Search for the rare decays
B
!
‘
þ
‘
and
B
0
!
‘
þ
‘
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
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
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
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
M. Franco Sevilla,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
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
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
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
S. Martellotti,
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
M. Morii,
26
A. Adametz,
27
U. Uwer,
27
H. M. Lacker,
28
P. D. Dauncey,
29
U. Mallik,
30
C. Chen,
31
J. Cochran,
31
W. T. Meyer,
31
S. Prell,
31
A. E. Rubin,
31
A. V. Gritsan,
32
N. Arnaud,
33
M. Davier,
33
D. Derkach,
33
G. Grosdidier,
33
F. Le Diberder,
33
A. M. Lutz,
33
B. Malaescu,
33
P. Roudeau,
33
A. Stocchi,
33
G. Wormser,
33
D. J. Lange,
34
D. M. Wright,
34
J. P. Coleman,
35
J. R. Fry,
35
E. Gabathuler,
35
D. E. Hutchcroft,
35
D. J. Payne,
35
C. Touramanis,
35
A. J. Bevan,
36
F. Di Lodovico,
36
R. Sacco,
36
G. Cowan,
37
J. Bougher,
38
D. N. Brown,
38
C. L. Davis,
38
A. G. Denig,
39
M. Fritsch,
39
W. Gradl,
39
K. Griessinger,
39
A. Hafner,
39
E. Prencipe,
39
R. J. Barlow,
40,
‡
G. D. Lafferty,
40
E. Behn,
41
R. Cenci,
41
B. Hamilton,
41
A. Jawahery,
41
D. A. Roberts,
41
R. Cowan,
42
D. Dujmic,
42
G. Sciolla,
42
R. Cheaib,
43
P. M. Patel,
43,
§
S. H. Robertson,
43
P. Biassoni,
44a,44b
N. Neri,
44a
F. Palombo,
44a,44b
L. Cremaldi,
45
R. Godang,
45,
∥
P. Sonnek,
45
D. J. Summers,
45
X. Nguyen,
46
M. Simard,
46
P. Taras,
46
G. De Nardo,
47a,47b
D. Monorchio,
47a,47b
G. Onorato,
47a,47b
C. Sciacca,
47a,47b
M. Martinelli,
48
G. Raven,
48
C. P. Jessop,
49
J. M. LoSecco,
49
K. Honscheid,
50
R. Kass,
50
J. Brau,
51
R. Frey,
51
N. B. Sinev,
51
D. Strom,
51
E. Torrence,
51
E. Feltresi,
52a,52b
M. Margoni,
52a,52b
M. Morandin,
52a
M. Posocco,
52a
M. Rotondo,
52a
G. Simi,
52a
F. Simonetto,
52a,52b
R. Stroili,
52a,52b
S. Akar,
53
E. Ben-Haim,
53
M. Bomben,
53
G. R. Bonneaud,
53
H. Briand,
53
G. Calderini,
53
J. Chauveau,
53
Ph. Leruste,
53
G. Marchiori,
53
J. Ocariz,
53
S. Sitt,
53
M. Biasini,
54a,54b
E. Manoni,
54a
S. Pacetti,
54a,54b
A. Rossi,
54a,54b
C. Angelini,
55a,55b
G. Batignani,
55a,55b
S. Bettarini,
55a,55b
M. Carpinelli,
55a,55b,
¶
G. Casarosa,
55a,55b
A. Cervelli,
55a,55b
F. Forti,
55a,55b
M. A. Giorgi,
55a,55b
A. Lusiani,
55a,55c
B. Oberhof,
55a,55b
E. Paoloni,
55a,55b
A. Perez,
55a
G. Rizzo,
55a,55b
J. J. Walsh,
55a
D. Lopes Pegna,
56
J. Olsen,
56
A. J. S. Smith,
56
R. Faccini,
57a,57b
F. Ferrarotto,
57a
F. Ferroni,
57a,57b
M. Gaspero,
57a,57b
L. Li Gioi,
57a
G. Piredda,
57a
C. Bu
̈
nger,
58
O. Gru
̈
nberg,
58
T. Hartmann,
58
T. Leddig,
58
C. Voß,
58
R. Waldi,
58
T. Adye,
59
E. O. Olaiya,
59
F. F. Wilson,
59
S. Emery,
60
G. Hamel de Monchenault,
60
G. Vasseur,
60
Ch. Ye
`
che,
60
F. Anulli,
61
D. Aston,
61
D. J. Bard,
61
J. F. Benitez,
61
C. Cartaro,
61
M. R. Convery,
61
J. Dorfan,
61
G. P. Dubois-Felsmann,
61
W. Dunwoodie,
61
M. Ebert,
61
R. C. Field,
61
B. G. Fulsom,
61
A. M. Gabareen,
61
M. T. Graham,
61
C. Hast,
61
W. R. Innes,
61
P. Kim,
61
M. L. Kocian,
61
D. W. G. S. Leith,
61
P. Lewis,
61
D. Lindemann,
61
B. Lindquist,
61
S. Luitz,
61
V. Luth,
61
H. L. Lynch,
61
D. B. MacFarlane,
61
D. R. Muller,
61
H. Neal,
61
S. Nelson,
61
M. Perl,
61
T. Pulliam,
61
B. N. Ratcliff,
61
A. Roodman,
61
A. A. Salnikov,
61
R. H. Schindler,
61
A. Snyder,
61
D. Su,
61
M. K. Sullivan,
61
J. Va’vra,
61
A. P. Wagner,
61
W. F. Wang,
61
W. J. Wisniewski,
61
M. Wittgen,
61
D. H. Wright,
61
H. W. Wulsin,
61
V. Ziegler,
61
W. Park,
62
M. V. Purohit,
62
R. M. White,
62
J. R. Wilson,
62
A. Randle-Conde,
63
S. J. Sekula,
63
M. Bellis,
64
P. R. Burchat,
64
T. S. Miyashita,
64
E. M. T. Puccio,
64
M. S. Alam,
65
J. A. Ernst,
65
R. Gorodeisky,
66
N. Guttman,
66
D. R. Peimer,
66
A. Soffer,
66
S. M. Spanier,
67
J. L. Ritchie,
68
A. M. Ruland,
68
R. F. Schwitters,
68
B. C. Wray,
68
J. M. Izen,
69
X. C. Lou,
69
F. Bianchi,
70a,70b
F. De Mori,
70a,70b
A. Filippi,
70a
D. Gamba,
70a,70b
S. Zambito,
70a,70b
L. Lanceri,
71a,71b
L. Vitale,
71a,71b
F. Martinez-Vidal,
72
A. Oyanguren,
72
P. Villanueva-Perez,
72
H. Ahmed,
73
J. Albert,
73
Sw. Banerjee,
73
F. U. Bernlochner,
73
H. H. F. Choi,
73
G. J. King,
73
R. Kowalewski,
73
M. J. Lewczuk,
73
T. Lueck,
73
I. M. Nugent,
73
J. M. Roney,
73
R. J. Sobie,
73
N. Tasneem,
73
T. J. Gershon,
74
P. F. Harrison,
74
T. E. Latham,
74
H. R. Band,
75
S. Dasu,
75
Y. Pan,
75
R. Prepost,
75
and S. L. Wu
75
(
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
PHYSICAL REVIEW D
88,
032012 (2013)
1550-7998
=
2013
=
88(3)
=
032012(16)
032012-1
Ó
2013 American Physical Society
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
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 V6T 1Z1, Canada
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics SB RAS, 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
Fakulta
̈
t Physik, Technische Universita
̈
t Dortmund, 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-44122 Ferrara, Italy
22b
