of 35
arXiv:1611.05624v1 [hep-ex] 17 Nov 2016
B
A
B
AR
-PUB-16/006
SLAC-PUB-16855
Measurement of the inclusive electron spectrum from
B
meson decays
and determination of
|
V
ub
|
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
INFN Sezione di Bari and Dipartimento di Fisica, Universit`
a di Bari, I-70126 Bari, Italy
G. Eigen
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
D. N. Brown and Yu. G. Kolomensky
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
V. E. Blinov
abc
, A. R. Buzykaev
a
, V. P. Druzhinin
ab
, V. B. Golubev
ab
, E. A. Kravchenko
ab
,
A. P. Onuchin
abc
, S. I. Serednyakov
ab
, Yu. I. Skovpen
ab
, E. P. Solodov
ab
, and K. Yu. Todyshev
ab
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630
090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 6300
92
c
, Russia
A. J. Lankford
University of California at Irvine, Irvine, California 926
97, USA
J. W. Gary and O. Long
University of California at Riverside, Riverside, Califor
nia 92521, USA
A. M. Eisner, W. S. Lockman, and W. Panduro Vazquez
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, J. Kim
,
T. S. Miyashita, P. Ongmongkolkul, F. C. Porter, and M. R ̈ohrken
California Institute of Technology, Pasadena, California
91125, USA
Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D. Sokoloff, and L. S
un
University of Cincinnati, Cincinnati, Ohio 45221, USA
J. G. Smith and S. R. Wagner
University of Colorado, Boulder, Colorado 80309, USA
D. Bernard and M. Verderi
2
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
, I. Garzia
ab
, E. Luppi
ab
, 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
A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Martellotti,
P. Patteri, I. M. Peruzzi, M. Piccolo, M. Rotondo, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
S. Passaggio and C. Patrignani
INFN Sezione di Genova, I-16146 Genova, Italy
B. Bhuyan
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, and S. Prell
Iowa State University, Ames, Iowa 50011, USA
H. Ahmed
Physics Department, Jazan University, Jazan 22822, Kingdo
m of Saudi Arabia
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, F. Le Diberder, A. M. Lutz, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
J. P. Coleman, E. Gabathuler, D. E. Hutchcroft, D. J. Payne, and
C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
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
Sw. Banerjee, 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 K.
R. Schubert
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
R. Cenci, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan
3
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib and S. H. Robertson
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
B. Dey
a
, 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,
§
and D. J. Summers
University of Mississippi, University, Mississippi 38677
, USA
P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo and C. Sciacca
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II, I-80126 Napoli, Italy
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
A. Gaz
a
, M. Margoni
ab
, M. Posocco
a
, G. Simi
ab
, 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, G. Calderini, J. C
hauveau, G. Marchiori, and J. Ocariz
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
M. Biasini
ab
, E. Manoni
a
, and A. Rossi
a
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
G. Casarosa
ab
, M. Chrzaszcz
a
, F. Forti
ab
,
M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, M. Rama
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
A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
F. Anulli
a
, R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, A. Pilloni
ab
, 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, S. Dittrich, O. Gr ̈unberg, M. Heß, T. Leddig, C. Voß,
and R. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
S. Emery and G. Vasseur
4
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
D. Aston, C. Cartaro, M. R. Convery, J. Dorfan, W. Dunwoodie, M
. Ebert, R. C. Field, B. G. Fulsom,
M. T. Graham, C. Hast, W. R. Innes, P. Kim, D. W. G. S. Leith, S. Luit
z, V. Luth, D. B. MacFarlane,
D. R. Muller, H. Neal, B. N. Ratcliff, A. Roodman, M. K. Sullivan, J. Va’vr
a, and W. J. Wisniewski
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
M. V. Purohit 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, and E. M. T. Puccio
Stanford University, Stanford, California 94305, USA
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 and R. F. Schwitters
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
, and D. Gamba
ab
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
L. Lanceri and L. Vitale
INFN Sezione di Trieste and Dipartimento di Fisica, Univers
it`a di Trieste, I-34127 Trieste, Italy
F. Martinez-Vidal and A. Oyanguren
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
J. Albert, A. Beaulieu, F. U. Bernlochner, G. J. King, R. Kowalewski,
T. Lueck, I. M. Nugent, J. M. Roney, and 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
R. Prepost and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
Based on the full
B
A
B
AR
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 CKM suppressed
B
X
u
decays from the CKM favored
B
X
c
decays, and from
various other backgrounds, and determine the total semilep
tonic branching fraction
B
(
B
Xeν
)
= (10
.
