Measurement of the inclusive electron spectrum from
B
meson decays
and determination of
j
V
ub
j
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3
G. Eigen,
4
D. N. Brown,
5
Yu. G. Kolomensky,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
V. E. Blinov,
8a,8b,8c
A. R. Buzykaev,
8a
V. P. Druzhinin,
8a,8b
V. B. Golubev,
8a,8b
E. A. Kravchenko,
8a,8b
A. P. Onuchin,
8a,8b,8c
S. I. Serednyakov,
8a,8b
Yu. I. Skovpen,
8a,8b
E. P. Solodov,
8a,8b
K. Yu. Todyshev,
8a,8b
A. J. Lankford,
9
J. W. Gary,
10
O. Long,
10
A. M. Eisner,
11
W. S. Lockman,
11
W. Panduro Vazquez,
11
D. S. Chao,
12
C. H. Cheng,
12
B. Echenard,
12
K. T. Flood,
12
D. G. Hitlin,
12
J. Kim,
12
T. S. Miyashita,
12
P. Ongmongkolkul,
12
F. C. Porter,
12
M. Röhrken,
12
Z. Huard,
13
B. T. Meadows,
13
B. G. Pushpawela,
13
M. D. Sokoloff,
13
L. Sun,
13
,
†
J. G. Smith,
14
S. R. Wagner,
14
D. Bernard,
15
M. Verderi,
15
D. Bettoni,
16a
C. Bozzi,
16a
R. Calabrese,
16a,16b
G. Cibinetto,
16a,16b
E. Fioravanti,
16a,16b
I. Garzia,
16a,16b
E. Luppi,
16a,16b
V. Santoro,
16a
A. Calcaterra,
17
R. de Sangro,
17
G. Finocchiaro,
17
S. Martellotti,
17
P. Patteri,
17
I. M. Peruzzi,
17
M. Piccolo,
17
M. Rotondo,
17
A. Zallo,
17
S. Passaggio,
18
C. Patrignani,
18
,
‡
B. Bhuyan,
19
U. Mallik,
20
C. Chen,
21
J. Cochran,
21
S. Prell,
21
H. Ahmed,
22
A. V. Gritsan,
23
N. Arnaud,
24
M. Davier,
24
F. Le Diberder,
24
A. M. Lutz,
24
G. Wormser,
24
D. J. Lange,
25
D. M. Wright,
25
J. P. Coleman,
26
E. Gabathuler,
26
D. E. Hutchcroft,
26
D. J. Payne,
26
C. Touramanis,
26
A. J. Bevan,
27
F. Di Lodovico,
27
R. Sacco,
27
G. Cowan,
28
Sw. Banerjee,
29
D. N. Brown,
29
C. L. Davis,
29
A. G. Denig,
30
M. Fritsch,
30
W. Gradl,
30
K. Griessinger,
30
A. Hafner,
30
K. R. Schubert,
30
R. J. Barlow,
31
,§
G. D. Lafferty,
31
R. Cenci,
32
A. Jawahery,
32
D. A. Roberts,
32
R. Cowan,
33
R. Cheaib,
34
S. H. Robertson,
34
B. Dey,
35a
N. Neri,
35a
F. Palombo,
35a,35b
L. Cremaldi,
36
R. Godang,
36
,¶
D. J. Summers,
36
P. Taras,
37
G. De Nardo,
38
C. Sciacca,
38
G. Raven,
39
C. P. Jessop,
40
J. M. LoSecco,
40
K. Honscheid,
41
R. Kass,
41
A. Gaz,
42a
M. Margoni,
42a,42b
M. Posocco,
42a
G. Simi,
42a,42b
F. Simonetto,
42a,42b
R. Stroili,
42a,42b
S. Akar,
43
E. Ben-Haim,
43
M. Bomben,
43
G. R. Bonneaud,
43
G. Calderini,
43
J. Chauveau,
43
G. Marchiori,
43
J. Ocariz,
43
M. Biasini,
44a,44b
E. Manoni,
44a
A. Rossi,
44a
G. Batignani,
45a,45b
S. Bettarini,
45a,45b
M. Carpinelli,
45a,45b
,**
G. Casarosa,
45a,45b
M. Chrzaszcz,
45a
F. Forti,
45a,45b
M. A. Giorgi,
45a,45b
A. Lusiani,
45a,45c
B. Oberhof,
45a,45b
E. Paoloni,
45a,45b
M. Rama,
45a
G. Rizzo,
45a,45b
J. J. Walsh,
45a
A. J. S. Smith,
46
F. Anulli,
47a
R. Faccini,
47a,47b
F. Ferrarotto,
47a
F. Ferroni,
47a,47b
A. Pilloni,
47a,47b
G. Piredda,
47a
,*
C. Bünger,
48
S. Dittrich,
48
O. Grünberg,
48
M. Heß,
48
T. Leddig,
48
C. Voß,
48
R. Waldi,
48
T. Adye,
49
F. F. Wilson,
49
S. Emery,
50
G. Vasseur,
50
D. Aston,
51
C. Cartaro,
51
M. R. Convery,
51
J. Dorfan,
51
W. Dunwoodie,
51
M. Ebert,
51
R. C. Field,
51
B. G. Fulsom,
51
M. T. Graham,
51
C. Hast,
51
W. R. Innes,
51
P. Kim,
51
D. W. G. S. Leith,
51
S. Luitz,
51
V. Luth,
51
D. B. MacFarlane,
51
D. R. Muller,
51
H. Neal,
51
B. N. Ratcliff,
51
A. Roodman,
51
M. K. Sullivan,
51
J. Va
’
vra,
51
W. J. Wisniewski,
51
M. V. Purohit,
52
J. R. Wilson,
52
A. Randle-Conde,
53
S. J. Sekula,
53
M. Bellis,
54
P. R. Burchat,
54
E. M. T. Puccio,
54
M. S. Alam,
55
J. A. Ernst,
55
R. Gorodeisky,
56
N. Guttman,
56
D. R. Peimer,
56
A. Soffer,
56
S. M. Spanier,
57
J. L. Ritchie,
58
R. F. Schwitters,
58
J. M. Izen,
59
X. C. Lou,
59
F. Bianchi,
60a,60b
F. De Mori,
60a,60b
A. Filippi,
60a
D. Gamba,
60a,60b
L. Lanceri,
61
L. Vitale,
61
F. Martinez-Vidal,
62
A. Oyanguren,
62
J. Albert,
63
A. Beaulieu,
63
F. U. Bernlochner,
63
G. J. King,
63
R. Kowalewski,
63
T. Lueck,
63
I. M. Nugent,
63
J. M. Roney,
63
N. Tasneem,
63
T. J. Gershon,
64
P. F. Harrison,
64
T. E. Latham,
64
R. Prepost,
65
and S. L. Wu
65
(
B
A
B
AR
Collaboration)
1
Laboratoire d
’
Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3
INFN Sezione di Bari and Dipartimento di Fisica, Università 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 Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
8b
Novosibirsk State University, Novosibirsk 630090, Russia
8c
Novosibirsk State Technical University, Novosibirsk 630092, Russia
9
University of California at Irvine, Irvine, California 92697, USA
10
University of California at Riverside, Riverside, California 92521, USA
11
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
12
California Institute of Technology, Pasadena, California 91125, USA
13
University of Cincinnati, Cincinnati, Ohio 45221, USA
14
University of Colorado, Boulder, Colorado 80309, USA
15
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
16a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
16b
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy
PHYSICAL REVIEW D
95,
072001 (2017)
2470-0010
