of 12
Measurement of
D
0
-

D
0
mixing and
CP
violation in two-body
D
0
decays
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
D. J. Asgeirsson,
7
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov,
9
A. R. Buzykaev,
9
V. P. Druzhinin,
9
V. B. Golubev,
9
E. A. Kravchenko,
9
A. P. Onuchin,
9
S. I. Serednyakov,
9
Yu. I. Skovpen,
9
E. P. Solodov,
9
K. Yu. Todyshev,
9
A. N. Yushkov,
9
M. Bondioli,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
H. Atmacan,
11
J. W. Gary,
11
F. Liu,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
B. Spaan,
18
K. R. Schubert,
19
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
P. J. Clark,
21
S. Playfer,
21
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
22a,22b
M. Munerato,
22a,22b
L. Piemontese,
22a
V. Santoro,
22a
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
P. Patteri,
23
I. M. Peruzzi,
23,
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
B. Bhuyan,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. J. Edwards,
27
A. Adametz,
28
U. Uwer,
28
H. M. Lacker,
29
T. Lueck,
29
P. D. Dauncey,
30
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
P. Roudeau,
34
M. H. Schune,
34
A. Stocchi,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
K. Griessinger,
40
A. Hafner,
40
E. Prencipe,
40
R. J. Barlow,
41,
G. Jackson,
41
G. D. Lafferty,
41
E. Behn,
42
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
R. Cheaib,
45
D. Lindemann,
45
P. M. Patel,
45,
§
S. H. Robertson,
45
P. Biassoni,
46a,46b
N. Neri,
46a
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
k
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
M. Simard,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
M. Martinelli,
50
G. Raven,
50
C. P. Jessop,
51
J. M. LoSecco,
51
W. F. Wang,
51
K. Honscheid,
52
R. Kass,
52
J. Brau,
53
R. Frey,
53
N. B. Sinev,
53
D. Strom,
53
E. Torrence,
53
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
G. Simi,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
S. Akar,
55
E. Ben-Haim,
55
M. Bomben,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
S. Sitt,
55
M. Biasini,
56a,56b
E. Manoni,
56a,56b
S. Pacetti,
56a,56b
A. Rossi,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b
M. Carpinelli,
57a,57b,
{
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
B. Oberhof,
57a,57b
E. Paoloni,
57a,57b
A. Perez,
57a
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
C. Bu
̈
nger,
60
O. Gru
̈
nberg,
60
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60,
§
C. Voss,
60
R. Waldi,
60
T. Adye,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
J. F. Benitez,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
M. Ebert,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
P. Lewis,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
R. H. Schindler,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
J. Va’vra,
63
A. P. Wagner,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
C. C. Young,
63
V. Ziegler,
63
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
A. Randle-Conde,
65
S. J. Sekula,
65
M. Bellis,
66
P. R. Burchat,
66
T. S. Miyashita,
66
E. M. T. Puccio,
66
M. S. Alam,
67
J. A. Ernst,
67
R. Gorodeisky,
68
N. Guttman,
68
D. R. Peimer,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
J. L. Ritchie,
70
A. M. Ruland,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
S. Zambito,
72a,72b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
F. Martinez-Vidal,
74
A. Oyanguren,
74
H. Ahmed,
75
J. Albert,
75
Sw. Banerjee,
75
F. U. Bernlochner,
75
H. H. F. Choi,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
I. M. Nugent,
75
J. M. Roney,
75
R. J. Sobie,
75
N. Tasneem,
75
T. J. Gershon,
76
P. F. Harrison,
76
T. E. Latham,
76
H. R. Band,
77
S. Dasu,
77
Y. Pan,
77
R. Prepost,
77
and S. L. Wu
77
PHYSICAL REVIEW D
87,
012004 (2013)
1550-7998
=
2013
=
87(1)
=
012004(12)
012004-1
Ó
2013 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, Universitat de Barcelona, Facultat de Fisica, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento 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
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
19
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
21
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
22b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711, USA
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
30
Imperial College London, London, SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
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
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London, E1 4NS, United Kingdom
38
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
40
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
41
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
46a
INFN Sezione di Milano, I-20133 Milano, Italy
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, Netherlands
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
012004 (2013)
012004-2
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
55
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
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-56127 Pisa, Italy
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
58
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 20 September 2012; published 3 January 2013)
We present a measurement of
D
0
-