34
±
0
.
04
stat
±
0
.
26
syst
)%, averaged over
B
±
and
B
0
mesons. We determine the spectrum and
branching fraction for charmless
B
X
u
decays and extract the CKM element
|
V
ub
|
, by relying
on four different QCD calculations based on the Heavy Quark Ex
pansion. While experimentally,
5
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 fou
r predictions on the measurements
of the electron spectrum, the branching fraction, and the ex
traction of the CKM matrix element
|
V
ub
|
are presented, with the lower limit on the electron momentum
varied from 0.8 GeV
/c
to the
kinematic endpoint. We determine
|
V
ub
|
using each of these different calculations and find,
|
V
ub
|
=
(3
.
794
±
0
.
107
exp
+0
.
292
0
.
219 SF
+0
.
078
0
.
068 theory
)
×
10
3
(DN), (4
.
563
±
0
.
126
exp
+0
.
230
0
.
208 SF
+0
.
162
0
.
163 theory
)
×
10
3
(BLNP), (3
.
959
±
0
.
104
exp
+0
.
164
0
.
154 SF
+0
.
042
0
.
079 theory
)
×
10
3
(GGOU), (3
.
848
±
0
.
108
exp
+0
.
084
0
.
070 theory
)
×
10
3
(DGE), where the stated uncertainties refer to the experime
ntal uncertainties of the partial
branching fraction measurement, the shape function parame
ters, and the theoretical calculations.
PACS numbers: 13.20.He, 12.15.Hh, 12.38.Qk, 14.40.Nd
I. INTRODUCTION
Semileptonic decays of
B
mesons proceed via lead-
ing 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] el-
ements
|
V
cb
|
and
|
V
ub
|
. 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 deter-
mine the angles,
|
V
cb
|
normalizes the length of the sides,
and the ratio
|
V
ub
|
/
|
V
cb
|
determines the side opposite the
well-measured angle
β
. Thus, precise measurements of
|
V
cb
|
and
|
V
ub
|
are crucial to studies of flavor physics and
CP-violation in the quark sector.
There are two methods to determine
|
V
cb
|
and
|
V
ub
|
,
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
meson, the other based on inclusive decays
B
Xeν
,
where
X
refers to either
X
c
or
X
u
,
i.e.
, to any hadronic
state with or without charm, respectively.
The extractions of
|
V
cb
|
and
|
V
ub
|
from measured in-
clusive or exclusive semileptonic
B
meson decays rely
on different experimental techniques to isolate the signal
and on different theoretical descriptions of QCD contri-
butions to the underlying weak decay processes. Thus,
they have largely independent uncertainties, and provide
important cross checks of the methods and our under-
standing of these decays in general. At present, these
two methods result in values for
|
V
cb
|
and
|
V
ub
|
that each
differ by approximately three standard deviations [2].
