of 15
Measurement of branching fractions and rate asymmetries in the rare decays
B
!
K
ðÞ
þ

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
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,46a
L. Cremaldi,
47
R. Godang,
47,
§
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,
k
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
86,
032012 (2012)
1550-7998
=
2012
=
86(3)
=
032012(15)
032012-1
Ó
2012 American Physical Society
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, 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, 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
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
Massachusetts Institute of Technology, Laboratory for Nuclear Science, 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
86,
032012 (2012)
032012-2
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 18 April 2012; published 24 August 2012)
In a sample of
471

10
6
B

B
events collected with the
BABAR
detector at the PEP-II
e
þ
e

collider we
study the rare decays
B
!
K
ðÞ
þ

, where
þ

is either
e
þ
e

or

þ


. We report results on partial
branching fractions and isospin asymmetries in seven bins of dilepton mass-squared. We further present
CP
and lepton-flavor asymmetries for dilepton masses below and above the
J=
c
resonance. We find no
evidence for
CP
or lepton-flavor violation. The partial branching fractions and isospin asymmetries are
consistent with the Standard Model predictions and with results from other experiments.
DOI:
10.1103/PhysRevD.86.032012
PACS numbers: 13.20.He
I. INTRODUCTION
The decays
B
!
K
ðÞ
þ

arise from flavor-changing
neutral-current processes that are forbidden at tree level in
the Standard Model (SM). The lowest-order SM processes
contributing to these decays are the photon penguin, the
Z
penguin and the
W
þ
W

box diagrams shown in Fig.
1
.
Their amplitudes are expressed in terms of hadronic form
factors and perturbatively calculable effective Wilson co-
efficients,
C
eff
7
,
C
eff
9
and
C
eff
10
, which represent the electro-
magnetic penguin diagram, and the vector part and the
axial-vector part of the linear combination of the
Z
penguin
and
W
þ
W

box diagrams, respectively [
1
]. In next-
to-next-to-leading order at a renormalization scale

¼
4
:
8 GeV
, the effective Wilson coefficients are
C
eff
7
¼

0
:
304
,
C
eff
9
¼
4
:
211
, and
C
eff
10
¼
4
:
103
[
2
].
Non-SM physics may add new penguin and box dia-
grams, which can contribute at the same order as the SM
*
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.
§
Now at University of South Alabama, Mobile, AL 36688,
USA.
k
Also with Universita
`
di Sassari, Sassari, Italy.
MEASUREMENT OF BRANCHING FRACTIONS AND RATE
...
PHYSICAL REVIEW D
86,
032012 (2012)
032012-3
diagrams [
3
5
]. Examples of new physics loop processes
are depicted in Fig.
2
. These contributions might modify
the Wilson coefficients from their SM expectations [
5
7
].
In addition, new contributions from scalar, pseudoscalar,
and tensor currents may arise that can modify, in particular,
the lepton-flavor ratios [
8
,
9
].
II. OBSERVABLES
We report herein results on exclusive partial branching
fractions and isospin asymmetries in six bins of
s

m
2
‘‘
,
defined in Table
I
. We further present results in the
s
bin
s
0
¼
1
:
0
6
:
0GeV
2
=c
4
chosen for calculations inspired by soft-
collinear effective theory [
10
]. In addition, we report on direct
CP
asymmetries and the ratio of rates to dimuon and dielec-
tron final states in the low
s
and high
s
regions separated by
the
J=
c
resonance. We remove regions of the long-distance
contributions around the
J=
c
and
c
ð
2
S
Þ
resonances. New
BABAR
results on angular observabl
es using the same data set
and similar event selection will be reported shortly.
The
B
!
K‘
þ

and
B
!
K

þ

total branching
fractions are predicted to be
ð
0
:
35

0
:
12
Þ
10

6
and
ð
1
:
19

0
:
39
Þ
10

6
(for
s>
0
:
1 GeV
2
=c
4
), respectively
[
5
]. The

30%
uncertainties are due to a lack of knowl-
edge about the form factors that model the hadronic effects
in the
B
!
K
and
B
!
K

transitions. Thus, measure-
ments of decay rates to exclusive final states are less suited
to searches for new physics than rate asymmetries, where
many theory uncertainties cancel.
For charged
B
decays and neutral
B
decays flavor-tagged
through
K

!
K
þ


[
11
], the direct
CP
asymmetry is
defined as
A
K
ðÞ
CP

B
ð

B
!

