arXiv:1303.6010v1 [hep-ex] 25 Mar 2013
B
A
B
AR
-PUB-12/33
SLAC-PUB-15401
A Search for the Rare Decays
B
→
πℓ
+
ℓ
−
and
B
0
→
ηℓ
+
ℓ
−
J. P. Lees, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules
(LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vie
ux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament
ECM, E-08028 Barcelona, Spain
A. Palano
ab
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
G. Eigen and B. Stugu
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, and G. Lynch
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, California 94720, USA
H. Koch and T. Schroeder
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. So
University of British Columbia, Vancouver, British Columb
ia, Canada V6T 1Z1
A. Khan
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kin
gdom
V. E. Blinov, A. R. Buzykaev, V. P. Druzhinin, V. B. Golubev, E. A. Kr
avchenko, A. P. Onuchin,
S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, K. Yu. Todysh
ev, and A. N. Yushkov
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630
090, Russia
D. Kirkby, A. J. Lankford, and M. Mandelkern
University of California at Irvine, Irvine, California 926
97, USA
B. Dey, J. W. Gary, O. Long, and G. M. Vitug
University of California at Riverside, Riverside, Califor
nia 92521, USA
C. Campagnari, M. Franco Sevilla, T. M. Hong, D. Kovalskyi, J. D. Rich
man, and C. A. West
University of California at Santa Barbara, Santa Barbara, C
alifornia 93106, USA
A. M. Eisner, W. S. Lockman, A. J. Martinez, B. A. Schumm, and A. S
eiden
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin, P. On
gmongkolkul, and F. C. Porter
California Institute of Technology, Pasadena, California
91125, USA
R. Andreassen, Z. Huard, B. T. Meadows, M. D. Sokoloff, and L. Su
n
University of Cincinnati, Cincinnati, Ohio 45221, USA
P. C. Bloom, W. T. Ford, A. Gaz, U. Nauenberg, J. G. Smith, and S. R
. Wagner
University of Colorado, Boulder, Colorado 80309, USA
R. Ayad
∗
and W. H. Toki
Colorado State University, Fort Collins, Colorado 80523, U
SA
2
B. Spaan
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44
221 Dortmund, Germany
K. R. Schubert and R. Schwierz
Technische Universit ̈at Dresden, Institut f ̈ur Kern- und T
eilchenphysik, D-01062 Dresden, Germany
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
S. Playfer
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
,
I. Garzia
ab
, E. Luppi
ab
, L. Piemontese
a
, and V. Santoro
a
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a
di Ferrara
b
, I-44122 Ferrara, Italy
R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,
S. Martellotti, P. Patteri, I. M. Peruzzi,
†
M. Piccolo, M. Rama, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
R. Contri
ab
, E. Guido
ab
, M. Lo Vetere
ab
, M. R. Monge
ab
, S. Passaggio
a
, C. Patrignani
ab
, and E. Robutti
a
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
B. Bhuyan and V. Prasad
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
M. Morii
Harvard University, Cambridge, Massachusetts 02138, USA
A. Adametz and U. Uwer
Universit ̈at Heidelberg, Physikalisches Institut, Philo
sophenweg 12, D-69120 Heidelberg, Germany
H. M. Lacker
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, Ne
wtonstr. 15, D-12489 Berlin, Germany
P. D. Dauncey
Imperial College London, London, SW7 2AZ, United Kingdom
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, W. T. Meyer, S. Prell, and A. E. Rubin
Iowa State University, Ames, Iowa 50011-3160, USA
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder,
A. M. Lutz, B. Malaescu, P. Roudeau, A. Stocchi, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, F
rance
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. P
ayne, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
3
A. J. Bevan, F. Di Lodovico, and R. Sacco
Queen Mary, University of London, London, E1 4NS, United Kin
gdom
G. Cowan
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
J. Bougher, D. N. Brown, and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, and E.
Prencipe
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Ker
nphysik, D-55099 Mainz, Germany
R. J. Barlow
‡
and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingd
om
E. Behn, R. Cenci, B. Hamilton, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan, D. Dujmic, and G. Sciolla
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib, P. M. Patel,
§
and S. H. Robertson
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
P. Biassoni
ab
, N. Neri
a
, and F. Palombo
ab
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
L. Cremaldi, R. Godang,
¶
P. Sonnek, and D. J. Summers
University of Mississippi, University, Mississippi 38677
, USA
X. Nguyen, M. Simard, and P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo
ab
, D. Monorchio
ab
, G. Onorato
ab
, and C. Sciacca
ab
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
M. Martinelli and G. Raven
NIKHEF, National Institute for Nuclear Physics and High Ene
rgy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
J. Brau, R. Frey, N. B. Sinev, D. Strom, and E. Torrence
University of Oregon, Eugene, Oregon 97403, USA
E. Feltresi
ab
, M. Margoni
ab
, M. Morandin
a
, M. Posocco
a
, M. Rotondo
a
, G. Simi
a
, F. Simonetto
ab
, and R. Stroili
ab
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand,
G. Calderini, J. Chauveau, Ph. Leruste, G. Marchiori, J. Ocariz, an
d S. Sitt
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
4
M. Biasini
ab
, E. Manoni
a
, S. Pacetti
ab
, and A. Rossi
ab
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06100 Perugia, Italy
C. Angelini
ab
, G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
∗∗
G. Casarosa
ab
, A. Cervelli
ab
, F. Forti
ab
,
M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, A. Perez
