of 15
Measurement of the time-dependent
CP
asymmetry
of partially reconstructed
B
0
!
D
D

decays
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
A. Palano,
3,4
G. Eigen,
5
B. Stugu,
5
D. N. Brown,
6
L. T. Kerth,
6
Yu. G. Kolomensky,
6
G. Lynch,
6
H. Koch,
7
T. Schroeder,
7
D. J. Asgeirsson,
8
C. Hearty,
8
T. S. Mattison,
8
J. A. McKenna,
8
R. Y. So,
8
A. Khan,
9
V. E. Blinov,
10
A. R. Buzykaev,
10
V. P. Druzhinin,
10
V. B. Golubev,
10
E. A. Kravchenko,
10
A. P. Onuchin,
10
S. I. Serednyakov,
10
Yu. I. Skovpen,
10
E. P. Solodov,
10
K. Yu. Todyshev,
10
A. N. Yushkov,
10
M. Bondioli,
11
D. Kirkby,
11
A. J. Lankford,
11
M. Mandelkern,
11
H. Atmacan,
12
J. W. Gary,
12
F. Liu,
12
O. Long,
12
G. M. Vitug,
12
C. Campagnari,
13
T. M. Hong,
13
D. Kovalskyi,
13
J. D. Richman,
13
C. A. West,
13
A. M. Eisner,
14
J. Kroseberg,
14
W. S. Lockman,
14
A. J. Martinez,
14
B. A. Schumm,
14
A. Seiden,
14
D. S. Chao,
15
C. H. Cheng,
15
B. Echenard,
15
K. T. Flood,
15
D. G. Hitlin,
15
P. Ongmongkolkul,
15
F. C. Porter,
15
A. Y. Rakitin,
15
R. Andreassen,
16
Z. Huard,
16
B. T. Meadows,
16
M. D. Sokoloff,
16
L. Sun,
16
P. C. Bloom,
17
W. T. Ford,
17
A. Gaz,
17
U. Nauenberg,
17
J. G. Smith,
17
S. R. Wagner,
17
R. Ayad,
18,
*
W. H. Toki,
18
B. Spaan,
19
K. R. Schubert,
20
R. Schwierz,
20
D. Bernard,
21
M. Verderi,
21
P. J. Clark,
22
S. Playfer,
22
D. Bettoni,
23
C. Bozzi,
23
R. Calabrese,
23,24
G. Cibinetto,
23,24
E. Fioravanti,
23,24
I. Garzia,
23,24
E. Luppi,
23,24
M. Munerato,
23,24
L. Piemontese,
23
V. Santoro,
23
R. Baldini-Ferroli,
25
A. Calcaterra,
25
R. de Sangro,
25
G. Finocchiaro,
25
P. Patteri,
25
I. M. Peruzzi,
25,
M. Piccolo,
25
M. Rama,
25
A. Zallo,
25
R. Contri,
26,27
E. Guido,
26,27
M. Lo Vetere,
26,27
M. R. Monge,
26,27
S. Passaggio,
26
C. Patrignani,
26,27
E. Robutti,
26
B. Bhuyan,
28
V. Prasad,
28
C. L. Lee,
29
M. Morii,
29
A. J. Edwards,
30
A. Adametz,
31
U. Uwer,
31
H. M. Lacker,
32
T. Lueck,
32
P. D. Dauncey,
33
U. Mallik,
34
C. Chen,
35
J. Cochran,
35
W. T. Meyer,
35
S. Prell,
35
A. E. Rubin,
35
A. V. Gritsan,
36
Z. J. Guo,
36
N. Arnaud,
37
M. Davier,
37
D. Derkach,
37
G. Grosdidier,
37
F. Le Diberder,
37
A. M. Lutz,
37
B. Malaescu,
37
P. Roudeau,
37
M. H. Schune,
37
A. Stocchi,
37
G. Wormser,
37
D. J. Lange,
38
D. M. Wright,
38
C. A. Chavez,
39
J. P. Coleman,
39
J. R. Fry,
39
E. Gabathuler,
39
D. E. Hutchcroft,
39
D. J. Payne,
39
C. Touramanis,
39
A. J. Bevan,
40
F. Di Lodovico,
40
R. Sacco,
40
M. Sigamani,
40
G. Cowan,
41
D. N. Brown,
42
C. L. Davis,
42
A. G. Denig,
43
M. Fritsch,
43
W. Gradl,
43
K. Griessinger,
43
A. Hafner,
43
E. Prencipe,
43
R. J. Barlow,
44,
G. Jackson,
44
G. D. Lafferty,
44
E. Behn,
45
R. Cenci,
45
B. Hamilton,
45
A. Jawahery,
45
D. A. Roberts,
45
C. Dallapiccola,
46
R. Cowan,
47
D. Dujmic,
47
G. Sciolla,
47
R. Cheaib,
48
D. Lindemann,
48
P. M. Patel,
48,
§
S. H. Robertson,
48
P. Biassoni,
49,50
N. Neri,
49
F. Palombo,
49,50
S. Stracka,
49,50
L. Cremaldi,
51
R. Godang,
51,
k
R. Kroeger,
51
P. Sonnek,
51
D. J. Summers,
51
X. Nguyen,
52
M. Simard,
52
P. Taras,
52
G. De Nardo,
53,54
D. Monorchio,
53,54
G. Onorato,
53,54
C. Sciacca,
53,54
M. Martinelli,
55
G. Raven,
55
C. P. Jessop,
56
J. M. LoSecco,
56
W. F. Wang,
56
K. Honscheid,
57
R. Kass,
57
J. Brau,
58
R. Frey,
58
N. B. Sinev,
58
D. Strom,
58
E. Torrence,
58
E. Feltresi,
59,60
N. Gagliardi,
59,60
M. Margoni,
59,60
M. Morandin,
59
M. Posocco,
59
M. Rotondo,
59
G. Simi,
59
F. Simonetto,
59,60
R. Stroili,
59,60
S. Akar,
61
E. Ben-Haim,
61
M. Bomben,
61
G. R. Bonneaud,
61
H. Briand,
61
G. Calderini,
61
J. Chauveau,
61
O. Hamon,
61
Ph. Leruste,
61
G. Marchiori,
61
J. Ocariz,
61
S. Sitt,
61
M. Biasini,
62,63
E. Manoni,
62,63
S. Pacetti,
62,63
A. Rossi,
62,63
C. Angelini,
64,65
G. Batignani,
64,65
S. Bettarini,
64,65
M. Carpinelli,
64,65,
{
G. Casarosa,
64,65
A. Cervelli,
64,65
F. Forti,
64,65
M. A. Giorgi,
64,65
A. Lusiani,
64,66
B. Oberhof,
64,65
E. Paoloni,
64,65
A. Perez,
64
G. Rizzo,
64,65
J. J. Walsh,
64
D. Lopes Pegna,
67
J. Olsen,
67
A. J. S. Smith,
67
A. V. Telnov,
67
F. Anulli,
68
R. Faccini,
68,63
F. Ferrarotto,
68
F. Ferroni,
68,63
M. Gaspero,
68,63
L. Li Gioi,
68
M. A. Mazzoni,
68
G. Piredda,
68
C. Bu
̈
nger,
70
O. Gru
̈
nberg,
70
T. Hartmann,
70
T. Leddig,
70
H. Schro
̈
der,
70,
**
C. Voss,
70
R. Waldi,
70
T. Adye,
71
E. O. Olaiya,
71
F. F. Wilson,
71
S. Emery,
72
G. Hamel de Monchenault,
72
G. Vasseur,
72
Ch. Ye
`
che,
72
D. Aston,
73
D. J. Bard,
73
R. Bartoldus,
73
J. F. Benitez,
73
C. Cartaro,
73
M. R. Convery,
73
J. Dorfan,
73
G. P. Dubois-Felsmann,
73
W. Dunwoodie,
73
M. Ebert,
73
R. C. Field,
73
M. Franco Sevilla,
73
B. G. Fulsom,
73
A. M. Gabareen,
73
M. T. Graham,
73
P. Grenier,
73
C. Hast,
73
W. R. Innes,
73
M. H. Kelsey,
73
P. Kim,
73
M. L. Kocian,
73
D. W. G. S. Leith,
73
P. Lewis,
73
B. Lindquist,
73
S. Luitz,
73
V. Luth,
73
H. L. Lynch,
73
D. B. MacFarlane,
73
D. R. Muller,
73
H. Neal,
73
S. Nelson,
73
M. Perl,
73
T. Pulliam,
73
B. N. Ratcliff,
73
A. Roodman,
73
A. A. Salnikov,
73
R. H. Schindler,
73
A. Snyder,
73
D. Su,
73
M. K. Sullivan,
73
J. Va’vra,
73
A. P. Wagner,
73
W. J. Wisniewski,
73
M. Wittgen,
73
D. H. Wright,
73
H. W. Wulsin,
73
C. C. Young,
73
V. Ziegler,
73
W. Park,
74
M. V. Purohit,
74
R. M. White,
74
J. R. Wilson,
74
A. Randle-Conde,
75
S. J. Sekula,
75
M. Bellis,
76
P. R. Burchat,
76
T. S. Miyashita,
76
E. M. T. Puccio,
76
M. S. Alam,
77
J. A. Ernst,
77
R. Gorodeisky,
78
N. Guttman,
78
D. R. Peimer,
78
A. Soffer,
78
P. Lund,
79
S. M. Spanier,
79
J. L. Ritchie,
80
A. M. Ruland,
80
R. F. Schwitters,
80
B. C. Wray,
80
J. M. Izen,
81
X. C. Lou,
81
F. Bianchi,
82,83
D. Gamba,
82,83
S. Zambito,
82,83
L. Lanceri,
84,85
L. Vitale,
84,85
F. Martinez-Vidal,
86
A. Oyanguren,
86
H. Ahmed,
87
J. Albert,
87
Sw. Banerjee,
87
F. U. Bernlochner,
87
H. H. F. Choi,
87
G. J. King,
87
R. Kowalewski,
87
M. J. Lewczuk,
87
I. M. Nugent,
87
J. M. Roney,
87
R. J. Sobie,
87
N. Tasneem,
87
T. J. Gershon,
88
P. F. Harrison,
88
T. E. Latham,
