Search for direct
CP
violation in singly Cabibbo-suppressed
D
!
K
þ
K
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
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
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
P. Villanueva-Perez,
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,
052010 (2013)
1550-7998
=
2013
=
87(5)
=
052010(12)
052010-1
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, Facultat de Fisica, Universitat de Barcelona, 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
Institute of Physics, University of Bergen, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Institut fu
̈
r Experimentalphysik 1, Ruhr Universita
̈
t Bochum, 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
Institute for Particle Physics, University of California at Santa Cruz, 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
Fakulta
̈
t Physik, Technische Universita
̈
t Dortmund, D-44221 Dortmund, Germany
19
Institut fu
̈
r Kern- und Teilchenphysik, Technische Universita
̈
t Dresden, 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 781039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711, USA
28
Physikalisches Institut, Universita
̈
t Heidelberg, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Institut fu
̈
r Physik, Humboldt-Universita
̈
t zu Berlin, Newtonstrasse 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
Royal Holloway and Bedford New College, University of London, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
40
Institut fu
̈
r Kernphysik, Johannes Gutenberg-Universita
̈
t Mainz, 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
Physique des Particules, Universite
́
de Montre
́
al, 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, The Netherlands
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
052010 (2013)
052010-2
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
School of Physics and Astronomy, Tel Aviv University, 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 11 December 2012; published 6 March 2013)
We report on a search for direct
CP
violation in the singly Cabibbo-suppressed decay
D
þ
!
K
þ
K
þ
using a data sample of
476 fb
1
of
e
þ
e
annihilation data accumulated with the
BABAR
detector at the
SLAC PEP-II electron-positron collider, running at and just below the energy of the
ð
4
S
Þ
resonance. The
integrated
CP
-violating decay rate asymmetry
A
CP
is determined to be
ð
0
:
37
0
:
30
0
:
15
Þ
%
. Model-
independent and model-dependent Dalitz plot analysis techniques are used to search for
CP
-violating
asymmetries in the various intermediate states. We find no evidence for
CP
-violation asymmetry.
DOI:
10.1103/PhysRevD.87.052010
PACS numbers: 11.30.Er, 13.25.Ft, 14.40.Lb
I. INTRODUCTION
Searches for
CP
violation (
CPV
) in charm meson decays
provide a probe of physics beyond the Standard Model.
Singly Cabibbo-suppressed (SCS) decays can exhibit direct
CP
asymmetries due to interference between tree-level
transitions and
j
C
j¼
1
penguin-level transitions if there
is both a strong and a weak phase difference between the
two amplitudes. In the Standard Model, the resulting asym-
metries are suppressed by
O
ðj
V
cb
V
ub
=V
cs
V
us
jÞ
10
3
,
where
V
ij
are elements of the Cabibbo-Kobayashi-
Maskawa quark-mixing matrix [
1
]. A larger measured value
of the
CP
asymmetry could be a consequence of the
*
Present address: University of Tabuk, Tabuk 71491, Saudi Arabia.
†
Also with Dipartimento di Fisica, Universita
`
di Perugia, Perugia, Italy.
‡
Present address: University of Huddersfield, Huddersfield HD1 3DH, UK.
§
Deceased.
k
Present address: University of South Alabama, Mobile, Alabama 36688, USA.
{
Also with Universita
`
di Sassari, Sassari, Italy.
SEARCH FOR DIRECT
CP
VIOLATION IN SINGLY
...
PHYSICAL REVIEW D
87,
052010 (2013)
052010-3
enhancement of penguin amplitudes in
D
meson decays due
to final-state interactions [
2
,
3
]orofnewphysics[
4
,
5
].
The LHCb and CDF Collaborations recently reported
evidence for a nonzero
CP
asymmetry in the difference of
the time-integrated
D
0
!
þ
and
D
0
!