a
, G. Rizzo
ab
, and J. J. Walsh
a
INFN Sezione di Pisa
a
; Dipartimento di Fisica, Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
D. Lopes Pegna, J. Olsen, and A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, M. Gaspero
ab
, L. Li Gioi
a
, and G. Piredda
a
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
C. B ̈unger, O. Gr ̈unberg, T. Hartmann, T. Leddig, C. Voß, and R
. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
S. Emery, G. Hamel de Monchenault, G. Vasseur, and Ch. Y`eche
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
F. Anulli
a
, D. Aston, D. J. Bard, J. F. Benitez, C. Cartaro, M. R. Convery,
J. Dorfan, G. P. Dubois-Felsmann,
W. Dunwoodie, M. Ebert, R. C. Field, B. G. Fulsom, A. M. Gabareen, M
. T. Graham, C. Hast,
W. R. Innes, P. Kim, M. L. Kocian, D. W. G. S. Leith, P. Lewis, D. Linde
mann, B. Lindquist, S. Luitz,
V. Luth, H. L. Lynch, D. B. MacFarlane, D. R. Muller, H. Neal, S. Nels
on, M. Perl, T. Pulliam,
B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, A. Snyder
, D. Su, M. K. Sullivan, J. Va’vra,
A. P. Wagner, W. F. Wang, W. J. Wisniewski, M. Wittgen, D. H. Wright,
H. W. Wulsin, and V. Ziegler
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
W. Park, M. V. Purohit, R. M. White, and J. R. Wilson
University of South Carolina, Columbia, South Carolina 292
08, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, T. S. Miyashita, and E. M. T. Puccio
Stanford University, Stanford, California 94305-4060, US
A
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Av
iv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie, A. M. Ruland, R. F. Schwitters, and B. C. Wray
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi
ab
, F. De Mori
ab
, A. Filippi
a
, D. Gamba
ab
, and S. Zambito
ab
INFN Sezione di Torino
a
; Dipartimento di Fisica Sperimentale, Universit`a di Tori
no
b
, I-10125 Torino, Italy
5
L. Lanceri
ab
and L. Vitale
ab
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
F. Martinez-Vidal, A. Oyanguren, and P. Villanueva-Perez
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
H. Ahmed, J. Albert, Sw. Banerjee, F. U. Bernlochner, H. H. F. Ch
oi, G. J. King, R. Kowalewski,
M. J. Lewczuk, T. Lueck, I. M. Nugent, J. M. Roney, R. J. Sobie, a
nd N. Tasneem
University of Victoria, Victoria, British Columbia, Canad
a V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4
7AL, United Kingdom
H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
(Dated: March 20, 2013)
We present the results of a search for the rare flavor-changin
g neutral-current decays
B
→
πℓ
+
ℓ
−
(
π
=
π
±
,π
0
and
ℓ
=
e,μ
) and
B
0
→
ηℓ
+
ℓ
−
using a sample of
e
+
e
−
→
Υ
(4
S
)
→
B
B
decays corre-
sponding to 428 fb
−
1
of integrated luminosity collected by the
B
A
B
AR
detector. No significant signal
is observed, and we set an upper limit on the isospin and lepto
n-flavor averaged branching fraction of
B
(
B →
πℓ
+
ℓ
−
)
<
7
.
0
×
10
−
8
and a lepton-flavor averaged upper limit of
B
(
B
0
→
ηℓ
+
ℓ
−
)
<
9
.
2
×
10
−
8
,
both at the 90% confidence level. We also report 90% confidence
level branching fraction upper
limits for the individual modes
B
+
→
π
+
e
+
e
−
,
B
0
→
π
0
e
+
e
−
,
B
+
→
π
+
μ
+
μ
−
,
B
0
→
π
0
μ
+
μ
−
,
B
0
→
ηe
+
e
−
, and
B
0
→
ημ
+
μ
−
.
PACS numbers: 13.20.He, 13.60.Hb
I. INTRODUCTION
In the standard model (SM), the decays
B
→
πℓ
+
ℓ
−
(
π
=
π
±
,π
0
and
ℓ
=
e,μ
) and
B
0
→
ηℓ
+
ℓ
−
proceed
through the quark-level flavor-changing neutral current
(FCNC) process
b
→
dℓ
+
ℓ
−
. Since all FCNC processes
are forbidden at tree level in the SM, the lowest order dia-
grams representing these transitions must involve loops.
For
b
→
dℓ
+
ℓ
−
, these are the electroweak semileptonic
penguin diagrams (Fig. 1(a)) and the
W
+
W
−
box dia-
grams (Fig. 1(b)). The
b
→
dℓ
+
ℓ
−
transition is similar
to
b
→
sℓ
+
ℓ
−
, but its rate is suppressed by the ratio
|
V
td
/V
ts
|
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
+
→
π
+
ℓ
+
ℓ
−
decay modes lie in the range of (1
.
4 – 3
.
3)
×
10
−
8
, when
the dilepton mass regions near the
J/ψ
and
ψ
(2
S
) are ex-
cluded in order to remove decays that proceed through
the intermediate charmonium resonances. The largest
source of uncertainty in these predictions arises from
∗
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia
†
Also with Universit`a di Perugia, Dipartimento di Fisica, P
erugia,
Italy
‡
Now at the University of Huddersfield, Huddersfield HD1 3DH,
UK
§
Deceased
¶
Now at University of South Alabama, Mobile, Alabama 36688,
USA
∗∗
Also with Universit`a di Sassari, Sassari, Italy
knowledge of the
B
→
π
form factors [3–5]. These
branching fractions imply that 5–15 events occur for each
B
→
πℓ
+
ℓ
−
decay channel in the
B
A
B
AR
data set (471
million
B
B
pairs). The predicted
B
0
→
ηℓ
+
ℓ
−
branching
fractions lie in the range (2
.
5 – 3
.
7)
×
10
−
8
where again
the dominant uncertainty is due to lack of knowledge of
the
B
0
→
η
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
→
dℓ
+
ℓ
−
and
b
→
sℓ
+
ℓ
−
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]. Mea-
surements in the
πℓ
+
ℓ
−
and
ηℓ
+
ℓ
−
systems complement
and provide independent searches of NP from those in
the
K
(
∗
)
ℓ
+
ℓ
−
channels [11–17], as physics beyond the
SM may have non-trivial flavor couplings [18]. The mea-
surement of observables as a function of the square of the
invariant dilepton mass
q
2
=
m
2
ℓℓ
for exclusive
b
→
dℓ
+
ℓ
−
decay modes allows for more thorough tests of SM pre-
dictions and deeper probes for NP but is currently not
possible due to the size of the data set.
Only one
b
→
dℓ
+
ℓ
−
decay has been observed to date,
with LHCb measuring the
B
+
→
π
+
μ
+
μ
−
branching
fraction to be (2
.
4
±
0
.
6
±
0
.