Dipartimento di Fisica e Scienze della Terra, Universita
`
di Ferrara, I-44122 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
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
28
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstrasse 15, D-12489 Berlin, Germany
29
Imperial College London, London SW7 2AZ, United Kingdom
30
University of Iowa, Iowa City, Iowa 52242, USA
31
Iowa State University, Ames, Iowa 50011-3160, USA
32
Johns Hopkins University, Baltimore, Maryland 21218, USA
33
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
34
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
35
University of Liverpool, Liverpool L69 7ZE, United Kingdom
36
Queen Mary, University of London, London E1 4NS, United Kingdom
37
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
38
University of Louisville, Louisville, Kentucky 40292, USA
39
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
40
University of Manchester, Manchester M13 9PL, United Kingdom
41
University of Maryland, College Park, Maryland 20742, USA
42
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
43
McGill University, Montre
́
al, Que
́
bec H3A 2T8, Canada
44a
INFN Sezione di Milano, I-20133 Milano, Italy
44b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
45
University of Mississippi, University, Mississippi 38677, USA
46
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec H3C 3J7, Canada
47a
INFN Sezione di Napoli, I-80126 Napoli, Italy
47b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
48
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
49
University of Notre Dame, Notre Dame, Indiana 46556, USA
50
Ohio State University, Columbus, Ohio 43210, USA
51
University of Oregon, Eugene, Oregon 97403, USA
52a
INFN Sezione di Padova, I-35131 Padova, Italy
52b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
53
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
54a
INFN Sezione di Perugia, I-06100 Perugia, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032012 (2013)
032012-2
54b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
55a
INFN Sezione di Pisa, I-56127 Pisa, Italy
55b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
55c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
56
Princeton University, Princeton, New Jersey 08544, USA
57a
INFN Sezione di Roma, I-00185 Roma, Italy
57b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
58
Universita
̈
t Rostock, D-18051 Rostock, Germany
59
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
60
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
61
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
62
University of South Carolina, Columbia, South Carolina 29208, USA
63
Southern Methodist University, Dallas, Texas 75275, USA
64
Stanford University, Stanford, California 94305-4060, USA
65
State University of New York, Albany, New York 12222, USA
66
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
67
University of Tennessee, Knoxville, Tennessee 37996, USA
68
University of Texas at Austin, Austin, Texas 78712, USA
69
University of Texas at Dallas, Richardson, Texas 75083, USA
70a
INFN Sezione di Torino, I-10125 Torino, Italy
70b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
71a
INFN Sezione di Trieste, I-34127 Trieste, Italy
71b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
72
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
73
University of Victoria, Victoria, British Columbia V8W 3P6, Canada
74
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
75
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 31 March 2013; published 27 August 2013)
We present the results of a search for the rare flavor-changing neutral-current decays
B
!
‘
þ
‘
(
¼
,
0
and
‘
¼
e
,
) and
B
0
!
‘
þ
‘
using a sample of
e
þ
e
!
ð
4
S
Þ!
B
B
decays
corresponding to
428 fb
1
of integrated luminosity collected by the
BABAR
detector. No significant
signal is observed, and we set an upper limit on the isospin and lepton-flavor averaged branching fraction
of
B
ð
B
!
‘
þ
‘
Þ
<
5
:
9
10
8
and a lepton-flavor averaged upper limit of
B
ð
B
0
!
‘
þ
‘
Þ
<
6
:
4
10
8
, both at the 90% confidence level. We also report 90% confidence level branching fraction upper
limits for the individual modes
B
þ
!
þ
e
þ
e
,
B
0
!
0
e
þ
e
,
B
þ
!
þ
þ
,
B
0
!
0
þ
,
B
0
!
e
þ
e
, and
B
0
!
þ
.
DOI:
10.1103/PhysRevD.88.032012
PACS numbers: 13.20.He, 13.60.Hb
I. INTRODUCTION
In the standard model (SM), the decays
B
!
‘
þ
‘
(
¼
,
0
and
‘
¼
e
,
) and
B
0
!
‘
þ
‘
proceed
through the quark-level flavor-changing neutral-current
process
b
!
d‘
þ
‘
. Since all flavor-changing neutral-
current processes are forbidden at tree level in the SM,
the lowest order diagrams representing these transitions
must involve loops. For
b
!
d‘
þ
‘
, these are the elec-
troweak semileptonic penguin diagrams [Fig.
1(a)
] and
the
W
þ
W
box diagrams [Fig.
1(b)
]. The
b
!
d‘
þ
‘
transition is similar to
b
!
s‘
þ
‘
, but its rate is sup-
pressed by the ratio
j
V
td
=V
ts
j
2
0
:
04
where
V
td
and
V
ts
are elements of the Cabibbo-Kobayashi-Maskawa quark
mixing matrix [
1
,
2
]. The predicted branching fractions
for the
B
þ
!
