of 16
Measurement of
CP
asymmetries and branching fractions in charmless
two-body
B
-meson decays to pions and kaons
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
M. Negrini,
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
P. K. Behera,
31
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
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
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
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
77
Y. Pan,
77
R. Prepost,
77
and S. L. Wu
77
PHYSICAL REVIEW D
87,
052009 (2013)
1550-7998
=
2013
=
87(5)
=
052009(16)
052009-1
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
Facultat de Fisica, Departament ECM, 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 781 039, 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
University of London, Royal Holloway and Bedford New College, 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,
052009 (2013)
052009-2
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 19 June 2012; published 6 March 2013)
We present improved measurements of
CP
-violation parameters in the decays
B
0
!

þ


,
B
0
!
K
þ


, and
B
0
!

0

0
, and of the branching fractions for
B
0
!

0

0
and
B
0
!
K
0

0
.
The results are obtained with the full data set collected at the

ð
4
S
Þ
resonance by the
BABAR
experiment
at the PEP-II asymmetric-energy
B
factory at the SLAC National Accelerator Laboratory, corresponding
to
ð
467

5
Þ
10
6
B

B
pairs. We find the
CP
-violation parameter values and branching fractions:
S

þ


¼
0
:
68

0
:
10

0
:
03
,
C

þ


¼
0
:
25

0
:
08

0
:
02
,
A
K


þ
¼
0
:
107

0
:
016
þ
0
:
006

0
:
004
,
C

0

0
¼
0
:
43

0
:
26

0
:
05
,
B
ð
B
0
!

0

0
Þ¼ð
1
:
83

0
:
21

0
:
13
Þ
10

6
,
B
ð
B
0
!
K
0

0
Þ¼
ð
10
:
1

0
:
6

0
:
4
Þ
10

6
, where in each case, the first uncertainties are statistical and the second are
systematic. We observe
CP
violation with a significance of 6.7 standard deviations for
B
0
!

þ


and
6.1 standard deviations for
B
0
!
K
þ


, including systematic uncertainties. Constraints on the unitarity
triangle angle

are determined from the isospin relations among the
B
!

rates and asymmetries.
Considering only the solution preferred by the Standard Model, we find

to be in the range [71

,109

]at
the 68% confidence level.
DOI:
10.1103/PhysRevD.87.052009
PACS numbers: 13.66.Bc, 13.25.Hw, 13.25.Jx, 14.40.Nd
*
Present address: University of Tabuk, Tabuk 71491, Saudi Arabia.
Also at Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
Present address: University of Huddersfield, Huddersfield HD1 3DH, United Kingdom.
§
Deceased.
k
Present address: University of South Alabama, Mobile, Alabama 36688, USA.
{
Also at Universita
`
di Sassari, Sassari, Italy.
MEASUREMENT OF
CP
ASYMMETRIES AND BRANCHING
...
PHYSICAL REVIEW D
87,
052009 (2013)
052009-3
I. INTRODUCTION
Large
CP
-violating effects [
1
] in the
B
-meson
system are among the most remarkable predictions of
the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing
model [
2
]. These predictions have been confirmed by the
BABAR
and Belle Collaborations, most precisely in
b
!
c

cs
decays of
B
0
mesons to
CP
eigenstates [
3
,
4
].
Effective constraints on physics beyond the Standard
Model (SM) are provided by high-precision measurements
of quantities whose SM predictions are subject to only
small theoretical uncertainties. Many experimental and
theoretical uncertainties partially cancel in the calculation
of
CP
-violating asymmetries. This makes
CP
-violation
measurements a sensitive probe for effects of yet-
undiscovered additional interactions and heavy particles
that are introduced by extensions to the SM. All measure-
ments of
CP
violation to date, including those involving
the decay modes studied here [
5
9
], are in agreement with
the indirect predictions from global SM fits [
10
,
11
], which
are based on measurements of the magnitudes of the ele-
ments
V
ij
of the CKM quark-mixing matrix. This strongly
constrains [
12
] the flavor structure of SM extensions.
The CKM-matrix unitarity triangle angle


arg
½
V
td
V

tb
=V
ud
V

ub

is measured through interference
between two decay amplitudes, where one amplitude in-
volves
B
0
-

B
0
mixing. Multiple measurements of

, with
different decays, further test the consistency of the CKM
model. The time-dependent asymmetry in
B
0
!

þ


decays is proportional to
sin 2

in the limit that only the
b
!
u
(‘‘tree’’) quark-level amplitude contributes to this
decay. In the presence of
b
!
d
(‘‘penguin’’) amplitudes, the
time-dependent asymmetry in
B
0
!

þ


is modified to
a
ð

t
Þ¼
j

A
ð

t
Þ
2
j
A
ð

t
Þj
2
j

A
ð

t
Þ
2
þj
A
ð

t
Þj
2
¼
S

þ


sin
ð

m
d

t
Þ
C

þ


cos
ð

m
d

t
Þ
;
(1)
where

t
is the difference between the proper decay times of
the
B
meson that undergoes the
B
!