K
ðÞ
þ

Þ
B
ð
B
!
K
ðÞ
þ

Þ
B
ð

B
!

K
ðÞ
þ

Þþ
B
ð
B
!
K
ðÞ
þ

Þ
(1)
and is expected to be
O
ð
10

3
Þ
in the SM. However
A
K
ðÞ
CP
may receive a significant enhancement from new physics
contributions at the electroweak scale [
12
].
For
s>
0
:
1 GeV
2
=c
4
, the ratio of rates to dimuon and
dielectron final states is defined as
R
K
ðÞ

B
ð
B
!
K
ðÞ

þ


Þ
B
ð
B
!
K
ðÞ
e
þ
e

Þ
:
(2)
In the SM,
R
K
ðÞ
is expected to be unity to within a few
percent [
13
] for dilepton invariant masses above the
dimuon kinematic threshold. In two-Higgs-doublet mod-
els, including supersymmetry, these ratios are sensitive to
the presence of a neutral Higgs boson. When the ratio of
neutral Higgs field vacuum expectation values
tan

is
large,
R
K
ðÞ
might be increased by up to 10% [
9
].
The
CP
-averaged isospin asymmetry is defined as
A
K
ðÞ
I

B
ð
B
0
!
K
ðÞ
0
þ

Þ
r

B
ð
B
þ
!
K
ðÞþ
þ

Þ
B
ð
B
0
!
K
ðÞ
0
þ

Þþ
r

B
ð
B
þ
!
K
ðÞþ
þ

Þ
;
(3)
where
r



B
0
=
B
þ
¼
1
=
ð
1
:
071

0
:
009
Þ
is the ratio of
B
0
and
B
þ
lifetimes [
14
].
A
K

I
has a SM expectation of
þ
6%
to
þ
13%
as
s
!
0
[
4
]. This is consistent with the
measured asymmetry
3

3%
in
B
!
K


[
15
]. A calcu-
lation of the predicted
K
and
K

0
rates integrated over
the low
s
region yields
A
K

I
¼
0
:
005

0
:
020
[
16
,
17
].
In the high
s
region, we may expect contributions from
charmonium states as an additional source of isospin asym-
metry. However the measured asymmetries in the
J=
c
K
ðÞ
and
c
ð
2
S
Þ
K
ðÞ
modes are all below 5% [
14
].
III.
BABAR
EXPERIMENT AND DATA SAMPLE
We use a data sample of
471

10
6
B

B
pairs collected at
the

ð
4
S
Þ
resonance with the
BABAR
detector [
18
] at the
PEP-II asymmetric-energy
e
þ
e

collider at the SLAC
National Accelerator Laboratory. Charged particle track-
ing is provided by a five-layer silicon vertex tracker and a
40-layer drift chamber in a 1.5 T solenoidal magnetic field.
We identify electrons with a CsI(Tl) electromagnetic calo-
rimeter, and muons using an instrumented magnetic flux
return. Electron and muon candidates are required to have
b
t,c,u
-
H
(a)
b
u
~
c
,
~
t
,
~
s
-
χ
(b)
b
d
~
s
,
~
b
,
~
s
0
χ
g
,
~
(c)
s
FIG. 2. Examples of new physics loop contributions to
b
!
s‘
þ

: (a) charged Higgs (
H

); (b) squark
ð
~
t;
~
c;
~
u
Þ
and chargino
(


); (c) squark
ð
~
b;
~
s;
~
d
Þ
and gluino (
~
g
) or neutralino (

0
).
q
q
bs
t,c,u
W
γ
, Z
l
+
l
q
q
bs
t,c,u
W
+
W
ν
l
l
+
FIG. 1. Lowest-order Feynman diagrams for
b
!
s‘
þ

.
TABLE I. The definition of seven
s
bins used in the analysis.
Here
m
B
and
m
K
ðÞ
are the invariant masses of
B
and
K
ðÞ
,
respectively. The low
s
region is given by
0
:
10
<s<
8
:
12 GeV
2
=c
4
, while the high
s
region is given by
s>
10
:
11 GeV
2
=c
4
.
s
bin
s
min (
GeV
2
=c
4
)
s
max (
GeV
2
=c
4
)
Low
s
1
0.10
2.00
s
2
2.00
4.30
s
3
4.30
8.12
High
s
4
10.11
12.89
s
5
14.21
16.00
s
6
16.00
ð
m
B

m
K
ðÞ
Þ
2
s
0
1.00
6.00
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032012 (2012)
032012-4
momenta
p>
0
:
3 GeV
=c
in the laboratory frame. We
combine up to three photons with electrons when they
are consistent with bremsstrahlung, and do not use elec-
trons that are associated with photon conversions to low-
mass
e
þ
e

pairs. We identify charged kaons using
a detector of internally reflected Cherenkov light, as
well as
d
E=
d
x
information from the drift chamber.
Charged tracks other than identified
e
,

and
K
candidates are treated as pions. Neutral
K
0
S
!