K
þ
K
decay
rates [
6
,
7
]. Searches for
CPV
in other SCS decays with
identical transitions
c
!
ud
d
and
c
!
us
s
are relevant to
an understanding of the origin of
CPV
[
8
–
10
].
We present here a study of the SCS decay
D
þ
!
K
þ
K
þ
[
11
], which is dominated by quasi-two-body
decays with resonant intermediate states. This allows us
to probe the Dalitz-plot substructure for asymmetries in
both the magnitudes and phases of the intermediate states.
The results of this study include a measurement of the
integrated
CP
asymmetry, the
CP
asymmetry in four re-
gions of the Dalitz plot, a comparison of the binned
D
þ
and
D
Dalitz plots, a comparison of the Legendre polynomial
moment distributions for the
K
þ
K
and
K
þ
systems,
and a comparison of parametrized fits to the Dalitz plots.
Previous measurements by the CLEO-c Collaboration
found no evidence for
CPV
in specific two-body ampli-
tudes or for the integrals over the entire phase space [
12
].
The LHCb Collaboration also finds no evidence for
CPV
in
a model-independent search [
13
].
II. THE
BABAR
DETECTOR AND DATA SAMPLE
The analysis is based on a sample of electron-positron
annihilation data collected at and just below the energy of
the
ð
4
S
Þ
resonance with the
BABAR
detector at the SLAC
PEP-II collider, corresponding to an integrated luminosity of
476 fb
1
.The
BABAR
detector is described in detail else-
where [
14
]. The following is a brief summary of the detector
subsystems important to this analysis. Charged-particle
tracks are detected, and their momenta measured, by means
of the combination of a 40-layer cylindrical drift chamber
(DCH) and a five-layer silicon vertex tracker, both operating
within a 1.5-T solenoidal magnetic field. Information from a
ring-imaging Cherenkov detector (detector of internally
reflected Cherenkov light) and specific energy-loss mea-
surements (
dE=dx
) in the silicon vertex tracker and DCH
are used to identify charged kaon and pion candidates.
For various purposes described below, we use samples of
Monte Carlo (MC) simulated events generated using the
JETSET [
15
] program. These events are passed through a
detector simulation based on the Geant4 toolkit [
16
].
Signal MC events refer to
D
þ
!
K
þ
K
þ
decays gen-
erated using JETSET as well as
D
þ
!
K
þ
K
þ
decays
generated using JETSET in combination with the PHOTOS
[
17
] program. In all cases when we simulate particle
decays, we include EvtGen [
18
].
III. EVENT SELECTION AND
D
þ
!
K
þ
K
þ
RECONSTRUCTION
The three-body
D
þ
!
K
þ
K
þ
decay is reconstructed
from events having at least three tracks with net charge
þ
1
.
Two oppositely charged tracks must be consistent with the
kaon hypothesis. Other charged tracks are assumed to be
pions. To improve particle identification performance,
there must be at least one photon in the detector of inter-
nally reflected Cherenkov light associated with each track.
Contamination from electrons is significantly reduced by
means of
dE=dx
information from the DCH. Pion candi-
dates must have transverse momentum
p
T
>
300 MeV
=c
.
For lower
p
T
values, tracks are poorly reconstructed.
Also, for lower
p
T
, differences in the nuclear cross sections
for positively charged and negatively charged particles
can lead to asymmetries. We form the invariant mass of
K
þ
K
þ
candidates and require it to lie within
1
:
82
–
1
:
92 GeV
=c
2
. The three tracks must originate from
a common vertex, and the vertex-constrained fit probability
(
P
vtx
) must be greater than 0.5%. The momentum in the
center-of-mass (CM) frame (
p
CM
) of the resulting
D
can-
didate must lie within the interval [2.4, 5.0]
GeV
=c
. The
lower limit on
p
CM
reduces background from
B
decays by
preferentially selecting
e
þ
e
!
c
c
events; this has tradi-
tionally been the way to reduce combinatoric background
due to
B
decays. To remove background from misidentified
D
þ
!