88
H. R. Band,
89
S. Dasu,
89
Y. Pan,
89
R. Prepost,
89
and S. L. Wu
89
PHYSICAL REVIEW D
86,
112006 (2012)
1550-7998
=
2012
=
86(11)
=
112006(15)
112006-1
Ó
2012 American Physical Society
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Departament ECM, Facultat de Fisica, Universitat de Barcelona, E-08028 Barcelona, Spain
3
INFN Sezione di Bari, I-70126 Bari, Italy
4
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
5
Institute of Physics, University of Bergen, N-5007 Bergen, Norway
6
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
7
Institut fu
̈
r Experimentalphysik 1, Ruhr Universita
̈
t Bochum, D-44780 Bochum, Germany
8
University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
9
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
10
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
11
University of California at Irvine, Irvine, California 92697, USA
12
University of California at Riverside, Riverside, California 92521, USA
13
University of California at Santa Barbara, Santa Barbara, California 93106, USA
14
Institute for Particle Physics, University of California at Santa Cruz, Santa Cruz, California 95064, USA
15
California Institute of Technology, Pasadena, California 91125, USA
16
University of Cincinnati, Cincinnati, Ohio 45221, USA
17
University of Colorado, Boulder, Colorado 80309, USA
18
Colorado State University, Fort Collins, Colorado 80523, USA
19
Fakulta
̈
t Physik, Technische Universita
̈
t Dortmund, D-44221 Dortmund, Germany
20
Institut fu
̈
r Kern-und Teilchenphysik, Technische Universita
̈
t Dresden, D-01062 Dresden, Germany
21
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
22
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
23
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
24
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
25
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
26
INFN Sezione di Genova, I-16146 Genova, Italy
27
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
28
Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India
29
Harvard University, Cambridge, Massachusetts 02138, USA
30
Harvey Mudd College, Claremont, California 91711, USA
31
Physikalisches Institut, Universita
̈
t Heidelberg, Philosophenweg 12, D-69120 Heidelberg, Germany
32
Institut fu
̈
r Physik, Humboldt-Universita
̈
t zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany
33
Imperial College London, London SW7 2AZ, United Kingdom
34
University of Iowa, Iowa City, Iowa 52242, USA
35
Iowa State University, Ames, Iowa 50011-3160, USA
36
Johns Hopkins University, Baltimore, Maryland 21218, USA
37
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
38
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
39
University of Liverpool, Liverpool L69 7ZE, United Kingdom
40
Queen Mary, University of London, London E1 4NS, United Kingdom
41
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
42
University of Louisville, Louisville, Kentucky 40292, USA
43
Institut fu
̈
r Kernphysik, Johannes Gutenberg-Universita
̈
t Mainz, D-55099 Mainz, Germany
44
University of Manchester, Manchester M13 9PL, United Kingdom
45
University of Maryland, College Park, Maryland 20742, USA
46
University of Massachusetts, Amherst, Massachusetts 01003, USA
47
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
48
McGill University, Montre
́
al, Que
́
bec H3A 2T8, Canada
49
INFN Sezione di Milano, I-20133 Milano, Italy
50
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
51
University of Mississippi, University, Mississippi 38677, USA
52
Physique des Particules, Universite
́
de Montre
́
al, Montre
́
al, Que
́
bec H3C 3J7, Canada
53
INFN Sezione di Napoli, I-80126 Napoli, Italy
54
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
55
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, Netherlands
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112006 (2012)
112006-2
56
University of Notre Dame, Notre Dame, Indiana 46556, USA
57
Ohio State University, Columbus, Ohio 43210, USA
58
University of Oregon, Eugene, Oregon 97403, USA
59
INFN Sezione di Padova, I-35131 Padova, Italy
60
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
61
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
62
INFN Sezione di Perugia, I-06100 Perugia, Italy
63
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
64
INFN Sezione di Pisa, I-56127 Pisa, Italy
65
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
66
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
67
Princeton University, Princeton, New Jersey 08544, USA
68
INFN Sezione di Roma, I-00185 Roma, Italy
69
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
70
Universita
̈
t Rostock, D-18051 Rostock, Germany
71
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
72
Centre de Saclay, CEA, Irfu, SPP, F-91191 Gif-sur-Yvette, France
73
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
74
University of South Carolina, Columbia, South Carolina 29208, USA
75
Southern Methodist University, Dallas, Texas 75275, USA
76
Stanford University, Stanford, California 94305-4060, USA
77
State University of New York, Albany, New York 12222, USA
78
School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
79
University of Tennessee, Knoxville, Tennessee 37996, USA
80
University of Texas at Austin, Austin, Texas 78712, USA
81
University of Texas at Dallas, Richardson, Texas 75083, USA
82
INFN Sezione di Torino, I-10125 Torino, Italy
83
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
84
INFN Sezione di Trieste, I-34127 Trieste, Italy
85
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
86
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
87
University of Victoria, Victoria, British Columbia V8W 3P6, Canada
88
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
89
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 8 August 2012; published 20 December 2012)
We present a new measurement of the time-dependent
CP
asymmetry of
B
0
!
D
D

