of 9
Branching fraction of


!


K
0
s
K
0
s
ð

0
Þ


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
86,
092013 (2012)
1550-7998
=
2012
=
86(9)
=
092013(9)
092013-1
Ó
2012 American Physical Society
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, Ge
`
rmany
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, 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, Boı
ˆ
te Postale 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
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, The Netherlands
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
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
092013 (2012)
092013-2
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 Saclayu, 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 2 August 2012; published 26 November 2012)
We present a study of


!


K
0
S
K
0
S
ð

0
Þ


and


!
K

K
0
S
K
0
S
ð

0
Þ


decays using a data set of
430 million

lepton pairs, corresponding to an integrated luminosity of
468 fb

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

storage rings. We measure branching fractions of
ð
2
:
31

0
:
04

0
:
08
Þ
10

4
and
ð
1
:
60

0
:
20

0
:
22
Þ
10

5
for the


!


K
0
S
K
0
S


and


!


K
0
S
K
0
S

0


decays, respectively. We find no evidence for


!
K

K
0
S
K
0
S


and


!
K

K
0
S
K
0
S

0


decays and place upper limits on the branching fractions of
6
:
3

10

7
and
4
:
0

10

7
at the 90% confidence level.
DOI:
10.1103/PhysRevD.86.092013
PACS numbers: 13.35.Dx, 14.60.Fg
The

lepton can be used as a high-precision probe of the
Standard Model and models of new physics. A recent
BABAR
paper, for example, presented a search for
CP
violation by measuring the decay-rate asymmetry of


!


K
0
S


decays [
1
]. One of the backgrounds in that
analysis is


!


K
0
S
K
0
S


, which has a large uncer-
tainty in the branching fraction [
2
]. The uncertainty in
the background from


!


K
0
S
K
0
S


decays was not a
limitation of the decay-rate asymmetry measurement, but
an improved measurement of the branching fraction and an
understanding of the decay dynamics will be required for a
future measurement at a high-luminosity
B
-factory.
This paper presents measurements of the branching
fractions of


!


K
0
S
K
0
S
ð

0
Þ


decays and the first
search for


!
K

K
0
S
K
0
S
ð

0
Þ


decays. In this work we
use the
K
0
S
!

þ


decay mode. Here and throughout the
paper, charge conjugation is implied.
Previously, ALEPH and CLEO measured the


!


K
0
S
K
0
S


branching fraction to be
ð
2
:
6

1
:
0

0
:
5
Þ
10

4
[
3
] and
ð
2
:
3

0
:
5

0
:
3
Þ
10

4
[
4
], respectively.
*
Present address: University of Tabuk, Tabuk 71491, Saudi
Arabia.
Also with 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 with Universita
`
di Sassari, Sassari, Italy.
BRANCHING FRACTION OF
...
PHYSICAL REVIEW D
86,
092013 (2012)
092013-3
ALEPH set an upper limit on the


!


K
0
S
K
0
S

0


branching fraction of
2

10

4
at the 95% confidence
level [
3
].
The present analysis uses data recorded by the
BABAR
detector at the PEP-II asymmetric-energy
e
þ
e

collider,
operated at center-of-mass (CM) energies of 10.58 and
10.54 GeV at the SLAC National Accelerator Laboratory.
The
BABAR
detector is described in detail in Ref. [
5
]. In
particular, charged particle momenta are measured with
a five-layer double-sided silicon vertex tracker and a
40-layer drift chamber, both within a 1.5 T supercon-
ducting solenoidal magnet. Charged kaons and pions are
separated by ionization (
dE=dx
) measurements in the sili-
con vertex detector and the drift chamber in combination
with an internally reflecting Cherenkov detector. An elec-
tromagnetic calorimeter made of thallium-doped cesium
iodide crystals provides energy measurements for electrons
and photons, and an instrumented flux return detector
identifies muons. Based on an integrated luminosity
of
468 fb

1
, the data sample contains approximately
430 million

-pair events.
Simulated event samples are used to estimate the selec-
tion efficiency and purity of the data sample. The produc-
tion of

pairs is simulated with the KK2F Monte Carlo
(MC) event generator [
6
]. Subsequent decays of the

lepton, continuum
q

q
events (where
q
¼
u
,
d
,
s
,
c
), and
final-state radiative effects are modeled with Tauola [
7
]
and EvtGen [
8
], JETSET [
9
], and PHOTOS [
10
], respec-
tively. Passage of the particles through the detector is
simulated by Geant4 [
11
].
The


!


K
0
S
K
0
S


decay is simulated with Tauola
using


!
K

K
0


. The


!


