Search for the rare decay
B
!
K
P. del Amo Sanchez,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
M. Martinelli,
3,4
A. Palano,
3,4
M. Pappagallo,
3,4
G. Eigen,
5
B. Stugu,
5
L. Sun,
5
M. Battaglia,
6
D. N. Brown,
6
B. Hooberman,
6
L. T. Kerth,
6
Yu. G. Kolomensky,
6
G. Lynch,
6
I. L. Osipenkov,
6
T. Tanabe,
6
C. M. Hawkes,
7
A. T. Watson,
7
H. Koch,
8
T. Schroeder,
8
D. J. Asgeirsson,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
A. Khan,
10
A. Randle-Conde,
10
V. E. Blinov,
11
A. R. Buzykaev,
11
V. P. Druzhinin,
11
V. B. Golubev,
11
A. P. Onuchin,
11
S. I. Serednyakov,
11
Yu. I. Skovpen,
11
E. P. Solodov,
11
K. Yu. Todyshev,
11
A. N. Yushkov,
11
M. Bondioli,
12
S. Curry,
12
D. Kirkby,
12
A. J. Lankford,
12
M. Mandelkern,
12
E. C. Martin,
12
D. P. Stoker,
12
H. Atmacan,
13
J. W. Gary,
13
F. Liu,
13
O. Long,
13
G. M. Vitug,
13
C. Campagnari,
14
T. M. Hong,
14
D. Kovalskyi,
14
J. D. Richman,
14
A. M. Eisner,
15
C. A. Heusch,
15
J. Kroseberg,
15
W. S. Lockman,
15
A. J. Martinez,
15
T. Schalk,
15
B. A. Schumm,
15
A. Seiden,
15
L. O. Winstrom,
15
C. H. Cheng,
16
D. A. Doll,
16
B. Echenard,
16
D. G. Hitlin,
16
P. Ongmongkolkul,
16
F. C. Porter,
16
A. Y. Rakitin,
16
R. Andreassen,
17
M. S. Dubrovin,
17
G. Mancinelli,
17
B. T. Meadows,
17
M. D. Sokoloff,
17
P. C. Bloom,
18
W. T. Ford,
18
A. Gaz,
18
M. Nagel,
18
U. Nauenberg,
18
J. G. Smith,
18
S. R. Wagner,
18
R. Ayad,
19,
*
W. H. Toki,
19
H. Jasper,
20
T. M. Karbach,
20
J. Merkel,
20
A. Petzold,
20
B. Spaan,
20
K. Wacker,
20
M. J. Kobel,
21
K. R. Schubert,
21
R. Schwierz,
21
D. Bernard,
22
M. Verderi,
22
P. J. Clark,
23
S. Playfer,
23
J. E. Watson,
23
M. Andreotti,
24,25
D. Bettoni,
24,25
C. Bozzi,
24,25
R. Calabrese,
24,25
A. Cecchi,
24,25
G. Cibinetto,
24,25
E. Fioravanti,
24,25
P. Franchini,
24,25
E. Luppi,
24,25
M. Munerato,
24,25
M. Negrini,
24,25
A. Petrella,
24,25
L. Piemontese,
24
R. Baldini-Ferroli,
26
A. Calcaterra,
26
R. de Sangro,
26
G. Finocchiaro,
26
M. Nicolaci,
26
S. Pacetti,
26
P. Patteri,
26
I. M. Peruzzi,
26,
†
M. Piccolo,
26
M. Rama,
26
A. Zallo,
26
R. Contri,
27,28
E. Guido,
27,28
M. Lo Vetere,
27,28
M. R. Monge,
27,28
S. Passaggio,
27
C. Patrignani,
27,28
E. Robutti,
27
S. Tosi,
27,28
B. Bhuyan,
29
V. Prasad,
29
C. L. Lee,
30
M. Morii,
30
A. Adametz,
31
J. Marks,
31
U. Uwer,
31
F. U. Bernlochner,
32
M. Ebert,
32
H. M. Lacker,
32
T. Lueck,
32
A. Volk,
32
P. D. Dauncey,
33
M. Tibbetts,
33
P. K. Behera,
34
U. Mallik,
34
C. Chen,
35
J. Cochran,
35
H. B. Crawley,
35
L. Dong,
35
W. T. Meyer,
35
S. Prell,
35
E. I. Rosenberg,
35
A. E. Rubin,
35
Y. Y. Gao,
36
A. V. Gritsan,
36
Z. J. Guo,
36
N. Arnaud,
37
M. Davier,
37
D. Derkach,
37
J. Firmino da Costa,
37
G. Grosdidier,
37
F. Le Diberder,
37
A. M. Lutz,
37
B. Malaescu,
37
A. Perez,
37
P. Roudeau,
37
M. H. Schune,
37
J. Serrano,
37
V. Sordini,
37,
‡
A. Stocchi,
37
L. Wang,
37
G. Wormser,
37
D. J. Lange,
38
D. M. Wright,
38
I. Bingham,
39
C. A. Chavez,
39
J. P. Coleman,
39
J. R. Fry,
39
E. Gabathuler,
39
R. Gamet,
39
D. E. Hutchcroft,
39
D. J. Payne,
39
C. Touramanis,
39
A. J. Bevan,
40
F. Di Lodovico,
40
R. Sacco,
40
M. Sigamani,
40
G. Cowan,
41
S. Paramesvaran,
41
A. C. Wren,
41
D. N. Brown,
42
C. L. Davis,
42
A. G. Denig,
43
M. Fritsch,
43
W. Gradl,
43
A. Hafner,
43
K. E. Alwyn,
44
D. Bailey,
44
R. J. Barlow,
44
G. Jackson,
44
G. D. Lafferty,
44
T. J. West,
44
J. Anderson,
45
R. Cenci,
45
A. Jawahery,
45
D. A. Roberts,
45
G. Simi,
45
J. M. Tuggle,
45
C. Dallapiccola,
46
E. Salvati,
46
R. Cowan,
47
D. Dujmic,
47
P. H. Fisher,
47
G. Sciolla,
47
M. Zhao,
47
D. Lindemann,
48
P. M. Patel,
48
S. H. Robertson,
48
M. Schram,
48
P. Biassoni,
49,50
A. Lazzaro,
49,50
V. Lombardo,
49
F. Palombo,
49,50
S. Stracka,
49,50
L. Cremaldi,
51
R. Godang,
51,
x
R. Kroeger,
51
P. Sonnek,
51
D. J. Summers,
51
X. Nguyen,
52
M. Simard,
52
P. Taras,
52
G. De Nardo,
53,54
D. Monorchio,
53,54
G. Onorato,
53,54
C. Sciacca,
53,54
G. Raven,
55
H. L. Snoek,
55
C. P. Jessop,
56
K. J. Knoepfel,
56
J. M. LoSecco,
56
W. F. Wang,
56
L. A. Corwin,
57
K. Honscheid,
57
R. Kass,
57
J. P. Morris,
57
N. L. Blount,
58
J. Brau,
58
R. Frey,
58
O. Igonkina,
58
J. A. Kolb,
58
R. Rahmat,
58
N. B. Sinev,
58
D. Strom,
58
J. Strube,
58
E. Torrence,
58
G. Castelli,
59,60
E. Feltresi,
59,60
N. Gagliardi,
59,60
M. Margoni,
59,60
M. Morandin,
59,60
M. Posocco,
59
M. Rotondo,
59
F. Simonetto,
59,60
R. Stroili,
59,60
E. Ben-Haim,
61
G. R. Bonneaud,
61
H. Briand,
61
G. Calderini,
61
J. Chauveau,
61
O. Hamon,
61
Ph. Leruste,
61
G. Marchiori,
61
J. Ocariz,
61
J. Prendki,
61
S. Sitt,
61
M. Biasini,
62,63
E. Manoni,
62,63
A. Rossi,
62,63
C. Angelini,
64,65
G. Batignani,
64,65
S. Bettarini,
64,65
M. Carpinelli,
64,65,
k
G. Casarosa,
64,65
A. Cervelli,
64,65
F. Forti,
64,65
M. A. Giorgi,
64,65
A. Lusiani,
64,66
N. Neri,
64,65
E. Paoloni,
64,65
G. Rizzo,
64,65
J. J. Walsh,
64
D. Lopes Pegna,
67