=
2017
=
95(7)
=
072001(23)
072001-1
© 2017 American Physical Society
17
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
18
INFN Sezione di Genova, I-16146 Genova, Italy
19
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
20
University of Iowa, Iowa City, Iowa 52242, USA
21
Iowa State University, Ames, Iowa 50011, USA
22
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
23
Johns Hopkins University, Baltimore, Maryland 21218, USA
24
Laboratoire de l
’
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11, Centre Scientifique
d
’
Orsay, F-91898 Orsay Cedex, France
25
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
26
University of Liverpool, Liverpool L69 7ZE, United Kingdom
27
Queen Mary, University of London, London, E1 4NS, United Kingdom
28
University of London, Royal Holloway and Bedford New College,
Egham, Surrey TW20 0EX, United Kingdom
29
University of Louisville, Louisville, Kentucky 40292, USA
30
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
31
University of Manchester, Manchester M13 9PL, United Kingdom
32
University of Maryland, College Park, Maryland 20742, USA
33
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
34
McGill University, Montréal, Québec, Canada H3A 2T8
35a
INFN Sezione di Milano, I-20133 Milano, Italy
35b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
36
University of Mississippi, University, Mississippi 38677, USA
37
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
38
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,
Università di Napoli Federico II, I-80126 Napoli, Italy
39
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
40
University of Notre Dame, Notre Dame, Indiana 46556, USA
41
Ohio State University, Columbus, Ohio 43210, USA
42a
INFN Sezione di Padova, I-35131 Padova, Italy
42b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
43
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS,
Université Pierre et Marie Curie-Paris6, Université Denis Diderot-Paris7,
F-75252 Paris, France
44a
INFN Sezione di Perugia, I-06123 Perugia, Italy
44b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
45a
INFN Sezione di Pisa, I-56127 Pisa, Italy
45b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
45c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
46
Princeton University, Princeton, New Jersey 08544, USA
47a
INFN Sezione di Roma, I-00185 Roma, Italy
47b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
48
Universität Rostock, D-18051 Rostock, Germany
49
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
50
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
51
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
52
University of South Carolina, Columbia, South Carolina 29208, USA
53
Southern Methodist University, Dallas, Texas 75275, USA
54
Stanford University, Stanford, California 94305, USA
55
State University of New York, Albany, New York 12222, USA
56
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
57
University of Tennessee, Knoxville, Tennessee 37996, USA
58
University of Texas at Austin, Austin, Texas 78712, USA
59
University of Texas at Dallas, Richardson, Texas 75083, USA
60a
INFN Sezione di Torino, I-10125 Torino, Italy
60b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
61
INFN Sezione di Trieste and Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
62
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
072001 (2017)
072001-2
63
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
64
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
65
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 22 November 2016; published 5 April 2017)
Based on the full
BABAR
data sample of 466.5 million
B
̄
B
pairs, we present measurements of the
electron spectrum from semileptonic
B
meson decays. We fit the inclusive electron spectrum to distinguish
Cabibbo-Kobayashi-Maskawa (CKM) suppressed
B
→
X
u
e
ν
decays from the CKM-favored
B
→
X
c
e
ν
decays, and from various other backgrounds, and determine the total semileptonic branching fraction
B
ð
B
→
Xe
ν
Þ¼ð
10
.
34
0
.
04
stat
0
.
26
syst
Þ
%
, averaged over
B
and
B
0
mesons. We determine the
spectrum and branching fraction for charmless
B
→
X
u
e
ν
decays and extract the CKM element
j
V
ub
j
,by
relying on four different QCD calculations based on the heavy quark expansion. While experimentally,
the electron momentum region above
2
.
1
GeV
=c
is favored, because the background is relatively low, the
uncertainties for the theoretical predictions are largest in the region near the kinematic endpoint. Detailed
studies to assess the impact of these four predictions on the measurements of the electron spectrum,
the branching fraction, and the extraction of the CKM matrix element
j
V
ub
j
are presented, with the lower
limit on the electron momentum varied from
0
.
8
GeV
=c
to the kinematic endpoint. We determine
j
V
ub
j
using each of these different calculations and find,
j
V
ub
j¼ð
3
.
794
0
.
107
exp
þ
0
.