2)
×
10
−
8
[19]. Both
B
A
B
AR
[20]
and Belle [21] have performed searches for
B
→
πℓ
+
ℓ
−
decays, but have observed no significant signal. For the
πℓ
+
ℓ
−
modes, the smallest upper limits from the
B
fac-
tories lie within an order of magnitude of the SM pre-
6
b
d
ℓ
+
ℓ
−
Z
0
, γ
W
−
u, c, t
b
d
ℓ
+
ℓ
−
u, c, t
W
−
̄
ν
W
+
(a)
(b)
FIG. 1: Lowest order Feynman diagrams describing the quark l
evel
b
→
dℓ
+
ℓ
−
transition in
B
meson decay: (a) electroweak
penguin diagrams and (b)
W
+
W
−
box diagrams.
dictions [3–5] and are beginning to exclude portions of
the NP parameter space. No previous searches for
B
0
→
ηℓ
+
ℓ
−
have been reported. Observation of
b
→
dℓ
+
ℓ
−
de-
cays at the
B
factories is currently limited by the size of
the available data sets. Additionally, for
B
+
→
π
+
ℓ
+
ℓ
−
,
background from
B
+
→
K
+
ℓ
+
ℓ
−
decays where the kaon
is misidentified as a pion must be treated carefully as
K
+
ℓ
+
ℓ
−
can appear very signal-like and occurs at a rate
approximately 25 times the expected
B
+
→
π
+
ℓ
+
ℓ
−
rate.
In this article we report on our study of the
B
→
πℓ
+
ℓ
−
and
B
0
→
ηℓ
+
ℓ
−
decays using the full
B
A
B
AR
data
set, presenting branching fraction upper limits for the
modes
B
+
→
π
+
e
+
e
−
,
B
0
→
π
0
e
+
e
−
,
B
+
→
π
+
μ
+
μ
−
,
B
0
→
π
0
μ
+
μ
−
,
B
0
→
ηe
+
e
−
, and
B
0
→
ημ
+
μ
−
. Charge
conjugation is implied throughout unless specified other-
wise. We also present upper limits for the lepton-flavor
averaged modes
B
+
→
π
+
ℓ
+
ℓ
−
,
B
0
→
π
0
ℓ
+
ℓ
−
, and
B
0
→
ηℓ
+
ℓ
−
, where we constrain the
e
+
e
−
and
μ
+
μ
−
branching fractions to be equal; for the isospin averaged
modes
B
→
πe
+
e
−
and
B
→
πμ
+
μ
−
, where the
B
+
→
π
+
ℓ
+
ℓ
−
decay rate is constrained to be twice the
B
0
→
π
0
ℓ
+
ℓ
−
decay rate; and for the isospin and lepton-flavor
averaged mode
B
→
πℓ
+
ℓ
−
. For the lepton-flavor av-
eraged measurements, we neglect differences 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 vari-
ables. All selection criteria are determined before the fit
was performed on data,
i.e.,
the analysis is performed
“blind”.
II.
B
A
B
AR
DETECTOR, SIMULATION, AND
DATA SETS
The results of this analysis are based upon a sample
of
e
+
e
−
→
Υ
(4
S
)
→
B
B
interactions provided by the
PEP-II asymmetric-energy storage rings and collected by
the
B
A
B
AR
detector located at SLAC National Accelera-
tor Laboratory. The
B
A
B
AR
data sample corresponds to
an integrated luminosity of 428 fb
−
1
containing 471 mil-
lion
B
B
decays. This is the full data set collected at the
Υ
(4
S
) resonance. A detailed description of the
B
A
B
AR
de-
tector can be found elsewhere [22]. Charged particle mo-
menta 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 im-
mersed 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 elec-
trons and photons are detected with an electromagnetic
calorimeter (EMC) constructed from a finely segmented
array of thallium-doped CsI scintillating crystals. The
steel flux return of the solenoid (IFR) was initially in-
strumented with resistive plate chambers (RPCs) and
functions primarily to identify muons. For the later data
taking periods, the RPCs of the IFR were replaced with
limited streamer tubes and brass to increase absorption.
The
B
A
B
AR
Monte Carlo (MC) simulation utilizes
the
Geant4
package [23] for detector simulation, and
EvtGen
[24] and
Jetset7.4
[25] for
B
B
and
e
+
e
−
→
q
q
(
q
=
u,d,s,c
) decays, respectively. The
B
B
and contin-
uum (
e
+
e
−
→
q
q
,
q
=
u,d,s,c
) MC samples correspond
to an effective luminosity of about ten times the data
sample collected at the
Υ
(4
S
) resonance. Simulated
B
→
πℓ
+
ℓ
−
signal decay samples are generated according
to the form-factor model of Ref. [26], with the Wilson
coefficients taken from Refs. [27–29], and the decay am-
plitudes calculated in Ref. [10]. The
B
0
→
ηℓ
+
ℓ
−
signal
MC samples utilize the same kinematics, Wilson coeffi-
cients, and form-factor model as the
πℓ
+
ℓ
−
modes. The
effects of the choice of form-factor model and the val-
ues of the Wilson coefficients are considered as sources
of systematic uncertainty in the signal efficiency. We
also make use of simulated
B
→
K
(
∗
)
ℓ
+
ℓ
−
,
B
→
J/ψX
,
and
B
→
ψ
(2
S
)
X
samples. Signal efficiencies, as well
as parameters of the fit model, are determined from sig-
nal and
K
(
∗
)
ℓ
+
ℓ
−
MC data sets. The
B
→
J/ψX
and
B
→
ψ
(2
S
)
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
7
B
→
J/ψπ/η
fit validation, as described later.
III. EVENT RECONSTRUCTION AND
CANDIDATE SELECTION
Event reconstruction begins by building dilepton can-
didates from two leptons (
e
+
e
−
or
μ
+
μ
−
). Leptons are
selected as charged tracks with momenta in the labo-
ratory reference (Lab) frame greater than 300 MeV
/c
.
Loose particle identification (PID) requirements are
placed upon the two leptons. More stringent PID require-
ments are applied later, and the optimization of these se-
lection criteria is discussed in Section V. The lepton pair
is fit to a common vertex to form a dilepton candidate
with the requirement that
m
ℓℓ
<
5
.
0 GeV
/c
2
[30]. We
also place a loose constraint on the
χ
2
probability of the
vertex fit by requiring it to be greater than 10
−
10
. For
electrons, we apply an algorithm which associates pho-
tons 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 open-
ing 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 requiring 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
π
0
candidates from two photons with invari-
ant diphoton mass
m
γγ
lying in the range 115
< m
γγ
<
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 recon-
struct
η
as
η
→
γγ
(
η
γγ
) and
η
→
π
+
π
−
π
0
(
η
3
π
), which
constitute 39.3% and 22.7% of the
η
branching fraction,
respectively. As in the case of the
π
0
, we require the
η
γγ
photon daughters to have energy greater than 50 MeV in
the Lab frame. Additionally, the photon energy asymme-
try
A
γ
=
|
E
1
,γ
−
E
2
,γ
|
/
(
E
1
,γ
+
E
2
,γ
) must be less than
0.8, where
E
1
,γ
and
E
2
,γ
are the energies of the photons
in the Lab frame. The invariant diphoton mass must lie
in the range 500
< m
γγ
<
575 MeV
/c
2
. For
η
3
π
, the pion
candidates are fit to a common vertex to form an
η
can-
didate. In the fit the
η
candidate mass is constrained to
the nominal
η
mass, while the invariant three-pion mass
is required to lie in the range 535
< m
3
π
<
565 MeV
/c
2
.