C. Lu,
67
J. Olsen,
67
A. J. S. Smith,
67
A. V. Telnov,
67
F. Anulli,
68
E. Baracchini,
68,69
G. Cavoto,
68
R. Faccini,
68,69
F. Ferrarotto,
68
F. Ferroni,
68,69
M. Gaspero,
68,69
L. Li Gioi,
68
M. A. Mazzoni,
68
G. Piredda,
68
F. Renga,
68,69
T. Hartmann,
70
T. Leddig,
70
H. Schro
̈
der,
70
R. Waldi,
70
T. Adye,
71
B. Franek,
71
E. O. Olaiya,
71
F. F. Wilson,
71
S. Emery,
72
G. Hamel de Monchenault,
72
G. Vasseur,
72
Ch. Ye
`
che,
72
M. Zito,
72
M. T. Allen,
73
D. Aston,
73
D. J. Bard,
73
R. Bartoldus,
73
J. F. Benitez,
73
C. Cartaro,
73
M. R. Convery,
73
J. Dorfan,
73
G. P. Dubois-Felsmann,
73
W. Dunwoodie,
73
R. C. Field,
73
M. Franco Sevilla,
73
B. G. Fulsom,
73
A. M. Gabareen,
73
M. T. Graham,
73
P. Grenier,
73
C. Hast,
73
W. R. Innes,
73
M. H. Kelsey,
73
H. Kim,
73
P. Kim,
73
M. L. Kocian,
73
D. W. G. S. Leith,
73
S. Li,
73
B. Lindquist,
73
S. Luitz,
73
V. Luth,
73
H. L. Lynch,
73
D. B. MacFarlane,
73
H. Marsiske,
73
D. R. Muller,
73
H. Neal,
73
S. Nelson,
73
C. P. O’Grady,
73
I. Ofte,
73
M. Perl,
73
T. Pulliam,
73
B. N. Ratcliff,
73
A. Roodman,
73
A. A. Salnikov,
73
V. Santoro,
73
R. H. Schindler,
73
J. Schwiening,
73
A. Snyder,
73
D. Su,
73
M. K. Sullivan,
73
S. Sun,
73
K. Suzuki,
73
J. M. Thompson,
73
J. Va’vra,
73
A. P. Wagner,
73
M. Weaver,
73
C. A. West,
73
W. J. Wisniewski,
73
PHYSICAL REVIEW D
82,
112002 (2010)
1550-7998
=
2010
=
82(11)
=
112002(10)
112002-1
Ó
2010 The American Physical Society
M. Wittgen,
73
D. H. Wright,
73
H. W. Wulsin,
73
A. K. Yarritu,
73
C. C. Young,
73
V. Ziegler,
73
X. R. Chen,
74
W. Park,
74
M. V. Purohit,
74
R. M. White,
74
J. R. Wilson,
74
S. J. Sekula,
75
M. Bellis,
76
P. R. Burchat,
76
A. J. Edwards,
76
T. S. Miyashita,
76
S. Ahmed,
77
M. S. Alam,
77
J. A. Ernst,
77
B. Pan,
77
M. A. Saeed,
77
S. B. Zain,
77
N. Guttman,
78
A. Soffer,
78
P. Lund,
79
S. M. Spanier,
79
R. Eckmann,
80
J. L. Ritchie,
80
A. M. Ruland,
80
C. J. Schilling,
80
R. F. Schwitters,
80
B. C. Wray,
80
J. M. Izen,
81
X. C. Lou,
81
F. Bianchi,
82,83
D. Gamba,
82,83
M. Pelliccioni,
82,83
M. Bomben,
84,85
L. Lanceri,
84,85
L. Vitale,
84,85
N. Lopez-March,
86
F. Martinez-Vidal,
86
D. A. Milanes,
86
A. Oyanguren,
86
J. Albert,
87
Sw. Banerjee,
87
H. H. F. Choi,
87
K. Hamano,
87
G. J. King,
87
R. Kowalewski,
87
M. J. Lewczuk,
87
I. M. Nugent,
87
J. M. Roney,
87
R. J. Sobie,
87
T. J. Gershon,
88
P. F. Harrison,
88
T. E. Latham,
88
E. M. T. Puccio,
88
H. R. Band,
89
S. Dasu,
89
K. T. Flood,
89
Y. Pan,
89
R. Prepost,
89
C. O. Vuosalo,
89
and S. L. Wu
89
(The
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
3
INFN Sezione di Bari, I-70126 Bari, Italy
4
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
5
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
6
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
7
University of Birmingham, Birmingham, B15 2TT, United Kingdom
8
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
9
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
10
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
12
University of California at Irvine, Irvine, California 92697, USA
13
University of California at Riverside, Riverside, California 92521, USA
14
University of California at Santa Barbara, Santa Barbara, California 93106, USA
15
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
16
California Institute of Technology, Pasadena, California 91125, USA
17
University of Cincinnati, Cincinnati, Ohio 45221, USA
18
University of Colorado, Boulder, Colorado 80309, USA
19
Colorado State University, Fort Collins, Colorado 80523, USA
20
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
21
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
22
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
23
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
24
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
25
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
26
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
27
INFN Sezione di Genova, I-16146 Genova, Italy
28
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
29
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
30
Harvard University, Cambridge, Massachusetts 02138, USA
31
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
32
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
33
Imperial College London, London, SW7 2AZ, United Kingdom
34
University of Iowa, Iowa City, Iowa 52242, USA
35
Iowa State University, Ames, Iowa 50011-3160, USA
36
Johns Hopkins University, Baltimore, Maryland 21218, USA
37
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
38
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
39
University of Liverpool, Liverpool L69 7ZE, United Kingdom
40
Queen Mary, University of London, London, E1 4NS, United Kingdom
41
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
42
University of Louisville, Louisville, Kentucky 40292, USA
