:
3
Þ
%
. The finite resolution of the
B
vertex reconstruction
smears the distributions described in Eqs. (
7
) and (
8
). This
measurement resolution is modeled as the sum of three
Gaussian functions described in Ref. [
31
], the parameters
of which are also determined from the
B
flav
sample.
We determine the
CP
asymmetry parameters in un-
binned ML fits to the
m
ES
,

t
, and in the case of
B
0
!
D
D

,
cos

tr
distributions. The

t
signal distributions
are given in Eqs. (
7
) and (
8
) convolved with the experi-
mental resolution. The

t
background distribution has both
zero and nonzero lifetime components which are con-
volved with the experimental resolution. The lifetime com-
ponent is allowed to have effective
CP
parameters and
lifetime, which are determined in the fits. The angular
measurement resolution, determined for the
CP
-odd frac-
tion measurement, is convolved with the signal angular
distribution. The efficiency moments are not modeled but
rather absorbed into an effective
R
?
, which is determined
in the fit. This procedure simplifies the
cos

tr
distribution
and does not introduce a bias. The peaking background for
the
B
0
!
D
ðÞ
D

channels shares the

t
background
distributions with the combinatorial background because
it originates from similar sources. The
B
0
!
D
D

peaking background has only a lifetime component, since
it originates from a specific
B
þ
decay. Untagged events are
also included in the fits to constrain the
m
ES
and
cos

tr
shapes but do not contribute to the determination of the
CP
parameters. We also allow the signal yield, the
m
ES
back-
ground shape, and the
cos

tr
background shape to vary in
the fits. Again we use high-statistics MC samples divided
into data-sized subsets to validate the fitting procedure and
find no significant bias.
The statistical uncertainties of the
CP
measurements
below are consistent with the expected uncertainties ob-
tained from MC studies that include the signal and back-
ground yields observed in data. The statistical uncertainty
for the
B
0
!
D
ðÞ
D

channels is essentially unchanged
or even slightly worse than our previous measurement [
11
].
We interpret this as a downward fluctuation in the statisti-
cal uncertainty of the previous measurement. Using MC
data, we estimate the probability of observing such a
fluctuation at about 20%. For each measurement that fol-
lows, the first uncertainty is statistical and the second is
systematic.
From the fit to the
B
0
!
D
D

data, we find
S
þ
¼
0
:
76

0
:
16

0
:
04
C
þ
¼þ
0
:
00

0
:
12

0
:
02
S
?
¼
1
:
80

0
:
70

0
:
16
C
?
¼þ
0
:
41

0
:
49

0
:
08
;
(11)
with an effective
R
?
¼
0
:
155

0
:
030
. If we perform the
fit with the additional constraints that
S
þ
¼
S
?
¼
S
D
D

and
C
þ
¼
C
?
¼
C
D
D

, we obtain
S
D
D

¼
0
:
70

0
:
16

0
:
03
C
D
D

¼þ
0
:
05

0
:
09

0
:
02
;
(12)
having an effective
R
?
¼
0
:
171

0
:
028
. Fitting the
B
0
!
D
þ
D

data yields
S
D
þ
D

¼
0
:
63

0
:
36

0
:
05
C
D
þ
D

¼
0
:
07

0
:
23

0
:
03
;
(13)
and fitting the
B
0
!
D

D

data yields
MEASUREMENTS OF TIME-DEPENDENT
CP
...
PHYSICAL REVIEW D
79,
032002 (2009)
032002-9