292
−
0
.
219
SF
þ
0
.
078
−
0
.
068
theory
Þ
×
10
−
3
(De Fazio and Neubert),
ð
4
.
563
0
.
126
exp
þ
0
.
230
−
0
.
208
SF
þ
0
.
162
−
0
.
163
theory
Þ
×
10
−
3
(Bosch, Lange, Neubert,
and Paz),
ð
3
.
959
0
.
104
exp
þ
0
.
164
−
0
.
154
SF
þ
0
.
042
−
0
.
079
theory
Þ
×
10
−
3
(Gambino, Giordano, Ossola, and Uraltsev),
ð
3
.
848
0
.
108
exp
þ
0
.
084
−
0
.
070
theory
Þ
×
10
−
3
(dressed gluon exponentiation), where the stated uncertainties refer
to the experimental uncertainties of the partial branching fraction measurement, the shape function
parameters, and the theoretical calculations.
DOI:
10.1103/PhysRevD.95.072001
I. INTRODUCTION
Semileptonic decays of
B
mesons proceed via leading
order weak interactions. They are expected to be free of
non-Standard-Model contributions and therefore play a
critical role in the determination of the Cabibbo-
Kobayashi-Maskawa (CKM) quark-mixing matrix
[1]
ele-
ments
j
V
cb
j
and
j
V
ub
j
. In the Standard Model (SM), the
CKM elements satisfy unitarity relations that can be
illustrated geometrically as triangles in the complex plane.
For one of these triangles,
CP
asymmetries determine the
angles,
j
V
cb
j
normalizes the length of the sides, and the
ratio
j
V
ub
j
=
j
V
cb
j
determines the side opposite the well-
measured angle
β
. Thus, precise measurements of
j
V
cb
j
and
j
V
ub
j
are crucial to studies of flavor physics and
CP
violation in the quark sector.
There are two methods to determine
j
V
cb
j
and
j
V
ub
j
, one
based on exclusive semileptonic
B
decays, where the
hadron in the final state is a
D; D
;D
or
π
;
ρ
;
ω
;
η
;
η
0
meson, the other based on inclusive decays
B
→
Xe
ν
,
where
X
refers to either
X
c
or
X
u
, i.e., to any hadronic state
with or without charm, respectively.
The extractions of
j
V
cb
j
and
j
V
ub
j
from measured
inclusive or exclusive semileptonic
B
meson decays rely
on different experimental techniques to isolate the signal
and on different theoretical descriptions of QCD contribu-
tions to the underlying weak decay processes. Thus, they
have largely independent uncertainties, and provide impor-
tant cross-checks of the methods and our understanding of
these decays in general. At present, these two methods
result in values for
j
V
cb
j
and
j
V
ub
j
that each differ by
approximately 3 standard deviations
[2]
.
In this paper, we present a measurement of the inclusive
electron momentum spectrum and branching fraction (BF)
for the sum of all semileptonic
B
→
Xe
ν
decays, as well as
measurements of the spectrum and partial BF for charmless
semileptonic
B
→
X
u
e
ν
decays. The total rate for the
B
→
X
u
e
ν
decays is suppressed by about a factor 50 compared
to the
B
→
X
c
e
ν
decays. This background dominates the
signal spectrum except near the high-momentum endpoint.
In the rest frame of the
B
meson, the electron spectrum for
B
→
X
u
e
ν
signal extends to
∼
2
.
6
GeV
=c
, while for the
background
B
→
X
c
e
ν
decays the kinematic endpoint is at
∼
2
.
3
GeV
=c
. In the
Υ
ð
4
S
Þ
rest frame, the two
B
mesons
are produced with momenta of
300
MeV
=c
which extends
the electron endpoint by about
200
MeV
=c
. The endpoint
region above
2
.
3
GeV
=c
, which covers only about 10% of
the total electron spectrum, is more suited for the exper-
imental isolation of the charmless decays.
*
Deceased
†
Present address: Wuhan University, Wuhan 43072, China.
‡
Present address: Università di Bologna and INFN Sezione di
Bologna, I-47921 Rimini, Italy.
§
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
¶
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
**
Present address: Università di Sassari, I-07100 Sassari, Italy.
MEASUREMENT OF THE INCLUSIVE ELECTRON
...
PHYSICAL REVIEW D
95,
072001 (2017)
072001-3
To distinguish contributions of the CKM suppressed
B
→
X
u
e
ν
decays from those of CKM-favored
B
→
X
c
e
ν
decays, and from various other backgrounds, we fit the
inclusive electron momentum spectrum, averaged over
B
and
B
0
mesons produced in the
Υ
ð
4
S
Þ
decays
[2,3]
. For this
fit, we need predictions for the shape of the
B
→
X
u
e
ν
spectrum. We have employed and studied four different
QCD calculations based on the heavy quark expansion
(HQE)
[4]
. The upper limit of the fitted range of the
momentum spectrum is fixed at
3
.
5
GeV
=c
, while the
lower limit extends down to
0
.
8
GeV
=c
, covering up to
90% of the total signal electron spectrum. From the fitted
spectrum we derive the partial BF for charmless
B
→
X
u
e
ν
decays and extract the CKM element
j
V
ub
j
. While the
experimental sensitivity to the
B
→
X
u
e
ν
spectrum and to
j
V
ub
j
is primarily determined from the spectrum above
2
.
1
GeV
=c
, due to very large backgrounds at lower
momenta, the uncertainties for the theoretical predictions
are largest in the region near the kinematic endpoint.
Studies of the impact of various theoretical predictions
on the measurements are presented.