þ
‘
þ
‘
decay modes lie in the range of
ð
1
:
4
–
3
:
3
Þ
10
8
, when the dilepton mass regions near
the
J=
c
and
c
ð
2
S
Þ
are excluded in order to remove
decays that proceed through the intermediate charmo-
nium resonances. The largest source of uncertainty in
these predictions arises from knowledge of the
B
!
form factors [
3
–
5
]. These branching fractions imply that
5–15 events occur for each
B
!
‘
þ
‘
decay channel
in the
BABAR
data set (471 million
B
B
pairs). The
predicted
B
0
!
‘
þ
‘
branching fractions lie in the
range
ð
2
:
5
–
3
:
7
Þ
10
8
where again the dominant
*
Present address: University of Tabuk, Tabuk 71491,
Saudi Arabia.
†
Also at Dipartimento di Fisica, Universita
`
di Perugia,
Perugia, Italy.
‡
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
§
Deceased.
∥
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
¶
Also at Universita
`
di Sassari, Sassari, Italy.
SEARCH FOR THE RARE DECAYS
...
PHYSICAL REVIEW D
88,
032012 (2013)
032012-3
uncertainty is due to lack of knowledge of the
B
0
!
form factors [
6
].
Many extensions of the SM predict the existence of new,
heavy particles which couple to the SM fermions and
bosons. The
b
!
d‘
þ
‘
and
b
!
s‘
þ
‘
decays provide
a promising avenue in which to search for new physics
(NP). Amplitudes from these NP contributions can inter-
fere with those from the SM, altering physical observables
(e.g., decay rates,
CP
, isospin, and forward-backward
asymmetries) from the SM predictions [
3
,
4
,
7
–
10
].
Measurements in the
‘
þ
‘
and
‘
þ
‘
systems comple-
ment and provide independent searches of NP from those
in the
K
ðÞ
‘
þ
‘
channels [
11
–
17
], as physics beyond the
SM may have nontrivial flavor couplings [
18
]. The
measurement of observables as a function of the square
of the invariant dilepton mass
q
2
¼
m
2
‘‘
for exclusive
b
!
d‘
þ
‘
decay modes allows for more thorough tests
of SM predictions and deeper probes for NP but is cur-
rently not possible due to the size of the data set.
Only one
b
!
d‘
þ
‘
decay has been observed to date,
with LHCb measuring the
B
þ
!
þ
þ
branching
fraction to be
ð
2
:
3
0
:
6
0
:
1
Þ
10
8
[
19
]. Both
BABAR
[
20
] and Belle [
21
] have performed searches for
B
!
‘
þ
‘
decays but have observed no significant sig-
nal. For the
‘
þ
‘
modes, the smallest upper limits from
the
B
factories lie within an order of magnitude of the SM
predictions [
3
–
5
] and are beginning to exclude portions of
the NP parameter space. No previous searches for
B
0
!
‘
þ
‘
have been reported. Observation of
b
!
d‘
þ
‘
decays at the
B
factories is currently limited by the size of
the available data sets. Additionally, for
B
þ
!
þ
‘
þ
‘
,
background from
B
þ
!
K
þ
‘
þ
‘
decays where the kaon
is misidentified as a pion must be treated carefully as
K
þ
‘
þ
‘
can appear very signal-like and occurs at a rate
approximately 25 times the expected
B
þ
!
þ
‘
þ
‘
rate.
In this article we report on our study of the
B
!
‘
þ
‘
and
B
0
!
‘
þ
‘
decays using the full
BABAR
data
set, presenting branching fraction upper limits for the
modes
B
þ
!
þ
e
þ
e
,
B
0
!
0
e
þ
e
,
B
þ
!
þ
þ
,
B
0
!
0
þ
,
B
0
!
e
þ
e
, and
B
0
!
þ
.
Charge conjugation is implied throughout unless specified
otherwise. We also present upper limits for the lepton-
flavor averaged modes
B
þ
!
þ
‘
þ
‘
,
B
0
!
0
‘
þ
‘
,
and
B
0
!
‘
þ
‘
, where we constrain the
e
þ
e
and
þ
branching fractions to be equal; for the isospin
averaged modes
B
!
e
þ
e
and
B
!
þ
, where
the
B
þ
!
þ
‘
þ
‘
decay rate is constrained to be twice
the
B
0
!
0
‘
þ
‘
decay rate; and for the isospin and
lepton-flavor averaged mode
B
!
‘
þ
‘
. For the
lepton-flavor averaged measurements, we neglect differ-
ences in available phase space due to the difference
between the electron and muon masses. The branching
fractions are based on signal yields that are extracted
through an unbinned, extended maximum likelihood fit to
two kinematic variables. All selection criteria are deter-
mined before the fit was performed on data, i.e., the
analysis is performed ‘‘blind.’’
II.
BABAR
DETECTOR, SIMULATION,
AND DATA SETS
The results of this analysis are based upon a sample of
e
þ
e
!
ð
4
S
Þ!
B
B
interactions provided by the PEP-II
asymmetric-energy storage rings and collected by the
BABAR
detector located at SLAC National Accelerator
Laboratory. The
BABAR
data sample corresponds to an
integrated luminosity of
428 fb
1
[
22
] containing 471
million
B
B
decays. This is the full data set collected at
the
ð
4
S
Þ
resonance. A detailed description of the
BABAR
detector can be found elsewhere [
23
]. Charged particle
momenta are measured with a five-layer, double-sided
silicon vertex tracker and a 40-layer drift chamber operated
in proportional mode. These two tracking systems are
immersed in the 1.5 T magnetic field of a superconducting
solenoid. A ring-imaging Cherenkov detector with fused
silica radiators, aided by ionization loss
d
E=
d
x
measure-
ments from the tracking system, provides identification of
charged particles. Electromagnetic showers from electrons
and photons are detected with an electromagnetic calo-
rimeter (EMC) constructed from a finely segmented array
of thallium-doped CsI scintillating crystals. The steel flux
return of the solenoid was initially instrumented with
resistive plate chambers and functions primarily to identify
FIG. 1. Lowest order Feynman diagrams describing the quark level
b
!
d‘
þ
‘
transition in
B
meson decay: (a) electroweak
penguin diagrams and (b)
W
þ
W
box diagrams.