D
0
mixing and
CP
violation using the ratio of lifetimes simultaneously
extracted from a sample of
D
0
mesons produced through the flavor-tagged process
D
!
D
0

þ
,where
D
0
decays to
K



,
K

K
þ
,or



þ
, along with the untagged decays
D
0
!
K



and
D
0
!
K

K
þ
.The
lifetimes of the
CP
-even, Cabibbo-suppressed modes
K

K
þ
and



þ
are compared to that of the
CP
-mixed
mode
K



in order to measure
y
CP
and

Y
. We obtain
y
CP
¼½
0
:
72

0
:
18
ð
stat
Þ
0
:
12
ð
syst
Þ
%
and

Y
¼½
0
:
09

0
:
26
ð
stat
Þ
0
:
06
ð
syst
Þ
%
,where

Y
constrains possible
CP
violation. The
y
CP
result
excludes the null mixing hypothesis at
3
:
3

significance. This analysis is based on an integrated luminosity
of
468 fb

1
collected with the
BABAR
detector at the PEP-II asymmetric-energy
e
þ
e

collider.
DOI:
10.1103/PhysRevD.87.012004
PACS numbers: 13.25.Ft, 11.30.Er, 12.15.Ff
I. INTRODUCTION
Several measurements [
1
6
] show evidence for mixing
in the
D
0
-

D
0
system consistent with predictions of possible
Standard Model (SM) contributions [
7
11
]. These results
also constrain many new physics models [
12
16
]. An
observation of
CP
violation (
CPV
) in the
D
0
-

D
0
system
at the present experimental sensitivity would provide pos-
sible evidence for physics beyond the SM [
17
21
].
*
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia.
Also with Universita
`
di Perugia, Dipartimento di Fisica,
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 with Universita
`
di Sassari, Sassari, Italy.
MEASUREMENT OF
D
0
-

D
0
MIXING AND
CP
...
PHYSICAL REVIEW D
87,
012004 (2013)
012004-3
One manifestation of
D
0
-

D
0
mixing is differing
D
0
decay time distributions for decays to different
CP
eigen-
states Ref. [
22
]. We present a measurement of charm
mixing using the ratio of lifetimes obtained from the
decays of neutral
D
mesons to
CP
-even and
CP
-mixed
two-body final states. We also present a search for indirect
CP
violation arising from a difference in
D
0
and

D
0
partial decay widths to
CP
-even eigenstates. Recently
the LHCb Collaboration has reported evidence for
CPV
in the difference of the time-integrated
CP
asymmetries
in
D
0
!
K

K
þ
and
D
0
!



þ
decays [
23
]. This
measurement is primarily sensitive to direct
CPV
.
As explained in Appendix
A
, we are not sensitive to effects
of direct
CP
violation at the level of the result reported by
LHCb, and we therefore assume no direct
CPV
in our
baseline model.
We measure the effective
D
0
lifetimes in three different
two-body final states:
K



,
K

K
þ
, and



þ
.We
make no distinction between the Cabibbo-favored
D
0
!
K


þ
and doubly Cabibbo-suppressed
D
0
!
K
þ


modes; in other words, we analyze and describe them
together. Given the current experimental evidence indicat-
ing a small mixing rate, the lifetime distribution for all
two-body final states is exponential to a good approxima-
tion. Decays in the
K



mode are to a
CP
-mixed final
state, and are assumed to be described by the average
D
0
width

. The singly Cabibbo-suppressed decays
D
0
(

D
0
)to
the
CP
-even
K

K
þ
and



þ
final states are described
by the partial decay rate

þ
(

þ
), where
þ
indicates the
CP
of the final state. We present in Appendix
A
a discus-
sion of the mixing formalism leading to the expressions
that are used to extract the mixing parameter
y
CP
and the
CPV
parameter