þ


can-
didates are required to have an invariant mass consistent
with the nominal
K
0
mass, and a flight distance from the
e
þ
e

interaction point that is more than 3 times its
uncertainty.
IV. EVENT SELECTION
We reconstruct
B
!
K
ðÞ
þ

signal events in the fol-
lowing eight final states:
(i)
B
0
!
K
0
S

þ


,
B
þ
!
K
þ

þ


,
B
0
!
K
0
S
e
þ
e

,
B
þ
!
K
þ
e
þ
e

,
B
þ
!
K
ð!
K
0
S

þ
Þ

þ


,
B
0
!
K

0
ð!
K
þ


Þ

þ


,
B
þ
!
K
ð!
K
0
S

þ
Þ
e
þ
e

,
B
0
!
K

0
ð!
K
þ


Þ
e
þ
e

.
We reconstruct
K
0
S
candidates in the

þ


final state. We
also study the
K
ðÞ
h



final states, where
h
is a charged
track with no particle identification requirement applied, to
characterize backgrounds from hadrons misidentified as
muons. We use a
K

e



sample to model the combina-
torial background from two random leptons. In each mode,
we utilize the kinematic variables
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
2
CM
=
4

p

2
B
q
and

E
¼
E

B

E
CM
=
2
, where
p

B
and
E

B
are the
B
momentum and energy in the

ð
4
S
Þ
center-of-mass (CM)
frame, and
E
CM
is the total CM energy.
For masses
m
ES
>
5
:
2 GeV
=c
2
we perform one-
dimensional fits of the
m
ES
distribution for
K‘
þ

modes. For
K

þ

modes, we include in addition the
K
mass region
0
:
72
<m
K
<
1
:
10 GeV
=c
2
in the fit.
We use the sideband
5
:
20
<m
ES
<
5
:
27 GeV
=c
2
to
characterize combinatorial background shapes and normal-
izations. For both the
e
þ
e

and

þ


modes, we
veto the
J=
c
ð
2
:
85
<m
‘‘
<
3
:
18 GeV
=c
2
Þ
and
c
ð
2
S
Þ
ð
3
:
59
<m
‘‘
<
3
:
77 GeV
=c
2
Þ
mass regions. The vetoed
events provide high-statistics control samples that we use
to validate the fit methodology.
The main backgrounds arise from random combinations
of leptons from semileptonic
B
and
D
decays. These
combinatorial backgrounds from either
B

B
events
(referred to as ‘‘
B

B
backgrounds’’) or continuum
q

q
events
(
e
þ
e

!
q

q
,
q
¼
u; d; s; c
, referred to as ‘‘
q

q
back-
grounds’’) are suppressed using bagged decision trees
(BDTs) [
19
]. We train eight separate BDTs as follows:
(i) suppression of
B

B
backgrounds for
e
þ
e

modes in
the low
s
region;
(ii) suppression of
B

B
backgrounds for
e
þ
e

modes in
the high
s
region;
(iii) suppression of
B

B
backgrounds for

þ


modes
in the low
s
region;
(iv) suppression of
B

B
backgrounds for

þ


modes
in the high
s
region;
(v) suppression of
q

q
backgrounds for
e
þ
e

modes in
the low
s
region;
(vi) suppression of
q

q
backgrounds for
e
þ
e

modes in
the high
s
region;
(vii) suppression of
q

q
backgrounds for

þ


modes
in the low
s
region;
(viii) suppression of
q

q
backgrounds for

þ


modes
in the high
s
region.
The BDT input parameters include the following
observables:
(i)

E
of the
B
candidate;
(ii) the ratio of Fox-Wolfram moments
R
2
[
20
] and the
ratio of the second-to-zeroth angular moments of
the energy flow
L
2
=L
0
[
21
], both event shape
parameters calculated using charged and neutral
particles in the CM frame;
(iii) the mass and