þ


decay (the
signal
B
) and the other
B
mesonintheevent(thetag
B
),

m
d
is the
B
0
-

B
0
mixing frequency,
A
is the
B
0
!

þ


decay amplitude,

A
is the
CP
-conjugate amplitude, and
C

þ


¼
j
A
j
2
j

A
j
2
j
A
j
2
þj

A
j
2
;
S

þ


¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1

C
2

þ


q
sin
ð
2


2


Þ
:
(2)
Both the direct
CP
asymmetry
C

þ


and the phase



may differ from zero due to the penguin contribution to the
decay amplitudes.
The magnitude and relative phase of the penguin con-
tribution to the asymmetry
S

þ


may be determined with
an analysis of isospin relations between the
B
!

decay
amplitudes [
13
]. The amplitudes
A
ij
of the
B
!

i

j
decays and

A
ij
of the

B
!

i

j
decays satisfy the relations
A
þ
0
¼
1
ffiffiffi
2
p
A
þ
þ
A
00
;

A

0
¼
1
ffiffiffi
2
p

A
þ
þ

A
00
:
(3)
The shapes of the triangles corresponding to these isospin
relations are determined from measurements of the branch-
ing fractions and time-integrated
CP
asymmetries for each
of the
B
!

decays. Gluonic penguin amplitudes do not
contribute to the

I
¼
3
=
2
decay
B

!



0
. Therefore,
neglecting electroweak (EW) penguin amplitudes, the am-
plitudes
A
þ
0
and

A

0
are equal. From the different shapes
of the triangles for the
B
and

B
decay amplitudes, a
constraint on



can be determined to within a fourfold
ambiguity.
The phenomenology of the
B
!

system has been
thoroughly studied in a number of theoretical frameworks
and models [
14
]. Predictions for the relative size and phase
of the penguin contribution vary considerably. Therefore,
increasingly precise measurements will help distinguish
among different theoretical approaches and add to our
understanding of hadronic
B
decays.
The measured rates and direct
CP
-violating asymme-
tries in
B
!
K
decays [
6
,
7
,
9
,
15
18
] reveal puzzling
features that could indicate significant contributions from
EW penguin amplitudes [
19
,
20
]. Various methods have
been proposed for isolating the SM contribution to this
process in order to test for signs of new physics. This
includes sum rules derived from
U
-spin symmetry, which
relate the rates and asymmetries for the decays of charged
or neutral
B
mesons to
K
þ


,
K
þ

0
,
K
0

0
, and
K
0

þ
[
21
,
22
], and
SU
ð
3
Þ
symmetry used to make predictions for
the
K
system based on hadronic parameters extracted
from the

system [
19
].
This article is organized as follows. The
BABAR
detector
and the data used in these measurements are described in
Sec.
II
. In Sec.
III
we outline the analysis method, includ-
ing the event selection and the fits used to extract the
parameters of interest. The results of the data analysis are
given in Sec.
IV
. The extraction of

and



is
described in Sec.
V
, and we summarize in Sec.
VI
.
II. THE
BABAR
DETECTOR AND DATA SET
In the
BABAR
detector [
23
], charged particles are
detected and their momenta are measured by the combi-
nation of a five-layer double-sided silicon vertex tracker
(SVT) and a 40-layer drift chamber (DCH) that covers
92% of the solid angle in the

ð
4
S
Þ
center-of-mass
(c.m.) frame, both operating in a 1.5-T uniform magnetic
field. Discrimination between charged pions, kaons, and
protons is obtained from ionization (
d
E=
d
x
) measurements
in the DCH and from an internally reflecting ring-imaging
Cherenkov detector (DIRC), which covers 84% of the c.m.
solid angle in the central region of the
BABAR
detector and
has a 91% reconstruction efficiency for pions and kaons
with momenta above
1
:
5 GeV
=c
. Photons and electrons
are identified and their energies are measured with
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
052009 (2013)
052009-4
an electromagnetic calorimeter (EMC) consisting of
6580 CsI(Tl) crystals. The photon energy resolution is

E
=E
¼f
2
:
3
=E
ð
GeV
Þ
1
=
4

1
:
4
g
%
, and the photon angular
resolution relative to the interaction point is


¼
4
:
16
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
ð
GeV
Þ
p
mrad
[
24
].
The data used in this analysis were collected during the
period 1999–2007 with the
BABAR
detector at the PEP-II
asymmetric-energy
B
-meson factory at the SLAC National
Accelerator Laboratory. A total of
ð
467

5
Þ
10
6
B

B
pairs were used. Relative to previous
BABAR
measure-
ments [
5
7
], roughly 22% more
B