K
0
S
K
0
S

0


decay is
simulated with EvtGen using


!
K

K
0

0


and


!
K

0
K
0




. As we later show, the


!
K

K
0


and


!
K

K
0

0


have a
K

ð
892
Þ
meson
that is observed in the


K
0
S
channel, and the


!
K

0
K
0




has a
K

ð
892
Þ
meson that is observed in the

0
K
0
S
channel.
The

pair is produced back-to-back in the
e
þ
e

CM
frame. As a result, the decay products of the two

leptons
can be separated from each other by dividing the event into
two hemispheres—referred to later as the ‘‘signal’’ hemi-
sphere and the ‘‘tag’’ hemisphere—using the plane per-
pendicular to the event thrust axis [
12
]. The event thrust
axis is calculated using all charged particles and all photon
candidates in the entire event.
We select events with one prompt track and two
K
0
S
!

þ


candidates reconstructed in the signal hemisphere,
and exactly one oppositely charged prompt track in the tag
hemisphere. All tracks are required to have the components
of momentum transverse to the
e

beam axis be greater
than
0
:
1 GeV
=c
in the laboratory frame. A prompt track is
defined to be a track with its point of closest approach to
the beam spot being less than 1.5 cm in the plane transverse
to the
e

beam axis and less than 2.5 cm in the direction of
the
e

beam axis. A
K
0
S
candidate is defined as a pair of
oppositely charged tracks where neither track is identified
as a prompt track. The invariant mass of the
K
0
S
candidate is
required to be between 0.475 and
0
:
525 GeV
=c
2
(see
Fig.
1
). Furthermore, the distance between the beam spot
and the

þ


vertex must be at least three times its
uncertainty (the di-pion pair will be referred to as the
‘‘
K
0
S
candidate daughters’’).
The charged hadron must be identified as a charged pion
or a charged kaon. The efficiency for selecting charged
pions and kaons is approximately 95 and 90%, respec-
tively. The probability of misidentifying a charged pion
(kaon) as a charged kaon (pion) is estimated to be 1% (5%).
The charged pion and kaon samples are divided into
samples with zero and one

0
mesons. Events with two or
more

0
mesons are rejected. The

0
candidate is recon-
structed from two clusters of energy deposits in the elec-
tromagnetic calorimeter that have no associated tracks.
The energy of each cluster is required to be greater than
30 MeV in the laboratory frame, and the invariant mass of
the two clusters must be between
0
:
115
and
0
:
150 GeV
=c
2
.
)
2
Mass (GeV/c
π
+
π
0.48
0.49
0.5
0.51
0.52
2
Entries/0.25 MeV/c
0
100
200
300
400
500
Data
0
S
K
0
S
K
π
0
π
0
S
K
0
S
K
π
Bkgd
)
2
Mass (GeV/c
π
+
π
0.48
0.49
0.5
0.51
0.52
2
Entries/0.5 MeV/c
0
20
40
60
80
100
Data
0
π
0
S
K
*-
K
-
π
0
S
K
*0
K
0
S
K
0
S
K
π
Bkgd
FIG. 1 (color online). The invariant mass of the two
K
0
S
!

þ


candidates in the


!


K
0
S
K
0
S


(top) and


!


K
0
S
K
0
S

0


(bottom) samples after all selection criteria
have been applied. The points are data and the histograms are the
prediction of the Monte Carlo simulation. For both plots, the
white histogram represents


!
K

K
0


decays, and the blue
(medium shaded) and beige (light shaded) histogram shows the


!
K

K
0

0


and


!
K

0
K
0




(


!


K
0
S
K
0
S

0


)
decays, respectively. The red (dark shaded) histogram is the
q

q
background.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
092013 (2012)
092013-4
The clusters in the electromagnetic calorimeter that are not
associated with a

0
candidate are ignored in the analysis.
To reduce backgrounds from non-

pair events, we
require that the momentum of the charged particle in the
tag hemisphere is less than
4 GeV
=c
in the CM frame and
be identified as either an electron or a muon. For momenta
above
1 GeV
=c
in the laboratory frame, electrons and
muons are identified with efficiencies of approximately
92 and 70%, respectively [
13
]. We also require the magni-
tude of the event thrust to be between 0.90 and 0.995.
The invariant mass of the charged hadron and the two
K
0
S
mesons is required to be less than
1
:
8 GeV
=c
2
.For


!