decays using
(
471

5
) million
B

B
pairs collected with the
BABAR
detector at the PEP-II
B
Factory at the SLAC
National Accelerator Laboratory. Using the technique of partial reconstruction, we measure the time-
dependent
CP
asymmetry parameters
S
¼
0
:
34

0
:
12

0
:
05
and
C
¼þ
0
:
15

0
:
09

0
:
04
. Using
the value for the
CP
-odd fraction
R
?
¼
0
:
158

0
:
028

0
:
006
, previously measured by
BABAR
with
fully reconstructed
B
0
!
D
D

events, we extract the
CP
-even components
S
þ
¼
0
:
49

0
:
18

0
:
07

0
:
04
and
C
þ
¼þ
0
:
15

0
:
09

0
:
04
. In each case, the first uncertainty is statistical and the
second is systematic; the third uncertainty on
S
þ
is the contribution from the uncertainty on
R
?
. The
measured value of the
CP
-even component
S
þ
is consistent with the value of
sin2

measured in
b
!
ð
c

c
Þ
s
transitions, and with the Standard Model expectation of small penguin contributions.
DOI:
10.1103/PhysRevD.86.112006
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh
I. INTRODUCTION
In the Standard Model (SM),
CP
violation arises from an
irreducible complex phase in the
3

3
quark mixing matrix
V
known as the Cabibbo-Kobayashi-Maskawa (CKM)
matrix [
1
,
2
]. Unitarity of the CKM matrix requires that
the relation
V
ud
V

ub
þ
V
cd
V

cb
þ
V
td
V

tb
¼
0
,whichdefines
the unitarity triangle, be satisfied. The aim of the
B
Factories
is to test the unitarity of the CKM matrix by the precise
*
Present Address: University of Tabuk, Tabuk 71491,
Saudi Arabia.
Also with Dipartimento di Fisica, Universita
`
di Perugia,
06123 Perugia, Italy.
Now at the University of Huddersfield, Huddersfield HD1
3DH, United Kingdom.
§
Deceased.
k
Now at University of South Alabama, Mobile, Alabama
36688, USA.
{
Also at Universita
`
di Sassari, Sassari 70100, Italy.
**
Deceased.
MEASUREMENT OF THE TIME-DEPENDENT
CP
...
PHYSICAL REVIEW D
86,
112006 (2012)
112006-3
measurement of the angles and sides of the above triangle,
whose nonvanishing area indicates violation of
CP
symmetry.
Both the
BABAR
and Belle collaborations have measured
the
CP
parameter
sin2

, where the angle

is defined as


arg
½
V
cd
V

cb
=V
td
V

tb

. The most accurate measure-
ments of
sin2

[
3
5
] use the
b
c

c
Þ
s
transition, in which
B
0
’s decay to charmonium final states. Measurement of
b
!
c

cd
transitions such as
B
0
!
D
ðÞþ
D
ðÞ
should yield
the same value of
sin2

to the extent that the contributions
from penguin processes may be neglected.
The leading and subleading order Feynman diagrams
contributing to
B
0
!
D
ðÞþ
D
ðÞ
decays are shown in
Fig.
1
. The effect of neglecting the penguin amplitude
has been estimated in models based on factorization and
heavy quark symmetry, and the corrections are found to be
a few percent [
6
,
7
]. Loops involving non-SM particles (for
example, charged Higgs or super symmetric particles)
could increase the contribution from penguin diagrams
and introduce additional phases.
In