B
candidates are reconstructed from a hadron candi-
date (
π
+
,
π
0
,
η
γγ
, or
η
3
π
) and a dilepton candidate (
e
+
e
−
or
μ
+
μ
−
). 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
=
√
(
s/
2 +
~p
B
·
~p
0
)
2
/E
2
0
−
p
2
B
(1)
∆
E
= (2
q
B
q
0
−
s
)
/
2
√
s
(2)
where
√
s
= 2
E
∗
beam
is the total energy of the
e
+
e
−
sys-
tem in the center of mass (CM) frame,
q
B
and
q
0
=
(
E
0
,~p
0
) are the four-vectors representing the momentum
of the
B
candidate and of the
e
+
e
−
system, respectively,
and
~p
B
is the three-momentum of the
B
candidate. In
the CM frame, these expressions simplify to
m
ES
=
√
E
∗
2
beam
−
p
∗
B
2
(3)
∆
E
=
E
∗
B
−
E
∗
beam
(4)
where the asterisk indicates evaluation in the CM 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
πℓ
+
ℓ
−
and
ηℓ
+
ℓ
−
branching fractions.
A large background is present from
B
→
J/ψX
and
B
→
ψ
(2
S
)
X
decays where
J/ψ
and
ψ
(2
S
) decay to
ℓ
+
ℓ
−
. Here
X
represents a hadronic state, typically
π
,
η
,
ρ
, or
K
(
∗
)
. These events are removed from our data
sample by rejecting any event with a value of
m
ℓℓ
consis-
tent with originating from a
J/ψ
or
ψ
(2
S
) decay. The
rejected
J/ψ
events are useful as they provide a con-
trol sample which can be used to test the fit model.
We also use these samples to estimate systematic uncer-
tainties and to correct for differences between data and
MC selection efficiencies. For the electron modes we re-
ject events in the following regions about the
J/ψ
mass:
2
.
90
< m
ℓℓ
<
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
μμ
<
3
.
20 GeV
/c
2
, or
m
μμ
<
3
.
00 GeV
/c
2
and
∆
E <
1
.
11
m
μμ
c
2
−
3
.
31 GeV. The rejection region about
the
ψ
(2
S
) mass is the same for electrons and muons:
3
.
60
< m
ℓℓ
<
3
.
75 GeV
/c
2
, or
m
ℓℓ
<
3
.
60 GeV
/c
2
and
∆
E < m
ℓℓ
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 ran-
dom combinations of particles from continuum events or
semileptonic
B
and
D
decays in
B
B
events. Contin-
uum events tend to be jet-like as the
q
q
pair is produced
back-to-back with relatively large momentum in the CM
frame. The topology of
B
B
decays is more isotropic as
the
B
mesons are produced nearly at rest in the
Υ
(4
S
)
rest frame. Semileptonic decays are characterized by the
presence of a neutrino,
e.g.,
missing energy in the event
and non-zero total transverse momentum of the event.
Due to the differences 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
8
one NN for each lepton flavor. We do not train sepa-
rate NNs for
π
+
,
π
0
, and
η
. 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
+
e
−
modes, one to reject
B
B
background in the
μ
+
μ
−
modes, one to reject continuum background in the
e
+
e
−
modes, and one to reject continuum background in
the
μ
+
μ
−
modes.
The signal training samples were assembled from equal
portions of correctly reconstructed
B
+
→
π
+
ℓ
+
ℓ
−
,
B
0
→
π
0
ℓ
+
ℓ
−
,
B
+
→
ρ
+
ℓ
+
ℓ
−
,
B
0
→
ρ
0
ℓ
+
ℓ
−
,
B
0
→
η
γγ
ℓ
+
ℓ
−
,
and
B
0
→
ωℓ
+
ℓ
−
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 per-
formance of the NNs. To increase the available statis-
tics the other events from the
ρℓ
+
ℓ
−
and
ωℓ
+
ℓ
−
modes
were added to the training samples. The
ρ
+
(
ρ
0
) was
reconstructed as
π
+
π
0
(
π
+
π
−
) with two-pion invariant
mass
m
ππ
in the range 0
.
455
< m
ππ
<
1
.
095 GeV
/c
2
(0
.
475
< m
ππ
<
1
.
075 GeV
/c
2
). The
ω
was reconstructed
as
π
+
π
−
π
0
and required to have a three-pion invaraint
mass lying within 50 MeV
/c
2
of the nominal
ω
mass. No
η
3
π
ℓ
+
ℓ
−
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
→
dℓ
+
ℓ
−
(global
NNs) modes were compared with NNs trained specifi-
cally for each of our four
B
→
πℓ
+
ℓ
−
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 [31]; the cosine of the polar angle of
the thrust axis [32] of the event; the cosine of the polar
angle of the thrust axis of the rest-of-the-event (ROE),
which consists of all particles in the event not associated
with the signal
B
candidate; the momentum weighted
polynomials
L
j
i
[33] computed using tracks and EMC
clusters; the cosine of the polar angle of the
B
candi-
date momentum; and the
χ
2
probability of the
B
can-
didate 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
χ
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 net-
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
continuum NN output
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
(a)
arbitrary units
(b)
arbitrary units
FIG. 2: Outputs of (a) the
e
+
e
−
B
B
neural network for a
sample of
B
+
→
π
+
e
+
e
−
signal (solid red) and
B
B
back-
ground (dashed blue) MC events, and (b) the
μ
+
μ
−
con-
tinuum neural network for a sample of
B
0
→
π
0
μ
+
μ
−
sig-
nal (solid red) and continuum background (dashed blue) MC
events (color available online). For both (a) and (b) the sig
nal
and background distributions are normalized to equal areas
.
works, shows the output of the
e
+
e
−
B
B
NN for a sam-
ple of signal and
B
B
background
π
+
e
+
e
−
MC events.