Measurements of the total inclusive lepton spectrum in
B
→
Xe
ν
decays have been performed by several experi-
ments operating at the
Υ
ð
4
S
Þ
resonance
[2]
. The best
estimate of this BF has been derived by HFAG
[3]
, based on
a global fit to moments of the lepton momentum and
hadron mass spectra in
B
→
Xe
ν
decays (corrected for
B
→
X
u
e
ν
decays) either with a constraint on the
c
-quark mass
or by including photon energy moments in
B
→
X
s
γ
decays
in the fit. Inclusive measurements of
j
V
ub
j
have been
performed at the
Υ
ð
4
S
Þ
resonance, by ARGUS
[5]
,
CLEO
[6,7]
,
BABAR
[8]
and Belle
[9]
, and experiments
at LEP operating at the
Z
0
resonance, L3
[10]
, ALEPH
[11]
, DELPHI
[12]
, and OPAL
[13]
. Among the
j
V
ub
j
measurements based on exclusive semileptonic decays
[2]
,
the most recent by the LHCb experiment at the LHC is
based on the baryon decay
Λ
b
→
p
μν
[14]
.
This analysis is based on methods similar to the one used
in previous measurements of the lepton spectrum near the
kinematic endpoint at the
Υ
ð
4
S
Þ
resonance
[5,6]
. The
results presented here supersede the earlier
BABAR
publication
[8]
, based on a partial data sample.
II. DATA SAMPLE
The data used in this analysis were recorded with the
BABAR
detector
[15]
at the PEP-II energy-asymmetric
e
þ
e
−
collider. A sample of 466.5 million
B
̄
B
events,
corresponding to an integrated luminosity of
424
.
9
fb
−
1
[16]
, was collected at the
Υ
ð
4
S
Þ
resonance. An additional
sample of
44
.
4
fb
−
1
was recorded at a center-of-mass (c.m.)
energy 40 MeV below the
Υ
ð
4
S
Þ
resonance, i.e., just below
the threshold for
B
̄
B
production. This off-resonance data
sample is used to subtract the non-
B
̄
B
background at the
Υ
ð
4
S
Þ
resonance. The relative normalization of the two
data samples has been derived from luminosity measure-
ments, which are based on the number of detected
μ
þ
μ
−
pairs and the QED cross section for
e
þ
e
−
→
μ
þ
μ
−
pro-
duction, adjusted for the small difference in center-of-mass
energy.
III. DETECTOR
The
BABAR
detector has been described in detail else-
where
[15]
. The most important components for this study
are the charged-particle tracking system, consisting of a
five-layer silicon vertex tracker and a 40-layer cylindrical
drift chamber, and the electromagnetic calorimeter consist-
ing of 6580 CsI(Tl) crystals. These detector components
operated in a 1.5 T magnetic field parallel to the beam.
Electron candidates are selected on the basis of the ratio of
the energy deposited in the calorimeter to the track
momentum, the shower shape, the energy loss in the drift
chamber, and the angle of signals in a ring-imaging
Cerenkov detector. Showers in the electromagnetic calo-
rimeter with energies below 50 MeV which are dominated
by beam background are not used in this analysis.
IV. SIMULATION
We use Monte Carlo (MC) techniques to simulate the
production and decay of
B
mesons and the detector
response
[17]
, to estimate signal and background efficien-
cies, and to extract the observed signal and background
distributions. The sample of simulated generic
B
̄
B
events
exceeds the
B
̄
B
data sample by about a factor of 3.
The MC simulations include radiative effects such as
bremsstrahlung in the detector material and QED initial and
final state radiation
[18]
. Information from studies of
selected control data samples on efficiencies and resolu-
tions is used to adjust and thereby improve the accuracy of
the simulation. Adjustments for small variations of the
beam energy over time have been included.
In the MC simulations, the BFs for hadronic
B
and
D
meson decays are based on values reported in the Review of
Particle Physics
[2]
. The simulation of inclusive charmless
semileptonic decays,
B
→
X
u
e
ν
, is based on calculations
by De Fazio and Neubert (DN)
[19]
. This simulation
produces a continuous mass spectrum of hadronic states
X
u
. To reproduce and test predictions by other authors
this spectrum is reweighted in the course of the analysis.
Three-body
B
→
X
u
e
ν
decays with low-mass hadrons,
X
u
¼
π
;
ρ
;
ω
;
η
;
η
0
, make up about 20% of the total charm-
less rate. They are simulated separately using the ISGW2
model
[20]
and added to samples of decays to nonresonant
and higher-mass resonant states
X
n
r
u
, so that the cumulative
distributions of the hadron mass, the momentum transfer
squared, and the electron momentum reproduce the inclu-
sive calculation as closely as possible. The hadronization of
X
u
with masses above
2
m
π
is performed according to
JETSET
[21]
.
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
072001 (2017)
072001-4
The MC-generated electron momentum distributions for
B
→
X
u
e
ν
decays are shown in Fig.
1
for individual decay
modes and for their sum. Here and throughout the paper,
the electron momentum and all other kinematic variables
are measured in the
Υ
ð
4
S
Þ
rest frame, unless stated
otherwise. Above
2
GeV
=
c, the significant signal contri-
butions are from decays involving the light mesons
π
,
ρ
,
ω
,
η
, and
η
0
, in addition to some lower mass nonresonant
states
X
n
r
u
.
The simulation of the dominant
B
→
X
c
e
ν
decays is
based on a variety of theoretical prescriptions. For
B
→
De
ν
and
B
→
D
e
ν
decays we use form factor para-
metrizations
[22
–
24]
, based on heavy quark effective
theory. Decays to pseudoscalar mesons are described in
terms of one form factor, with a single parameter
ρ
2
D
. The
differential decay rate for
B
→
D
e
ν
is described by three
amplitudes, with decay rates depending on three parame-
ters:
ρ
2
D
,
R
1
, and
R
2
. These parameters have been measured
by many experiments; we use the average values presented
in Table
I
.
For the simulation of decays to higher-mass
L
¼
1
resonances,
D
, i.e., two wide states
D
0
ð
2400
Þ
,
D
0
1
ð
2430
Þ
, and two narrow states
D
1
ð
2420
Þ
,
D
2
ð
2460
Þ
,
we have adopted the parametrizations by Leibovich
et al.