ð
4
S
Þ!
B
0

B
0
events the time-dependent decay rate
for
B
0
!
D
D

is given by
P
S
tag

ð

t
Þ¼
e
j

t
j
=
b
4

b
1
þ
S
tag
S

sin
ð

m
d

t
Þ
þ
S
tag
C
cos
ð

m
d

t
Þ
;
(1)
where

b
is the
B
0
lifetime averaged over the two mass
eigenstates,

m
d
is the
B
0

B
0
mixing frequency, and

t
is
the time interval between the
B
0
!
D
D

decay (
B
rec
)
and the decay of the other
B
(
B
tag
) in the event. The
parameter
S
tag
¼þ
1
ð
1
Þ
in Eq. (
1
) indicates the flavor
of the
B
tag
as a
B
0
(

B
0
), while

¼
1
indicates the
CP
eigenvalue of the
B
0
!
D
D

final state. The parame-
ters
C
and
S

are given by
C
¼
1
j

j
2
1
þj

j
2
;
S

¼

2
=
m
ð

Þ
1
þj

j
2
;

¼
q
p

A
A
;
(2)
where
A
ð

A
Þ
is the matrix element of the
B
0
(

B
0
) decay and
p
and
q
are the coefficients appearing in the expression of
the physical mass eigenstates
B
L
,
B
H
in terms of the flavor
eigenstates
B
,

B
as
j
B
L
p
j
B
q
j

B
ij
B
H
p
j
B
i
q
j

B
i
:
Since
B
0
!
D
D

is the decay of a scalar to two
vector mesons, the final state is a mixture of
CP
eigen-
states. The
CP
-odd and
CP
-even fractions have been pre-
viously measured from the angular analysis of completely
reconstructed events [
8
,
9
].
A large deviation of the measured parameter
S

in
Eq. (
2
) from the value of
sin2

measured in
b
c

c
Þ
s
transitions or a nonzero value of direct
CP
violation
[
10
12
] would be strong evidence of new physics.
Both the
BABAR
[
8
] and Belle [
9
] collaborations have
studied the
CP
asymmetries of
B
0
!
D
D

decays
using fully reconstructed events. In this article we report
a new measurement based on the technique of partial
reconstruction, which allows us to gain a factor of
5
in
the number of selected signal events with respect to the
most recent
BABAR
full reconstruction analysis in Ref. [
8
].
This result is complementary to the latter measurement,
because the statistics used are largely independent of
each other.
II. THE
BABAR
DETECTOR AND DATASET
The data sample used in this analysis has been collected
with the
BABAR
detector [
13
] operating at the PEP-II
asymmetric-energy
B
Factory located at the SLAC
National Accelerator Laboratory. We have analyzed the full
BABAR
data set collected at the

ð
4
S
Þ
mass peak,
ffiffiffi
s
p
¼
10
:
58 GeV
, corresponding to an integrated luminosity of
429
:
0fb

1
. In addition, we have used
44
:
8fb

1
of data
taken off-resonance to evaluate the background from events
e
þ
e

!
q

q
,where
q
represents a
u
,
d
,
s
or
c
quark (‘‘con-
tinuum’’). To study backgrounds and validate the analysis
procedure, we use a
GEANT4
-based [
14
] Monte Carlo simu-
lation in which coherent
B

B
production is simulated using
the package
EVTGEN
[
15
].
The asymmetric energies of the PEP-II beams are an
ideal environment to study time-dependent
CP
phenomena
in the
B
0
-

B
0
system. The boost of the

ð
4
S
Þ
in the labo-
ratory frame by

¼
0
:
56
increases the separation
between the vertices of the two
B
meson daughters, allow-
ing their precise measurement.
The
BABAR
detector is described in detail in Ref. [
13
].
We give here only a brief description of the main compo-
nents and their use in this analysis. Tracking is provided by
a five-layer silicon vertex detector (SVT) and a drift cham-
ber (DCH). The SVT provides precise position measure-
ments close to the interaction region that are used in vertex
reconstruction and low-momentum track reconstruction.
The DCH provides excellent momentum measurement of
charged particles.
Particle identification of kaons and pions is obtained
from ionization losses in the SVT and DCH and from
measurements of photons produced in a ring-imaging
Cherenkov light detector (the Detector of Internally
Reflected Cherenkov light). A CsI(Tl) crystal-based elec-
tromagnetic calorimeter (EMC) enables measurement of
FIG. 1. Leading and subleading order Feynman graphs for the

B
0
!
D
ðÞþ
D
ðÞ
decays.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112006 (2012)
112006-4
photon energies and electron identification. These systems
all operate inside a 1.5 T superconducting solenoid, whose
iron flux return is instrumented for muon detection, ini-
tially with resistive plate chambers and more recently with
limited streamer tubes [
16
].
III. ANALYSIS METHOD
A. Partial reconstruction
In the partial reconstruction of a
B
0
!
D
D

candi-
date, we reconstruct fully only one of the two
D

mesons
in the decay chain
D

!
D
0

[
17
], by identifying
D
0
candidates in one of four final states:
K
,
K
0
,
K
,
K
0
S

. The vertexing algorithm fits the two-step
decay tree simultaneously, correctly calculating correla-
tions among all candidates. In the first three
D
0
decay
modes, assumed to represent Cabibbo-favored decays,
charged kaon tracks are selected using particle identifica-
tion information from the Detector of Internally Reflected
Cherenkov light, SVT and DCH. In the last decay mode,
K
0
S
candidates are selected by constraining pairs of oppo-
sitely charged tracks to a common vertex.
Since the kinetic energy available in the decay
D

!
D
0

is small, we combine one reconstructed
D

with
an oppositely charged low-momentum (slow) pion

s
,
assumed to originate from the decay of the unreconstructed
D

, and evaluate the mass
m
rec
of the recoiling
D
0
meson
by using the momenta of the two particles. For signal
events
m
rec
peaks at the nominal
D
0
mass [
18
] with an
rms width of about
3 MeV
=c
2
, while for background
events no such peak is visible. Thus,
m
rec
is the primary
variable to discriminate signal from background. The cal-
culation of
m
rec
proceeds as follows (refer to Fig.
2
for
definitions of the various momenta and angles that we use).
The cosine of the angle between the momenta in the

ð
4
S
Þ
center of mass (CM) frame of the
B
and the recon-
structed
D

is readily computed as
cos

BD

¼

M
2
B
0
þ
E
CM
E
D

2
p
B
j
~
p
D

j
;
(3)
where all particle masses are set to their nominal values
[
18
],
E
D

and
~
p
D

are the measured energy and momentum
of the reconstructed
D

in the

ð
4
S
Þ
CM frame,
E
CM
=
2
is
the energy of each beam in the CM frame, and
p
B
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
2
CM
=
4