Also shown is the output of the
μ
+
μ
−
continuum NN for
a sample of signal and continuum background
π
0
μ
+
μ
−
MC events. Requirements on the NN outputs are opti-
mized for each of our eight modes to produce the lowest
branching fraction upper limit. A description of the op-
timization procedure is given in Section V.
Due to their similarity to signal,
B
→
K
(
∗
)
ℓ
+
ℓ
−
decays
constitute a background that mimics signal by peaking in
either one or both
m
ES
and ∆
E
. The
b
→
sℓ
+
ℓ
−
transi-
tion occurs at a rate approximately 25 times greater than
the SM
b
→
dℓ
+
ℓ
−
rate, and due to particle misiden-
tification and event misreconstruction, its contribution
is expected to be of the same order as the
πℓ
+
ℓ
−
sig-
nal in the
B
A
B
AR
data sample. In the charged pion
modes,
B
+
→
K
+
ℓ
+
ℓ
−
peaks in
m
ES
as
π
+
ℓ
+
ℓ
−
signal
but in ∆
E
near
−
70 MeV due to the misidentification
of the kaon as a pion. There are also contributions from
9
B
0
→
K
0
S
ℓ
+
ℓ
−
, where one of the pions from the
K
0
S
decay
is missed, and from
B
→
K
∗
(
→
K
+
π
)
ℓ
+
ℓ
−
, where the
pion from the
K
∗
decay is missed. In the case of
K
0
S
ℓ
+
ℓ
−
,
the remaining pion and the two leptons are reconstructed
as
π
+
ℓ
+
ℓ
−
. For
K
∗
(
→
K
+
π
)
ℓ
+
ℓ
−
, the
K
+
is misiden-
tified as
π
+
and reconstructed with the two leptons as
π
+
ℓ
+
ℓ
−
. In both cases, the decays peak in
m
ES
like sig-
nal but at ∆
E <
−
140 MeV due to the missing pion. For
K
∗
ℓ
+
ℓ
−
the ∆
E
peak occurs at even lower values due to
the kaon misidentification. For
B
0
→
π
0
ℓ
+
ℓ
−
, there is a
similar background from
B
0
→
K
0
S
(
→
π
0
π
0
)
ℓ
+
ℓ
−
decays
where one
π
0
is reconstructed along with the lepton pair
as
π
0
ℓ
+
ℓ
−
. These events produce a peak in
m
ES
in the
same location as
π
0
ℓ
+
ℓ
−
signal, but peak at smaller val-
ues of ∆
E
due to the missing pion from the decay. In all
three cases (
K
+
ℓ
+
ℓ
−
in
π
+
ℓ
+
ℓ
−
,
K
0
S
(
→
π
+
π
−
)
ℓ
+
ℓ
−
and
K
∗
(
→
K
+
π
)
ℓ
+
ℓ
−
in
π
+
ℓ
+
ℓ
−
, and
K
0
S
(
→
π
0
π
0
)
ℓ
+
ℓ
−
in
π
0
ℓ
+
ℓ
−
) we include a separate component in the fit model
to account for the corresponding contribution.
For
πe
+
e
−
and
η
γγ
e
+
e
−
, there is an additional back-
ground that originates from two-photon events, given by
the process
e
+
e
−
→
e
+
e
−
γγ
→
(
e
+
e
−
)
q
q
where
q
is a
u
,
,
.
or
s
quark. The background is characterized by a small
transverse momentum of the pion and a large lepton-
lepton opening angle
θ
ℓ
+
ℓ
−
. There is also a correlation
between the polar angles of the electron,
θ
e
−
, and of the
positron,
θ
e
+
. The
e
−
tends to be in the forward direction
while the
e
+
tends to be in the backward direction, con-
sistent with the
e
+
e
−
beam particles scattering into the
detector. Events of this type are rejected using the fol-
lowing requirements. For
π
+
e
+
e
−
,
π
0
e
+
e
−
, and
η
γγ
e
+
e
−
we require
p
∗
had
>
750 MeV
/c
and
N
trk
>
4 where
p
∗
had
is the hadron momentum in the CM frame and
N
trk
is
the number of charged tracks in the event. Additionally,
for
π
+
e
+
e
−
we require
E
1
,
neut
<
1
.
75 GeV, cos
θ
ℓ
+
ℓ
−
>
−
0
.
95, and
θ
e
−
>
(0
.
57
θ
e
+
−
0
.
7 rad) where
E
1
,
neut
is the
energy of the highest energy neutral cluster in the event
in the Lab frame. Similarly,
π
0
e
+
e
−
candidates must
satisfy
θ
e
−
>
(0
.
64
θ
e
+
−
0
.
8 rad), and
η
γγ
e
+
e
−
candi-
dates are required to have
θ
e
−
>
(0
.
6
θ
e
+
−
0
.
55 rad) and
cos
θ
ℓ
+
ℓ
−
>
−
0
.
95. These criteria were determined by
maximizing the quantity
ε/
√
N
SB
, where
ε
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
side-
band 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, in-
cluding those on the NN outputs.
To guard against possible background from
B
→
Dπ
and
B
→
Dη
decays where
D
→
Kπ
,
ππ
, or
ηπ
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
μ
+
μ
−
,
μ
±
π
, or
μ
±
η
with invariant mass in the range (1.83–1.89) GeV
/c
2
. The
probability of misidentifying a hadron as an electron is
negligible, and this requirement is therefore only applied
to the
μ
+
μ
−
modes.
Hadronic decays such as
B
+
→
π
+
π
−
π
+
, where two
pions are misidentified as muons, peak in both
m
ES
and
∆
E
similarly to signal due to the relatively small differ-
ence 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 deter-
mine its normalization and shape. This sample is con-
structed from events where one lepton candidate passes
the muon identification requirements but the other does
not. The events in these samples are weighted with par-
ticle misidentification probabilities determined from con-
trol samples in
B
A
B
AR
data. Studies of MC samples in-
dicate that this background is consequential only for the
πμ
+
μ
−
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
π
+
e
+
e
−
and
π
0
e
+
e
−
(
η
γγ
e
+
e
−
and
η
3
π
e
+
e
−
) candi-
dates, and 5–10% (25–30%) of
π
+
μ
+
μ
−
and
π
0
μ
+
μ
−
(
η
γγ
μ
+
μ
−
and
η
3
π
μ
+
μ
−
) candidates. There tend to be
more events containing multiple candidates in the
e
+
e
−
modes due to the bremsstrahlung recovery. For instance,
there may be multiple candidates arising from the same
π
+
e
+
e
−
combination where the bremsstrahlung photons
associated with the
e
+
or
e
−
are different.