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032012 (2013)
032012-4
muons. For the later data taking periods, the resistive plate
chambers of the steel flux return of the solenoid were
replaced with limited streamer tubes and brass to increase
absorption.
The
BABAR
Monte Carlo (MC) simulation utilizes the
GEANT4
package [
24
] for detector simulation, and EvtGen
[
25
] and Jetset7.4 [
26
] for
B
B
and
e
þ
e
!
q
q
(
q
¼
u
,
d
,
s
,
c
) decays, respectively. The
B
B
and continuum
(
e
þ
e
!
q
q
,
q
¼
u
,
d
,
s
,
c
) MC samples correspond to
an effective luminosity of about ten times the data sample
collected at the
ð
4
S
Þ
resonance. Simulated
B
!
‘
þ
‘
signal decay samples are generated according to the form-
factor model of Ref. [
27
], with the Wilson coefficients
taken from Refs. [
28
–
30
], and the decay amplitudes calcu-
lated in Ref. [
10
]. The
B
0
!
‘
þ
‘
signal MC samples
utilize the same kinematics, Wilson coefficients, and form-
factor model as the
‘
þ
‘
modes. The effects of the
choice of form-factor model and the values of the Wilson
coefficients are considered as sources of systematic uncer-
tainty in the signal efficiency. We also make use of
simulated
B
!
K
ðÞ
‘
þ
‘
,
B
!
J=
c
X
, and
B
!
c
ð
2
S
Þ
X
samples. Signal efficiencies, as well as parameters of the fit
model, are determined from signal and
K
ðÞ
‘
þ
‘
MC data
sets. The
B
!
J=
c
X
and
B
!
c
ð
2
S
Þ
X
MC samples allow
us to study background from these decays and also serve as
the data sets from which we fix the parameters of the
fit model used in the
B
!
J=
c
=
fit validation, as
described later.
III. EVENT RECONSTRUCTION
AND CANDIDATE SELECTION
Event reconstruction begins by building dilepton candi-
dates from two leptons (
e
þ
e
or
þ
). Leptons are
selected as charged tracks with momenta in the laboratory
reference (lab) frame greater than
300 MeV
=c
. Loose
particle identification (PID) requirements are placed upon
the two leptons. More stringent PID requirements are
applied later, and the optimization of these selection crite-
ria is discussed in Sec.
V
. The lepton pair is fit to a common
vertex to form a dilepton candidate with the requirement
that
m
‘‘
<
5
:
0 GeV
=c
2
[
31
]. We also place a loose con-
straint on the
2
probability of the vertex fit by requiring it
to be greater than
10
10
. For electrons, we apply an algo-
rithm which associates photons with electron candidates in
an attempt to recover energy lost through bremsstrahlung,
allowing at most one photon to be associated with each
electron. The photon trajectory is required to lie within a
small cone of opening angle 0.035 rad about the initial
momentum vector of the electron, and the photon energy in
the lab frame must be greater than 30 MeV. Additionally,
we suppress background from photon conversions by re-
quiring that the invariant mass of the electron (or positron)
paired with any other oppositely charged track in the event
be greater than
30 MeV
=c
2
.
Charged pion candidates are charged tracks passing pion
PID requirements which retain approximately 90%–95%
of charged pions and only 2%–5% of charged kaons. We
reconstruct
0
candidates from two photons with invariant
diphoton mass
m
lying in the range
115
<m
<
150 MeV
=c
2
. A minimum value of 50 MeV is required
for the lab energy of each photon. Photons are detected as
EMC clusters not associated with a charged track. The
clusters are also required to have a lateral shower profile
consistent with originating from a photon. We reconstruct
as
!
(
) and
!
þ
0
(
3
), which
constitute 39.3% and 22.7% of the
branching fraction,
respectively. As in the case of the
0
, we require the
photon daughters to have energy greater than 50 MeV in
the lab frame. Additionally, the photon energy asymmetry
A
¼j
E
1
;
E
2
;
j
=
ð
E
1
;
þ
E
2
;
Þ
must be less than 0.8,
where
E
1
;
and
E
2
;
are the energies of the photons in
the lab frame. The invariant diphoton mass must lie in the
range
500
<m
<
575 MeV
=c
2
.For
3
, the pion can-
didates are fit to a common vertex to form an
candidate.
In the fit the
candidate mass is constrained to the nominal
mass, while the invariant three-pion mass is required to
lie in the range
535
<m
3
<
565 MeV
=c
2
.
B
candidates are reconstructed from a hadron candidate
(
þ
,
0
,
,or
3
) and a dilepton candidate (
e
þ
e
or
þ
). The hadron and dilepton candidates are fit to a
common vertex, and the entire decay chain is refit. We
make use of two kinematic, Lorentz-invariant quantities,
m
ES
and
E
, defined as
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s=
2
þ
~
p
B
~
p
0
Þ
2
=E
2
0
p
2
B
q
(1)
E
¼ð
2
q
B
q
0
s
Þ
=
2
ffiffiffi
s
p
;
(2)
where
ffiffiffi
s
p
¼
2
E
beam
is the total energy of the
e
þ
e
system
in the c.m. frame,
q
B
and
q
0
¼ð
E
0
;
~
p
0
Þ
are the four-vectors
representing the momentum of the
B
candidate and of the
e
þ
e
system, respectively, and
~
p
B
is the three-momentum
of the
B
candidate. In the c.m. frame, these expressions
simplify to
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
2
beam
p
B
2
q
(3)
E
¼
E
B
E
beam
;
(4)
where the asterisk indicates evaluation in the c.m. frame.
These variables make use of precisely measured beam
quantities. All
B
candidates are required to have
m
ES
>
5
:
1 GeV
=c
2
and
300
<
E<
250 MeV
. The distribu-
tions of these two variables are later fit to extract the
‘
þ
‘
and
‘
þ
‘
branching fractions.
A large background is present from
B
!
J=
c
X
and
B
!
c
ð
2
S
Þ
X
decays where
J=
c
and
c
ð
2
S
Þ
decay to
‘
þ
‘
. Here
X
represents a hadronic state, typically
,
,
,or
K
ðÞ
. These events are removed from our data sample
SEARCH FOR THE RARE DECAYS
...