M
2
B
0
q
is the
B
meson CM momentum. Events
are required to be in the physical region
j
cos

BD

j
<
1
.
Given
cos

BD

and the measured momenta of the
D

and oppositely charged slow pion, the
B
four-momentum
can be calculated up to an unknown azimuthal angle

around
~
p
D

. For any chosen value of

, conservation laws
determine the unreconstructed
D
0
four-momentum
q
D
ð

Þ
,
and one can thus compute the corresponding

-dependent
invariant mass
m
ð

Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j
q
D
ð

Þj
2
p
. The value of

is not
constrained by kinematics and may be chosen arbitrarily, to
the extent that the shape of the resulting
m
ð

Þ
distribution
may still be described by the type of functions used in our
fits. We have chosen the value
cos

¼
0
:
62
, which is the
median of the corresponding Monte Carlo distribution for
signal events obtained using generated momenta, and
define the recoiling
D
0
mass
m
rec

m
ð
cos

¼
0
:
62
Þ
.
We use the same convention to obtain the direction of the
unreconstructed
D
0
meson.
B. Backgrounds and event selection
Backgrounds to the
B
0
!
D
D

process include the
following:
(i) Combinatorial
B

B
background, defined as decays
other than
B
0
!
D
D

, for which the
m
rec
distri-
bution is approximately flat.
(ii) Peaking
B

B
background, defined as decays other
than
B
0
!
D
D

, in which the
m
rec
distribution
peaks in the signal region. It will be shown later that
the contribution from this background is negligible.
(iii) Background from non-
b

b
events.
Combinatorial
B

B
background events are reduced by the
following requirements. For the
K
0
S

mode, we require the
invariant mass of the pion pair to be within
25 MeV
=c
2
of
the
K
0
S
mass [
18
]. The corresponding vertex must be separated
by more than 3 mm from the beam axis. For the
K
0
mode,

0
candidates are formed from pairs of photons detected in
the EMC, with energies greater than 40 MeV, for which
the invariant mass differs by less than
20 MeV
=c
2
from the
nominal

0
mass [
18
]. The reconstructed
D
0
mass must be
FIG. 2. Momenta and angles in the

ð
4
S
Þ
center of mass frame
used in partial reconstruction. The orthogonal axes
u
and
v
are
normal to the momentum
~
p
D

of the reconstructed
D

, and
u
lies
in the plane defined by the momenta of the
D

and slow pion,
~
p
D

and
~
p
s
. The angle

is measured in the
u

v
plane.
MEASUREMENT OF THE TIME-DEPENDENT
CP
...
PHYSICAL REVIEW D
86,
112006 (2012)
112006-5
equal to the nominal one [
18
] within 2 or 2.5 standard
deviations, depending on the
D
0
reconstruction mode.
The momenta in the

ð
4
S
Þ
CM frame of the reconstructed
D

and

s
from the missing
D
0
must be, respectively, in the
range
1
:
3
2
:
1 GeV
=c
and smaller than
0
:
6 GeV
=c
. The
difference

M
¼j
M
D


M
D
0

M

j
must be equal to
the nominal [
18
] value within 1 or
1
:
5 MeV
=c
2
, according
to the presence or absence of DCH hits in the pion track
appearing in the reconstructed decay
D

!
D
0

. The
probability of the vertex fits must be greater than
10

2
,
for both the
D
0
and the
D

reconstruction.
The requirement on the
D
0
vertex fit probability intro-
duces a small but measurable bias toward lower values of
the
B
lifetime. Because of the partial reconstruction, the
tracks used to make the
D
0
vertex may originate from the
same or different
B
mesons. In the latter case, since not all
tracks are from the same point in space, the
2
of the vertex
fit tends to be bigger. This effect worsens with increasing
distance between the two
B
decay vertices, causing verti-
ces further apart to be rejected more frequently. We have
verified this on signal Monte Carlo events, for which we
have measured a lifetime lower than the generated value.
Consequently, for the signal

t
probability distribution
functions (PDF’s) we use the value of

b
fitted to signal
Monte Carlo.
In events passing this selection we find more than one
candidate decay chain in about 25% of the cases, usually
differing only in the slow pion

s
, but sometimes in the
components of the reconstructed
D

. When this happens,
we choose one candidate chain, based respectively on the
largest number of DCH hits in the

s
, or according to a
2
based on the reconstructed
D
0
mass and

M
quantity
above. For signal Monte Carlo, the probability for this
candidate chain to be the correct one is 0.95.
The main suppression of continuum background is
obtained by requiring that the ratio
R
2
of the 2nd to
the 0th Fox-Wolfram moment [
19
], computed using all
charged particles and EMC clusters not matched to tracks,
be less than 0.3.
C. Fisher discriminant
To further reduce continuum background, we combine
several event-shape variables into a Fisher discriminant
[
20
]
F
. Discriminating power originates from the observa-
tion that
q

q
events tend to be jet-like, whereas
B

B
events
have a more spherical energy distribution. Rather than
applying requirements on
F
, we use the corresponding
distribution in the fits described in Sec.
III E
.
Our Fisher discriminant is a linear combination of vari-
ables chosen, according to Monte Carlo studies, to max-
imize the separation between
B

B
and continuum events.
The first nine variables describe the energy flow inside
nine concentric cones centered around the direction of the
reconstructed
D