D
0
þ
decays, we require
m
ð
K
þ
K
þ
Þ
m
ð
K
þ
Þ
m
ð
þ
Þ
>
15 MeV
=c
2
, where the pion and
kaon masses are set to the nominal values [
19
]. Finally,
for events with multiple
D
candidates, the combination
with the largest value of
P
vtx
is selected. We perform a
separate kinematic fit in which the
D
mass is constrained
to its nominal value [
19
]. The result of the fit is used in the
Dalitz plot and moments analyses described below.
To aid in the discrimination between signal and back-
ground events, we use the joint probability density function
(PDF) for
L
xy
, the distance between the primary event
vertex and the
D
meson decay vertex in the plane transverse
to the beam direction, and
p
CM
, to form a likelihood ratio,
R
L
¼
P
s
ð
p
CM
Þ
P
s
ð
L
xy
Þ
P
s
ð
p
CM
Þ
P
s
ð
L
xy
Þþ
P
b
ð
p
CM
Þ
P
b
ð
L
xy
Þ
:
(1)
Since the two variables have little correlation, we construct
the two-dimensional PDF as simply the product of their one-
dimensional PDFs; these one-dimensional PDFs for signal
(
P
s
) and background (
P
b
) are estimated from data. The
background PDFs are determined from events in the
D
þ
mass sidebands, while those for the signal are estimated
from events in the
D
þ
signal region after background is
subtracted using estimates from the sidebands. The signal
region is defined by the
m
ð
K
þ
K
þ
Þ
interval
1
:
86
–
1
:
88 GeV
=c
2
, while the sideband regions are the
1
:
83
–
1
:
84 GeV
=c
2
and
1
:
90
–
1
:
91 GeV
=c
2
intervals. The
selection on
R
L
is adjusted to maximize signal significance,
and the resulting signal is fairly pure (see Fig.
3
in Sec.
VI
).
The reconstruction efficiency for
D
þ
decays is deter-
mined from a sample of MC events in which the decay
is generated according to phase space (i.e., the Dalitz plot
is uniformly populated). To parametrize the selection
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
052010 (2013)
052010-4
efficiency, we use the distribution of reconstructed events
as a function of the cosine of the polar angle of the
D
meson in the CM frame [
cos
ð
CM
Þ
] and the
m
2
ð
K
þ
Þ
versus
m
2
ð
K
þ
K
Þ
Dalitz plot. The selection efficiency is
determined as the ratio of
N
Reco
=N
Gen
in intervals of
cos
ð
CM
Þ
and separately in intervals of the Dalitz plot,
where
N
Reco
is the number of selected events in an interval
and
N
Gen
is the number of events generated in the same
interval. The binned Dalitz-plot efficiency is parametrized
with a feed-forward artificial neural network (ANN) [
20
]
consisting of two hidden layers with three and five nodes.
Use of an ANN procedure allows us to adequately model
the efficiency near the edges of the Dalitz plots. The ANN
efficiency function is tested by creating separate training
and validation samples, which are satisfactorily fit by
the ANN.
IV. CORRECTIONS TO SIMULATED EVENTS
In order to describe accurately the reconstruction effi-
ciency, we apply corrections to the reconstructed MC events
to account for known differences between simulated events
and data. The differences arise in the reconstruction asym-
metry of charged-pion tracks and in the production model
for charm mesons. Differences in kaon particle identifica-
tion efficiency have a negligible asymmetry effect since the
K
þ
and
K
are common to
D
þ
and
D
decays.
To correct the production model used in the simulation,
we construct the ratio of the two-dimensional
p
CM
versus
cos
ð
CM
Þ
PDFs between data and simulation and apply
this ratio as a correction to the reconstructed MC events
before calculating the efficiency. For this procedure the
signal PDF for data is background subtracted, while the
signal MC events are weighted by the Dalitz plot amplitude
squared, determined from data (see Sec.
VIII
).