43
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
44
University of Manchester, Manchester M13 9PL, United Kingdom
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
112002 (2010)
112002-2
45
University of Maryland, College Park, Maryland 20742, USA
46
University of Massachusetts, Amherst, Massachusetts 01003, USA
47
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
48
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
49
INFN Sezione di Milano, I-20133 Milano, Italy
50
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
51
University of Mississippi, University, Mississippi 38677, USA
52
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
53
INFN Sezione di Napoli, I-80126 Napoli, Italy
54
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
55
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
56
University of Notre Dame, Notre Dame, Indiana 46556, USA
57
Ohio State University, Columbus, Ohio 43210, USA
58
University of Oregon, Eugene, Oregon 97403, USA
59
INFN Sezione di Padova, I-35131 Padova, Italy
60
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
61
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
62
INFN Sezione di Perugia, I-06100 Perugia, Italy
63
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
64
INFN Sezione di Pisa, I-56127 Pisa, Italy
65
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
66
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
67
Princeton University, Princeton, New Jersey 08544, USA
68
INFN Sezione di Roma, I-00185 Roma, Italy
69
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
70
Universita
̈
t Rostock, D-18051 Rostock, Germany
71
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
72
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
73
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
74
University of South Carolina, Columbia, South Carolina 29208, USA
75
Southern Methodist University, Dallas, Texas 75275, USA
76
Stanford University, Stanford, California 94305-4060, USA
77
State University of New York, Albany, New York 12222, USA
78
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
79
University of Tennessee, Knoxville, Tennessee 37996, USA
80
University of Texas at Austin, Austin, Texas 78712, USA
81
University of Texas at Dallas, Richardson, Texas 75083, USA
82
INFN Sezione di Torino, I-10125 Torino, Italy
83
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
84
INFN Sezione di Trieste, I-34127 Trieste, Italy
85
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
86
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
87
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
88
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
89
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 10 September 2010; published 8 December 2010)
We present a search for the rare decays
B
þ
!
K
þ
and
B
0
!
K
0
using
459
10
6
B
B
pairs
collected with the
BABAR
detector at the SLAC National Accelerator Laboratory. Flavor-changing
neutral-current decays such as these are forbidden at tree level but can occur through one-loop diagrams
in the standard model (SM), with possible contributions from new physics at the same order. The presence
of two neutrinos in the final state makes identification of signal events challenging, so reconstruction in
the semileptonic decay channels
B
!
D
ðÞ
l
of the
B
meson recoiling from the signal
B
is used to
*
Now at Temple University, Philadelphia, PA 19122, USA.
†
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
‡
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy.
x
Now at University of South AL, Mobile, AL 36688, USA.
k
Also with Universita
`
di Sassari, Sassari, Italy.
SEARCH FOR THE RARE DECAY
B
!
K
PHYSICAL REVIEW D
82,
112002 (2010)
112002-3
suppress backgrounds. We set an upper limit at the 90% confidence level (CL) of
1
:
3
10
5
on the total
branching fraction for
B
þ
!
K
þ
, and
5
:
6
10
5
for
B
0
!
K
0
. We additionally report 90% CL
upper limits on partial branching fractions in two ranges of dineutrino mass squared for
B
þ
!
K
þ
.
DOI:
10.1103/PhysRevD.82.112002
PACS numbers: 13.25.Hw, 12.15.
y
The decays
B
!
K
arise from flavor-changing neu-
tral currents (FCNC), which are forbidden at tree level in
the SM. The lowest-order SM processes contributing to
these decays are the
W
box and the
Z
penguin diagrams
shown in Fig.
1
. New physics contributions may enter at
the same order as the SM. These contributions, some of
which could increase the branching fraction by up to 10
times relative to the SM, include: unparticle models [
1
],
minimal supersymmetric extension of the SM at large
tan
[
2
], models with a single universal extra dimension [
3
],
scalar weakly interacting massive particle (WIMP) dark
matter [
4
] and WIMP-less dark matter [
5
]. A recent SM
prediction (ABSW model [
6
]) for the total
B
!