B
pairs have been added
to the analyzed data set, and improvements have been
introduced to the analysis technique, boosting the signal
significance. These improvements include better recon-
struction of charged-particle tracks, improved hadroniden-
tification and flavor-tagging algorithms, and optimal
selection of tracks and calorimeter clusters for calculation
of event-shape variables.
Samples of Monte Carlo (MC) simulated events are
analyzed with the same reconstruction and analysis proce-
dures as used for the data, following a Geant4-based [
25
]
detailed detector simulation [
23
]. The MC samples include
e
þ
e

!
q

q
continuum background events generated with
JETSET [
26
] and

ð
4
S
Þ!
B

B
decays generated with
EvtGen [
27
] and JETSET, including both signal and back-
ground
B
-meson decays.
III. EVENT SELECTION AND ANALYSIS METHOD
Many elements of the measurements discussed in this
paper are common to the decay modes [
28
]
B
0
!
h
þ
h
0
(where
h
,
h
0
¼

or
K
),
B
0
!

0

0
, and
B
0
!
K
0
S

0
. The
signal
B
-meson candidates (
B
rec
) are formed by combining
two particles, each of which is a charged-particle track, a

0
candidate, or a
K
0
S
candidate. The event selection differs
for each mode and is described below.
The number of
B
decays and the corresponding
CP
asymmetries are determined with extended unbinned
maximum likelihood (ML) fits to variables described be-
low. The likelihood is given by the expression
L
¼
exp


X
M
i
n
i

Y
N
j

X
M
i
n
i
P
i
ð
~
x
j
;
~

i
Þ

;
(4)
where
N
is the number of events, the sums are over the
event categories
M
,
n
i
is the event yield for each category
as described below, and the probability-density function
(PDF)
P
i
describes the distribution of the variables
~
x
j
in
terms of parameters
~

i
. The PDF functional forms are
discussed in Secs.
III C
and
III D
.
A. Track and
K
0
S
selection
In the
B
0
!
h
þ
h
0
mode, we require charged-particle
tracks to have at least 12 DCH hits and to lie in the
polar-angle region
0
:
35
<<
2
:
40
with respect to the
beam direction. The track impact parameter relative to
the
e
þ
e

collision axis must be smaller than 1.5 cm in
the plane perpendicular to the beam axis and 2.5 cm in the
direction along the axis.
In order for DIRC information to be used for particle
identification, we require that each track have its associated
Cherenkov angle (

C
) measured with at least six
Cherenkov photons, where the value of

C
is required to
be within 4.0 standard deviations (

) of either the pion or
kaon hypothesis. This removes candidates containing
a high-momentum proton. Tracks from electrons are
removed based primarily on a comparison of the track
momentum and the associated energy deposition in the
EMC, with additional information provided by DCH
d
E=
d
x
and DIRC

C
measurements.
The ionization energy loss in the DCH is used either in
combination with DIRC information or alone. This leads to
a 35% increase in the
B
0
!
h
þ
h
0
reconstruction effi-
ciency relative to the use of only tracks with good DIRC
information. A detailed DCH
d
E=
d
x
calibration developed
for the
B
0
!
h
þ
h
0
analysis takes into account variations
in the mean and resolution of
d
E=
d
x
measurement values
with respect to changes in the DCH running conditions
over time, as well as the track’s charge, polar and azimu-
thal angles, and number of ionization samples. The
calibration is performed with large high-purity samples
(with more than
10
6
events) of protons from

!
p

,
pions and kaons from
D
!
D
0

þ
ð
D
0
!
K


þ
Þ
, and
K
0
S
!

þ


decays that occur in the vicinity of the inter-
action region.
Candidates for the decay
K
0
S
!

þ


are reconstructed
from pairs of oppositely charged tracks. The two-track
combinations are required to form a vertex with a

2
probability greater than 0.001 and a

þ


invariant
mass within
11
:
2 MeV
=c
2
, corresponding to
3
:
7

, of the
nominal
K
0
S
mass [
29
].
B.

0
selection
We form

0
!

candidates from pairs of clusters in
the EMC that are isolated from any charged track. Clusters
are required to have a lateral profile of energy deposition
consistent with that of a photon and to have an energy
E

>
30 MeV
for
B
0
!

0

0
and
E

>
50 MeV
for
B
0
!
K
0
S

0
. We require

0
candidates to lie in the
invariant-mass range
110
<m

<
160 MeV
=c
2
.
For the
B
0
!