[25]
and the HFAG averages
[3]
for the BFs. For decays to
nonresonant charm states
B
→
D
ðÞ
π
e
ν
, we rely on the
prescription by Goity and Roberts
[26]
and the
BABAR
and
Belle measurements of the BFs
[3]
. The simulations of
these decays include the full angular dependence of
the rate.
The shapes of the MC-generated electron spectra for
individual
B
→
X
c
e
ν
decays are shown in Fig.
2
.Above
2
GeV
=c
the dominant contributions are from semileptonic
decays involving the lower-mass charm mesons,
D
and
D
.
Higher-mass and nonresonant charm states are expected to
contribute at lower electron momenta. The relative con-
tributions of the individual
B
→
X
c
e
ν
decay modes have
been adjusted to the results of the fit to the observed
spectrum (see Sec.
VI B 2
).
The difference between the measured exclusive decays
B
→
ð
D
ðÞ
;D
;D
ðÞ
π
Þ
l
ν
and the inclusive rate for semi-
leptonic
B
decays to charm final states is
ð
1
.
40
0
.
28
Þ
%
[27]
. The decay rate for
̄
B
→
D
ðÞ
π
þ
π
−
l
−
̄
ν
was measured
by
BABAR
[28]
. Based on these results it was estimated that
̄
B
→
D
ðÞ
ππ
l
−
̄
ν
decays account for up to half the differ-
ence between measured inclusive and the sum of previously
measured exclusive branching fractions. Beyond these
observed decays, there are missing decay modes, such as
B
→
D
0
ð
2550
Þ
e
ν
and
B
→
D
0
ð
2600
Þ
e
ν
. Candidates for
the 2S radial excitations were first observed by
BABAR
[29]
and recently confirmed by LHCb
[30]
. We have adopted the
masses and widths (
130
18
MeV
=c
2
and
93
14
MeV
=c
2
)
measured by
BABAR
[29]
, and have simulated these decays
using the form factor predictions
[27]
. Both
D
and
D
0ðÞ
may contribute by their decays to
D
ðÞ
ππ
to
̄
B
→
D
ðÞ
ππ
l
−
̄
ν
Electron Momentum (GeV/c)
0
0.5
1
1.5
2
2.5
3
GeV/c
1
dp
dN
N
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
FIG. 1. MC-generated electron momentum spectra in the
Υ
ð
4
S
Þ
rest frame for charmless semileptonic
B
decays. The full
spectrum (solid line) is normalized to 1.0. The largest contribu-
tion is from decays involving higher-mass resonances and
nonresonant states (
X
n
r
u
) (dash-three-dotted). The exclusive de-
cays (scaled by a factor of 5) are
B
→
π
e
ν
(dash-dotted),
B
→
ρ
e
ν
(dashed),
B
→
ω
e
ν
(dotted),
B
→
η
e
ν
(long-dashed),
B
→
η
0
e
ν
(long-dash-dotted).
Electron Momentum (GeV/c)
0
0.5
1
1.5
2
2.5
3
GeV/c
1
dp
dN
N
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
FIG. 2. MC-generated electron momentum spectra for semi-
leptonic decays to charm mesons,
B
→
X
c
e
ν
with the total rate
(solid line) normalized to 1.0. The individual components are:
B
→
De
ν
(dash-dotted),
B
→
D
e
ν
(dashed),
B
→
D
e
ν
þ
B
→
D
ðÞ
π
e
ν
(dotted). The highly suppressed
B
→
X
u
e
ν
signal
spectrum (long dashed) is shown for comparison.
TABLE I. Average measured values
[3]
of the form factor
parameters for
B
→
De
ν
and
B
→
D
e
ν
decays, as defined by
Caprini, Lellouch, and Neubert
[23]
.
B
→
De
ν
B
→
D
e
ν
ρ
2
D
1
.
185
0
.
054
ρ
2
D
1
.
207
0
.
026
R
1
1
.
406
0
.
033
R
2
0
.
853
0
.
020
MEASUREMENT OF THE INCLUSIVE ELECTRON
...
PHYSICAL REVIEW D
95,
072001 (2017)
072001-5
decays. The decay rate for
D
1
→
D
ππ
was measured by
Belle
[31]
and LHCb
[32]
, LHCb also measured the decay
rate for
D
2
→
D
ππ
. We account for contributions from
̄
B
→
D
e
−
̄
ν
,
̄
B
→
D
0ðÞ
e
−
̄
ν
, and
̄
B
→
D
ðÞ
π
e
−
̄
ν
decays to
̄
B
→
D
ðÞ
ππ
e
−
̄
ν
final states.
The main sources of secondary electrons are semilep-
tonic charm meson decays and
J=
ψ
→
e
þ
e
−
decays. The
J=
ψ
momentum distribution was determined from this data
set and the MC simulation was adjusted to reproduce these
measured spectra. The momentum spectra of
D
and
D
s
mesons produced in
B
̄
B
decays were measured earlier by
BABAR
[33]
and the MC simulated spectra were adjusted to
reproduce these measurements.
V. CALCULATIONS OF
B
→
X
u
l
ν
DECAY RATE
While at the parton level the rate for
b
→
u
l
ν
decays can
be reliably calculated, the theoretical description of inclu-
sive semileptonic
B
→
X
u
l
ν
decays is more challenging.
Based on HQE the total inclusive rate can be predicted with
an uncertainty of about 5%, however, this rate is very
difficult to measure due to very large background from the
CKM-favored
B
→
X
c
l
ν
decays. On the other hand, in the
endpoint region where the signal to background ratio is
much more favorable, calculations of the differential decay
rates are much more complicated. They require the inclu-
sion of additional perturbative and nonperturbative effects.