To choose the best candidate we construct a ratio
L
R
from the
B
B
and continuum NN classifier output distri-
butions of the signal and background samples. The ratio
L
R
is defined as
L
R
(
x,y
) =
P
sig
B
B
(
x
) +
P
sig
cont
(
y
)
(
P
sig
B
B
(
x
) +
P
sig
cont
(
y
)) + (
P
bkg
B
B
(
x
) +
P
bkg
cont
(
y
))
(5)
where
P
sig
B
B
(
x
) (
P
sig
cont
(
y
)) is the probability that a sig-
nal candidate has a
B
B
(continuum) NN output value
of
x
(
y
). The quantities
P
bkg
B
B
(
x
) and
P
bkg
cont
(
y
) are de-
fined analogously for background events. Signal-like can-
didates have values of
L
R
near 1 while more background-
like 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
πℓ
+
ℓ
−
and 75–80% of the time for
ηℓ
+
ℓ
−
. 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 un-
binned 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 com-
ponents corresponding to the different contributions in
the data set. To model the various components, we use a
10
combination of products of one-dimensional parametric
PDFs, two-dimensional histograms, and two-dimensional
non-parametric shapes determined by a Gaussian ker-
nel density estimation algorithm (KEYS PDF) [34]. 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 compo-
nents.
A.
B
+
→
π
+
ℓ
+
ℓ
−
The
π
+
ℓ
+
ℓ
−
fit model involves four components: sig-
nal,
K
+
ℓ
+
ℓ
−
background,
K
0
S
/K
∗
ℓ
+
ℓ
−
background, and
combinatoric background. There is an additional compo-
nent in
B
+
→
π
+
μ
+
μ
−
representing the
B
+
→
π
+
π
+
π
−
hadronic peaking background. The
K
+
ℓ
+
ℓ
−
background
arises from decays where the kaon is misidentified as a
pion. The
K
+
misidentification rate is such that the
K
+
ℓ
+
ℓ
−
background in
π
+
ℓ
+
ℓ
−
is approximately the
same size as the expected SM
π
+
ℓ
+
ℓ
−
signal. Since the
K
+
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
+
→
π
+
ℓ
+
ℓ
−
candi-
dates and the
B
+
→
K
+
ℓ
+
ℓ
−
candidates in our data
set. The
K
+
misidentification background to
B
+
→
K
+
ℓ
+
ℓ
−
is included in the fit at a level fixed to the
B
+
→
K
+
ℓ
+
ℓ
−
yield using the known misidentification prob-
ability (which depends on the momentum of the kaon).
The
B
+
→
K
+
ℓ
+
ℓ
−
branching fraction that is measured
from the simultaneous fit of the
B
+
→
π
+
ℓ
+
ℓ
−
and
B
+
→
K
+
ℓ
+
ℓ
−
data samples provides an additional valida-
tion of our procedure, since this branching fraction has
been previously measured [37].
The
K
+
ℓ
+
ℓ
−
sample is selected in exactly the same
way as the
π
+
ℓ
+
ℓ
−
sample except the charged pion iden-
tification requirements are reversed and the
J/ψ
and
ψ
(2
S
) 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
π
+
e
+
e
−
surrounding the
J/ψ
mass,
m
μμ
>
3
.
20 GeV
/c
2
and 1
.
11
m
μμ
c
2
−
3
.
614
<
∆
E <
m
μμ
c
2
−
2
.
925 GeV for
π
+
μ
+
μ
−
surrounding the
J/ψ
mass, and
m
ℓℓ
>
3
.
75 GeV
/c
2
and 1
.
11
m
ℓℓ
c
2
−
4
.
305
<
∆
E < m
ℓℓ
c
2
−
3
.
525 GeV for both modes surrounding
the
ψ
(2
S
) mass. Also, the ∆
E
window is
−
200
<
∆
E <
250 MeV for
K
+
e
+
e
−
and
−
100
<
∆
E <
250 MeV for
K
+
μ
+
μ
−
.
The
π
+
ℓ
+
ℓ
−
and
K
+
ℓ
+
ℓ
−
background
m
ES
and ∆
E
distributions are modeled by products of one-dimensional
PDFs. The
π
+
ℓ
+
ℓ
−
signal and
K
+
ℓ
+
ℓ
−
background
m
ES
distributions are described by a Crystal Ball function
[35]. The
π
+
e
+
e
−
∆
E
signal distribution is modeled
by the sum of a Crystal Ball function and a Gaussian
which share a common mean, while the
π
+
μ
+
μ
−
signal
and both the
K
+
e
+
e
−
and
K
+
μ
+
μ
−
∆
E
distributions are
modeled by a modified Gaussian with tail parameters
whose functional form is given by
f
(∆
E
) = exp
[
−
(∆
E
−
μ
)
2
2
σ
L,R
α
L,R
+
α
L,R
(∆
E
−
μ
)
]
(6)
where
σ
L
and
α
L
(
σ
R
and
α
R
) are the width and tail pa-
rameters used when ∆
E < μ
(∆
E > μ
), respectively. A
two-dimensional histogram models the contribution from
B
→
K
0
S
/K
∗
ℓ
+
ℓ
−
decays. Combinatoric background is
described by the product of an ARGUS function [36] in
m
ES
with endpoint fixed to 5.29 GeV
/c
2
and a second-
order polynomial in ∆
E
. The
π
+
μ
+
μ
−
hadronic peaking
background component is modeled by a two-dimensional
KEYS PDF [34].
The PDF fit to the
K
+
ℓ
+
ℓ
−
sample contains a simi-
lar set of components. Signal
K
+
ℓ
+
ℓ
−
distributions are
modeled by the product of a Crystal Ball function in
m
ES
and the line shape of Eq. 6 in ∆
E
. The contri-
bution from other
b
→
sℓ
+
ℓ
−
decays is dominated by
B
→
K
∗
(
K
+
π
)
ℓ
+
ℓ
−
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
+
e
+
e
−
and a second-order polynomial for
K
+
μ
+
μ
−
in ∆
E
. A KEYS PDF models the hadronic
peaking background in
K
+
μ
+
μ
−
.