E
of the other
B
meson in the event
(referred to as the ‘‘rest of the event’’) computed in
the laboratory frame by summing the momenta and
energies of all charged particles and photons that
are not used to reconstruct the signal candidate;
(iv) the magnitude of the total transverse momentum of
the event in the laboratory frame;
(v) the probabilities that the
B
candidate and the dilep-
ton candidate, respectively, originate from a single
point in space;
(vi) the cosine values of four angles: the angle between
the
B
candidate momentum and the beam axis, the
angle between the event thrust axis and the beam
axis, the angle between the thrust axis of the rest of
the event and the beam axis, and the angle between
the event thrust axis and the thrust axis of the rest of
the event, all defined in the CM frame.
Figure
3
shows the output distributions of the BDTs for
Monte Carlo (MC) simulated signal and combinatorial
background for the
e
þ
e

sample below the
J=
c
reso-
nance. The distributions are histograms normalized to
unit area. The selections on BDT outputs are further opti-
mized to maximize the statistical significance of the signal
events, as shown later.
Another source of background arises from
B
!
D
ð!
K
ðÞ

Þ

decays if both pions are misidentified
as leptons. Determined from data control samples with
high purity [
18
], the misidentification rates for muons
and electrons are

3%
and
&
0
:
1%
per candidate, respec-
tively. Thus, this background is only significant for

þ


MEASUREMENT OF BRANCHING FRACTIONS AND RATE
...
PHYSICAL REVIEW D
86,
032012 (2012)
032012-5
final states. We veto these events by requiring the invariant
mass of the
K
ðÞ

system to be outside the range
1
:
84
1
:
90 GeV
=c
2
after assigning the pion mass hypothe-
sis to the muon candidates. Any remaining residual back-
grounds from this type of contribution are parameterized
using control samples obtained from data.
After applying all selection criteria about 85% of signal
events contain more than one
B
candidate. These candi-
dates differ typically in one charged or neutral hadron. The
average number of candidates per signal event is about six.
To choose the best candidate, we define the ratio


P
B

B
sig
þ
P
q

q
sig
P
B

B
sig
þ
P
q

q
sig
þ
P
B

B
bkg
þ
P
q

q
bkg
;
(4)
where
P
sig
and
P
bkg
are probabilities calculated from the
corresponding
B

B
and
q

q
BDT output distributions for
signal and background, respectively. We select the candi-
date with the largest

as the best candidate. The proba-
bility for a correctly reconstructed signal event to be
selected as the best candidate is mode-dependent and
varies between about 80% and 95% for
s
bins below the
J=
c
mass, while for
s
bins above the
c
ð
2
S
Þ
mass it varies
between about 60% and 90%.
V. SELECTION OPTIMIZATION
To optimize the

E
selection, we simultaneously vary
the upper and lower bounds of the

E
interval to find the
values that maximize the ratio
S=
ffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
p
in the signal
region (
m
ES
>
5
:
27 GeV
=c
2
, and for
K

modes in addition
0
:
78
<m
K
<
0
:
97 GeV
=c
2
), where
S
and
B
are the
expected numbers [
14
] of signal and combinatorial back-
ground events, respectively. We perform separate optimi-
zations for dilepton masses below and above the
J=
c
mass. For some modes, the optimization tends to select
very narrow intervals, which leads to small signal effi-
ciency. To prevent this, we require the magnitudes of the

E
upper and lower bounds to be 0.04 GeVor larger. (Note
that the lower bound is always negative and the upper
bound always positive.)
We also optimize the lower bounds on the BDT
B

B
and
q

q
intervals (the upper bounds on these intervals are al-
ways 1.0). We perform fits to extract signal yields using the
fit model described in Sec.
VI
. For each mode, the lower
bound on the BDT interval is optimized by maximizing the
expected signal significance defined as the fitted signal
yield divided by its associated uncertainty. We determine
these from 500 pseudoexperiments using branching frac-
tion averages [
14
]. The optimized BDT lower bounds are
listed in Tables
II
and
III
for
K‘
þ

and
K

þ

, respec-
tively. Figure
4
shows the expected experimental signifi-
cance in the
B

B
BDT versus the
q

q
BDT plane for
B
0
!
K
þ



þ


in bin
s
2
. The signal selection effi-
ciency and the cross-feed fraction (defined in Sec.
VI
)in
each mode and
s
bin after the final event selection are also
listed in Tables
II
and
III
. The selection efficiencies
determined in simulations vary from
11
:
4