These calculations rely on HQE and QCD factorization
[34]
and separate perturbative and nonperturbative effects
by using an expansion in powers of
1
=m
b
and a non-
perturbative shape function (SF) which is
a priori
unknown. This function accounts for the motion of the
b
quark inside the
B
meson, and to leading order, it should be
universal for all transitions of a
b
quark to a light
quark
[35,36]
. It is modeled using arbitrary functions for
which low-order moments are constrained by measurable
parameters.
For the extraction of
j
V
ub
j
, we rely on
Δ
B
ð
Δ
p
Þ
, the
partial BF for
B
→
X
u
e
ν
decays measured in the momen-
tum interval
Δ
p
, and
Δ
ζ
ð
Δ
p
Þ¼
Γ
theory
×
f
u
ð
Δ
p
Þ
=
j
V
ub
j
2
,
the theoretical predictions for partial decay rate normalized
by
j
V
ub
j
2
, measured in units of ps
−
1
:
j
V
ub
j¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Δ
B
ð
Δ
p
Þ
τ
b
Δ
ζ
ð
Δ
p
Þ
s
:
ð
1
Þ
Here
τ
b
¼ð
1
.
580
0
.
005
Þ
ps is the average of the
B
0
and
B
þ
lifetimes
[2]
.
Γ
theory
is the total predicted decay rate and
f
u
ð
Δ
p
Þ
refers to the fraction of the predicted decay rate for
the momentum interval
Δ
p
.
In the following, we briefly describe four different
theoretical methods to derive predictions for the partial
and total BFs. In the original work by De Fazio and Neubert
[19]
and Kagan and Neubert
[37]
the determination of
j
V
ub
j
relies on the measurement of the electron spectrum for
B
→
X
u
e
ν
and on the radiative decays
B
→
X
s
γ
to derive
the parameters of the leading SF. More comprehensive
calculations were performed by Bosch, Lange, Neubert,
and Paz (BLNP)
[38
–
44]
. Calculations in the kinetic
scheme were introduced by Gambino, Giordano, Ossola,
Uraltsev (GGOU)
[45,46]
. BLNP and GGOU use
B
→
X
c
l
ν
and
B
→
X
s
γ
decays to derive the parameters of the
leading SF. Inclusive spectra for
B
→
X
u
e
ν
decays based
on a calculation of nonperturbative functions using
Sudakov resummation are presented in the dressed gluon
exponentiation (DGE) by Andersen and Gardi
[47
–
50]
.
We assess individual contributions to the uncertainty of
the predictions of the decay rates by the different theoretical
approaches. For this purpose, the authors of these calcu-
lations have provided software to compute the differential
rates and to provide guidance for the assessment of the
uncertainties on the rate and thereby
j
V
ub
j
. We differentiate
uncertainties originating from the SF parametrization,
including the sensitivity to
m
b
, the
b
-quark mass, from
the impact of the other purely theoretical uncertainties. The
uncertainty on
m
b
, the
b
-quark mass, has a large impact.
Weak annihilation could contribute significantly at high-
momentum transfers (
q
2
). The impact of weak annihilation
is generally assumed to be asymmetric, specifically, it is
estimated to decrease
j
V
ub
j
by
O
ð
1
–
2
Þ
%
[51]
.
A. DN calculations
While the calculations by BLNP are to supersede
the earlier work by DN, we use DN predictions for
comparisons with previous measurements based on
these predictions and also for comparisons with other
calculations.
The early DN calculations
[19]
predict the differential
spectrum with
O
ð
α
s
Þ
corrections to leading order in HQE.
This approach is based on a parametrization of the leading-
power nonperturbative SF. The long-distance interaction is
described by a single light-cone distribution. In the region
close to phase-space boundaries these nonperturbative
corrections to the spectrum are large. The prediction for
the decay distribution is obtained by a convolution of the
parton model spectrum with the SF. The SF is described by
two parameters
̄
Λ
SF
¼
M
B
−
m
b
and
λ
SF
1
which were
determined from the measured photon energy moments
in
B
→
X
s
γ
decays
[37]
. We use
BABAR
measurements
[52]
of the SF parameters,
m
SF
b
¼ð
4
.
79
þ
0
.
06
−
0
.
10
Þ
GeV and
λ
SF
1
¼
−
0
.
24
þ
0
.
09
−
0
.
18
GeV
2
with 94% correlation.
DN predict the shape of the differential electron spec-
trum, but they do not provide a normalization. Thus to
determine the partial rates
Δ
ζ
ð
Δ
p
Þ
, we rely on the DN
predictions for
f
u
ð
Δ
p
Þ
, the fractions of
B
→
X
u
e
ν
decays
in the interval
Δ
p
, and an independent prediction for the
normalized total decay rate
ζ
¼ð
65
.
7
þ
2
.
4
−
2
.
7
Þ
ps
−
1
[48]
[the
current value of
m
MS
b
¼ð
4
.
18
0
.
03
Þ
GeV
[2]
is used to
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
072001 (2017)
072001-6
calculate
ζ
]. Earlier determinations of
ζ
can be found in
[51,53
–
58]
.
The uncertainty on
j
V
ub
j
due to the application of the
shape function is derived from 10% variations of
̄
Λ
SF
and
λ
SF
1
, as prescribed by the authors. The estimated total
theoretical uncertainty on
j
V
ub
j
is about 2.1% (for
p
e
>
0
.
8
GeV
=c
).
B. BLNP predictions
The BLNP calculations incorporate all known perturba-
tive and power corrections and interpolation between the
HQE and SF regions
[38
–
40]
. The differential and partially
integrated spectra for the inclusive
B
→
X
u
l
ν
decay are
calculated in perturbative theory at next-to-leading order
(NLO) in renormalization-group, and at the leading
power in the heavy quark expansion. Formulas for the
triple differential rate of
B
→
X
u
l
ν
and for the
B
→
X
s
γ
photon spectrum are convolution integrals of weight
functions with the shape function renormalized at the
intermediate scale
μ
i
. The ansatz for the leading SF
depends on two parameters,
m
b
and
μ
2
π
; subleading SFs
are treated separately.