0

0
mode, we also use

0
candidates
from a single EMC cluster containing two adjacent
photons (a merged

0
), or one EMC cluster and two tracks
from a photon conversion to an
e
þ
e

pair inside the
detector. To reduce the background from random
photon combinations, the angle


between the photon
momentum vector in the

0
rest frame and the

0
momentum vector in the laboratory frame is required to
satisfy
j
cos


j
<
0
:
95
. The

0
candidates are fitted
MEASUREMENT OF
CP
ASYMMETRIES AND BRANCHING
...
PHYSICAL REVIEW D
87,
052009 (2013)
052009-5
kinematically with their mass constrained to the nominal

0
mass [
29
].
Photon conversions are selected from pairs of oppositely
charged electron-candidate tracks with an invariant mass
below
30 MeV
=c
2
whose combined momentum vector
points away from the beam spot. The conversion point is
required to lie within detector material layers. Converted
photons are combined with photons from single EMC
clusters to form

0
candidates.
Single EMC clusters containing two photons are
selected with the transverse second moment,
S
¼
P
i
E
i


i
Þ
2
=E
, where
E
i
is the energy in each CsI(Tl)
crystal and


i
is the angle between the cluster centroid
and the crystal. The second moment is used to distinguish
merged

0
candidates from both single photons and neutral
hadrons.
C.
B
0
!

þ


,
B
0
!
K
þ


, and
B
0
!

0

0
Two kinematic variables are used in the
B
0
!
h
þ
h
0
and
B
0
!

0

0
analyses to separate
B
-meson decays from
the large
e
þ
e

!
q

q
ð
q
¼
u; d; s; c
Þ
combinatoric back-
ground [
23
]. One variable is the beam-energy-substituted
mass
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s=
2
þ
p
i
p
B
Þ
2
=E
2
i

p
2
B
q
, where
ffiffiffi
s
p
is the
total
e
þ
e

c
:
m
:
energy,
ð
E
i
;
p
i
Þ
is the four-momentum of
the initial
e
þ
e

system in the laboratory frame, and
p
B
is
the laboratory momentum of the
B
candidate. The second
variable is

E
¼
E

B

ffiffiffi
s
p
=
2
, where
E

B
is the energy of
the
B
candidate in the c.m. frame.
To further separate
B
decays from the
q

q
background,
we use two additional topological variables that take
advantage of the two-jet nature of
q

q
events and the
isotropic particle distribution of
e
þ
e

!
B

B
events. The
first variable is the absolute value of the cosine of the angle

S
between the sphericity axis [
30
] of the decay products of
the
B
candidate and the sphericity axis of the remaining
tracks and neutral clusters in the event, computed in
the c.m. frame. The distribution of this variable peaks at
1 for the jetlike
q

q
events and is uniform for
B
decays. We
require
j
cos

S
j
<
0
:
91
for
B
0
!
h
þ
h
0
and
j
cos

S
j
<
0
:
7
for
B
0
!

0

0
, where a tighter requirement is needed
due to the higher background. For the
B
0
!
h
þ
h
0
mode, we remove a small remaining background from
e
þ
e

!

þ


events by further requiring that the normal-
ized second Fox-Wolfram moment [
31
] satisfy
R
2
<
0
:
7
.
To improve the discrimination against
q

q
events, a
Fisher discriminant
F
is formed as a linear combination
of the sums
L
T
0

P
i
j
p

i
j
and
L
T
2

P
i
j
p

i
j
cos
2


i
, where
p

i
are the momenta and


i
are the angles with respect to
the thrust axis [
32
] of the
B
candidate, both in the c.m.
frame, of all tracks and clusters not used to reconstruct the
signal
B
-meson candidate. The
F
variable takes advantage
of the fact that much of the momentum flow in
q

q
events is
along the thrust axis. In the case of
B
0
!

0

0
, we im-
prove the sensitivity to signal events by combining
F
with
three other event-shape variables in a neural network. The
first variables is
j
cos

S
j
, described above. The second is
j
cos


B
j
, where


B
is the angle between the momentum
vector of the signal
B
and the beam axis. The
j
cos


B
j
distribution of
q

q
events is uniform, while that of signal
events is proportional to
sin
2


B
. The third variable is
j
cos


T
j
, where


T
is the angle between the thrust axis of
the signal
B
-meson’s daughters and the beam axis. Both


B
and


T
are calculated in the c.m. frame. The characteristics
of the
j
cos


T
j
distributions are similar to those of
j
cos

S
j
.
1.
B
0
!

þ


and
B
0
!
K
þ


We reconstruct the candidate decays
B
rec
!
h
þ
h
0
from
pairs of oppositely charged tracks that are consistent with
originating from a common decay point with a

2
proba-
bility of at least 0.001. The remaining particles are exam-
ined to infer whether the other
B
meson in the event (
B
tag
)
decayed as a
B
0
or

B
0
(flavor tag). We perform an unbinned
extended ML fit to separate
B
0
!

þ


and
B
0
!
K
þ


decays and determine simultaneously their
CP
-violating
asymmetries
S

þ


,
C

þ


, and
A
K


þ
¼
B
ð
B
!
K


þ
Þ
B
ð
B
!
K
þ


Þ
B
ð
B
!
K


þ
Þþ
B
ð
B
!
K
þ


Þ
;
(5)
as well as the signal and background yields and PDF
parameters. The fit uses

C
,
d
E=
d
x
,

E
,
m
ES
,
F
,
B
tag
flavor, and

t
information.
The value of

E
is calculated assuming that both tracks
are charged pions. The
B
0
!