PHYSICAL REVIEW D
88,
032012 (2013)
032012-5
by rejecting any event with a value of
m
‘‘
consistent with
originating from a
J=
c
or
c
ð
2
S
Þ
decay. The rejected
J=
c
events are useful as they provide a control sample which
can be used to test the fit model. We also use these samples
to estimate systematic uncertainties and to correct for
differences between data and MC selection efficiencies.
For the electron modes we reject events in the following
regions about the
J=
c
mass:
2
:
90
<m
‘‘
<
3
:
20 GeV
=c
2
,
or
m
ee
<
2
:
90 GeV
=c
2
and
E<m
ee
c
2
2
:
875 GeV
.
For the muon modes the region is
3
:
00
<m
<
3
:
20 GeV
=c
2
,or
m
<
3
:
00 GeV
=c
2
and
E<
1
:
11
m
c
2
3
:
31 GeV
. The rejection region about the
c
ð
2
S
Þ
mass is the same for electrons and muons:
3
:
60
<
m
‘‘
<
3
:
75 GeV
=c
2
,or
m
‘‘
<
3
:
60 GeV
=c
2
and
E<
m
‘‘
c
2
3
:
525 GeV
. Introducing
E
dependence into
the region boundaries allows us to account for some of
the effects of track mismeasurement and energy lost due to
bremsstrahlung.
The largest source of background comes from random
combinations of particles from continuum events or semi-
leptonic
B
and
D
decays in
B
B
events. Continuum events
tend to be jetlike as the
q
q
pair is produced back-to-back
with relatively large momentum in the c.m. frame. The
topology of
B
B
decays is more isotropic as the
B
mesons
are produced nearly at rest in the
ð
4
S
Þ
rest frame.
Semileptonic decays are characterized by the presence of
a neutrino, e.g., missing energy in the event and nonzero
total transverse momentum of the event. Due to the differ-
ences in these two background types we train separate
artificial neutral networks (NNs) to reject each of them.
By selecting inputs to the NNs which are independent of
the final state we are able to train only one NN for each
lepton flavor. We do not train separate NNs for
þ
,
0
,
and
. This increases the size of the training samples,
improving the performance of the NNs. We train four
NNs: one to reject
B
B
background in the
e
þ
e
modes,
one to reject
B
B
background in the
þ
modes, one to
reject continuum background in the
e
þ
e
modes, and one
to reject continuum background in the
þ
modes.
The signal training samples were assembled from equal
portions of correctly reconstructed
B
þ
!
þ
‘
þ
‘
,
B
0
!
0
‘
þ
‘
,
B
þ
!
þ
‘
þ
‘
,
B
0
!
0
‘
þ
‘
,
B
0
!
‘
þ
‘
, and
B
0
!
!‘
þ
‘
MC events. The size of the
training samples, particularly the background training
samples, that could be formed from events reconstructed
as one of our signal modes was a limiting factor in the
performance of the NNs. To increase the available statistics
the other events from the
‘
þ
‘
and
!‘
þ
‘
modes were
added to the training samples. The
þ
(
0
) was recon-
structed as
þ
0
(
þ
) with two-pion invariant mass
m
in the range
0
:
455
<m
<
1
:
095 GeV
=c
2
(
0
:
475
<
m
<
1
:
075 GeV
=c
2
). The
!
was reconstructed as
þ
0
and required to have a three-pion invaraint
mass lying within
50 MeV
=c
2
of the nominal
!
mass.
No
3
‘
þ
‘
events were used in the training due to very
low statistics for the background
B
B
and continuum
samples for these modes. For background we combined
the MC data sets, either
B
B
or continuum depending upon
the classifier to be trained, from the six modes listed above
and randomly select events from this data set to form the
training sample. The performances of the NNs trained with
samples from several different
b
!
d‘
þ
‘
(global NNs)
modes were compared with NNs trained specifically for
each of our four
B
!
‘
þ
‘
modes (single mode NNs).
The background rejection of the global NNs at a fixed
signal efficiency was found to be similar to that of the
single mode NNs.
The input variables to the continuum NNs are related
mostly to event topology and include the ratios of Fox-
Wolfram moments [
32
]; the cosine of the polar angle of the
thrust axis [
33
] of the event; the cosine of the polar angle of
the thrust axis of the rest-of-the-event (ROE), which con-
sists of all particles in the event not associated with the
signal
B
candidate; the momentum weighted polynomials
L
j
i
[
34
] computed using tracks and EMC clusters; the
cosine of the polar angle of the
B
candidate momentum;
and the
2
probability of the
B
candidate vertex fit.
The input variables to the
B
B
NNs reflect the effort to
reject background from semileptonic
B
and
D
decays and
include
m
ES
and
E
constructed from the ROE, total
momentum of the event transverse to the beam, missing
energy in the event, momentum of the ROE transverse
to the beam direction, momentum of the ROE transverse
to the thrust axis of the event, cosine of the polar angle of
the
B
candidate momentum, and
2
probability of the
B
candidate and dilepton candidate vertex fits. The NN
outputs show only weak correlation with the fit variables
m
ES
and
E
.
Figure
2
, as representative of the several neural
networks, shows the output of the
e
þ
e
B
B
NN for a
sample of signal and
B
B
background
þ
e
þ
e
MC events.
Also shown is the output of the
þ
continuum NN for a
sample of signal and continuum background
0
þ
MC
events. Requirements on the NN outputs are optimized for
each of our eight modes to produce the lowest branching
fraction upper limit. A description of the optimization
procedure is given in Sec.
V
.
Due to their similarity to signal,
B
!
K
ðÞ
‘
þ
‘
decays
constitute a background that mimics signal by peaking in
either one or both
m
ES
and
E
. The
b
!
s‘
þ
‘
transition
occurs at a rate approximately 25 times greater than the SM
b
!
d‘
þ
‘
rate, and due to particle misidentification and
event misreconstruction, its contribution is expected to be
of the same order as the
‘
þ
‘
signal in the
BABAR
data
sample. In the charged pion modes,
B
þ
!
K
þ
‘
þ
‘
peaks
in
m
ES
as
þ
‘
þ
‘
signal but in
E
near
70 MeV
due to
the misidentification of the kaon as a pion. There are
also contributions from
B
0
!
K
0
S
‘
þ
‘
, where one of the
pions from the
K
0
S
decay is missed, and from
B
!
K
ð!