K
0
S
K
0
S

0


decays, we do not include the

0
in the mass
calculation. The


K
0
S
K
0
S
invariant mass is shown in
Figs.
2
and
3
. The


K
0
S
K
0
S

0
invariant mass is also shown
in Fig.
3
. We also require the pseudomass to be less than
1.9 and
2
:
1 GeV
=c
2
for the


!


K
0
S
K
0
S


and


!


K
0
S
K
0
S

0


samples, respectively (the

0
meson is
included in the pseudomass calculation). The pseudomass
is defined to be
M
pseudo
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
M
2
h
þ
2
ð
ffiffiffi
s
p

E
h
Þð
E
h

P
h
Þ
q
where
E
h
and
P
h
are the energy and magnitude of the
momentum of the hadronic final state in the laboratory
frame [
14
].
The invariant mass distribution predicted by the MC for
the hadronic final state particles and for their combinations
does not perfectly describe the data. In particular, the peak
of the (


K
0
S
K
0
S
) invariant mass distribution in the MC is
found to peak approximately 5% lower than the peak
observed in the data. To improve the modeling of the
data we have weighted the


!


K
0
S
K
0
S


in Tauola
using the Dalitz plot distribution for the


K
0
S
invariant
mass (shown for the data sample in Fig.
2
). The weighting
function is from a two-dimensional (
9

9
) matrix using
M
2
ð


K
0
S
Þ
with both


K
0
S
combinations (the matrix is
constructed to be symmetric). The weighted events are
used in all the mass plots and we observe an improvement
in the modeling of the data.
The branching fractions of the two charged pion modes
are determined simultaneously to take into account the
cross feed of each decay mode into the other sample. The
branching fraction is
B
j
¼
X
i


1
ji
ð
N
data
i

N
bkgd
i
Þ
=
ð
2
N

Þ
where
j
represents the


!


K
0
S
K
0
S


and


!


K
0
S
K
0
S

0


decay modes;
i
represents the (


K
0
S
K
0
S
)
or (


K
0
S
K
0
S

0
) reconstruction modes;
N
data
i
and
N
bkgd
i
are
2
)
2
) (GeV/c
0
S
K
-
π
(
2
M
0.4
0.6
0.8
1
1.2
1.4
1.6
2
)
2
) (GeV/c
0
S
K
-
π
(
2
M
0.4
0.6
0.8
1
1.2
1.4
1.6
)
2
Mass (GeV/c
0
S
K
0
S
K
π
1
1.2
1.4
1.6
1.8
2
2.2
2
Entries/0.02 GeV/c
0
200
400
600
Data
0
S
K
0
S
K
π
0
π
0
S
K
0
S
K
π
Bkgd
)
2
Mass (GeV/c
0
S
K
π
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
2
Entries/0.01 GeV/c
0
200
400
600
800
1000
)
2
Mass (GeV/c
0
S
K
0
S
K
1
1.1
1.2
1.3
1.4
1.5
2
Entries/0.01 GeV/c
0
100
200
300
FIG. 2 (color online). The Dalitz plot of the (


K
0
S
) system, and the (


K
0
S
K
0
S
), (


K
0
S
) and (
K
0
S
K
0
S
) invariant mass distributions for
events that pass the


!


K
0
S
K
0
S


selection criteria. The invariant mass requirement is not required for the plot of the (


K
0
S
K
0
S
)
invariant mass. There are two entries per event in the Dalitz plot and in the (


K
0
S
) mass plot. The points are data and the histograms
are the prediction of the Monte Carlo simulation. The signal decays are represented by the white histogram (


!
K

K
0


). The
beige (light shaded) histogram shows the


!
K

K
0

0


and


!
K

0
K
0




(


!


K
0
S
K
0
S

0


) decays. The red (dark
shaded) histogram is the
q

q
background. The mass plots use


!


K
0
S
K
0
S


events that have been weighted based on the Dalitz plot
distributions in the top left plot.
BRANCHING FRACTION OF
...
PHYSICAL REVIEW D
86,
092013 (2012)
092013-5
the number of data and background events in the
i
th data
sample;


1
is the inverse of the selection efficiency matrix
(

ij
is the probability to select an event of type
j
with the
selection criteria
i
); and
N

is the number of

-pair
candidates determined from the integrated luminosity and
the
e

e

!
cross section.
The columns in Table
I
give the number of data and
background events for each reconstruction mode. Table
I
also gives the selection efficiency matrix, where the
horizontal row gives the efficiency for selecting the true
decay for each reconstructed mode. For example, the effi-
ciency for selecting a true


!