þ


signal is described by
a Gaussian distribution for

E
, with a resolution of
29 MeV. For each kaon in the final state, the

E
peak
position is shifted from zero by an amount that depends on
the kaon momentum, with an average shift of

45 MeV
.
We require
j

E
j
<
0
:
150 GeV
. The wide range in

E
allows us to separate
B
0
decays to the four final states

þ


,
K
þ


,

þ
K

, and
K
þ
K

in a single fit. The
analysis is not optimized for measuring the
K
þ
K

final
state, which is treated as background. The
m
ES
resolution is
2
:
6 MeV
=c
2
. We require
m
ES
>
5
:
20 GeV
=c
2
, with events
in the large range below the signal peak allowing the fit to
effectively determine the background shape parameters.
We construct

C
PDFs for the pion and kaon hypotheses,
and
d
E=
d
x
PDFs for the pion, kaon, and proton hypotheses,
separately for each charge. The
K
-

separations provided
by

C
and
d
E=
d
x
are complementary: for

C
, the separa-
tion varies from
2
:
5

at
4
:
5 GeV
=c
to
13

at
1
:
5 GeV
=c
,
while for
d
E=
d
x
it varies from less than
1
:
0

at
1
:
5 GeV
=c
to
1
:
9

at
4
:
5 GeV
=c
(Fig.
1
). For more details, see
Ref. [
5
].
We use a multivariate technique [
33
] to determine the
flavor of the
B
tag
. Separate neural networks are trained to
identify leptons from
B
decays, kaons from
D
decays, and
soft pions from
D

decays. Events are assigned to one of
seven mutually exclusive tagging categories (one category
being untagged events) based on the estimated average
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
052009 (2013)
052009-6
mistag probability and the source of the tagging informa-
tion. The quality of tagging is expressed in terms of the
effective efficiency
Q
¼
P
k

k
ð
1

2
w
k
Þ
2
, where

k
and
w
k
are the efficiencies and mistag probabilities, respectively,
for events tagged in category
k
. The difference between the
mistag probabilities for
B
0
and

B
0
mesons is given by

w
¼
w
B
0

w

B
0
. Table
I
summarizes the tagging per-
formance measured in a large data sample of fully recon-
structed neutral
B
flav
decays to
D
ðÞ
ð

þ
;
þ
;a
þ
1
Þ
[
34
].
The time difference

t
¼

z= c
is obtained from the
known boost of the
e
þ
e

system (

¼
0
:
56
) and the
measured distance

z
along the beam (
z
) axis between
the
B
rec
and
B
tag
decay vertices. A description of the
inclusive reconstruction of the
B
tag
vertex is given in
Ref. [
35
]. We require
j

t
j
<
20 ps
and


t
<
2
:
5ps
,
where


t
is the uncertainty on

t
estimated separately
for each event. The signal

t
PDF for
B
0
!

þ


is
given by
f

k
ð

t
meas
Þ¼
e
j

t
j
=
4

1

w
Þð
1

2
w
k
Þ
S

þ


sin
ð

m
d

t
Þ

C

þ


cos
ð

m
d

t
Þg
R
ð

t
meas


t
Þ
;
(6)
where
f
þ
k
(
f

k
) indicates a
B
0
(

B
0
) flavor tag and the index
k
indicates the tagging category. The resolution function
R
ð

t
meas


t
Þ
for signal candidates is a sum of three
Gaussian functions, identical to the one described in
Ref. [
35
], with parameters determined from a fit to the
B
flav
sample, which includes events in all seven tagging
categories. The background

t
distribution is modeled as
the sum of three Gaussians, with parameters, common for
all tagging categories, determined simultaneously with the
CP
-violation parameters in the ML fit to the
B
rec
!
h
þ
h
0
sample.
The ML fit PDF includes 28 components. Of these, 24
components correspond to
B
0
signal decays and back-
ground events with the final states

þ


,
K
þ


,
K


þ
, and
K
þ
K

, where either the positively charged
track, the negatively charged track, or both have good
DIRC information (
2

4

3
¼
24
components). Four
additional components correspond to
p

,
pK

,

þ

p
,
and
K
þ

p
background events, where the (anti)proton has no
DIRC information. The
K


event yields
n
K


are
parametrized in terms of the asymmetry
A
raw
K


þ
and av-
erage yield
n
K
as
n
K


¼
n
K
ð
1
A
raw
K


þ
Þ
=
2
. All
other event yields are products of the fraction of events
in each tagging category taken from
B
flav
events, and the
total event yield. The background PDFs are a threshold
function [
36
] for
m
ES
and a second-order polynomial
for

E
. The
F
PDF is a sum of two asymmetric
Gaussians for both signal and background. We use large
samples of simulated
B
decays to investigate the effects
of backgrounds from other
B
decays on the determination
of the
CP
-violating asymmetries in
B
0
!