K
þ
Þ
‘
þ
‘
, where the pion from the
K
decay is
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032012 (2013)
032012-6
missed. In the case of
K
0
S
‘
þ
‘
, the remaining pion and
the two leptons are reconstructed as
þ
‘
þ
‘
.For
K
ð!
K
þ
Þ
‘
þ
‘
, the
K
þ
is misidentified as
þ
and
reconstructed with the two leptons as
þ
‘
þ
‘
. In both
cases, the decays peak in
m
ES
like signal but at
E<
140 MeV
due to the missing pion. For
K
‘
þ
‘
the
E
peak occurs at even lower values due to the kaon misiden-
tification. For
B
0
!
0
‘
þ
‘
, there is a similar background
from
B
0
!
K
0
S
ð!
0
0
Þ
‘
þ
‘
decays where one
0
is
reconstructed along with the lepton pair as
0
‘
þ
‘
.
These events produce a peak in
m
ES
in the same location
as
0
‘
þ
‘
signal but peak at smaller values of
E
due to the missing pion from the decay. In all three
cases [
K
þ
‘
þ
‘
in
þ
‘
þ
‘
,
K
0
S
ð!
þ
Þ
‘
þ
‘
and
K
ð!
K
þ
Þ
‘
þ
‘
in
þ
‘
þ
‘
, and
K
0
S
ð!
0
0
Þ
‘
þ
‘
in
0
‘
þ
‘
] we include a separate component in the fit model
to account for the corresponding contribution.
For
e
þ
e
and
e
þ
e
, there is an additional back-
ground that originates from two-photon events, given by
the process
e
þ
e
!
e
þ
e
!ð
e
þ
e
Þ
q
q
where
q
is a
u
,
d
,or
s
quark. The background is characterized by a small
transverse momentum of the pion and a large lepton-lepton
opening angle
‘
þ
‘
. There is also a correlation between
the polar angles of the electron,
e
and of the positron,
e
þ
. The
e
tends to be in the forward direction while the
e
þ
tends to be in the backward direction, consistent with
the
e
þ
e
beam particles scattering into the detector.
Events of this type are rejected using the following require-
ments. For
þ
e
þ
e
,
0
e
þ
e
, and
e
þ
e
we require
p
had
>
750 MeV
=c
and
N
trk
>
4
where
p
had
is the hadron
momentum in the c.m. frame and
N
trk
is the number of
charged tracks in the event. Additionally, for
þ
e
þ
e
we
require
E
1
;
neut
<
1
:
75 GeV
,
cos
‘
þ
‘
>
0
:
95
, and
e
>
ð
0
:
57
e
þ
0
:
7 rad
Þ
where
E
1
;
neut
is the energy of the
highest energy neutral cluster in the event in the lab
frame. Similarly,
0
e
þ
e
candidates must satisfy
e
>
ð
0
:
64
e
þ
0
:
8 rad
Þ
, and
e
þ
e
candidates are required
to have
e
>
ð
0
:
6
e
þ
0
:
55 rad
Þ
and
cos
‘
þ
‘
>
0
:
95
.
These criteria were determined by maximizing the quantity
"=
ffiffiffiffiffiffiffiffiffi
N
SB
p
, where
"
is the signal efficiency and
N
SB
is the
number of events lying in the sideband region
5
:
225
<
m
ES
<
5
:
26 GeV
=c
2
in data. We assume that the two-
photon background in the
m
ES
sideband occurs similarly
to the two-photon background in the region
m
ES
>
5
:
26 GeV
=c
2
. The optimization was carried out with all
other selection criteria applied, including those on the NN
outputs.
To guard against possible background from
B
!
D
and
B
!
D
decays where
D
!
K
,
,or
and
the kaon or pions are misidentified as leptons, we assign
the lepton candidates either a kaon or pion mass
and discard any event with a combination of
þ
,
,or
with invariant mass in the range
ð
1
:
83
–
1
:
89
Þ
GeV
=c
2
. The probability of misidentifying a
hadron as an electron is negligible, and this requirement is
therefore only applied to the
þ
modes.
Hadronic decays such as
B
þ
!
þ
þ
, where two
pions are misidentified as muons, peak in both
m
ES
and
E
similarly to signal due to the relatively small difference
between the pion and muon masses. This hadronic peaking
background is modeled by a component in the fit.
A dedicated data control sample is used to determine its
normalization and shape. This sample is constructed from
events where one lepton candidate passes the muon iden-
tification requirements but the other does not. The events in
these samples are weighted with particle misidentification
probabilities determined from control samples in
BABAR
data. Studies of MC samples indicate that this background
is consequential only for the
þ
modes.
After applying all selection criteria there are sometimes
multiple candidates within a given mode remaining in
an event. This occurs for approximately 20%–25%
(35%–40%) of
þ
e
þ
e
and
0
e
þ
e
(
e
þ
e
and
3
e
þ
e
) candidates and 5%–10% (25%–30%) of
NN output
B
B
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
0.3
(a)
NN output
B
B
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
arbitrary units
0
0.05
0.1
0.15
0.2
0.25
0.3
(a)
continuum NN output
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
arbitrary units
0
0.1
0.2
0.3
0.4
0.5
(b)
FIG. 2 (color online). Outputs of (a) the
e
þ
e
B
B
neural
network for a sample of
B
þ
!
þ
e
þ
e
signal (solid red) and
B
B
background (dashed blue) MC events and (b) the
þ
continuum neural network for a sample of
B
0
!
0
þ
signal (solid red) and continuum background (dashed blue)
MC events. For both (a) and (b) the signal and background
distributions are normalized to equal areas.
SEARCH FOR THE RARE DECAYS
...
PHYSICAL REVIEW D
88,
032012 (2013)
032012-7
þ
þ
and
0
þ
(
þ
and
3
þ
) can-
didates. There tend to be more events containing multiple
candidates in the
e
þ
e
modes due to the bremsstrahlung
recovery. For instance, there may be multiple candidates
arising from the same
þ
e
þ
e
combination where the
bremsstrahlung photons associated with the
e
þ
or
e
are
different.