K
branching fraction is
ð
4
:
5
0
:
7
Þ
10
6
, while an earlier
prediction (BHI model [
7
]), based on a different form
factor model, is
ð
3
:
8
þ
1
:
2
0
:
6
Þ
10
6
. The BHI model was
used by previous analyses [
8
,
9
] and provides a baseline
for comparison between results. The current experimental
upper limit (UL) on the total branching fraction for
B
þ
!
K
þ
(charge conjugation is implied throughout) is
1
:
4
10
5
at the 90% CL from the Belle Collaboration [
8
],
while an earlier
BABAR
analysis set an UL of
5
:
2
10
5
(90% CL) [
9
]. The only existing UL on the total branching
fraction for
B
0
!
K
0
is
1
:
6
10
4
(90% CL) from
Belle [
8
].
We report results of a search for
B
þ
!
K
þ
and
B
0
!
K
0
, with branching fractions for both decays as well as
for the combination
B
!
K
. We also report on partial
branching fractions for
B
þ
!
K
þ
in two regions of
dineutrino invariant mass squared (
q
2
). The low-
q
2
region
(
q
2
<
0
:
4
m
2
B
) is selected by requiring
p
K
þ
>
1
:
5 GeV
=c
and the high-
q
2
region (
q
2
>
0
:
4
m
2
B
)by
p
K
þ
<
1
:
5 GeV
=c
in the
ð
4
S
Þ
center-of-mass system (CMS) [
10
], where
m
B
is the mass of the
B
meson and
p
K
þ
is the magnitude of the
CMS 3-momentum of the signal
K
þ
candidate. The
high-
q
2
region is of theoretical interest because the partial
branching fraction in this region could be enhanced under
some new physics models [
6
].
This analysis is based on a data sample of
ð
459
:
0
5
:
1
Þ
10
6
B
B
pairs, corresponding to an integrated lumi-
nosity of
418 fb
1
of
e
þ
e
colliding-beam data and
recorded at the
ð
4
S
Þ
resonance with the
BABAR
detector
[
11
] at the SLAC PEP-II asymmetric-energy
B
factory.
Charged particle tracking is provided by a five-layer silicon
vertex tracker and a 40-layer drift chamber in a 1.5 T
magnetic field. A CsI(Tl) electromagnetic calorimeter
(EMC) is used to measure photon energies and directions
and to identify electrons. All quantities in this paper that
are measured by the EMC are required to exceed a mini-
mum 20 MeV cluster energy, unless a higher threshold is
explicitly noted. The magnetic flux return from the sole-
noid, instrumented with resistive plate chambers and lim-
ited streamer tubes (IFR), provides muon identification.
We identify
K
þ
candidates by using a detector of internally
reflected Cherenkov light (DIRC) as well as ionization
energy loss information from the tracking system.
Because of the presence of two neutrinos in the
B
!
K
final state, it is not possible to exploit the kinematic
constraints on the
B
mass and energy that are typically used
to distinguish signal and background events in
B
meson
decays at the
ð
4
S
Þ
. Instead, before looking for the signal
decay, we first reconstruct a
B
decay (
B
rec
) in one of several
exclusive
D
ðÞ
l
semileptonic final states. We then search
for the signal
B
!
K
among the remaining charged and
neutral particles in the detector that are not part of the
B
rec
.
We collectively refer to these remaining particles as
B
roe
for rest of the event. This strategy is common to several
BABAR
analyses [
12
,
13
] and has the advantage of higher
efficiency compared with reconstruction of the
B
rec
in
hadronic decay modes [
9
].
We reconstruct the
D
candidates in the following decay
modes:
K
þ
,
K
þ
þ
,
K
þ
þ
,
K
þ
0
,
K
0
S
þ
, and
K
0
S
þ
. The
K
0
S
candidates, reconstructed
in the
K
0
S
!
þ
mode, are required to have a
þ
invariant mass within
25 MeV
=c
2
of the nominal
K
0
S
mass.
D
candidates are similarly required to have a reconstructed
invariant mass within
60 MeV
=c
2
of the nominal value
[
14
], except for the
K
þ
0
mode where the range is
100 MeV
=c
2
. We form
D
0
!
D
0
0
,
D
þ
!
D
0
þ
, and
D
þ
!
D
þ
0
candidates with a required mass difference
ð
m
ð
D
Þ
m
ð
D
ÞÞ
in the range
130
–
170 MeV
=c
2
. In addi-
tion, we combine
D
and
candidates to form
D
candi-
dates with a required mass difference in the range
120
–
170 MeV
=c
2
.A
D
ðÞ
candidate is combined with an
identified electron or muon with momentum above
0
:
8 GeV
=c
in the CMS to form a
B
rec
candidate. In events
with multiple reconstructed
B
rec
candidates, we select the
FIG. 1. Lowest-order Feynman diagrams for
B
!
K
, with
the
W
box on the left and
Z
penguin on the right.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
112002 (2010)
112002-4
candidate with the highest probability that the daughter
tracks originate from a common vertex. After a
B
rec
can-
didate has been identified, the remaining charged and
neutral decay products are used to classify the
B
roe
as either
a background event or a possible signal candidate.
As a first step in refining the selection of
B
roe
candidates,
we veto
K
candidates, which, when combined with a re-
maining charged or neutral pion candidate, have a
K
invariant mass within
75 MeV
=c
2
of the nominal
K
ð
892
Þ
mass. We also veto events where a remaining charged track
can be combined with a
0
candidate to yield a
þ
candi-
date, with a mass window
0
:
45
<m
ð
þ
Þ
<
1
:
10 GeV
=c
2
.
Similarly vetoed are events where three remaining charged
tracks can be combined to yield an
a
þ
1
candidate, with a
mass window
0
:
6
<m
ð
a
þ
1
Þ
<
2
:
0 GeV
=c
2
. These vetoes
eliminate, with little loss of signal efficiency, sizable back-
grounds that consist mostly of random track combinations.