In this paper, we present a measurement of the inclu-
Now at: Wuhan University, Wuhan 43072, China
Now at: Universit`a di Bologna and INFN Sezione di Bologna,
I-47921 Rimini, Italy
Now at: University of Huddersfield, Huddersfield HD1 3DH, UK
§
Now at: University of South Alabama, Mobile, Alabama 36688,
USA
Also at: Universit`a di Sassari, I-07100 Sassari, Italy
∗∗
Deceased
sive electron momentum spectrum and branching frac-
tion (BF) for the sum of all semileptonic
B
Xeν
de-
cays, as well as measurements of the spectrum and partial
BF for charmless semileptonic
B
X
u
decays. The
total rate for the
B
X
u
decays is suppressed by
about a factor 50 compared to the
B
X
c
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
signal extends to
2
.
6 GeV
/c
, while for the back-
ground
B
X
c
decays the kinematic endpoint is at
2
.
3 GeV
/c
. In the
Υ
(4
S
) 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.
To distinguish contributions of the CKM suppressed
B
X
u
decays from those of CKM favored
B
X
c
decays, and from various other backgrounds, we fit the
inclusive electron momentum spectrum, averaged over
B
±
and
B
0
mesons produced in the
Υ
(4
S
) decays [2, 4].
For this fit, we need predictions for the shape of the
B
X
u
spectrum. We have employed and stud-
ied four different QCD calculations based on the Heavy
Quark Expansion (HQE) [3]. 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
decays and extract the CKM el-
ement
|
V
ub
|
. While the experimental sensitivity to the
B
X
u
spectrum and to
|
V
ub
|
is primarily deter-
mined 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
Xeν
decays have been performed by several ex-
periments operating at the
Υ
(4
S
) resonance [2]. The
best estimate of this BF has been derived by HFAG [4],
6
based on a global fit to moments of the lepton momentum
and hadron mass spectra in
B
Xeν
decays (corrected
for
B
X
u
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
|
V
ub
|
have been performed at the
Υ
(4
S
) resonance, by
ARGUS [5], CLEO [6, 7],
B
A
B
AR
[8] and Belle [9], and ex-
periments at LEP operating at the
Z
0
resonance, L3 [10],
ALEPH [11], DELPHI [12], and OPAL [13]. Among the
|
V
ub
|
measurements based on exclusive semileptonic de-
cays [2], the most recent by the LHCb experiment at the
LHC is based on the baryon decay
Λ
b
pμν
[14].
This analysis is based on methods similar to the
one used in previous measurements of the lepton spec-
trum near the kinematic endpoint at the
Υ
(4
S
) reso-
nance [5, 6]. The results presented here supersede the
earlier
B
A
B
AR
publication [8], based on a partial data
sample.
II. DATA SAMPLE
The data used in this analysis were recorded with the
B
A
B
AR
detector [15] at the PEP-II energy-asymmetric
e
+
e
collider. A sample of 466.5 million
B
B
events, cor-
responding to an integrated luminosity of 424.9 fb
1
[16],
was collected at the
Υ
(4
S
) resonance. An additional sam-
ple of 44.4 fb
1
was recorded at a center-of-mass (c.m.)
energy 40 MeV below the
Υ
(4
S
) resonance,
i.e.
, just be-
low the threshold for
B
B
production. This off-resonance
data sample is used to subtract the non-
B
B
background
at the
Υ
(4
S
) resonance. The relative normalization of the
two data samples has been derived from luminosity mea-
surements, which are based on the number of detected
μ
+
μ
pairs and the QED cross section for
e
+
e
μ
+
μ
production, adjusted for the small difference in center-of-
mass energy.
III. DETECTOR
The
B
A
B
AR
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 cylin-
drical drift chamber, and the electromagnetic calorimeter
consisting of 6580 CsI(Tl) crystals. These detector com-
ponents 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 electro-
magnetic calorimeter 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 effi-
ciencies, and to extract the observed signal and back-
ground distributions. The sample of simulated generic
B
B
events exceeds the
B
B
data sample by about a fac-
tor of three.