þ


and
B
0
!
K
þ


, and find them to be negligible.
2.
B
0
!

0

0
B
0
!

0

0
events are identified with a ML fit to the
variables
m
ES
,

E
, and the output
NN
of the event-shape
neural network. We require
m
ES
>
5
:
20 GeV
=c
2
and
j

E
j
<
0
:
2 GeV
. Since tails in the EMC response produce
a correlation between
m
ES
and

E
, a two-dimensional
binned PDF derived from the signal MC sample is used
to describe signal PDF. The
NN
distribution is divided into
ten bins (with each bin approximately equally populated by
signal events) and described by a nine-bin step-function
PDF with values taken from the MC and fixed in the
fit.
B
flav
data are used to verify that the MC accurately
reproduces the
NN
distribution. The
q

q
background PDFs
are a threshold function [
36
] for
m
ES
, a second-order
polynomial for

E
, and a parametric step function for
NN
.For
q

q
events,
NN
is not distributed uniformly
across the bins but rises sharply toward the highest bins.
We see a small correlation of 2.5% between the shape
parameter of the
m
ES
threshold function and the
NN
bin
number, and this relation is taken into account in the fit. All
q

q
background PDF-parameter values are determined by
the ML fit.
TABLE I. Average tagging efficiency

, average mistag
fraction
w
, mistag fraction difference

w
¼
w
ð
B
0
Þ
w
ð

B
0
Þ
,
and effective tagging efficiency
Q
for signal events in each
tagging category (except the untagged category).
Category

ð
%
Þ
w
ð
%
Þ

w
ð
%
Þ
Q
ð
%
Þ
LEPTON
8
:
96

0
:
07 2
:
9

0
:
30
:
2

0
:
57
:
95

0
:
11
KAON I
10
:
81

0
:
07 5
:
3

0
:
30
:
0

0
:
68
:
64

0
:
14
KAON II
17
:
18

0
:
09 14
:
5

0
:
30
:
4

0
:
68
:
64

0
:
17
KAON PION
13
:
67

0
:
08 23
:
3

0
:
4

0
:
6

0
:
73
:
91

0
:
12
PION
14
:
19

0
:
08 32
:
6

0
:
45
:
1

0
:
71
:
73

0
:
09
OTHER
9
:
55

0
:
07 41
:
5

0
:
53
:
8

0
:
80
:
28

0
:
04
Total
31
:
1

0
:
3
p (GeV/c)
1.5
2
2.5
3
3.5
4
4.5
)
σ
separation (
π
DIRC K-
2
4
6
8
10
12
14
)
σ
separation (
π
DCH K-
0.5
1
1.5
2
DCH dE/dx
DIRC
FIG. 1 (color online). The average expected
K
-

separation,
in units of uncertainty, provided by the DIRC angle

C
and
DCH
d
E=
d
x
for kaons and pions from
B
0
!
K
þ


decays in
the laboratory-frame polar angle range
0
:
35
<<
2
:
40
,asa
function of laboratory-frame momentum.
MEASUREMENT OF
CP
ASYMMETRIES AND BRANCHING
...
PHYSICAL REVIEW D
87,
052009 (2013)
052009-7
The decays
B
þ
!
þ

0
and
B
0
!
K
0
S

0
ð
K
0
S
!

0

0
Þ
add
71

10
background events to
B
0
!

0

0
and are
included as an additional component in the ML fit. We
model these
B
-decay background events with a two-
dimensional binned PDF in
m
ES
and

E
, and with a step
function for
NN
. The shapes of these PDFs are taken from
MC simulation, and their event yields and asymmetries are
fixed in the fit and are later varied to evaluate systematic
uncertainties.
The time-integrated
CP
asymmetry is measured by the
B
-flavor tagging algorithm described above. The fraction
of events in each tagging category is constrained to the
corresponding fraction determined from MC simulation.
The PDF event yields for the
B
0
!

0

0
signal are given
by the expression
n

0

0
;k
¼
1
2
f
k
N

0

0
½
1

s
j
ð
1

2

Þð
1

2
w
k
Þ
C

0

0

;
(7)
where
f
k
is the fraction of events in tagging category
k
,
N

0

0
is the number of
B
0
!

0

0
candidate decays,

is the time-integrated
B
0
mixing probability [
29
],
s
j
¼þ
1
ð
1
Þ
when the
B
tag
is a
B
0
(

B
0
), and
C

0

0
¼
j
A
00
j
2
j

A
00
j
2
j
A
00
j
2
þj

A
00
j
2
(8)
is the direct
CP
asymmetry in
B
0
!