To correct for differences in the reconstruction asymme-
try of charged-pion tracks, we use a sample of
e
þ
e
!
þ
events in which one
decays leptonically via
!
, while the other
decays hadronically via
!
h
h
h
. We tag events with a single isolated
muon on one side of the event and reconstruct the hadronic
decay in the opposite hemisphere. We refer to this sample
as the ‘‘Tau31’’ sample. We further require two of the three
hadrons to have an invariant mass consistent with the rho
mass to within
100 MeV
=c
2
. Due to tracking inefficien-
cies, tau decays to three tracks are sometimes reconstructed
with only two tracks. We use the two-dimensional distri-
butions of
cos
and
p
T
(with respect to the beam axis)
of the rho-decay pions for two-hadron and three-hadron
events to determine the pion inefficiency and asymmetry.
We allow for a different efficiency for positive and negative
tracks (
"
) by introducing the asymmetry
a
ð
p
Lab
Þ
as a
function of pion laboratory momentum (
p
Lab
),
a
ð
p
Lab
Þ¼
"
þ
ð
p
Lab
Þ
"
ð
p
Lab
Þ
"
þ
ð
p
Lab
Þþ
"
ð
p
Lab
Þ
:
(2)
The results for
a
ð
p
Lab
Þ
are shown in Fig.
1
: the average
value for
0
<p
Lab
<
4 GeV
=c
is
ð
0
:
10
0
:
26
Þ
%
, which is
consistent with zero [
21
]. We use linear interpolation be-
tween data points, or extrapolation beyond the first and last
data points, to obtain the ratio of track-efficiency asymme-
tries between data and MC as a function of momentum.
This ratio is then used to correct track efficiencies deter-
mined from signal MC.
V. INTEGRATED
CP
ASYMMETRY AS A
FUNCTION OF
cos
ð
CM
Þ
The production of
D
þ
(and
D
) mesons from the
e
þ
e
!
c
c
process is not symmetric in
cos
ð
CM
Þ
; this
forward-backward (FB) asymmetry, coupled with the
asymmetric acceptance of the detector, results in different
yields for
D
þ
and
D
events. The FB asymmetry, to first
order, arises from the interference of the separate annihi-
lation processes involving a virtual photon and a
Z
0
boson.
We define the charge asymmetry
A
in a given interval of
cos
ð
CM
Þ
by
A
ð
cos
ð
CM
ÞÞ
N
D
þ
=
D
þ
N
D
=
D
N
D
þ
=
D
þ
þ
N
D
=
D
;
(3)
where
N
D
and
D
are the yield and efficiency, respec-
tively, in the given
cos
ð
CM
Þ
bin. We remove the FB
asymmetry by averaging
A
over four intervals symmetric
in
cos
ð
CM
Þ
, i.e., by evaluating
A
CP
A
ð
cos
ð
CM
ÞÞ þ
A
ð
cos
ð
CM
ÞÞ
2
:
(4)
The interval boundaries in
cos
ð
CM
Þ
are defined as 0, 0.2,
0.4, 0.6, 1.0. The
D
yields are determined from fits to the
reconstructed
K
K
mass distributions, as described in
Sec.
VI
. This technique has been used in previous
BABAR
measurements in both three-body and two-body decays
) (GeV/c)
±
π
(
Lab
p
01234567
-
ε
+
+
ε
-
ε
-
+
ε
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
FIG. 1 (color online). Charged pion tracking efficiency
asymmetry [defined in Eq. (
2
)] as a function of the pion
momentum in the laboratory frame determined from the decays
of
leptons. The horizontal error bars indicate the range of pion
momentum [
21
].
SEARCH FOR DIRECT
CP
VIOLATION IN SINGLY
...
PHYSICAL REVIEW D
87,
052010 (2013)
052010-5
[
22
–
24
]. The weighted average of values obtained using
Eq. (
4
)is
A
CP
¼ð
0
:
37
0
:
30
0
:
15
Þ
%
, where the uncer-
tainties are statistical and systematic, respectively, with a
probability of 21% that the asymmetries are null in all four
intervals (Fig.