. In addition, we use the momenta of the
charged and the neutral particle closest to the cone axis,
the polar angles in the CM of the reconstructed
D

momen-
tum and the thrust axis
T
for charged tracks in the
B
tag
vertex (see next paragraph), the angle between the recon-
structed
D

momentum and
T
, and the sum
S
¼

i
p
i

P
2
ð
cos

i
Þ
over the
B
tag
charged tracks, in which
p
i
is
momentum,
P
2
is the 2nd Legendre polynomial of argument
cos

i
,and

i
is the angle between track
i
at the origin and
T
.
D. Flavor tagging and decay time measurement
For this analysis, two measurements are needed: the
difference

t
between the proper decay times of the par-
tially reconstructed
B
meson and the other
B
meson in the
event, and the flavor of the latter.
The flavor tagging algorithm is based on tracks identi-
fied as electrons, muons or kaons. The electron and muon
tags contribute equally to the total sample and, since these
events are kinematically almost indistinguishable and have
very similar effective tagging efficiency, we treat them as
one homogeneous ‘‘lepton’’ sample.
The tagging tracks must be chosen among those not used
in
B
rec
reconstruction and must originate from within 4 mm
(3 cm) of the interaction point in the transverse (longitudinal)
view. The momentum of the lepton candidates is required to
be greater than
1
:
1GeV
=c
in order to reject most leptons
from charmed meson decays. If one or more lepton candi-
dates are qualified, the tag flavor is assigned based on the
charge of the lepton with the highest center-of-mass momen-
tum. If two or more qualified kaons are present, the event is
used only if the flavor is unambiguous. If both a lepton and a
kaon tag are available, the lepton tag is used.
The time difference

t
is calculated using

t
¼

z=c
, where

z
¼
z
rec

z
tag
is the difference between
the
z
-coordinates of the partially reconstructed
B
rec
and
B
tag
vertices and the boost parameters are calculated using
the measured beam energies. The uncertainty

t
on

t
is
calculated from the results of the
z
rec
and
z
tag
vertex fits.
We require
j

t
j
<
20 ps
and

t
<
2
:
5ps
.
We define the
B
rec
vertex as the decay point of the fully
reconstructed
D

. The

s
track from the other
D

is not
used, since it undergoes significant multiple Coulomb
scattering and hence does not improve the
z
rec
measure-
ment resolution.
The
B
tag
vertex reconstruction depends on the tagging
category. For kaon-tagged events, we obtain
z
tag
from a
beam spot constrained vertex fit of all charged tracks in the
event, excluding those from the
B
rec
meson, and excluding
also tracks within 1 rad of the unreconstructed
D
0
momen-
tum in the CM frame, which presumably originate from the
D
0
decay. We require the probability of this fit to be greater
than
10

2
. For lepton tagged events, we use the lepton
track parameters and errors, and the measured beam spot
position and size in the plane perpendicular to the beams
(the
x
-
y
plane). We find the position of the point in space
for which the sum of the
2
contributions from the lepton
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112006 (2012)
112006-6
track and the beam spot is minimum. The
z
-coordinate of
this point is taken as
z
tag
.
The beam spot is measured on a run-by-run basis using
2-prong events (Bhabha and
þ

), and has an rms size
of approximately
120
m
in the horizontal dimension (
x
),
5
m
in the vertical dimension (
y
), and 8.5 mm along the
beam direction (
z
). The average
B
meson flight distance in
the
x
-
y
plane is
30
m
. To account for the
B
flight distance
in the beam spot constrained vertex fit,
30
m
are added in
quadrature to the effective
x
and
y
sizes.
E. Probability distribution functions
We use two PDF’s,
P
on
for on-resonance, and
P
off
for
off-resonance data. The former depends on the variables
m
rec
,
F
,

t
,

t
,
S
tag
, and is given by the sum of the PDF’s
for the different event types described above,
P
on
¼
f
B

B
½
f
sig
P
sig
þð
1

f
sig
Þ
P
comb
þð
1

f
B

B
Þ
P
q

q
;
(4)
where
P
sig
,
P
comb
, and
P
q

q
are respectively the PDF’s for
signal events, for combinatorial background from
B

B
, and
for continuum. Moreover,
f
B

B
is the fraction of
B

B
events
in our sample, and
f
sig
is the fraction of signal events in
B

B
events. The PDF for off-resonance data,
P
off
, is reduced to
just one component,
P
q

q
, as the off-peak sample contains
only continuum events.
According to Monte Carlo, the distributions of
B
0

B
0
and
B
þ
B

combinatorial background events are very similar
and can be described well by the same PDF.
We do not consider the fraction of
B

B
events a free
parameter, but fix it to
f
B

B
¼
1

f
q

q
,where
f
q

q
is the
fraction of continuum events in the on-peak sample and is
defined by
f
q

q
¼
N
off
-
peak
N
on
-
peak
L
on
-
peak
L
off
-
peak
;
(5)
where
N
’s arethenumberofeventsleftbyourselectioninthe
on- and off-peak samples and
L
’s are the integrated on- and
off-peak luminosities.
Each of the
P
i
(
i
¼
sig
, comb,
q

q
) can be expressed as
the product of three one-dimensional PDF’s,
P
i
ð
m
rec
;F;

t;

t
;S
tag
Þ¼
M
i
ð
m
rec
Þ
F
i
ð
F
Þ
T
0
i
ð

t;

t
;S
tag
Þ
;
(6)
that are the probability distributions of the recoil
D
0
mass
M
i
ð
m
rec
Þ
, the Fisher discriminant function
F
i
ð
F
Þ
, and the
decay time difference function
T
0
i
ð

t;

t
;S
tag
Þ
. This fol-
lows from extensive Monte Carlo studies showing that the
correlations among these variables are negligible.
1.
M
ð
m
rec
Þ
and
F
ð
F
Þ
PDF’s
The
m
rec
distribution of all sample components can be
well modeled in the lower region of the spectrum with a so
called ‘‘Argus function’’ [
21
],
A
ð
m
rec
Þ¼
m
rec
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
m
rec
=m
ep
Þ
2
q

e
c

m
rec
=m
ep
;
(7)
where
m
ep
is the kinematic endpoint (
m
rec
m
ep
) and
c
is
a free parameter describing the slope. This function alone,
however, is not sufficient to account for the abrupt fall of
the
m
rec
spectrum near the kinematic endpoint. For the
signal sample we model this shoulder with an asymmetric
error function with widths
l
and
r
, tapered off at low
m
rec
by an exponential factor with decay constant
a
,
E
ð
m
rec
Þ
¼
8
<
:
e
m
rec
=a
½
1

erf
ð
m
rec

m
ep
Þ
=
ð
ffiffiffi
2
p
l
Þ
;m
rec
<m
ep
e
m
rec
=a
½
1

erf
ð
m
rec

m
ep
Þ
=
ð
ffiffiffi
2
p
r
Þ
;m
rec
>m
ep
:
Thus, we describe the signal
m
rec
distribution with a com-
bination of three functions: a Gaussian
G
having average
m
G
and standard deviation
G
for the well reconstructed
peaking component; an Argus function, mainly for events
in which the right
D

is combined with a low-momentum
pion from another decay chain; and the
E
function
M
sig
ð
m
rec
Þ¼
f
A
sig