In both the
π
+
ℓ
+
ℓ
−
and
K
+
ℓ
+
ℓ
−
PDFs, the sig-
nal and combinatoric background yields float along with
the shapes of the combinatoric background PDFs. The
K
+
ℓ
+
ℓ
−
background yield in the
π
+
ℓ
+
ℓ
−
sample is con-
strained so that the
B
+
→
K
+
ℓ
+
ℓ
−
branching fractions
measured in the
π
+
ℓ
+
ℓ
−
and
K
+
ℓ
+
ℓ
−
samples are equal.
All fixed shapes and yields are determined from exclu-
sive MC samples except for the hadronic peaking back-
ground which uses a data control sample. Normalizations
of the
K
0
S
/K
∗
ℓ
+
ℓ
−
component of the
π
+
ℓ
+
ℓ
−
PDF and
of
K
∗
ℓ
+
ℓ
−
component in the
K
+
ℓ
+
ℓ
−
PDF are fixed
from efficiencies determined from MC samples and world
average branching fractions [37].
B.
B
0
→
π
0
ℓ
+
ℓ
−
The
B
0
→
π
0
ℓ
+
ℓ
−
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
(
→
π
0
π
0
)
ℓ
+
ℓ
−
decays is modeled by a
two-dimensional histogram. The product of an ARGUS
shape in
m
ES
with an exponential function in ∆
E
mod-
els the combinatoric background distribution. As in the
π
+
μ
+
μ
−
and
K
+
μ
+
μ
−
PDFs, there is an additional com-
ponent in the
π
0
μ
+
μ
−
fit model devoted to hadronic
peaking background which is described by a KEYS PDF.
In the fit, only the signal
π
0
ℓ
+
ℓ
−
and combinatoric
background yields along with the ARGUS slope parame-
ter and argument of the exponential float. The signal and
K
0
S
(
→
π
0
π
0
)
ℓ
+
ℓ
−
shapes are determined from fits to MC
samples, and the
K
0
S
(
→
π
0
π
0
)
ℓ
+
ℓ
−
normalization comes
11
from efficiencies taken from MC samples and world aver-
age branching fractions [37]. The shape and normaliza-
tion of the peaking hadronic component are determined
from a data control sample.
C.
B
0
→
ηℓ
+
ℓ
−
The
ηℓ
+
ℓ
−
fit model is simple, consisting of only three
components, and is the same for all four
ηℓ
+
ℓ
−
chan-
nels. 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 con-
taining a signal decay where the signal
B
is incorrectly
reconstructed, 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 con-
tribution is represented by a two-dimensional histogram
and its normalization is a fixed fraction of the signal
yield with the fraction determined from signal MC. The
self-cross-feed-to-signal ratio varies from 0.1–0.15 for the
η
γγ
channels to 0.25–0.3 for the
η
3
π
channels. Combi-
natoric background 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 indica-
tion of potential peaking background contributions from
b
→
sℓ
+
ℓ
−
decays or any other sources. The
η
γγ
ℓ
+
ℓ
−
yield and the
η
3
π
ℓ
+
ℓ
−
yield are constrained in the fit to
be consistent with the same
B
0
→
ηℓ
+
ℓ
−
branching frac-
tion. The signal yield, combinatoric 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
→
πℓ
+
ℓ
−
and
B
0
→
ηℓ
+
ℓ
−
modes we also present lepton-flavor averaged, isospin av-
eraged, and lepton-flavor and isospin averaged results.
The lepton-flavor averaged measurement of
B
(
B
+
→
π
+
ℓ
+
ℓ
−
) is the branching fraction obtained from a si-
multaneous fit to the
π
+
e
+
e
−
and
π
+
μ
+
μ
−
samples sub-
ject to the constraint
B
(
B
+
→
π
+
e
+
e
−
) =
B
(
B
+
→
π
+
μ
+
μ
−
). Here we have neglected the difference be-
tween the electron and muon masses. The measure-
ments of
B
(
B
0
→
π
0
ℓ
+
ℓ
−
) and
B
(
B
0
→
ηℓ
+
ℓ
−
) are
subject to a similar set of constraints and are deter-
mined in an analogous way. The isospin averaged branch-
ing fraction
B
(
B
→
πe
+
e
−
) is the measured value
of
B
(
B
+
→
π
+
e
+
e
−
) after simultaneously fitting the
π
+
e
+
e
−
and
π
0
e
+
e
−
samples subject to the constraint
B
(
B
+
→
π
+
e
+
e
−
) = (
τ
B
0
/
2
τ
B
+
)
B
(
B
0
→
π
0
e
+
e
−
)
where
τ
B
0
and
τ
B
+
are the mean lifetimes of the neutral
and charged
B
mesons, respectively [37]. An analogous
expression is applied for the
B
(
B
→
πμ
+
μ
−
) measure-
ment. The lepton-flavor and isospin averaged measure-
ment of
B
(
B
→
πℓ
+
ℓ
−
) is the value of
B
(
B
+
→
π
+
ℓ
+
ℓ
−
)
determined from a simultaneous 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 follow-
ing a method which utilizes the profile likelihood. Upper
limits at the
α
confidence level (CL) are set by scanning
the profile likelihood
λ
as a function of the signal branch-
ing fraction to determine where
−
2 ln
λ
changes by
α
per-
centile of a
χ
2
random variable with one degree of free-
dom. For
α
= 0
.
9 we look for a change in
−
2 ln
λ
of 1.642.
If the measured branching fraction is negative, we begin
our scan from zero rather than the minimum [38]. This
is a conservative approach that always produces physi-
cal,
i.e.,
non-negative, upper limits, even in the case of
low statistics. Systematic uncertainties are incorporated
into the limit by convolving the profile likelihood with a
Gaussian distribution whose width is equal to the total
systematic uncertainty.
V. OPTIMIZATION OF SELECTION
We simultaneously optimize the selection criteria for
the two NN outputs and the PID selection criteria for the
charged pions and leptons.
B
A
B
AR
employs algorithms
which use outputs from one or more multivariate clas-
sifiers to identify charged particle species. A few (3-6)
standard selections on the outputs of these algorithms
are used to identify particles of a given species with dif-
ferent efficiencies. Greater identification efficiencies typ-
ically imply greater misidentification rates. Due to this
trade-off, it is not clear
a priori
which selection is best for
a particular analysis. Therefore for each charged particle
type (
e
−
,
μ
−
,
π
+
) we optimize the PID requirements for
the leptons and pions along with the NN output criteria.