Y
,
y
CP
¼

þ
þ

þ
2

1
;
(1)

Y
¼

þ


þ
2
;
(2)
from the experimentally measured
CP
-mixed and
CP
-even
lifetimes. This definition of

Y
is opposite in sign to
that in our previous measurement [
2
] and is now con-
sistent with that used by the Heavy Flavor Averaging
Group [
24
].
Tagged decays refer to
D
0
mesons coming from
D
!
D
0

þ
decays [
25
], while untagged decays refer to
D
0
mesons where no
D
parent was found. The charge of
the
D

is used to split the
K

K
þ
and



þ
samples into
those originating from
D
0
and from

D
0
mesons in order to
measure the
CP
-violating parameter

Y
. The requirement
of a
D
parent strongly suppresses backgrounds; hence
untagged decays are reconstructed only in
K



and
K

K
þ
because of the relatively poor signal-to-background
ratio in the untagged



þ
final state. In summary, we
study seven modes: two untagged and five tagged.
In addition to the increased integrated luminosity of the
new dataset compared to that used in our earlier results
[
2
,
3
], this analysis benefits from improved charged-particle
track reconstruction, and a more inclusive and optimized
event selection. The particle identification selection effi-
ciency was sizably increased both for pions and kaons in
the high-momentum-spectrum range by improving the
algorithms that combine the information coming from the
detector. We implement an improved background model,
and we simultaneously fit both the tagged and untagged
datasets.
II. EVENT RECONSTRUCTION AND SELECTION
We use
468 fb

1
of
e
þ
e

colliding-beam data recorded
at, and slightly below, the

ð
4
S
Þ
resonance (
e
þ
e

center-
of-mass [CM] energy
ffiffiffi
s
p

10
:
6 GeV
) with the
BABAR
detector [
26
] at the SLAC National Accelerator Laboratory
PEP-II asymmetric-energy
B
Factory. To avoid potential
bias, we finalize our data selection criteria, as well as the
procedures for fitting, extracting statistical limits, and
determining systematic uncertainties, prior to examining
the results.
We reconstruct charged tracks and vertices with a five-
layer, double-sided silicon vertex tracker (SVT) and a
40-layer drift chamber. We select
D
0
candidates by pairing
oppositely charged tracks, requiring each track to satisfy
particle identification criteria based on specific ionization
energy loss (
d
E=
d
x
) from the SVT and drift chamber, and
Cherenkov angle measurements from a ring-imaging
Cherenkov detector. We then refit the
D
0
daughter tracks,
requiring them to originate from a common vertex. To
reduce contributions from
D
0
’s produced via
B
-meson
decay to a negligible level, we require each
D
0
to have
momentum in the CM frame
p
CM
>
2
:
5 GeV
=c
.
For tagged decays, we reconstruct
D
candidates by
combining a
D
0
candidate with a slow pion track

þ
s
,
requiring them to originate from a common vertex con-
strained to the
e
þ
e

interaction region. We require the

þ
s
momentum to be greater than
0
:
1 GeV
=c
in the laboratory
frame and less than
0
:
45 GeV
=c
in the CM frame. We
reject a positron that fakes a

þ
s
candidate by using
d
E=
d
x
information and veto any

þ
s
candidate that may have
originated from a reconstructed photon conversion or

0
Dalitz decay. The distribution of the difference

m
between the reconstructed
D
and
D
0
masses peaks
near

m

0
:
1455 GeV
=c
2
. Backgrounds are suppressed
by retaining only tagged candidates in the range
0
:
1447
<

m<
0
:
1463 GeV
=c
2
.
To determine the proper time
t
and its error

t
for each
D
0
candidate, we perform a combined fit to the
D
0
pro-
duction and decay vertices. We constrain the production
point to be within the
e
þ
e

interaction region, which we
determine using Bhabha and di-muon events from triggers
close in time to any given signal candidate event. We retain
only candidates with a