0

0
.
D.
B
0
!
K
0
S

0
CP
-violation parameters for
B
0
!
K
0
S

0
have been
reported in Ref. [
4
]. Here we describe the measurement
of the branching fraction for this mode.
For each
B
0
!
K
0
S

0
candidate, two independent
kinematic variables are computed. The first variable is
the invariant mass
m
B
of the
B
rec
. The second variable is
the invariant (missing) mass
m
miss
of the
B
tag
, computed
from the magnitude of the difference between the four-
momentum of the initial
e
þ
e

system and that of the
B
rec
,
after applying a
B
0
-mass constraint to the
B
rec
[
37
]. For
signal decays,
m
B
and
m
miss
peak near the
B
0
mass with
resolutions of about 36 and
5
:
3 MeV
=c
2
, respectively.
Since the linear correlation coefficient between
m
B
and
m
miss
vanishes, these variables yield better separation of
signal from background than
m
ES
and

E
. Both the
m
B
and
m
miss
distributions exhibit a low-side tail due to leakage of
energy out of the EMC. We select candidates within the
ranges
5
:
13
<m
B
<
5
:
43 GeV
=c
2
and
5
:
11
<m
miss
<
5
:
31 GeV
=c
2
, which include a signal peak and a
‘‘sideband’’ region for background characterization.
In events with more than one reconstructed candidate
(0.8% of the total), we select the candidate with the small-
est

2
¼
P
i
¼

0
;K
0
S
ð
m
i

m
0
i
Þ
2
=
2
m
i
, where
m
i
(
m
0
i
) is the
measured (nominal) mass and

m
i
is the estimated uncer-
tainty on the measured mass of particle
i
.
We exploit topological observables computed in the c.m.
frame to discriminate jetlike
e
þ
e

!
q

q
events from the
nearly spherical
B

B
events. In order to reduce the number
of background events, we require
L
2
=L
0
<
0
:
55
, where
L
j

P
i
j
p

i
j
cos
j


i
and


i
are computed with respect to
the sphericity axis [
30
] of the
B
rec
candidate. Taking ad-
vantage of the fact that signal events follow a
1

cos
2


B
distribution while the background is flat, we select events
with
j
cos


B
j
<
0
:
9
. Using a full detector simulation, we
estimate that our selection retains
34
:
2%

1
:
2%
of the
signal events, where the uncertainty includes both statisti-
cal and systematic contributions. The selected sample of
B
0
!
K
0
S

0
candidates is dominated by random
K
0
S

0
combinations from
e
þ
e

!
q

q
events. Using large
samples of simulated
B

B
events, we find that backgrounds
from other
B
-meson decays are small, of order 0.1%.
Therefore, this type of background is not included in the
fit described below, and this is accounted for in the evalu-
ation of systematic uncertainties (see Sec.
IV C
).
We extract the signal yield from an extended unbinned
ML fit to
m
B
,
m
miss
,
L
2
=L
0
,
cos


B
, the flavor tag, and the
decay time and its error. The use of tagging and decay-time
information in the ML fit further improves discrimination
between signal and background. Since in the
B
0
!
K
0
S

0
decay no charged particles originate from the decay vertex,
we compute the decay point of the
B
rec
using the
K
0
S
trajectory obtained from the reconstructed
K
0
S
decay vertex
and momentum vector, and the average
e
þ
e

interaction
point [
38
]. We have verified that all correlations between
the fit variables are negligible and so construct the like-
lihood function as a product of one-dimensional PDFs.
Residual correlations are taken into account in the system-
atic uncertainty, as explained below.
The PDFs for signal events are parametrized based on a
large sample of fully reconstructed
B
decays in data and
from simulated events. For background PDFs, we take the
functional form from the background-dominated sideband
regions in the data. The likelihood function is
L
ð
S
K
0
S

0
;C
K
0
S

0
;N
S
;N
B
;f
g
S
;f
g
B
;~

Þ
¼
e
N
S
þ
N
B
Þ
N
!
Y
i
2
g
½
N
S
f
g
S

c
S
P
S
ð
~
x
i
;
~
y
i
;
S
K
0
S

0
;C
K
0
S

0
Þ
þ
N
B
f
g
B

c
B
P
B
ð
~
x
i
;
~
y
i
;
~

Þ
Y
i
2
b
½
N
S
f
b
S

c
S
P
0
S
ð
~
x
i
;
C
K
0
S

0
Þ
þ
N
B
f
b
B

c
B
P
0
B
ð
~
x
i
;
~

Þ
;
(9)
where the
N
selected events are partitioned into two sub-
sets: the index
i
2
g
indicates events that have

t
infor-
mation, while
i
2
b
events do not have

t
information.
Here,
f
g
S
(
f
g
B
) is the fraction of signal (background) events
that are in the subset
g
, and
f
b
S
¼
1

f
g
S
(
f
b
B
¼
1

f
g
B
)
are the corresponding signal (background) fractions in
the subset
b
. The parameter
N
S
(
N
B
) is the number of
signal (background) events. The probabilities
P
S
and
P
B
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
052009 (2013)
052009-8
are products of PDFs for the signal and background
hypotheses evaluated for the measurements
~
x
i
¼
f
m
B
;m
miss
;L
2
=L
0
;
cos


B
;
flavor tag
;
tagging category
g
and
~
y
i
¼f

t; 

t
g
. The corresponding PDFs for events
without

t
information are
P
0
S
and
P
0
B
. Detailed descrip-
tions of
P
S
,
P
B
,
P
0
S
, and
P
0
B
are given in Ref. [
4
].
The vector
~

represents the set of parameters that define
the shapes of the PDFs. Along with the
CP
asymmetries
S
K
0
S

0
and
C
K
0
S

0
, the fit extracts the yields
N
S
and
N
B
, the
fraction of events
f
g
S
and
f
g
B
, and the parameters of the
background PDFs.
IV. RESULTS AND SYSTEMATIC UNCERTAINTIES
A.
B
0
!