After the vetoes,
B
þ
(
B
0
) signal candidate events are re-
quired to possess
K
þ
(
K
0
S
!
þ
) candidates, accompa-
nied by at most two (one) additional charged tracks, which
are assumed to have been incorrectly left out of the
B
rec
.For
the
K
þ
final state, the
B
rec
lepton daughter and the
K
þ
are
also required to be oppositely charged. For the
K
0
S
final
state, signal candidates are required to have a
þ
invari-
ant mass within
25 MeV
=c
2
of the nominal
K
0
S
mass.
At this stage of the selection, each event has a
B
rec
candidate representing a
B
meson reconstructed in a semi-
leptonic decay and a
B
roe
candidate formed from the rest of
the event, with the latter representing the signal decay. In
simulated
K
þ
(
K
0
S
) signal events that have passed this
selection, 99% (92%) of events have a correctly identified
signal
K
þ
(
K
0
S
). However, a large background still remains.
Further background suppression is achieved using a multi-
variate event selection algorithm, a bagged decision tree
(BDT) [
15
,
16
], that can leverage many weak discriminat-
ing variables to achieve high background rejection. Such
an algorithm needs to be trained with simulated signal and
background events, henceforth referred to as Monte Carlo
(MC) events. We use a GEANT4 [
17
] detector simulation
to obtain large samples of simulated signal events gener-
ated with a pure phase-space model (which are later re-
scaled to the BHI signal model), as well as samples of
nonresonant
e
þ
e
!
q
q
ð
q
¼
u; d; s; c
Þ
,
B
B
, and
þ
background events, whose sizes are one (
uds
), two (
c
c
),
three (
B
B
), and one (
þ
) times luminosity. These back-
ground events are augmented with a separate sample, with
a size 13 times luminosity, of simulated
B
B
doubly semi-
leptonic events, the largest source of background.
We construct two ensembles of BDTs, one for the
K
þ
signal mode and one for the
K
0
S
. To create an ensemble, we
repeatedly divide the total signal and background datasets
in half randomly, creating 20 distinct BDT training and
validation datasets, where each dataset has a 50% correla-
tion with any other because approximately 50% of the
events are shared. This procedure makes optimal use of
the limited statistics of MC events that pass the initial event
selection and results in a more statistically precise un-
biased estimate of background contributions. Use of the
ensemble of 20 BDTs created for each final state also
averages out the variations in BDT response compared to
a single BDT trained and validated with a single division of
the simulated signal and background datasets [
18
,
19
]. The
choice of 20 divisions, instead of a lower or higher number,
represents a balance between minimizing the variation
versus minimizing the overhead of multiple BDTs.
Each BDT of the
K
þ
(
K
0
) ensemble uses 26 (38) dis-
criminating variables, described in the Appendix. These
variables fall into four general categories: quantities re-
lated to the missing energy in the event, to the overall event
properties, to the signal kinematics, and to the overall
reconstruction quality of the
B
rec
. Some quantities are
given in two different frames and thus allow the BDTs to
extract from them additional discriminating power. Several
additional variables were initially considered but were
pruned during the BDT optimization process because
they were found to add little additional sensitivity.
‘‘Missing Energy’’ quantities relate to the fact that signal
events are expected to possess significant missing energy
and momentum because the signal decay includes two
neutrinos. In contrast, the dominant background events
usually acquire missing energy and momentum as a result
of particles passing outside of the detector fiducial
acceptance, with the result that distributions of quantities
related to missing energy differ between signal and
background.
After the
B
rec
and
K
or
K
0
s
signal candidate have been
identified, signal events are expected to have little or no
additional activity in the detector, other than a few low-
energy clusters in the calorimeter resulting from hadronic
shower remnants, beam backgrounds, or similar sources.
In contrast, background events arising from higher-
multiplicity
B
decays typically possess additional
charged or neutral particles within the detector. Vari-
ables which characterize this additional detector activity
can provide discriminating power between signal and
background, and are indicated by the term ‘‘extra’’ in
the following.
The strongest discriminant for both
K
þ
and
K
0
ensem-
bles is
E
extra
, the sum of all detector activity not explicitly
associated with either the
B
rec
or
K
signal candidate,
followed by
p
K
þ
for the
K
þ
ensemble and by the lab
energy of the signal
K
0
S
for the
K
0
ensemble. The recon-
structed mass of the
D
from the
B
rec
is the third ranking
variable for both channels.
Figure
2
shows signal, background, and data distribu-
tions from the validation set of
K
þ
and
K
0
BDT output for
a BDT randomly selected from the 20 BDTs in the en-
semble. The other 19 BDTs are similar to that shown.
We choose as the target signal efficiency the one that
maximizes expected signal significance averaged over the
SEARCH FOR THE RARE DECAY
B
!
K
PHYSICAL REVIEW D
82,
112002 (2010)
112002-5
20 BDTs, under the assumption of a branching fraction of
3
:
8
10
6
. This signal significance is
s=
ffiffiffiffiffiffiffiffiffiffiffiffi
s
þ
b
p
, where
s
is the number of signal events, and
b
is the number of
background events. Optimization using a figure of merit
based upon signal efficiency and independent of assumed
branching fraction yields similar results. For each BDT, a
BDT output value that yields the target signal efficiency is
calculated. For example, the BDToutput cuts for the BDTs
shown in Fig.
2
are 0.976 for the
K
þ
BDTand 0.955 for the
K
0
BDT. The mean background for target signal efficiency
is obtained by averaging the individual background esti-
mates from each of the 20 BDTs. Thus, we treat each
ensemble of 20 BDTs as a set of correlated estimators
for the numbers of signal and background events in a signal
region defined by the target signal efficiency.
The low-
q
2
(high-
q
2
) measurement uses the
K
þ
en-
semble but only includes events with
p
K
þ
>
1
:
5 GeV
=c
(
p
K
þ
<
1
:
5 GeV
=c
), which means that only those events
are used to calculate the signal efficiency and the back-
ground prediction. The low-
q
2
measurement has the same
BDT output cuts and background prediction as the primary
K
þ
measurement, with only the signal efficiency changed
by the restriction on
p
K
þ
. On the other hand, the high-
q
2
measurement has its own set of BDT output cuts based
upon its own optimized signal efficiency, along with its
own background prediction.