0
:
2%
for
K
0
S

þ
e
þ
e

in
s
6
to
33
:
3

0
:
3%
for
K
þ

þ


in
s
5
,
where the uncertainties are statistical.
VI. FIT METHODOLOGY
We perform one-dimensional fits in
m
ES
for
K‘
þ

modes and two-dimensional fits in
m
ES
and
m
K
for
K

þ

modes to extract the signal yields. The probability
density function (PDF) for signal
m
ES
is parametrized by a
Gaussian function with mean and width fixed to values
obtained from fits to the vetoed
J=
c
events in the data
control samples. For
m
K
, the PDF is a relativistic Breit-
Wigner line shape [
22
]. True signal events are those where
all generator-level final-state daughter particles are cor-
rectly reconstructed and are selected to form a
B
candidate.
For the combinatorial background, the
m
ES
PDF is mod-
eled with a kinematic threshold function whose shape is a
free parameter in the fits [
23
], while the
m
K
PDF shape is
FIG. 3 (color online). The (a)
B

B
and (b)
q

qe
þ
e

BDT
outputs for simulated events in the low
s
region. Shown are
the distributions for
B

B
background (red dashed line),
q

q
background (red dotted line), and signal (blue solid line) event
samples, normalized to unit area.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032012 (2012)
032012-6
characterized with the
K

e



sample mentioned in Sec.
IV
.
We parameterize the combinatorial
m
K
distributions with
nonparametric Gaussian kernel density estimator shapes [
24
]
(referred to as the ‘‘KEYS PDFs’’) drawn from the
K

e



sample in the full
m
ES
fit region. Since the correlation be-
tween
m
K
and

E
is weak, we accept all
K

e



events
within
j

E
j
<
0
:
3GeV
, rather than imposing a stringent

E
selection, in order to enhance sample sizes.
Signal cross feed consists of misreconstructed signal
events, in which typically a low-momentum


or

0
is
swapped, added, or removed in the
B
candidate reconstruc-
tion. We distinguish among different categories of cross
feed: ‘‘self-cross-feed’’ is when a particle is swapped
within one mode, ‘‘feed-across’’ is when a particle is
swapped between two signal modes with the same final-
state multiplicity, and ‘‘feed-up (-down)’’ is when a parti-
cle is added (removed) from a lower (higher) multiplicity
b
!
s‘
þ

mode. We use both exclusive and inclusive
b
!
s‘
þ

MC samples to evaluate the contributions of
the different categories. The cross-feed
m
ES
distribution is
typically broadened compared to correctly reconstructed
signal decays. We combine the cross-feed contributions
from all sources into a single fit component that is modeled
as a sum of weighted histograms with a single overall
normalization, which is allowed to scale as a fixed fraction
of the observed correctly reconstructed signal yield. This
fixed fraction is presented as the ‘‘cross-feed fraction’’ in
Tables
II
and
III
. The modeling of cross-feed contributions
is validated using fits to the vetoed
J=
c
K
ðÞ
and
c
ð
2
S
Þ
K
ðÞ
events, in which the cross-feed contributions are relatively
large compared to all other backgrounds.
Exclusive
B
hadronic decays may be misreconstructed
as
B
!
K
ðÞ
þ

, since hadrons can be misidentified as
muons. Following a procedure similar to that described in
Ref. [
25
], we determine this background by selecting a
sample of
K
ðÞ


h

events, in which the muon is identi-
fied as a muon and the hadron is inconsistent with an
electron. Requiring identified kaons and pions, we select
subsamples of
K
ðÞ

þ


,
K
ðÞ
K
þ


,
K
ðÞ

þ
K

, and
K
ðÞ
K
þ
K

. We obtain weights from data control samples
where a charged particle’s species can be identified with
high precision and accuracy without using particle identi-
fication information. The weights are then applied to this
data set to characterize the contribution expected in our fits
TABLE II. Optimized lower bounds on the BDT intervals, signal reconstruction efficiency, and cross-feed fraction, by
K‘
þ