K
0
S
K
0
S


decay is
)
2
Mass (GeV/c
0
S
K
0
S
K
π
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
2
2
Entries/0.05 GeV/c
0
20
40
60
80
100
Data
0
π
0
S
K
*-
K
-
π
0
S
K
*0
K
0
S
K
0
S
K
π
Bkgd
)
2
Mass (GeV/c
0
π
0
S
K
0
S
K
π
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
2
2.1
2.2
2
Entries/0.05 GeV/c
0
20
40
60
80
100
)
2
Mass (GeV/c
0
S
K
π
0.6
0.7
0.8
0.9
1
1.1
1.2
2
Entries/0.03 GeV/c
0
20
40
60
80
100
120
140
160
180
200
)
2
Mass (GeV/c
0
S
K
0
π
0.6
0.7
0.8
0.9
1
1.1
1.2
2
Entries/0.03 GeV/c
0
20
40
60
80
100
120
140
160
180
200
FIG. 3 (color online). The (


K
0
S
K
0
S
), (


K
0
S
K
0
S

0
), (


K
0
S
), and (

0
K
0
S
) invariant mass distributions that pass the


!


K
0
S
K
0
S

0


selection criteria [except for the plot of the (


K
0
S
K
0
S
) invariant mass where the selection requirement on the mass
is not included]. There are two entries per event in the (


K
0
S
) and (

0
K
0
S
) mass plots. The points are data and the histograms are the
predictions of the Monte Carlo simulation. The two signal channels are shown in the white (


!
K

K
0

0


) and beige (light
shaded) (


!
K

0
K
0




) histograms. The dark blue (medium shaded) histogram is


!


K
0
S
K
0
S


(


!
K

K
0


) decays.
The red (dark shaded) histogram is the
q

q
background. The mass plots use


!


K
0
S
K
0
S


events that have been weighted based on
the Dalitz plot distributions shown in Fig.
2
.
TABLE I. Results for the charged pion decays. The background events are primarily
q

q
events.
Decay mode


!


K
0
S
K
0
S




!


K
0
S
K
0
S

0


Branching fraction
ð
2
:
31

0
:
04

0
:
08
Þ
10

4
ð
1
:
60

0
:
20

0
:
22
Þ
10

5
Events
Data
4985
409
Estimated background
98

17
35

7
Selection efficiency


!


K
0
S
K
0
S


ð
4
:
93

0
:
02
Þ
%
ð
0
:
21

0
:
01
Þ
%


!


K
0
S
K
0
S

0


ð
3
:
04

0
:
10
Þ
%
ð
2
:
65

0
:
09
Þ
%
Fractional systematic errors
Selection efficiency
0.008
0.12
Background
0.004
0.04
Common systematics
0.034
0.03
Total
0.035
0.13
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
092013 (2012)
092013-6
ð
4
:
93

0
:
02
Þ
%
and
ð
0
:
21

0
:
01
Þ
%
with the (


K
0
S
K
0
S
)
and (


K
0
S
K
0
S

0
) selection criteria, respectively.
We measure the


!


K
0
S
K
0
S


and


!


K
0
S
K
0
S

0


branching fractions to be
B
ð


!


K
0
S
K
0
S


Þ¼ð
2
:
31

0
:
04

0
:
08
Þ
10

4
;
B
ð


!


K
0
S
K
0
S

0


Þ¼ð
1
:
60

0
:
20

0
:
22
Þ
10

5
;
where the first error is statistical and the second is system-
atic. The statistical correlation parameter for the two mea-
surements is found to be

0
:
21
. The results have been
corrected for the
K
0
S
!

þ


branching fraction [
2
].
The systematic uncertainties (see Table
I
) are divided
into the selection efficiency, background, and common
systematic components. The uncertainties on the elements
of the efficiency matrix only include the errors specific to
that decay and those selection criteria. Uncertainties that
are common to all matrix elements are included in the
common systematic errors.
The efficiency for selecting


!


K
0
S
K
0
S


events is
found to be
ð
4
:
93

0
:
02
Þ
%
and
ð
0
:
21

0
:
01
Þ
%
for the
samples with zero and one

0
candidate, respectively. The
uncertainty on the first efficiency is from the MC statistical
error. The uncertainty on the second efficiency also
includes the MC statistical error and an error that takes
into account the uncertainty for finding a fake

0
meson in


!


K
0
S
K
0
S


decays. The uncertainty for finding a
fake

0
is estimated to be 6% and is determined by
comparing the number of


!


K
0
S
K
0
S


decays that
have two neutral clusters in the data and MC samples
where the invariant mass of the two neutral clusters must
not be near the

0
mass.
The efficiency for selecting


!