The total optimized signal efficiency for the
K
þ
ð
K
0
Þ
mode is 0.16% (0.06%), while the efficiency for the
K
þ
low-
q
2
(high-
q
2
) region is 0.24% (0.28%). The uncertainty
in the signal efficiency is discussed below. Figure
3
shows
the BDT selection efficiency versus
p
K
for the
K
þ
,
K
0
, and
high-
q
2
measurements, where the BDT selection efficiency
considers only the effect of the BDT output cut.
To measure the branching fractions, we use the value
obtained from simulated events of the predicted back-
ground in the signal region, the number of observed data
events, and the signal efficiency, as shown by the following
equation:
B
¼ð
N
obs
N
bkg
Þ
=N
B
, where
B
is the branch-
ing fraction,
N
obs
is the number of observed data events,
N
bkg
is the number of predicted background events,
is the
total signal efficiency, and
N
B
is the number of
B
mesons,
either charged or neutral [
20
], that are relevant to the
branching fraction. We account for the 50% correlation
between each of the datasets when computing the statisti-
cal uncertainty of the estimated background contribution
by using a standard method for combining correlated
uncertainties [
19
].
Data control samples are used to ensure that both
signal-like and background-like events in actual data are
classified similarly to simulated events. The vetoed
a
þ
1
events offer a high-statistics control sample, which can be
used to compare the
K
þ
and
K
0
BDT output distributions
Single BDT Output
+
K
0
0.2
0.4
0.6
0.8
1
Number of Events
10
2
10
3
10
4
10
-4
10
-3
10
-2
10
-1
10
1
Signal MC
Background MC
Data
Fraction of Events
(a)
Single BDT Output
S
0
K
0
0.2
0.4
0.6
0.8
1
Number of Events
1
10
2
10
3
10
4
10
5
10
-4
10
-3
10
-2
10
-1
10
1
Signal MC
Background MC
Data
Fraction of Events
(b)
FIG. 2 (color online). (a)
K
þ
and (b)
K
0
BDT output for data (diamonds), background MC (solid), and signal MC (dotted) events.
For each plot, the scale for the data and background events is on the left axis, and the scale for the signal events is on the right axis.
The distribution of signal MC events is normalized to unit area.
(GeV/c)
K
*
p
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
BDT Signal Efficiency
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(a)
(GeV/c)
K
*
p
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
BDT Signal Efficiency
0
0.1
0.2
0.3
0.4
0.5
0.6
(b)
(GeV/c)
K
*
p
0.4
0.6
0.8
1
1.2
1.4
BDT Signal Efficiency
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(c)
FIG. 3. BDT selection efficiency in the signal region versus
p
K
for (a)
K
þ
, (b)
K
0
S
, and (c) high-
q
2
K
þ
simulated signal events,
considering only the effect of the BDT output cut.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
112002 (2010)
112002-6
for background events in both simulated and actual data.
We find good agreement between data and MC events in
the BDT output distribution for both final states, with only
a
ðþ
5
2
Þ
%
data-MC discrepancy. For the
K
þ
mode we
make a
þ
5%
adjustment to the expected number of
background events, based upon a weighting technique
that corrects data-MC discrepancy in the sideband
K
þ
BDT output next to the signal region, and we assign the
full adjustment as a systematic uncertainty. Likewise, for
the high-
q
2
K
þ
measurement, we make a
þ
25%
correc-
tion to the expected number of background events and
assign the full correction as a systematic uncertainty. In
the
K
0
S
final state, we find a
ðþ
10
3
Þ
%
data-MC dis-
crepancy in the sideband BDT output next to the signal
region, and we make a
þ
10%
correction and assign the
full correction as a systematic uncertainty.
To validate our signal efficiency estimates and assess
their systematic uncertainties, we use high-purity samples
of
B
þ
!
K
þ
J=
c
ð!
‘
þ
‘
Þ
decays (where
‘
þ
‘
¼
e
þ
e
,
þ
). The two leptons from the
J=
c
are discarded in
order to model the unseen neutrinos of the signal decay,
and then the events are subjected to the same selection
requirements as other signal candidates. Classifying
J=
c
K
data and MC events, we find only a
ð
10
10
Þ
%
data-MC
discrepancy in the BDT output distribution. Although we
do not make any correction, we assign a 10% systematic
uncertainty to the estimated signal efficiency for all four
measurements (
K
þ
,
K
0
S
, low-
q
2
K
þ
, high-
q
2
K
þ
) based on
these results. We also assign a signal efficiency systematic
uncertainty of 10% to account for the theoretical uncer-
tainties of the signal models. Adding these in quadrature,
we assign a total uncertainty of 14% in the estimation of
signal efficiency for both final states. Table
I
summarizes
all of the systematic uncertainties.
Table
II
shows the total signal efficiencies and the ex-
pected number of signal and background events in the data.
We performed a blind analysis where data events with BDT
outputs above the optimized values were not counted or
plotted until the analysis methodology and sources of
systematic uncertainty were fixed as described above.
Table
III
shows our results. The noninteger number of
observed events results from averaging the integer yields
from the 20 BDTs of each type. We calculate two-sided
68% confidence intervals for the number of excess events
based on the statistical and systematic uncertainties in the
background estimates and the statistical uncertainty on
the number of events observed in the data. Figure
4
shows
the averaged BDT outputs in the signal region for
K
þ
,
K
0
,
and high-
q
2
K
þ
data overlaid with the background and
signal contributions, while Fig.