2
-based probability for the fit
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
012004 (2013)
012004-4
P
ð

2
Þ
>
0
:
1%
, and with

2
<t<
4ps
and

t
<
0
:
5ps
.
For tagged decays, this fit does not incorporate any

þ
s
information in order to ensure that the lifetime resolution
models for tagged and untagged signal decays are very
similar. The most probable value of

t
for signal events is

40%
of the nominal
D
0
lifetime [
27
].
If an event contains a tagged
D
0
decay, we exclude all
untagged
D
0
candidates from that event in the final sample.
For a given final state, when multiple
D
0
(for the untagged
modes) or
D
(for the tagged modes) candidates in an
event share one or more tracks, we retain only the candi-
date with the highest
P
ð

2
Þ
. The fraction of events with
multiple
D
0
candidates with overlapping daughter tracks is

1%
for all final states.
III. INVARIANT-MASS FITS
We characterize the
D
0
invariant-mass (
M
) distribution
for each of the seven modes with an extended unbinned
maximum likelihood fit to
D
0
and

D
0
samples. We allow
the parameters governing the shapes of the probability
density functions (PDFs), as well as the expected signal
and background candidate yields, to vary in the fits. For
the tagged
CP
-even modes we fit the
D
0
and

D
0
samples
simultaneously, sharing all parameters except for the
expected signal and background candidate yields.
We fit the tagged



þ
invariant-mass distribution in
the fit range
1
:
82
<M

<
1
:
93 GeV
=c
2
using a sum of
two Gaussians with independent means and widths for the
signal PDF, along with a first-order Chebychev polynomial
for the total background.
The fit model for the tagged
K

K
þ
invariant-mass
distribution is similar to



þ
, except that the fit range
is
1
:
82
<M
KK
<
1
:
91 GeV
=c
2
, and the signal PDF is the
sum of two independent Gaussians and a modified
Gaussian with a power-law tail [
28
], which aids in better
modeling of the lower tail of the distribution.
The signal PDF for the untagged
K

K
þ
mode and for
both tagged and untagged
K



modes is a sum of three
independent Gaussians: the background is modeled using a
second-order Chebychev polynomial. The mass fit range is
1
:
82
<M
KK
<
1
:
91 GeV
=c
2
for the untagged
K

K
þ
mode,
1
:
81
<M
K
<
1
:
92 GeV
=c
2
for the untagged
K



mode, and
1
:
80
<M
K
<
1
:
93 GeV
=c
2
for the
tagged
K



mode. In these modes, we do not distinguish
D
0
from

D
0
candidates, and therefore determine only the
total signal and total background yields, in addition to the
signal and background shape parameters.
The reconstructed
D
0
invariant-mass distributions and
the fit results are shown in Fig.
1
, together with a plot of the
corresponding normalized Poisson pulls [
29
].
IV. SIGNAL AND SIDEBAND REGIONS
For the lifetime fit, we determine the regions in
two-body invariant mass that maximize signal significance,
minimize systematic effects due to backgrounds, and mini-
mize the effect of the correlation between the
D
0
invariant
mass and proper time. We refer to these regions as the
lifetime-fit mass regions. Based on these studies, the optimal
lifetime-fit mass region is
34 MeV
=c
2
wide for all tagged
modes and untagged
K



events,
1
:
847
<M<
1
:
881 GeV
=c
2
. Because ofthe smaller signal-to-background
ratio for the untagged
K