K
0
S
K
0
S

0


events
is found to be
ð
3
:
04

0
:
10
Þ
%
and
ð
2
:
65

0
:
09
Þ
%
for the
samples with zero and one

0
candidate, respectively. The
uncertainties include the MC statistical error and an uncer-
tainty for the

0
identification. The uncertainty for identi-
fying a

0
meson is estimated to be 3% based on studies
with tau lepton and
D
meson data and MC control samples.
We observe that the efficiency for selecting


!


K
0
S
K
0
S

0


decays with and without a

0
is approxi-
mately equal, and hence we assign a 3% uncertainty on the
efficiency for selecting


!


K
0
S
K
0
S

0


decays with-
out reconstructing the

0
meson.
The background in the charged pion modes is predicted
by the MC simulation to be entirely from
e
þ
e

!
q

q
events. The background in the charged kaon modes is cross
fed from the charged pion modes where a charged pion is
misidentified as the charged kaon. The background in the
charged pion sample is confirmed with data and MC simu-
lation control samples. The control samples are created
using the nominal selection criteria except that the invari-
ant mass and pseudomass requirements are reversed to
eliminate the

-pair events and enhance
q

q
events. The
ratio of selected events in the data to MC control samples is
found to be consistent with unity within 15% for both


!


K
0
S
K
0
S


and


!


K
0
S
K
0
S

0


samples. The
15% value is added to the MC statistical uncertainty of the
number of background events.
A number of systematic uncertainties are common to
both the


!


K
0
S
K
0
S


and


!


K
0
S
K
0
S

0


branching fractions’ measurements. They can be catego-
rized into two components: tracking and particle identifi-
cation reconstruction uncertainties, and topological
selection uncertainties.
The tracking and particle identification reconstruction
uncertainties include the uncertainty on the track recon-
struction efficiency (0.5%). They also include the uncer-
tainties on the efficiencies of the particle identification
algorithms: lepton identification (combined electron and
muon) (1.6%), charged pion particle identification (0.5%),
and
K
0
S
identification (1.8% for two
K
0
S
). The particle
identification algorithms used in this work are based on
standard
BABAR
routines and the uncertainties are deter-
mined using control data and MC samples [
5
,
15
]. The
uncertainty on the efficiency for selecting

0
mesons is
included in the elements of the selection efficiency matrix.
The topological selection u
ncertainties include a 2% un-
certainty associated with the topological selection criteria
that impose requirements that the prompt tracks be associ-
ated with the primary vertex. Also included is the uncertainty
in the product of the luminosity multiplied by the
e
þ
e

!

þ


cross section (1%). If the weighting of the invariant
mass distribution of the


!


K
0
S
K
0
S


MC decays is not
included (or another weighting scheme is used), we find the
change in the measured branching ratios to be negligible
compared with the other systematic uncertainties.
In Fig.
2
we plot the (


K
0
S
K
0
S
), (


K
0
S
), and (
K
0
S
K
0
S
)
invariant mass distributions. The contribution of the
K

ð
892
Þ
resonance (
K

!


K
0
S
) is observed in the
(


K
0
S
) invariant mass plot and the Dalitz plot in Fig.
2
.
The


!


K
0
S
K
0
S


branching fraction is in good
agreement with the previous measurements of
ð
2
:
6

1
:
0

0
:
5
Þ
10

4
[
3
] and
ð
2
:
3

0
:
5

0
:
3
Þ
10

4
[
4
].
The theoretical prediction for the


!


K
0
S
K
0
S


branching fraction is
4
:
8

10

4
[
16
]. Decays involving
a pion and two kaon mesons can have contributions from
both axial and vector currents at the same time, and the
vector contribution for


!


K
0
S
K
0
S


is estimated to
be
1
:
4

10

4
[
16
].
Assuming isospin symmetry [
17
] and using other
measurements, we can estimate the


!


K
0
S
K
0
L


branching fraction. The


!


K
0

K
0


and


!


K
þ
K



branching fractions are equal if isospin is an
exact symmetry (the


!


K
0
S
K
0
S


and


!


K
0
L
K
0
L


branching fractions are also equal).
Hence
B
ð


!


K
0
S
K
0
L


Þ¼
B
ð


!


K
þ
K



Þ
2
B
ð


!


K
0
S
K
0
S


Þ
and we obtain
B
ð


!


K
0
S
K
0
L


Þ¼ð
9
:
8

0
:
5
Þ
10

4
BRANCHING FRACTION OF
...
PHYSICAL REVIEW D
86,
092013 (2012)
092013-7