For the optimization we assume that
B
→
πℓ
+
ℓ
−
and
B
0
→
ηℓ
+
ℓ
−
occur near the center of the branching frac-
tion ranges expected in the SM. Under this assumption,
no statistically significant signal is expected, and the se-
lection is optimized to produce the smallest branching
fraction upper limit. We divide the
B
B
and continuum
NN output space into a grid and generate 2,500 paramet-
rically simulated data sets per grid point according to our
fit model. Each simulated data set is fit, and a branch-
ing fraction upper limit is calculated. The figure of merit
(FOM) for each point is the average branching fraction
upper limit determined from the 2,500 data sets, and we
take the combination of PID and NN output selection
producing the smallest FOM as optimal.
The results of the optimization show that the upper
limits are rather insensitive to the PID selection. Also,
12
in the two-dimensional NN output space, there is a re-
gion about the optimal selection where the FOM changes
slowly, giving confidence that our optimization procedure
is robust because the expected limits do not depend crit-
ically on the NN selection requirements.
The
e
+
e
−
(
μ
+
μ
−
) modes use the same electron (muon)
selection, while more efficient charged pion selection is
favored for
π
+
e
+
e
−
and
η
3
π
e
+
e
−
than
π
+
μ
+
μ
−
and
η
3
π
μ
+
μ
−
. Tighter selection is favored on the continuum
NN output than the
B
B
NN output. The optimization
favors looser requirements for the
ηℓ
+
ℓ
−
modes as the
size of the background in these channels is much smaller
than for
πℓ
+
ℓ
−
.
VI. FIT VALIDATION
We validate our fit methodology in three ways: (1)
generating an ensemble of data sets from our fit model
and fitting them with the same model (“pure pseudo-
experiments”), (2) generating and fitting an ensemble of
data sets with signal events from the
B
A
B
AR
MC simu-
lation embedded into the data set (“embedded pseudo-
experiments”), (3) extracting
B
→
J/ψπ
and
B
0
→
J/ψη
branching fractions from the
B
A
B
AR
data sample.
From our studies of both pure and embedded pseudo-
experiments, we find no significant source of bias in our
fit. Distributions of branching fractions and their errors
obtained from fits to these data sets are consistent with
expectations.
Measuring the
B
+
→
J/ψπ
+
,
B
0
→
J/ψπ
0
,
B
0
→
J/ψη
, and
B
+
→
J/ψK
+
branching fractions in the con-
trol sample of vetoed charmonium events allows us to val-
idate our fit methodology on data. We employ the same
fit model to extract these branching fractions as we do
for the
π
+
ℓ
+
ℓ
−
,
π
0
ℓ
+
ℓ
−
,
K
+
ℓ
+
ℓ
−
, and
ηℓ
+
ℓ
−
branching
fractions. Fixed shape parameters and yields are deter-
mined through fits to exclusive MC samples. We find
that all measurements are in good agreement with world
averages [37].
VII. SYSTEMATIC UNCERTAINTIES
Systematic uncertainties are included in the branching
fraction upper limit calculation by convolving the pro-
file likelihood with a Gaussian whose width is equal to
the total systematic uncertainty. The systematic uncer-
tainties are divided into “multiplicative” uncertainties,
which scale with the true value of the branching fraction,
and “additive” uncertainties, which are added to the true
value of the branching fraction, independent of its value.
A. Multiplicative uncertainties
We list the sources of multiplicative systematic uncer-
tainty below and their assigned values for each of the
πℓ
+
ℓ
−
and
ηℓ
+
ℓ
−
signal modes in Table I.
The systematic uncertainty in the measured number of
B
B
pairs is estimated to be 0.6% [39].
The difference between the
π
0
reconstruction efficiency
in data and MC has been studied in
τ
+
τ
−
decays where
one
τ
decays via the channel
τ
±
→
e
±
ν
ν
and the other
τ
decays via
τ
±
→
π
±
ν
or
τ
±
→
ρ
±
ν
with
ρ
±
recon-
structed as
π
±
π
0
. The
τ
±
→
ρ
±
ν
yields are roughly pro-
portional to the product of the
π
±
and
π
0
reconstruction
efficiencies, while the
τ
±
→
π
±
ν
yields are proportional
to the
π
±
reconstruction efficiencies. A correction pro-
portional to the ratio of the
τ
→
ρν
to
τ
→
πν
yields in
the data and MC samples is applied to better reproduce
the data reconstruction efficiency in MC simulation. The
uncertainty due to this correction is estimated as 3.0%
per
π
0
. We take the uncertainty in the
η
γγ
reconstruc-
tion efficiency associated with this correction to also be
3.0% per
η
γγ
.
A correction to the MC tracking efficiency was devel-
oped from the study of
τ
+
τ
−
decays where one
τ
has
a single charged daughter (1-prong decays) allowing the
event to be identified as a
τ
+
τ
−
event and the other
τ
has
three charged daughters (3-prong decays). By measuring
the event yields where the 3-prong
τ
has either two or
three tracks reconstructed, the track reconstruction effi-
ciency can be measured. This efficiency can be used to
correct the MC to match the efficiency measured in data.
The systematic uncertainty associated with this correc-
tion is estimated to be 0.3% per charged track taken to
be 100% correlated among tracks in the event.
We correct for the difference between the lepton PID
selection efficiencies in data and MC by measuring the
B
+
→
J/ψK
+
yields in data and
J/ψK
+
MC control
samples with and without the PID selection requirements
applied to both leptons. The ratios of the yields are
used to correct the lepton particle identification selection
efficiency derived from MC to match data. The error
on the correction is taken as the associated systematic
uncertainty, which ranges from 1.3–1.5%. The available
statistics in the samples used to calculate the correction
determine the size of the error which is associated with
it.
In an analogous procedure, we correct for the differ-
ence between the charged pion PID selection efficiency
obtained by measuring signal yields in high statistics
B
0
→
J/ψK
∗
0
(
→
K
−
π
+
) data and exclusive MC con-
trol samples with and without pion PID selection criteria
applied. A correction is derived and the error on the cor-
rection is taken as the associated systematic uncertainty.
These uncertainties are approximately 2.5% and 3.5% for
e
+
e
−
and
μ
+
μ
−
modes, respectively.
The high statistics of the
B
+
→
J/ψK
+
data and MC
control samples are again exploited to derive a correc-
tion for the NN output selection efficiency on MC. The
J/ψK
+
signal yields were measured with only the
B
B
NN output selection applied, only the continuum NN out-
put selection applied, and with both selections applied.
The error on the correction is taken as the associated