K
þ
events, the lifetime-fit
mass region for this mode is only
24 MeV
=c
2
in width,
)
2
Entries / ( 1.10 MeV/c
0
500
1000
1500
2000
*
D
)
2
(GeV/c
π
π
M
1.82 1.84 1.86 1.88
1.9
1.92
Pull
-2
+2
)
2
Entries / ( 1.10 MeV/c
0
500
1000
1500
2000
+
*
D
π
ππ
π
)
2
(GeV/c
π
π
M
1.82 1.84 1.86 1.88
1.9
1.92
Pull
-2
+2
)
2
Entries / ( 0.90 MeV/c
0
1000
2000
3000
4000
*
D
KK
)
2
(GeV/c
KK
M
1.82
1.84
1.86
1.88
1.9
Pull
-2
+2
)
2
Entries / ( 0.90 MeV/c
0
1000
2000
3000
4000
+
*
D
KK
)
2
(GeV/c
KK
M
1.82
1.84
1.86
1.88
1.9
Pull
-2
+2
)
2
Entries / ( 0.90 MeV/c
0
10
20
30
3
10
×
unt
KK
)
2
(GeV/c
KK
M
1.82
1.84
1.86
1.88
1.9
Pull
-2
+2
)
2
Entries / ( 1.30 MeV/c
0
20
40
60
80
100
3
10
×
±
*
D
π
K
)
2
(GeV/c
π
K
M
1.8 1.82 1.84 1.86 1.88 1.9 1.92
Pull
-2
+2
)
2
Entries / ( 1.10 MeV/c
0
100
200
300
400
3
10
×
unt
π
K
)
2
(GeV/c
π
K
M
1.82 1.84 1.86 1.88
1.9
1.92
Pull
-2
+2
FIG. 1 (color online). The reconstructed two-body invariant-
mass distributions for the seven modes. The vertical lines show
the lifetime-fit mass region, defined in Sec.
IV
. The shaded
regions are the background contributions. The normalized
Poisson pulls for each fit are shown under each plot: ‘‘unt’’
refers to the untagged datasets.
MEASUREMENT OF
D
0
-

D
0
MIXING AND
CP
...
PHYSICAL REVIEW D
87,
012004 (2013)
012004-5
1
:
852
<M<
1
:
876 GeV
=c
2
. For the tagged modes, a mass
difference sideband
0
:
151
<

m<
0
:
159 GeV
=c
2
is used,
along with a low- (high-) invariant-mass sideband,
1
:
819
ð
1
:
890
Þ
<M<
1
:
839
ð
1
:
910
Þ
GeV
=c
2
. The low-
(high-) mass sideband used for the untagged modes,
1
:
810
ð
1
:
899
Þ
<M<
1
:
830
ð
1
:
919
Þ
GeV
=c
2
, is displaced
from the tagged sideband in order to reduce the signal
component there. The contribution of the signal events in
the sideband regions is in general very small compared to the
background; however, it has been considered when extract-
ing the combinatorial-background PDF. The signal purities
in the lifetime-fit mass regions range from

75%
for the
untagged
K

K
þ
sample to

99
:
8%
for the tagged
K



events.
We classify
D
0
candidate decays in the lifetime-fit mass
region as follows:
D
0
signal decays; misreconstructed-
charm decays, i.e., those in which the candidate-
D
0
daugh-
ter tracks are decay products of a nonsignal weak charm
decay; and random combinatorial background. Table
I
gives the composition of the misreconstructed-charm
backgrounds expected from simulated events [
30
] in each
final state.
V. LIFETIME FIT
The lifetimes are determined from an extended
unbinned maximum likelihood fit to
t
and

t
for candi-
dates in the lifetime-fit mass region. All modes are fit
simultaneously using shared signal-resolution-function
parameters. The signal, misreconstructed-charm, and
combinatorial components are described by their own
set of PDFs, which in the tagged modes can also depend
on the charm flavor.
The lifetime PDF for the signal is an exponential
function convolved with a resolution function, which is
the sum of three Gaussian functions whose widths are
proportional to

t
. The explicit form of the signal lifetime
PDF is
R
T
F;L
ð
t; 
t
Þ¼
f
t
1
D
ð
t; 
t
;
S
0
T
S
F
s
1
;t
0
;
L
Þ
þð
1