5
shows similar plots for
the
p
K
distribution in the signal region. Figure
6
shows the
integrated numbers of events (observed, predicted back-
ground, and excess over background) in the signal region
for
K
þ
,
K
0
, and high-
q
2
K
þ
data for each of the 20 BDTs
of each type. Table
IV
gives the branching fraction central
values, along with corresponding 90% and 95% CL upper
limits, assuming the BHI signal model (the ABSW model
gives similar results). The upper limits are calculated using
a frequentist method [
21
]. The quoted uncertainties in-
clude all statistical and systematic uncertainties. Our
results constrain the
B
!
K
branching fraction at the
90% CL to a few times the SM expectation, with limits
of
1
:
3
10
5
for
B
þ
!
K
þ
and
5
:
6
10
5
for
B
0
!
K
0
.
We are grateful for the extraordinary contributions of our
PEP-II colleagues in achieving the excellent luminosity and
machine conditions that have made this work possible. The
success of this project also relies critically on the expertise
and dedication of the computing organizations that support
BABAR
. The collaborating institutions wish to thank SLAC
for its support and the kind hospitality extended to them.
This work is supported by the U.S. Department of Energy
and National Science Foundation, the Natural Sciences and
Engineering Research Council (Canada), the Commissariat
a
`
l’Energie Atomique and Institut National de Physique
TABLE I. Systematic uncertainties
Category
Uncertainty
Signal efficiency
14%
K
þ
background prediction
5%
High-
q
2
K
þ
background prediction
25%
K
0
S
background prediction
10%
TABLE II. Total signal efficiencies and MC expectations of
the number of data events. The uncertainties shown are system-
atic for
N
sgnl
, with statistical negligible, and statistical followed
by systematic for
N
bkgd
.
Mode
(in %)
N
sgnl
N
bkgd
K
þ
0.16
2
:
9
0
:
417
:
6
2
:
6
0
:
9
K
0
S
0.06
0
:
5
0
:
13
:
9
1
:
3
0
:
4
low-
q
2
K
þ
0.24
2
:
9
0
:
417
:
6
2
:
6
0
:
9
high-
q
2
K
þ
0.28
2
:
1
0
:
3
187
10
46
TABLE III. Observed and excess data events, with statistical
uncertainties [
21
] shown for
N
obs
and combined statistical and
systematic uncertainties shown for
N
excess
. The last column
shows the probability that excess events could be due solely to
a background fluctuation.
Mode
N
obs
N
excess
Prob.
K
þ
19
:
4
þ
4
:
4
4
:
4
1
:
8
þ
6
:
2
5
:
1
38%
K
0
6
:
1
þ
4
:
0
2
:
2
2
:
2
þ
4
:
1
2
:
8
23%
low-
q
2
K
þ
19
:
4
þ
4
:
4
4
:
4
1
:
8
þ
6
:
2
5
:
1
38%
high-
q
2
K
þ
164
þ
13
13
23
þ
49
48
33%
SEARCH FOR THE RARE DECAY
B
!
K
PHYSICAL REVIEW D
82,
112002 (2010)
112002-7
Nucle
́
aire et de Physique des Particules (France), the
Bundesministerium fu
̈
r Bildung und Forschung and
Deutsche Forschungsgemeinschaft (Germany), the Istituto
Nazionale di Fisica Nucleare (Italy), the Foundation for
Fundamental Research on Matter (The Netherlands), the
Research Council of Norway, the Ministry of Education and
Science of the Russian Federation, Ministerio de Ciencia e
Innovacio
́
n (Spain), and the Science and Technology
Facilities Council (United Kingdom). Individuals have re-
ceived support from the Marie-Curie IEF program
(European Union), the A. P. Sloan Foundation (USA) and
the Binational Science Foundation (USA-Israel).
BDT Output
0.96 0.965 0.97 0.975 0.98 0.985 0.99 0.995
1
Average Number of Events
0
2
4
6
8
10
12
Data
Background MC
Signal MC
(a)
BDT Output
0.94
0.95
0.96
0.97
0.98
0.99
1
Average Number of Events
0
1
2
3
4
5
6
Data
Background MC
Signal MC
(b)
BDT Output
0.75
0.8
0.85
0.9
0.95
1
Average Number of Events
0
10
20
30
40
50
60
Data
Background MC
Signal MC X 10
(c)
FIG. 4 (color online). Averaged BDT signal-region output for (a)
K
þ
, (b)
K
0
S
, and (c) high-
q
2
K
þ
data, with expected signal and
background contributions. The signal estimate assumes a branching fraction of
3
:
8
10
6
.
(GeV/c)
K
*
p
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Average Number of Events
0
2
4
6
8
10
Data
Background MC
Signal MC
(a)
(GeV/c)
K
*
p
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Average Number of Events
0
1
2
3
4
5
6
7
8
9
10
Data
Background MC
Signal MC
(b)
(GeV/c)
K
*
p
0.6 0.7 0.8 0.9
1
1.1 1.2 1.3 1.4 1.5
Average Number of Events
0
5
10
15
20
25
Data
Background MC
Signal MC X 10
(c)
FIG. 5 (color online). Averaged
p
K
signal-region output for (a)
K
þ
, (b)
K
0
S
, and (c) high-
q
2
K
þ
data, with expected signal and
background contributions. The signal estimate assumes a branching fraction of
3
:
8
10
6
.
BDT Number
0
5
10
15
20
Number of Events
-10
-5
0
5
10
15
20
25
30
(a)
BDT Number
0
5
10
15
20
Number of Events
-2
0
2
4
6
8
10
12
(b)
BDT Number
0
5
10
15
20
Number of Events
-50
0
50
100
150
200
(c)
FIG. 6 (color online). Integrated numbers of observed (red triangles), expected background (black circles), and excess events (blue
squares) for data for each BDT: (a)
K
þ
, (b)
K
0
S
, and (c) high-
q
2
K
þ
. The individual uncertainties are purely statistical and assume no
correlation between data sets. The horizontal dashed lines show the sum of the statistical and systematic uncertainties on the mean
number of excess events.
TABLE IV. Branching fraction (BF) central values and upper
limits. The low- and high-
q
2
values are partial BFs, while the
rest are total BFs.