To choose the best candidate we construct a ratio
L
R
from the
B
B
and continuum NN classifier output distribu-
tions of the signal and background samples. The ratio
L
R
is
defined as
L
R
ð
x; y
Þ¼
P
sig
B
B
ð
x
Þþ
P
sig
cont
ð
y
Þ
ð
P
sig
B
B
ð
x
Þþ
P
sig
cont
ð
y
ÞÞþð
P
bkg
B
B
ð
x
Þþ
P
bkg
cont
ð
y
ÞÞ
;
(5)
where
P
sig
B
B
ð
x
Þ
[
P
sig
cont
ð
y
Þ
] is the probability that a signal
candidate has a
B
B
(continuum) NN output value of
x
(
y
).
The quantities
P
bkg
B
B
ð
x
Þ
and
P
bkg
cont
ð
y
Þ
are defined analo-
gously for background events. Signal-like candidates
have values of
L
R
near 1 while more backgroundlike
candidates have values near 0. If multiple candidates are
present in an event, we choose the candidate with the
greatest value of
L
R
as the best candidate. For events
containing multiple candidates, this procedure chooses
the correct candidate approximately 90%–95% of the
time for
‘
þ
‘
and 75%–80% of the time for
‘
þ
‘
.
The ratio
L
R
is used only to select a best candidate.
IV. BRANCHING FRACTION MEASUREMENT
AND UPPER LIMIT CALCULATION
Branching fractions are extracted through an unbinned
extended maximum likelihood fit to
m
ES
and
E
with
the fit region defined as
m
ES
>
5
:
225 GeV
=c
2
and
300
<
E<
250 MeV
. The probability density functions (PDFs)
in the fit model contain several components corresponding
to the different contributions in the data set. To model the
various components, we use a combination of products of
one-dimensional parametric PDFs, two-dimensional histo-
grams, and two-dimensional nonparametric shapes deter-
mined by a Gaussian kernel density estimation algorithm
(KEYS PDF) [
35
]. For components that are described by
the product of one-dimensional PDFs, we are allowed to
use such a model because
m
ES
and
E
are uncorrelated for
these components.
A.
B
þ
!
þ
‘
þ
‘
The
þ
‘
þ
‘
fit model involves four components:
signal,
K
þ
‘
þ
‘
background,
K
0
S
=K
‘
þ
‘
background,
and combinatoric background. There is an additional
component in
B
þ
!
þ
þ
representing the
B
þ
!
þ
þ
hadronic peaking background. The
K
þ
‘
þ
‘
background arises from decays where the kaon is misiden-
tified as a pion. The
K
þ
misidentification rate is such that
the
K
þ
‘
þ
‘
background in
þ
‘
þ
‘
is approximately the
same size as the expected SM
þ
‘
þ
‘
signal. Since the
K
þ
misidentification probability is well measured, it is
possible to measure this background contribution directly
from our data. This is done by simultaneously fitting two
data samples, comprised by the
B
þ
!
þ
‘
þ
‘
candidates
and the
B
þ
!
K
þ
‘
þ
‘
candidates in our data set. The
K
þ
misidentification background to
B
þ
!
K
þ
‘
þ
‘
is in-
cluded in the fit at a level fixed to the
B
þ
!
K
þ
‘
þ
‘
yield using the known misidentification probability (which
depends on the momentum of the kaon). The
B
þ
!
K
þ
‘
þ
‘
branching fraction that is measured from the
simultaneous fit of the
B
þ
!
þ
‘
þ
‘
and
B
þ
!
K
þ
‘
þ
‘
data samples provides an additional validation
of our procedure, since this branching fraction has been
previously measured [
36
].
The
K
þ
‘
þ
‘
sample is selected in exactly the same way
as the
þ
‘
þ
‘
sample except the charged pion identifica-
tion requirements are reversed and the
J=
c
and
c
ð
2
S
Þ
rejection window includes the following regions:
m
ee
>
3
:
20 GeV
=c
2
and
1
:
11
m
ee
c
2
3
:
67
<
E<m
ee
c
2
2
:
875 GeV
for
þ
e
þ
e
surrounding the
J=
c
mass,
m
>
3
:
20 GeV
=c
2
and
1
:
11
m
c
2
3
:
614
<
E<
m
c
2
2
:
925 GeV
for
þ
þ
surrounding the
J=
c
mass, and
m
‘‘
>
3
:
75 GeV
=c
2
and
1
:
11
m
‘‘
c
2
4
:
305
<
E<m
‘‘
c
2
3
:
525 GeV
for both modes surrounding the
c
ð
2
S
Þ
mass. Also, the
E
window is
200
<
E<
250 MeV
for
K
þ
e
þ
e
and
100
<
E<
250 MeV
for
K
þ
þ
.
The
þ
‘
þ
‘
and
K
þ
‘
þ
‘
background
m
ES
and
E
distributions are modeled by products of one-dimensional
PDFs. The
þ
‘
þ
‘
signal and
K
þ
‘
þ
‘
background
m
ES
distributions are described by a Crystal Ball function [
37
].
The
þ
e
þ
e
E
signal distribution is modeled by the sum
of a Crystal Ball function and a Gaussian which share a
common mean, while the
þ
þ
signal and both the
K
þ
e
þ
e
and
K
þ
þ
E
distributions are modeled by a
modified Gaussian with tail parameters whose functional
form is given by
f
ð
E
Þ¼
exp
ð
E
Þ
2
2
L;R
L;R
þ
L;R
ð
E
Þ
;
(6)
where
L
and
L
(
R
and
R
) are the width and tail
parameters used when
E<
(
E>
), respectively.
A two-dimensional histogram models the contribution
from
B
!
K
0
S
=K
‘
þ
‘
decays. Combinatoric background
is described by the product of an ARGUS function [
38
]in
m
ES
with endpoint fixed to
5
:
29 GeV
=c
2
and a second-
order polynomial in
E
. The
þ
þ
hadronic peaking
background component is modeled by a two-dimensional
KEYS PDF [
35
].
The PDF fit to the
K
þ
‘
þ
‘
sample contains a similar set
of components. Signal
K
þ
‘
þ
‘
distributions are modeled
by the product of a Crystal Ball function in
m
ES
and the line
shape of Eq. (
6
)in
E
. The contribution from other
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032012 (2013)
032012-8
b
!
s‘
þ
‘
decays is dominated by
B
!