mode
and
s
bin. The uncertainties are statistical only.
Mode
s
bin
B

B
BDT
q

q
BDT
Efficiency [%]
Cross-feed fraction [%]
B
0
!
K
0
S

þ


s
1
0.20
0.80
19
:
9

0
:
2
8
:
9

0
:
3
s
2
0.70
0.85
22
:
2

0
:
2
8
:
6

0
:
2
s
3
0.20
0.85
25
:
2

0
:
1
8
:
9

0
:
2
s
4
0.70
0.70
24
:
3

0
:
2
9
:
4

0
:
2
s
5
0.70
0.80
22
:
2

0
:
2
12
:
0

0
:
5
s
6
0.75
0.80
16
:
6

0
:
1
21
:
7

0
:
7
s
0
0.50
0.85
22
:
7

0
:
1
8
:
8

0
:
1
B
þ
!
K
þ

þ


s
1
0.30
0.85
21
:
3

0
:
2
0
:
3

0
:
0
s
2
0.15
0.85
27
:
0

0
:
2
0
:
3

0
:
0
s
3
0.15
0.85
30
:
9

0
:
1
0
:
3

0
:
0
s
4
0.80
0.85
31
:
0

0
:
2
0
:
4

0
:
0
s
5
0.65
0.85
33
:
3

0
:
3
2
:
1

0
:
1
s
6
0.05
0.85
30
:
5

0
:
2
10
:
4

0
:
2
s
0
0.05
0.85
13
:
6

0
:
1
0
:
3

0
:
0
B
0
!
K
0
S
e
þ
e

s
1
0.25
0.80
22
:
1

0
:
2
8
:
3

0
:
3
s
2
0.25
0.80
25
:
2

0
:
2
9
:
4

0
:
3
s
3
0.65
0.80
24
:
3

0
:
1
9
:
4

0
:
2
s
4
0.50
0.85
24
:
1

0
:
2
10
:
9

0
:
4
s
5
0.05
0.65
23
:
0

0
:
2
18
:
5

0
:
9
s
6
0.25
0.70
16
:
5

0
:
1
35
:
0

1
:
1
s
0
0.85
0.85
21
:
3

0
:
1
9
:
2

0
:
2
B
þ
!
K
þ
e
þ
e

s
1
0.35
0.85
22
:
8

0
:
2
0
:
4

0
:
1
s
2
0.10
0.85
28
:
8

0
:
2
0
:
4

0
:
0
s
3
0.10
0.85
30
:
8

0
:
1
0
:
5

0
:
0
s
4
0.30
0.80
32
:
7

0
:
2
1
:
1

0
:
1
s
5
0.25
0.80
31
:
7

0
:
3
4
:
3

0
:
2
s
6
0.50
0.85
25
:
1

0
:
2
12
:
0

0
:
3
s
0
0.40
0.85
29
:
6

0
:
1
0
:
5

0
:
0
MEASUREMENT OF BRANCHING FRACTIONS AND RATE
...
PHYSICAL REVIEW D
86,
032012 (2012)
032012-7
due to misidentified muon candidates. We characterize the
misidentification backgrounds using the KEYS PDFs, with
normalizations obtained by construction directly from the
weighted data.
Some charmonium events may escape the charmonium
vetoes and appear in our fit region. Typically, this occurs
when electrons radiate a photon or a muon candidate is a
misidentified hadron and the missing energy is accounted
for by a low-energy


or

0
. The largest background
contributions from this source are expected in the
K


þ


and
K

e
þ
e

channels. We model this back-
ground using the charmonium MC samples and determine
the leakage into
s
bins on either side of the
J=
c
and
c
ð
2
S
Þ
resonances. We see a notable charmonium contribution
(about five events) for
B
0
!
K
þ



þ


in bin
s
3
. This
leakage is typically caused by a swap between the

þ
and

þ
in a single
B
!
J=
c
ð!

þ


Þ
K
þ
candidate,
where both the

þ
and

þ
are misidentified.
Hadronic peaking background from
B
!
K


0
and
B
!
K

in which the

0
or
decays via Dalitz pairs
shows a small peaking component in
m
ES
in bin
s
1
.Because
of the requirement
s>
0
:
1GeV
2
=c
4
, contributions of

conversions from
B
!
K


events beyond the photon
pole region are found to be negligible.
Fit model for rate asymmetries
Using the PDFs described above, we perform simulta-
neous fits across different
K
ðÞ
þ

modes. Since
efficiency-corrected signal yields are shared across various
decay modes, we can extract rate asymmetries directly
from the fits. The fitted signal yields in
B
þ
modes are
corrected by the lifetime ratio

B
0
=
B
þ
. We also correct
the signal yields for
B
ð
K

!
K
Þ
in
K

modes and
B
ð
K
0
S
!