Mode
BF
90% CL
95% CL
10
5
10
5
10
5
K
þ
0
:
2
þ
0
:
8
0
:
7
1.3
1.6
K
0
1
:
7
þ
3
:
1
2
:
1
5.6
6.7
Comb.
K
þ
,
K
0
0
:
5
þ
0
:
7
0
:
7
1.4
1.7
Low-
q
2
K
þ
0
:
2
þ
0
:
6
0
:
5
0.9
1.1
High-
q
2
K
þ
1
:
8
þ
3
:
8
3
:
8
3.1
4.6
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
112002 (2010)
112002-8
APPENDIX: DEFINITIONS OF BDT VARIABLES
In the following the notation
½
K
þ
or
½
K
0
indicates that
a variable is used only by that ensemble; otherwise it is
used by both BDT ensembles.
BDT input variables related to missing 4-momentum
The event missing 4-momentum is computed from the
difference between the 4-momentum of the combined
e
þ
e
beams and the 4-momenta of all charged and neutral
particles reconstructed in the detector.
(i) Energy component of missing momentum 4-vector
(ii) Energy component of missing momentum 4-vector
(CMS)
(iii) Magnitude of the missing momentum 3-vector
(iv) Magnitude of the missing momentum 3-vector
(CMS)
(v) Cosine of the angle with respect to the beam axis of
the missing momentum 3-vector
(vi) Cosine of the angle with respect to the beam axis of
the 3-momentum vector representing the difference
betweenthe initial event momentumand the summed
momenta of the
B
rec
and
B
roe
candidates
½
K
0
BDT input variables related to overall event properties
(i)
E
extra
¼
i
E
i
, where
E
i
is the energy of an isolated
EMC cluster or a charged track and the sum is over
all tracks or clusters which are not part of the
B
rec
or
the
B
roe
(ii) Total energy of all reconstructed charged and
neutral particles in the event
(iii) Minimum invariant mass obtained from the combi-
nation of any three charged tracks in the event
(iv) Total charge of all tracks in the event
½
K
0
(v) Total charge of all tracks matched to EMC energy
deposits
½
K
0
(vi) Number of extra EMC clusters
(vii) Number of
K
L
candidates in the EMC
(viii) Number of IFR
K
L
candidates
½
K
þ
(ix) Number of extra reconstructed tracks
(x) Magnitude of the 3-momentum of a candidate
ð
4
S
Þ
computed from the
B
rec
and
B
roe
4-momenta
½
K
0
(xi) Angle with respect to the beam axis of a candidate
ð
4
S
Þ
3-momentum vector computed from the
B
rec
and
B
roe
4-momenta
½
K
0
(xii) Normalized second Fox-Wolfram moment of the
overall event
BDT input variables related to signal kinematics
(i) Cosine of the angle between the signal
K
and the
event thrust axis
(ii) Cosine of the angle between the signal
K
and the
Dl
thrust axis
(iii) Energy of the signal kaon
½
K
0
(iv) Reconstructed invariant mass of the signal
K
0
S
½
K
0
(v) Magnitude of the 3-momentum of the signal kaon
(vi) Magnitude of the CMS 3-momentum of the signal
kaon
(vii) Cosine of the angle with respect to the beam axis of
the 3-momentum vector of the signal kaon
(viii) Uncertainty in the
x
-component of the signal
K
point of closest approach to the
e
þ
e
interac-
tion point, as determined from a three dimen-
sional fit, with the
x
-axis defined perpendicular
to the beam axis in the horizontal plane of the
detector
½
K
0
(ix) Uncertainty in the
x
-component of the signal
K
point of closest approach to the
e
þ
e
interaction
point, as determined by a fit in the
xy
-plane, with
the
x
-axis defined perpendicular to the beam axis
(
z
) in the horizontal plane of the detector
½
K
0
BDT input variables related to
B
rec
reconstruction
(i)
2
per degree of freedom of the vertex fit of the
tracks making up the
B
rec
(ii)
cos
BY
ð
2
E
beam
E
Dl
m
2
Bn
m
2
Dl
Þ
=
ð
2
p
Dl
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
2
beam
m
2
Bn
q
Þ
, where
E
beam
is one half the total
CMS energy,
m
Bn
is the nominal
B
meson mass [
14
]
and
E
Dl
,
m
Dl
and
p
Dl
are the CMS energy, invariant
mass and 3-momentum magnitude of the
D
—lepton
combination used in the reconstruction of the
B
rec
(iii)
cos
BY
recalculated with the addition of a photon
to the
Dl
candidate such that
100
<
ð
m
ð
D
0
;
Þ
m
ð
D
0
ÞÞ
<
150 MeV
=c
2
(iv) Reconstructed decay mode of the
D
from the
B
rec
(v) Uncertainty in the
x
-component of the point of
closest approach to the
e
þ
e
interaction point of
the leading pion daughter from the
D
meson, with
the
x
-axis defined perpendicular to the beam axis in
the horizontal plane of the detector
(vi) Number of daughters possessed by the recon-
structed
D
from the
B
rec
(vii) Number of extra
0
candidates satisfying
0
:
115
<
m
ð
Þ
<
0
:
150 GeV
=c
2
and
E
>
30 MeV
(viii) Reconstructed invariant mass of the
B
rec
(ix) Reconstructed invariant mass of the
D
from the
B
rec
(x) Magnitude of the CMS 3-momentum of the
B
rec
½
K
0
(xi) Magnitude of the CMS 3-momentum of the
D
candidate from the
B
rec
(xii) Magnitude of the 3-momentum of the lepton from
the
B
rec
½
K
0
(xiii) Magnitude of the CMS 3-momentum of the lepton
from the
B
rec
SEARCH FOR THE RARE DECAY
B
!
K
PHYSICAL REVIEW D
82,
112002 (2010)
112002-9
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et al.
(
BABAR
Collaboration),
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479
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et al.
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[20] Equal branching fractions for
ð
4
S
Þ!
B
0
B
0
and
ð
4
S
Þ!
B
þ
B
are assumed in this paper.
[21] R. Barlow,
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P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
112002 (2010)
112002-10