þ


and
B
0
!
K
þ


results
The event yields and
CP
-violation parameters are listed
in Table
II
. The correlation coefficient between
S

þ


and
C

þ


is found to be

0
:
056
, and the correlation between
C

þ


and
A
K


þ
is 0.019. We show the
m
ES
,

E
, and
F
distribution for the
B
!

,
B
!
K
, and
q

q
background
in Fig.
2
, where the
s
P
lots [
39
] weighting and background-
subtraction technique is used to display a distribution for a
particular type of event. The direct
CP
asymmetry in
B
0
!
K
þ


is apparent in the

E
distributions, which
are plotted separately for
B
0
and

B
0
decays in Fig.
3
.We
show the distributions of

t
for
B
0
!
K


signal and
background decays in Fig.
4
. In Fig.
5
, we show the
distribution of

t
separately for
B
0
!

þ


events
TABLE II. Results for the
B
0
!
h
þ
h
0
decay modes.
Uncertainties on the signal yields
N
sig
are statistical. For the
CP
-violation parameters, the first uncertainties are statistical,
and the second are systematic.
Mode
N
sig
CP
-violation parameters
B
0
!

þ


1394

54
S

þ


¼
0
:
68

0
:
10

0
:
03
C

þ


¼
0
:
25

0
:
08

0
:
02
B
0
!
K
þ


5410

90
A
K


þ
¼
0
:
107

0
:
016
þ
0
:
006

0
:
004
B
0
!
K
þ
K

7

17
5.27
5.275
5.28
5.285
5.29
0
50
100
150
200
250
300
)
2
(GeV/c
ES
m
)
2
(GeV/c
ES
m
5.27
5.275
5.28
5.285
5.29
)
2
Events / (1 MeV/c )
2
Events / (1 MeV/c
0
50
100
150
200
250
300
E (GeV)
-0.1
0
0.1
0
50
100
150
200
E (GeV)
-0.1
0
0.1
Events / (10 MeV)
0
50
100
150
200
F
-2
0
2
0
100
200
300
F
-2
0
2
Events / bin
0
100
200
300
BABAR
Preliminary
)
2
(GeV/c
ES
m
5.27
5.275
5.28
5.285
5.29
0
100
200
300
400
500
600
700
800
900
)
2
(GeV/c
ES
m
5.27
5.275
5.28
5.285
5.29
)
2
Events / (1 MeV/c )
2
Events / (1 MeV/c
0
100
200
300
400
500
600
700
800
900
E (GeV)
-0.1
0
0.1
0
100
200
300
400
E (GeV)
-0.1
0
0.1
Events / (6 MeV)
0
100
200
300
400
-2
0
2
Events / bin
0
200
400
600
F
-2
0
2
0
200
400
600
)
2
(GeV/c
ES
m
5.2
5.22
5.24
5.26
5.28
5.3
0
2000
4000
6000
8000
10000
)
2
(GeV/c
ES
m
5.2
5.22
5.24
5.26
5.28
5.3
)
2
Events / (2 MeV/c )
2
Events / (2 MeV/c
0
2000
4000
6000
8000
10000
E (GeV)
-0.1
0
0.1
0
2000
4000
6000
E (GeV)
-0.1
0
0.1
Events / (5 MeV)
0
2000
4000
6000
F
-2
0
2
Events / bin
0
5000
10000
15000
F
-2
0
2
0
5000
10000
15000
FIG. 2 (color online).
s
P
lots of the (left column)
m
ES
, (center column)

E
, and (right column) Fisher discriminant
F
distributions
for (top row)
B
0
!

þ


, (middle row)
B
0
!
K
þ


, and (bottom row)
q

q
background candidates. The points with error bars show
the data, and the lines represent the PDFs used in the fit and reflect the fit result. The structure to the left of the signal

E
peak for
B
0
!

þ


is consistent with the expected background from other charmless modes, which is negligible for

E>

0
:
10 GeV
.In
the calculation of

E
for
B
0
!
K
þ


, the kaon candidate is assigned the pion mass.
MEASUREMENT OF
CP
ASYMMETRIES AND BRANCHING
...
PHYSICAL REVIEW D
87,
052009 (2013)
052009-9