2
).
VI.
D
þ
MASS FIT
The
K
þ
K
þ
mass distribution is fitted with a double-
Gaussian function with a common mean and a linear
background (Fig.
3
), plus a function describing radiative
decays
D
þ
!
K
þ
K
þ
. The PDF for radiative decays is
obtained from the reconstructed mass distribution of
K
þ
K
þ
events selected at the generator level in our
MC additionally convolved with a Gaussian of width
2
:
26 MeV
=c
2
and accounts for 1.5% of the signal. The fit
to data gives a
D
þ
mass value of
1869
:
70
0
:
01 MeV
=c
2
,
where the uncertainty is statistical only. The signal region
is defined to lie within
2
D
þ
of the peak, where
D
þ
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f
1
2
1
þð
1
f
1
Þ
2
2
q
is
5
:
04 MeV
=c
2
, and contains a total
of 227874 events;
1
ð
2
Þ
is the standard deviation of the
first (second) Gaussian component and
f
1
¼
0
:
63
is the
fraction of the signal in the first Gaussian component.
Separate fits to the
K
þ
K
þ
and
K
þ
K
distributions
yield
N
D
þ
¼
113037
469
and
N
D
¼
110663
467
events, respectively. The ratio of efficiency-corrected
yields (
N=
)is
R
N
D
þ
=
D
þ
N
D
=
D
¼
1
:
020
0
:
006
. This ratio
is used to account for remaining asymmetries that arise
from physics- or detector-related processes, such as an
insufficiently accurate simulation of the FB asymmetry
or a residual detector asymmetry. Also, it is a less accurate
measure of the asymmetry when the efficiency varies sig-
nificantly as a function of
cos
ð
CM
Þ
, as for our experiment.
VII. MODEL-INDEPENDENT SEARCHES FOR
CP
VIOLATION IN THE DALITZ PLOTS
Model-independent techniques to search for
CP
violation in the Dalitz plots are presented in Ref. [
22
].
The techniques include a comparison of the moment dis-
tributions and the asymmetry in the
D
þ
and
D
yields in
various regions of the Dalitz plot. We scale the
D
yields
by the factor
R
described in Sec.
VI
. By applying this
correction, we remove residual detector-induced asymme-
tries and decouple, as far as possible, the search for
CPV
in
the Dalitz plot from the search for
CPV
integrated over the
phase space, which was described in Sec.
V
. We measure
the
CP
asymmetry in the four regions of the Dalitz plot
labeled A, B, C, and D in Fig.
4
. We report the fitted yields,
2
) GeV/c
±
π
-
K
+
m(K
1.82
1.84
1.86
1.88
1.9
1.92
)
2
Events / (1.0 MeV/c
0
5000
10000
15000
20000
→
signal
←
2
) GeV/c
±
π
-
K
+
m(K
1.82
1.84
1.86
1.88
1.9
1.92
)
2
Events / (1.0 MeV/c
1
10
2
10
3
10
4
10
FIG. 3 (color online). Combined reconstructed invariant mass
distribution
m
ð
K
þ
K
Þ
and projection of the fit result. The
points show the data, the solid curve the fit model, and the
dashed curve shows the background PDF. The signal region is
indicated by the dashed vertical lines, and the sideband regions
by the solid vertical lines. The lower figure shows the fit on a
logarithmic scale with the radiative component of the signal PDF
shown separately as a smooth curve.
)|
CM
θ
|cos(
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
CP
A
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
FIG. 2 (color online).
CP
asymmetry as a function of
j
cos
ð
CM
Þj
. The solid line represents the central value of
A
CP
and the dashed lines the
1
standard deviation statistical uncer-
tainty, determined from a
2
fit to a constant value.
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
052010 (2013)
052010-6