þ


Þ
in the modes with a
K
0
S
. In the fits for
A
CP
, we share the efficiency-corrected signal yield
N
B
as
a floating variable for
Bq

b
,
q
¼
u; d
events across differ-
ent flavor-tagging
K
ðÞ
þ

modes by assuming lepton-
flavor and isospin symmetries. The efficiency-corrected
signal yield
N

B
for

B
ð

qb
Þ
events is then defined by
N

B
¼
N
B
1
þ
A
CP
Þ
Þ
=
ð
1

A
CP
Þ
and is also shared across
corresponding modes. For the lepton-flavor ratios
R
K
ðÞ
,
we share the efficiency-corrected signal yield
N
ee
as a floating variable for the two
B
!
Ke
þ
e

or
TABLE III. Optimized lower bounds on the BDT intervals, signal reconstruction efficiency, and cross-feed fraction, by
K

þ

mode and
s
bin. The uncertainties are statistical only.
Mode
s
bin
B

B
BDT
q

q
BDT
Efficiency [%]
Cross-feed fraction [%]
B
þ
!
K
0
S

þ

þ


s
1
0.55
0.85
13
:
6

0
:
1
14
:
0

0
:
5
s
2
0.80
0.85
14
:
6

0
:
2
19
:
2

0
:
7
s
3
0.85
0.80
14
:
9

0
:
1
20
:
7

0
:
5
s
4
0.85
0.85
14
:
7

0
:
1
28
:
0

0
:
7
s
5
0.15
0.85
16
:
4

0
:
2
59
:
3

1
:
3
s
6
0.10
0.85
14
:
3

0
:
1
110
:
8

1
:
9
s
0
0.80
0.85
14
:
5

0
:
1
18
:
9

0
:
5
B
0
!
K
þ



þ


s
1
0.80
0.85
16
:
2

0
:
1
4
:
9

0
:
2
s
2
0.80
0.85
19
:
6

0
:
2
7
:
8

0
:
3
s
3
0.75
0.85
21
:
3

0
:
1
10
:
1

0
:
2
s
4
0.85
0.85
20
:
9

0
:
1
13
:
8

0
:
3
s
5
0.75
0.85
22
:
8

0
:
2
31
:
7

0
:
6
s
6
0.80
0.80
19
:
5

0
:
2
61
:
0

0
:
9
s
0
0.60
0.85
20
:
4

0
:
1
8
:
9

0
:
2
B
þ
!
K
0
S

þ
e
þ
e

s
1
0.45
0.70
16
:
6

0
:
2
17
:
8

0
:
6
s
2
0.85
0.85
13
:
7

0
:
2
20
:
7

0
:
8
s
3
0.55
0.85
16
:
0

0
:
1
27
:
5

0
:
7
s
4
0.40
0.85
15
:
4

0
:
1
41
:
6

0
:
9
s
5
0.80
0.45
13
:
1

0
:
2
68
:
6

1
:
8
s
6
0.60
0.85
11
:
4

0
:
2
133
:
4

2
:
9
s
0
0.70
0.85
16
:
0

0
:
1
23
:
1

0
:
5
B
0
!
K
þ


e
þ
e

s
1
0.80
0.85
16
:
5

0
:
2
6
:
8

0
:
2
s
2
0.85
0.85
18
:
6

0
:
2
10
:
9

0
:
3
s
3
0.80
0.80
18
:
5

0
:
1
11
:
2

0
:
3
s
4
0.55
0.65
21
:
9

0
:
2
25
:
6

0
:
4
s
5
0.75
0.80
19
:
0

0
:
2
50
:
4

0
:
9
s
6
0.05
0.80
15
:
1

0
:
2
110
:
9

1
:
8
s
0
0.80
0.85
19
:
7

0
:
1
10
:
8

0
:
2
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032012 (2012)
032012-8
B
!
K

e
þ
e

modes by assuming isospin symmetry. The
efficiency-corrected signal yield
N

shared across the
corresponding
B
!
K
ðÞ

þ


modes is then defined by
N

¼
N
ee

R
K
ðÞ
. For the isospin asymmetry
A
K
ðÞ
I
,we
share the efficiency-corrected signal yield
N
B
þ
as a floating
variable for the two
B
þ
!
K
þ
þ

or
B
þ
!
K
þ

modes by assuming lepton-flavor symmetry. The
efficiency-corrected signal yield
N
B
0
shared across the
corresponding
B
0
!
K