A
ð
m
rec
Þþð
1

f
A
sig
Þ½
f
G

G
ð
m
rec
Þ
þð
1

f
G
Þ
E
ð
m
rec
Þ
:
(8)
In Eq. (
8
)
f
A
sig
is the fraction of events described by the
Argus component and
f
G
is the fraction of events in the
Gaussian peak relative to the non-Argus component.
For the background, both combinatorial and continuum,
we set the fraction of the Gaussian component to zero, and
model the distribution at the endpoint with a simple error
function of width
. However, for the case of combinato-
rial background in kaon-tagged events, we find that two
different Argus components (
A
1
and
A
2
) are needed to
correctly describe the entire reconstructed mass spectrum.
We thus define two PDF’s according to
M
comb
ð
m
rec
Þ¼
f
erf
comb

erf
ð
m
rec

m
ep
;
comb
Þ
þð
1

f
erf
comb
Þ½
f
A
1
comb

A
1
ð
m
rec
Þ
þð
1

f
A
1
comb
Þ
A
2
ð
m
rec
Þ
;
(9)
M
q

q
ð
m
rec
Þ¼
f
erf
q

q

erf
ð
m
rec

m
ep
Þ
;
q

q
Þ
þð
1

f
erf
q

q
Þ
A
1
ð
m
rec
Þ
:
(10)
The parameter
m
ep
represents simultaneously the two
Argus endpoints and the error function inflection point.
The Fisher discriminant PDF
F
i
is parametrized by two
Gaussian functions for each event type
i
¼ð
B

B; q

q
Þ
, hav-
ing standard deviations
L
i
and
R
i
, and common mean
i
,
F
i
ð
F
Þ/
8
<
:
exp
½ð
F

i
Þ
2
=
2
ð
L
i
Þ
2

F<
i
exp
½ð
F

i
Þ
2
=
2
ð
R
i
Þ
2

F>
i
:
(11)
Since the Fisher variable is designed to discriminate
between
q

q
and
B

B
events, we expect the Fisher
MEASUREMENT OF THE TIME-DEPENDENT
CP
...
PHYSICAL REVIEW D
86,
112006 (2012)
112006-7
discriminant for signal events to be indistinguishable from
that of
B

B
combinatorial events. We have verified this
expectation with Monte Carlo studies, and thus use the
same Fisher discriminant to describe both event types.
2.

t
PDF’s
The

t
-dependent part of the PDF is a convolution of
the form
T
0
i
ð

t;

t
;S
tag
Þ¼
Z
d

t
true
T
i
ð

t
true
;S
tag
Þ
R
i
ð

t


t
true
;

t
Þ
;
(12)
where
T
is the distribution of

t
true
, the true decay time
difference, and
R
is a resolution function that parametrizes
detector resolution and systematic offsets in the measured
positions of vertices.
Taking into account the mistag probability and the effect
of tags due to the unreconstructed
D
0
, the

t
true
signal PDF
in Eq. (
12
) can be written as
T
sig
¼
1
4

b
e
j

t
true
j
=
b
f
1

S
tag

!
ð
1

Þ
þ
S
tag
ð
1

2
!
Þð
1

Þ½
C
cos
ð

m
d

t
true
Þ
þ
S
sin
ð

m
d

t
true
Þg
;
(13)
where the time-dependent
CP
asymmetry parameters
S
and
C
are the object of the measurement discussed in the
present article and
(see Sec.
IV B
) is the fraction of
events in which the tagging track is from the unrecon-
structed
D
0
. We parametrize possible detector effects lead-
ing to a small difference between the mistag probability of
B
0
tags (
!
þ
) and that of

B
0
tags (
!

), by using the average
mistag rate
!
!
þ
þ
!

Þ
=
2
and the mistag rate differ-
ence

!

!
þ

!

as parameters of the PDF.
Since the
B

B
combinatorial background is dominated by
non-
CP
final states, the
CP
asymmetry is expected to be
negligible. However, we allow the PDF to accommodate
some contamination from
CP
final states. Therefore, we
parametrize the
B

B
background

t
true
distribution with a
PDF similar to that for signal events given in Eq. (
13
).
We also add a fraction
f
of a
-function, to allow for a
zero-lifetime component,
T
comb
¼
f
comb

ðj

t
true
jÞð
1

S
tag

!
comb
Þ
þð
1

f
comb
Þ
1
4

comb
e
j

t
true
j
=
comb
f
1

S
tag

!
comb
þ
S
tag
C
comb
cos
ð

m
d

t
true
Þ
þ
S
comb
sin
ð

m
d

t
true
Þg
:
(14)
The second term of the PDF is obtained from Eq. (
13
) with
!
¼
¼
0
, as these are not defined for background
events. The
C
comb
,
S
comb
parameters describe small fluctu-
ations in the

t
true
distribution of background events and
possible
CP
event contamination, leading to a small effec-
tive
CP
violation value.
The

!
parameters, which for signal events is the
difference in the mistag probabilities for
B
0
and

B
0
, allow
for differences in the number of events tagged as a
B
0
or

B
0
in the same background sample. We use this PDF to
describe both the
B
0

B
0
and
B
þ
B

components.
The PDF for the background due to continuum events is
modeled with a simple exponential decay distribution plus
a fraction
f
of a
-function,
T
q

q
¼
f
q

q
1

S
tag

!
q

q
Þ
ðj

t
true
þð
1

f
q

q
Þð
1

S
tag

!
q

q
Þ
1
4

q

q
e
j

t
true
j
=
q

q
;
(15)
where the parameters

!
q

q
and

!
q

q
allow for differ-
ences in the number of events tagged as a
B
0
or

B
0
in
this sample.
3. Resolution functions
The functions
T
0
i
of the measured time difference

t
,to
be used in the fits, are obtained by convolving the
T
i
PDF’s
of Eqs. (
13
)–(
15
), with the appropriate resolution function
for events of type
i
(
i
¼
sig
, comb,
q

q
).
The resolution functions are parametrized as the sum of
three Gaussian functions,
R
i
ð
t
r
;

t
Þ¼
f
n
i
G
n
i
ð
t
r
;

t
Þþð
1

f
n
i

f
o
i
Þ
G
w
i
ð
t
r
;