K
ð
K
þ
Þ
‘
þ
‘
where the pion is lost. We use a two-dimensional histogram
to model this background. Combinatoric background is
modeled by the product of an ARGUS distribution in
m
ES
and by an exponential function for
K
þ
e
þ
e
and a
second-order polynomial for
K
þ
þ
in
E
. A KEYS
PDF models the hadronic peaking background in
K
þ
þ
.
In both the
þ
‘
þ
‘
and
K
þ
‘
þ
‘
PDFs, the signal and
combinatoric background yields float along with the
shapes of the combinatoric background PDFs. The
K
þ
‘
þ
‘
background yield in the
þ
‘
þ
‘
sample is con-
strained so that the
B
þ
!
K
þ
‘
þ
‘
branching fractions
measured in the
þ
‘
þ
‘
and
K
þ
‘
þ
‘
samples are equal.
All fixed shapes and yields are determined from exclusive
MC samples except for the hadronic peaking background
which uses a data control sample. Normalizations of the
K
0
S
=K
‘
þ
‘
component of the
þ
‘
þ
‘
PDF and of
K
‘
þ
‘
component in the
K
þ
‘
þ
‘
PDF are fixed from
efficiencies determined from MC samples and world
average branching fractions [
36
].
B.
B
0
!
0
‘
þ
‘
The
B
0
!
0
‘
þ
‘
signal distribution is modeled by the
product of a Crystal Ball function in
m
ES
and by the
line shape given in Eq. (
6
)in
E
. Background from
B
0
!
K
0
S
ð!
0
0
Þ
‘
þ
‘
decays is modeled by a two-
dimensional histogram. The product of an ARGUS shape
in
m
ES
with an exponential function in
E
models the
combinatoric background distribution. As in the
þ
þ
and
K
þ
þ
PDFs, there is an additional component in
the
0
þ
fit model devoted to hadronic peaking back-
ground which is described by a KEYS PDF.
In the fit, only the signal
0
‘
þ
‘
and combinatoric
background yields along with the shape of the com-
binatoric background PDF float. The signal and
K
0
S
ð!
0
0
Þ
‘
þ
‘
shapes are determined from fits to
MC samples, and the
K
0
S
ð!
0
0
Þ
‘
þ
‘
normalization
comes from efficiencies taken from MC samples and world
average branching fractions [
36
]. The shape and normal-
ization of the peaking hadronic component are determined
from a data control sample.
C.
B
0
!
‘
þ
‘
The
‘
þ
‘
fit model is simple, consisting of only three
components, and is the same for all four
‘
þ
‘
channels.
The signal component is modeled by the product of a
Crystal Ball function in
m
ES
and the line shape of Eq. (
4
)
in
E
. We include a component for events containing a
signal decay where the signal
B
is incorrectly recon-
structed, which we refer to as self-cross-feed. In these
events the signal decay is typically reconstructed as a
combination of particles from the
B
decaying to our signal
mode and the other
B
. In most self-cross-feed events the
dilepton pair is correctly reconstructed, and the hadron is
misreconstructed. The self-cross-feed contribution is rep-
resented by a two-dimensional histogram, and its normal-
ization is a fixed fraction of the signal yield with the
fraction determined from signal MC. The self-cross-feed-
to-signal ratio varies from 0.1 to 0.15 for the
channels
to 0.25–0.3 for the
3
channels. Combinatoric back-
ground is described by the product of an ARGUS function
in
m
ES
and an exponential function in
E
. From studies of
MC samples, we find no indication of potential peaking
background contributions from
b
!
s‘
þ
‘
decays or any
other sources. The
‘
þ
‘
yield and the
3
‘
þ
‘
yield
are constrained in the fit to be consistent with the same
B
0
!
‘
þ
‘
branching fraction. The signal yield, combi-
natoric background yield, ARGUS slope and exponential
argument float in the fit. All other parameters are fixed
from MC samples.
D. Lepton-flavor averaged and isospin averaged fits
In addition to branching fraction measurements and
upper limits for the
B
!
‘
þ
‘
and
B
0
!
‘
þ
‘
modes
we also present lepton-flavor averaged, isospin averaged,
and lepton-flavor and isospin averaged results. The lepton-
flavor averaged measurement of
B
ð
B
þ
!
þ
‘
þ
‘
Þ
is the
branching fraction obtained from a simultaneous fit to the
þ
e
þ
e
and
þ
þ
samples subject to the constraint
B
ð
B
þ
!
þ
e
þ
e
Þ¼
B
ð
B
þ
!
þ
þ
Þ
. Here we
have neglected the difference between the electron and
muon masses. The measurements of
B
ð
B
0
!
0
‘
þ
‘
Þ
and
B
ð
B
0
!
‘
þ
‘
Þ
are subject to a similar set of
constraints and are determined in an analogous way.
The isospin averaged branching fraction
B
ð
B
!
e
þ
e
Þ
is the measured value of
B
ð
B
þ
!
þ
e
þ
e
Þ
after
simultaneously fitting the
þ
e
þ
e
and
0
e
þ
e
samples
subject to the constraint
B
ð
B
þ
!
þ
e
þ
e
Þ¼
ð
B
0
=
2
B
þ
Þ
B
ð
B
0
!
0
e
þ
e
Þ
where
B
0
and
B
þ
are the
mean lifetimes of the neutral and charged
B
mesons,
respectively [
36
]. An analogous expression is applied for
the
B
ð
B
!
þ
Þ
measurement. The lepton-flavor and
isospin averaged measurement of
B
ð
B
!
‘
þ
‘
Þ
is the
value of
B
ð
B
þ
!
þ
‘
þ
‘
Þ
determined from a simulta-
neous fit to all four samples subject to both the lepton
flavor and isospin constraints listed above.
E. Upper limit calculation
We set upper limits on the branching fractions following
a method which utilizes the profile likelihood. Upper limits
at the
confidence level (CL) are set by scanning the
profile likelihood
as a function of the signal branching
fraction to determine where
2ln
changes by
percen-
tile of a
2
random variable with 1 degree of freedom.
For
¼
0
:
9
we look for a change in
2ln
of 1.642.
If the measured branching fraction is negative, we begin
our scan from zero rather than the minimum [
39
]. This is a
conservative approach that always produces physical,
i.e., non-negative, upper limits, even in the case of low
SEARCH FOR THE RARE DECAYS
...
PHYSICAL REVIEW D
88,
032012 (2013)
032012-9