0
þ

modes is then defined by
N
B
0
¼
N
B
þ
1
þ
A
K
ðÞ
I
Þ
=
ð
1

A
K
ðÞ
I
Þ
.
VII. FIT VALIDATION
We validate the fit methodology with charmonium con-
trol samples obtained from the dilepton mass regions
around the
J=
c
and
c
ð
2
S
Þ
resonances that are vetoed in
the
B
!
K
ðÞ
þ

analysis. We measure the
J=
c
K
ðÞ
and
c
ð
2
S
Þ
K
ðÞ
branching fractions in each final state with the
optimized BDT selections in bins
s
3
and
s
4
, respectively.
Our measurements agree well with the world averages [
14
]
for all final states. Typical deviations, based on statistical
uncertainties only, are less than 1 standard deviation (
).
The largest deviation, in the
K
þ



þ


mode, is
1
:
7
.
For
J=
c
K
ðÞ
modes, the statistical uncertainties are con-
siderably smaller than those of the world averages. We
float the Gaussian means and widths of the signal PDFs in
the fits for the
J=
c
K
ðÞ
modes. The associated uncertain-
ties obtained from the fits are then used as a source of
systematic variation for the signal PDFs. The typical signal
width in
m
ES
is
2
:
5 MeV
=c
2
.
We further validate our fitting procedure by applying it
to charmonium events to extract the rate asymmetries. The
measured
CP
asymmetries
A
CP
, lepton-flavor ratios
R
K
ðÞ
and isospin asymmetries
A
I
are in good agreement with
Standard Model expectations or world averages for
A
I
.
We also test the methodology with fits to ensembles of
data sets where signal and background events are generated
from appropriately normalized PDFs (‘‘pure pseudoexperi-
ments’’). We perform fits to these pseudoexperiments in
each mode and
s
bin using the full fit model described
previously. For ensembles of 1000 pure pseudoexperi-
ments, the pull distributions for the signal yields show
negligible biases. We further fit ensembles of pseudoex-
periments in which the signal events are drawn from
properly normalized exclusive MC samples (‘‘embedded
pseudoexperiments’’). The pull distributions also show the
expected performance.
We perform fits to ensembles of pure pseudoexperiments
in order to estimate the statistical sensitivity of, and biases
related to, the various rate asymmetry measurements. The
pull distributions for
A
CP
and
R
K
ðÞ
for the low and high
s
regions show minimal biases. For
A
I
, we test a series of
A
I
input values (

0
:
6
,

0
:
3
, 0.0, 0.3, 0.6) in each
s
bin
using pure pseudoexperiments to ensure we obtain un-
biased fits under different assumptions of isospin asymme-
try. The
A
K
I
pulls are generally well-behaved. In the worst
case, the test fits for
A
K
I
are slightly biased due to very low
signal yield expectations in the
K
0
S
þ

final states.
VIII. SYSTEMATIC UNCERTAINTIES
Since some systematic uncertainties largely cancel in
ratios, it is useful to separate the discussion of systematic
uncertainties on partial branching fractions from that on
rate asymmetries.
A. Branching Fraction Uncertainties
Systematic uncertainties for branching fractions arise
from multiplicative systematic uncertainties involving the
determination of the signal efficiency, and from additive
systematic uncertainties arising from the extraction of
signal yields in the data fits. The multiplicative systematic
errors include contributions from the
(i) Number of
B

B
pairs: This uncertainty is 0.6%.
(ii) Tracking efficiency for charged particles: We assign
a correlated uncertainty of 0.3% for each lepton, and
0.4% for each charged hadron including daughter
pions from
K
0
S
decay [
26
].
(iii) Charged particle identification (PID) efficiencies:
We employ a data-driven method to correct PID
efficiencies in simulated events. We estimate the
systematic uncertainties from the change in signal
efficiency for simulated
J=
c
K
ðÞ
events after turn-
ing off the PID corrections. The systematic uncer-
tainties are mode-dependent and vary between
0.3% and 1.6%.
(iv)
K
0
S
identification efficiency: This is determined
as a function of flight distance after applying
K
0
S
efficiency corrections. An uncertainty of 0.9% is
obtained by varying the
K
0
S
selection algorithm.
(v) Event selection efficiency: We measure the effi-
ciency of the BDT selection in charmonium data
BDT
B
B
BDT
q
q
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.1
1.2
1.3
1.4
1.5
0.8
0.9
0.7
0.6
0.5
0.4
0.3
0.2
0.1
FIG. 4 (color online). Expected statistical significance of the
number of fitted signal events as a function of BDT interval
lower bounds for
B
0
!
K
þ



þ


in bin
s
2
. The star marks
the optimized pair of lower bounds.
MEASUREMENT OF BRANCHING FRACTIONS AND RATE
...
PHYSICAL REVIEW D
86,
032012 (2012)
032012-9