The SF parameters in the kinetic scheme are determined
by fits to moments of the hadron mass and lepton
energy spectra from inclusive
B
→
X
c
l
ν
decays and
either additional photon energy moments in
B
→
X
s
γ
decays or by applying a constraint on the
c
-quark mass,
m
MS
c
ð
3
GeV
Þ¼
0
.
998
0
.
029
GeV
=c
2
. These parameters
are translated from the kinetic to the SF mass scheme
[42]
.
The impact of the uncertainties in these SFs are
estimated by varying the scale parameters
μ
i
and choices
of different subleading SF. The next-to-next-to-leading
order (NNLO) corrections were studied in detail
[44]
.In
extractions of
j
V
ub
j
, the choice
μ
i
¼
1
.
5
GeV introduces
for the NNLO corrections significant shifts to lower values
of the partial decay rates, by
∼
15%
–
20%
, while at the same
time reducing the perturbative uncertainty on the scale
μ
h
.
At NLO, small changes of the value of
μ
i
impact the
agreement between the NLO and NNLO results. We
adopt the authors
’
recommendation and use values
μ
i
¼
2
.
0
GeV and
μ
h
¼
4
.
25
GeV, as the default. The results
obtained in the SF mass scheme with the
m
c
constraint
and
μ
i
¼
2
.
0
GeV are
m
SF
b
¼ð
4
.
561
0
.
023
Þ
GeV and
μ
2
SF
π
¼ð
0
.
149
0
.
040
Þ
GeV
2
[59]
. The
1
σ
contours for
different choices of these parameters are presented in
Fig.
3
.
In the BLNP framework, the extraction of
j
V
ub
j
is based
on the predicted partial rate
ζ
ð
Δ
p
Þ
[43]
for
B
→
X
u
e
ν
decays and the measurement of
Δ
B
. The predictions for
total decay rate are
ζ
¼ð
73
.
5
1
.
9
SF
þ
5
.
5
−
4
.
9
theory
Þ
ps
−
1
m
c
constraint
;
μ
i
¼
2
.
0
GeV
;
ð
2
Þ
ζ
¼ð
70
.
4
1
.
9
SF
þ
6
.
4
−
5
.
2
theory
Þ
ps
−
1
m
c
constraint
;
μ
i
¼
1
.
5
GeV
;
ð
3
Þ
ζ
¼ð
74
.
5
2
.
7
SF
þ
5
.
5
−
4
.
9
theory
Þ
ps
−
1
X
s
γ
constraint
;
μ
i
¼
2
.
0
GeV
;
ð
4
Þ
ζ
¼ð
71
.
4
2
.
7
SF
þ
6
.
5
−
5
.
3
theory
Þ
ps
−
1
X
s
γ
constraint
;
μ
i
¼
1
.
5
GeV
:
ð
5
Þ
The estimated SF uncertainty and total theoretical uncer-
tainty on
j
V
ub
j
are about 5.0% and 3.6%, respectively
(for
p
e
>
0
.
8
GeV
=c
).
C. GGOU predictions
The GGOU calculations
[45,46]
of the triple differ-
ential decay rate include all perturbative and nonpertur-
bative effects through
O
ð
α
2
s
β
0
Þ
and
O
ð
1
=m
3
b
Þ
.TheFermi
motion is parametrized in terms of a single light-cone
function for each structure function and for any value of
q
2
, accounting for all subleading effects. The calculations
are based on the kinetic mass scheme, with a hard cutoff
at
μ
¼
1
GeV.
(GeV)
b
m
4.5 4.52 4.54 4.56 4.58 4.6 4.62 4.64 4.66 4.68 4.7
)
2
(GeV
2
0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
0.54
kinetic
(GeV)
b
m
4.5 4.52 4.54 4.56 4.58 4.6 4.62 4.64 4.66 4.68 4.7
)
2
(GeV
2
0.05
0.1
0.15
0.2
0.25
0.3
0.35
shape function
FIG. 3. The shape function parameters
m
b
and
μ
2
π
in the kinetic
scheme (HFAG 2014): fit to
X
c
data with constraint on the
c
-quark mass (solid line, solid triangle); fit to
X
c
þ
X
s
γ
data
(
μ
i
¼
1
.
5
GeV,
μ
¼
μ
i
) (dotted line, solid square). Translation
of fit to
X
c
data with constraint on the
c
-quark mass (short dashed
line, open triangle); translation of fit to
X
c
þ
X
s
γ
data with
μ
i
¼
2
.
0
GeV,
μ
¼
μ
i
(dash-dotted line, open square). The
previous
BABAR
endpoint analysis
[8]
was based on a
X
s
þ
X
c
fit (long dashed line, open circle). The contours represent
Δ
χ
2
¼
1
.
MEASUREMENT OF THE INCLUSIVE ELECTRON
...
PHYSICAL REVIEW D
95,
072001 (2017)
072001-7
The SF parameters are determined by fits to moments
of the hadron mass and lepton energy spectra from
inclusive
B
→
X
c
l
ν
decays, and either including photon
energy moments in
B
→
X
s
γ
decays or by applying a
constraint on the
c
-quark mass. The results obtained in the
kinetic scheme with the
m
c
constraint are
m
kin
b
ð
1
.
0
GeV
Þ¼
ð
4
.
560
0
.
023
Þ
GeV and
μ
2
kin
π
ð
1
.
0
GeV
Þ¼ð
0
.
453
0
.
036
Þ
GeV
2
[59]
. The
1
σ
contours for the resulting SF
parameters are presented in Fig.
3
.
The uncertainties are estimated as prescribed in
[46]
.
To estimate the uncertainties of the higher order perturba-
tive corrections, the hard cutoff is varied in the range
0
.