f
t
1
Þ½
f
t
2
D
ð
t; 
t
;
S
0
T
S
F
s
2
;t
0
;
L
Þ
þð
1

f
t
2
Þ
D
ð
t; 
t
;
S
0
T
S
F
s
3
;t
0
;
L
Þ
;
(3)
where
f
ti
(with
i
¼
1
, 2) parametrizes the contribution
of each individual Gaussian,
s
i
(with
i
¼
1
,2,3)isa
scaling factor associated with each Gaussian, and
t
0
is an
offset of the mean of the resolution function. The function
D
ð
t; 
t
;
s; t
0
;
Þ
is given by
D
ð
t;
t
;
s;t
0
;
Þ¼
C

t
Z
exp
ð
t
true
=
Þ

exp


ð
t

t
true
þ
t
0
Þ
2
2
ð
s

t
Þ
2

dt
true
;
(4)
where the normalization coefficient
C

t
is chosen such that
Z
D
ð
t; 
t
;
s; t
0
;
Þ
dt
¼
1
for each

t
:
(5)
With this definition, the product
H
sig

t
ð

t
Þ
D
ð
t; 
t
;
s; t
0
;
Þ
is a properly normalized two-dimensional conditional
PDF, where
H
sig

t
ð

t
Þ
is a PDF characterizing the

t
distri-
bution, described below. To account for small differences
in the resolution function for the different final states we
introduce additional mode-dependent scale factors
S
F
,
F
¼
K
,
KK
,

. We also allow for differences between
the resolution functions for tagged and untagged modes by
means of scale factors
S
0
T
,
T
¼
tag
(tagged) or unt
(untagged). We fix
S
K
and
S
0
unt
to 1.
The three lifetime parameters are

L
¼f

þ
;


þ
;
K
g
,
where

K
is extracted from the tagged and untagged
K



modes, while

þ
and


þ
are extracted from the
tagged and untagged
CP
-even modes. Approximately
0.4% of the tagged
CP
-even samples contain correctly
reconstructed
D
0
candidates combined with an unrelated

þ
s
: this fraction has been estimated from simulated events
and verified in data by an earlier
BABAR
analysis [
1
].
These candidates have the same resolution and lifetime
behavior as those from correctly reconstructed
D
decays, but about half of them will be tagged as the wrong
flavor. Therefore, the tagged
CP
-even
D
0
proper-time dis-
tributions are modeled as the weighted sum of PDFs for
correctly tagged and untagged candidates, characterized by
the lifetime parameters

þ
and


þ
, respectively, and a
mistag fraction
f
tag
¼
0
:
2%
. The tagged
CP
-even

D
0
proper-time distributions are modeled in a similar fashion,
where now the correctly tagged and mistagged PDFs are
characterized by the lifetime parameters


þ
and

þ
,
respectively. The untagged
K

K
þ
proper-time distribution
is modeled as a weighted sum of two PDFs characterized
by the lifetime parameters

þ
and


þ
, respectively, and a
weighting fraction
f
D
0
¼
0
:
5
. These parametrizations
assume no direct
CPV
, and allow for
CPV
in the interfer-
ence between decays with and without mixing character-
ized by a mode-independent weak phase

. Both
f
tag
and
TABLE I. Expected composition (in %) of the
misreconstructed-charm backgrounds. Only misreconstructed-
charm background channels that have
>
1%
contribution in at
least one signal mode are listed. For the tagged modes, the yields
are the sum of the separate
D
0
and

D
0
tags.
Tagged Modes
Untagged Modes
Mode



þ
K

K
þ
K



K

K
þ
K



D
0
!
X‘
15.4 10.3 29.9
7.2
2
D
0
!
K


þ
80.8 14.9 57.1
8.8
35.8
D
0
!

0

þ
K

1.1
70.3
1.7
63.3
6.9
D
þ
!

þ

þ
K

1
2.9
1
11.8
2
D
0
!
K
þ
K

1
1
1.3
1
3.5
D
0
!

þ


1.8
1
2.2
1
3.1
D
0
!

þ



0
1
1
7.0
1
17.3

decays
1
1
1
4.9
2.6
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
012004 (2013)
012004-6