t
Þ
þ
f
o
i
G
o
i
ð
t
r
Þ
;
(16)
where
t
r
¼

t


t
true
is the residual of the

t
measure-
ment, and
G
n
i
,
G
w
i
, and
G
o
i
are the ‘‘narrow,’’ ‘‘wide,’’ and
‘‘outlier’’ Gaussian functions. The narrow and wide
Gaussian functions incorporate information from the

t
uncertainty

t
, and account for systematic offsets in
the estimation of

t
and the

t
measurement. They
have the form
G
k
i
ð
t
r
;

t
Þ
1
ffiffiffiffiffiffiffi
2

p
s
k
i

t

exp


ð
t
r

b
k
i

t
Þ
2
2
ð
s
k
i

t
Þ
2

;
(17)
where the index
k
takes the values
k
¼
n
,
w
for the narrow
and wide Gaussian funcions, and
b
k
i
and
s
k
i
are parameters
determined by fits. The outlier Gaussian function, describ-
ing a small fraction of events with badly measured

t
, has
the form
G
o
i
ð
t
r
Þ
1
ffiffiffiffiffiffiffi
2

p
s
o
i
exp


ð
t
r

b
o
i
Þ
2
2
ð
s
o
i
Þ
2

:
(18)
In all fits, the values of
b
o
i
and
s
o
i
are fixed to 0 and 8 ps,
respectively, and are later varied to evaluate systematic
uncertainties.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112006 (2012)
112006-8
F. Analysis procedure
After the event selection described in Sec.
III B
is com-
plete, the rest of the analysis proceeds with a series of
unbinned maximum-likelihood fits, performed simulta-
neously on the on- and off-resonance data samples and
independently for the lepton tagged and kaon-tagged
events. The procedure can be logically divided in the
following three steps, which we shall discuss in detail in
the following paragraphs:
(1) In the first step we determine the signal fraction
f
sig
in Eq. (
4
) and the shape of
M
ð
m
rec
Þ
and
F
ð
F
Þ
in
Eq. (
6
) for the different classes of events (signal and
backgrounds, kaon and lepton tagging categories).
This is done by fitting data with the PDF
P
i
ð
m
rec
;F
Þ¼
M
i
ð
m
rec
Þ
F
i
ð
F
Þ
;
(19)
ignoring the time dependence; we refer to this step
as the kinematic fit.
(2) In the second step we determine the tagging dilution
due to wrong tag assignments.
(3) In the last step we perform the time-dependent fit to
the data. We fix all parameter values obtained in the
previous steps and use the full PDF of Eq. (
6
)to
determine the parameters of the resolution func-
tions,
T
0
i
ð

t;

t
;S
tag
Þ
, and the
CP
asymmetry val-
ues
C
,
S
of the signal and of the
B

B
combinatorial
background component.
The fitting procedure has been validated using both full
Monte Carlo and, where the requested number of events
would be too large, the technique of ‘‘toy’’ Monte Carlo. In
a toy Monte Carlo, events are described by a small number
of variables which are generated according to our PDF’s.
IV. RESULTS
Event selection yields the numbers of events listed in the
top two rows of Table
I
. The third and fourth rows show the
number of continuum and
B

B
events calculated, using
Eq. (
5
), from the number of off-peak events in the second
row. The numbers of signal events in the last line of the
table are calculated using the signal fractions obtained
from the kinematic fit described in the next section.
A. Kinematic fit
We begin by fitting the shape of our signal,
M
sig
ð
m
rec
Þ
,
using a large sample of Monte Carlo signal events. The
parameters most relevant to determine directly the signal
fraction in the data, and consequently our final result for
S
and
C
, will be released again in the final kinematic fit. They
are [refer to Eq. (
8
)]: the Gaussian fraction
f
G
, mean value
m
G
, and standard deviation
G
, and are shown in the last
section of Table
II
.
Next we fit the Fisher
F
q

q
and recoil mass
M
q

q
distri-
bution to the off-peak data sample. As the number of off-
resonance events selected in the lepton tagged sample is
too small to yield convergence, we set the lepton tag
sample parameters to the corresponding values obtained
from the fit to the kaon tag sample. Because of the small
continuum fraction in the lepton sample, we judge that this
does not introduce any significant systematic effect. The
F
q

q
parameters are fixed in all subsequent fits.
We initialize the parameters of the
B

B
combinatorial
background PDF directly from the data, using a sample of
events in which the contribution of signal events is much
reduced. We obtain this sample by combining a
D

with a
pion of wrong sign charge (WS sample). We have verified,
both on Monte Carlo and in the
m
rec
sideband for data
(
1
:
836
1
:
856 GeV
=c
2
), that the shape of the
M
ð
m
rec
Þ
distribution for combinatorial
B

B
background is well
described by that of the WS data sample.
To evaluate a possible contribution from a peaking
component in the
B

B
background events, we have allowed
the Gaussian fraction
f
G
in Eq. (
8
) to float in a fit to a
sample of Monte Carlo background events; this fraction is
found to be
0
:
000

0
:
002
, and is therefore set to zero.
Finally we fit the on-peak data sample, leaving as free
parameters the fraction
f
sig
of signal events in the
B

B
com-
ponent, some of the shape parameters of the continuum and
B

B
combinatorial background
M
comb
, some of the signal
parameters in
M
sig
, and the shape parameters of the Fisher
discriminant
F
B

B
. Table
II
summarizes the results and pro-
vides information about which parameters are released in the
fit (statistical uncertainties given) and which ones are taken
from previous fits (no uncertainty given).
The final results of the kinematic fits for the kaon and
lepton tagged sample are shown in Figs.
3
and
4
.
B. Determination of mistag probabilities
A common problem of analyses using the partial recon-
struction technique is that a fraction of the tracks used in
tagging may belong to the unreconstructed
D
0
, leading to a
mistag of the event. As the tracks originating from the
missing
D
0
tend to align to its direction of flight, this
fraction can be reduced by applying a constraint on the
TABLE I. Event selection yield. The first uncertainty shown is
statistical, while the second uncertainty on the number of contin-
uum events accounts for a 1% relative uncertainty on the on-peak
and off-peak luminosities.
Number of events
Kaon tag
Lepton tag
On-peak
61179
20855
Off-peak
1025
51
Continuum
9814

307

196
488

68

10
B

B
51365

364
20367

69
N
sig
3843

397
1129

218
MEASUREMENT OF THE TIME-DEPENDENT
CP
...
PHYSICAL REVIEW D
86,
112006 (2012)
112006-9