7
<
μ
<
1
.
3
GeV. Combined with an estimate of 40% of
the uncertainty in
α
2
s
β
0
corrections, this is taken as the
overall uncertainty of these higher order perturbative and
nonperturbative calculations. The uncertainty due to weak
annihilation is assumed to be asymmetric, i.e., it tends to
decrease
j
V
ub
j
. The uncertainty in the modeling of the tail
of the
q
2
distribution is estimated by comparing two
different assumptions for the range
ð
8
.
5
–
13
.
5
Þ
GeV
2
.
The extraction of
j
V
ub
j
is based on the measured partial
BF
Δ
B
ð
Δ
p
Þ
, and the GGOU prediction for the partial
normalized rate
ζ
ð
Δ
p
Þ
. The predictions for the total decay
rate are
ζ
¼ð
67
.
2
1
.
6
SF
þ
2
.
5
−
1
.
3
theory
Þ
ps
−
1
m
c
constraint
;
ð
6
Þ
ζ
¼ð
67
.
9
2
.
3
SF
þ
2
.
8
−
5
.
1
theory
Þ
ps
−
1
X
s
γ
constraint
:
ð
7
Þ
The estimated uncertainties on
j
V
ub
j
for the SF and the total
theoretical uncertainty are about 4.1% and 2.0%, respec-
tively (for
p
e
>
0
.
8
GeV
=
c).
D. DGE predictions
The DGE
[47]
is a general formalism for inclusive
distributions near the kinematic boundaries. In this
approach, the on-shell calculation, converted to hadronic
variables, is directly used as an approximation to the decay
spectrum without the use of a leading-power nonperturba-
tive function. The perturbative expansion includes
NNLO resummation in momentum space as well as full
O
ð
α
s
Þ
and
O
ð
α
2
s
β
0
Þ
corrections. The triple differential rate
of
B
→
X
u
l
ν
was calculated
[48,50]
. The DGE calculations
rely on the
MS renormalization scheme.
Based on the prescriptions by the authors
[50]
,wehave
estimated the uncertainties in these calculations and their
impact on
j
V
ub
j
. The theoretical uncertainty is obtained by
accounting for the uncertainty in
α
s
¼
0
.
1184
0
.
0007
and
m
MS
b
¼ð
4
.
18
0
.
03
Þ
GeV
[2]
. The renormalization
scale factor
μ
=m
b
¼
1
.
0
is varied between 0.5 and 2.0, and
the default values of
ð
C
3
=
2
;f
pv
Þ¼ð
1
.
0
;
0
.
0
Þ
are changed
to
ð
C
3
=
2
;f
pv
Þ¼ð
6
.
2
;
0
.
4
Þ
to assess the uncertainties in the
nonperturbative effects.
DGE predict the shape of differential electron spectrum,
but do not provide a normalization. Thus we rely on the
DGE predictions for
f
u
ð
Δ
p
Þ
, the fraction of
B
→
X
u
e
ν
decays in the interval
Δ
p
, and an independent prediction
for the normalized total decay rate,
ζ
¼ð
65
.
7
þ
2
.
4
−
2
.
7
Þ
ps
−
1
[48]
to derive
Δ
ζ
ð
Δ
p
Þ
[the current value of
m
MS
b
¼ð
4
.
18
0
.
03
Þ
GeV
[2]
is used to calculate
ζ
].
The estimated total theoretical uncertainty on
j
V
ub
j
for
DGE calculations is about 2.2% (for
p
e
>
0
.
8
GeV
=c
).
VI. ANALYSIS
A. Event Selection
To select
B
̄
B
events with a candidate electron from a
semileptonic
B
meson decay, we apply the following criteria:
Electron selection:
We select events with at least one electron
candidate in the c.m. momentum range
0
.
8
<p
cms
<
5
.
0
GeV
=c
and within the polar angle acceptance in the
laboratory frame of
−
0
.
71
<
cos
θ
e
<
0
.
90
. Within these
constraints the identification efficiency for electrons exceeds
94%. The average hadron misidentification rate is about 0.1%.
Track multiplicity:
To suppress background from non-
B
̄
B
events, primarily low-multiplicity QED processes, includ-
ing
τ
þ
τ
−
pair production and
e
þ
e
−
→
q
̄
q
ð
γ
Þ
annihilation
(
q
represents a
u
,
d
,
s
or
c
quark), we reject events with
fewer than four charged tracks.
J=
ψ
suppression
: To reject electrons from the decay
J=
ψ
→
e
þ
e
−
, we combine the selected electron with other
electron candidates of opposite charge and reject the event
if the invariant mass of any pair is consistent with a
J=
ψ
decay,
3
.
00
<m
e
þ
e
−
<
3
.
15
GeV
=c
2
.
If an event in the remaining sample has more than one
electron that passes this selection, the one with the highest
momentum is chosen as the signal candidate.
To further suppress non-
B
̄
B
events we build a neural
network (NN) with the following input variables which rely
on the momenta of all charged particles and energies of
photons above 50 MeV detected in the event:
(i)
R
2
, the ratio of the second to the zeroth Fox-
Wolfram moments
[60]
, calculated from all detected
particles in the event [Fig.
4(a)
].
(ii)
l
2
¼
P
i
p
i
cos
2
θ
i
=
2
E
beam
, where the sum includes
all detected particles except the electron, and
θ
i
is the
angle between the momentum of particle
i
and the
direction of the electron momentum [Fig.
4(b)
].
(iii) cos
θ
e
−
roe
, the cosine of the angle between the
electron momentum and the axis of the thrust of
the rest of the event [Fig.
4(c)
].
The distribution of the NN output is shown in Fig.
5
.
Only events with positive output values are retained, this
selects
∼
90%
of
B
→
X
u
e
ν
and
∼
20%
non-
B
̄
B
events. The
positive output corresponds the selection with maximum
significance level.
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
072001 (2017)
072001-8