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 charm-
less semileptonic decays,
B
X
u
, is based on calcu-
lations by De Fazio and Neubert (DN) [19]. This simu-
lation 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
decays with low-mass
hadrons,
X
u
=
π,ρ,ω,η,η
, make up about 20% of the
total charmless rate. They are simulated separately using
the ISGW2 model [20] and added to samples of decays
to non-resonant 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 mo-
mentum reproduce the inclusive calculation as closely as
possible. The hadronization of
X
u
with masses above
2
m
π
is performed according to JETSET [21].
The MC-generated electron-momentum distributions
for
B
X
u
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
(4
S
) rest frame, unless
stated otherwise. Above 2 GeV/c, the significant signal
contributions are from decays involving the light mesons
π
,
ρ
,
ω
,
η
, and
η
, in addition to some lower mass non-
resonant states
X
n
r
u
.
The simulation of the dominant
B
X
c
decays
is based on a variety of theoretical prescriptions. For
B
Deν
and
B
D
decays we use form factor
parameterizations [22–24], based on heavy quark effec-
tive theory (HQET). Decays to pseudoscalar mesons are
described in terms of one form factor, with a single pa-
rameter
ρ
2
D
. The differential decay rate for
B
D
is described by three amplitudes, with decay rates de-
pending on three parameters:
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
= 1 res-
onances,
D
∗∗
,
i
.
e
.
, two wide states
D
0
(2400),
D
1
(2430),
7
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
(4
S
) rest frame for charmless semileptonic
B
decays. The
full spectrum (solid line) is normalized to 1.0. The largest
con-
tribution is from decays involving higher-mass resonances
and
non-resonant states (
X
n
r
u
) (dash-three-dots). The exclusive
decays (scaled by a factor of five) are:
B
πeν
(dash-dots),
B
ρeν
(dashes),
B
ωeν
(dots),
B
ηeν
(long-dashes),
B
η
(long-dash-dots).
TABLE I: Average measured values [4] of the form factor
parameters for
B
Deν
and
B
D
decays, as defined
by Caprini, Lellouch, and Neubert [23].
B
Deν B
D
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
and two narrow states
D
1
(2420),
D
2
(2460), we have
adopted the parameterizations by Leibovich et al. [25]
and the HFAG averages [4] for the BFs. For decays to
non-resonant charm states
B
D
(
)
πeν
, we rely on the
prescription by Goity and Roberts [26] and the
B
A
B
AR
and Belle measurements of the BFs [4]. 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
decays are shown in Fig. 2. Above
2 GeV
/c
the dominant contributions are from semilep-
tonic decays involving the lower-mass charm mesons,
D
and
D
. Higher-mass and non-resonant charm states are
expected to contribute at lower electron momenta. The
relative contributions of the individual
B
X
c
decay
modes have been adjusted to the results of the fit to the
observed spectrum (see Section VI B 2).
The difference between the measured exclusive decays
B
(
D
(
)
,D
∗∗
,D
(
)
π
)
ℓν
and the inclusive rate for
semileptonic
B
decays to charm final states is (1
.
40
±
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
semileptonic decays to charm mesons,
B
X
c
with the
total rate (solid line) normalized to 1.0. The individual co
m-
ponents are:
B
Deν
(dash-dotted),
B
D
(dashed),
B
D
∗∗
+
B
D
(
)
πeν
(dotted). The highly suppressed
B
X
u
signal spectrum (long dashed) is shown for com-
parison.
0
.
28)% [27]. The decay rate for
̄
B
D
(
)
π
+
π
̄
ν
was measured by
B
A
B
AR
[28]. Based on these results
it was estimated that
̄
B
D
(
)
ππℓ
̄
ν
decays account
for up to half the difference between measured inclusive
and the sum of previously measured exclusive branch-
ing fractions. Beyond these observed decays, there are
missing decay modes, such as
B
D
(2550)
and
B
D
′∗
(2600)
. Candidates for the 2S radial excita-
tions were first observed by
B
A
B
AR
[31] and recently con-
firmed by LHCb [32]. We have adopted the masses and
widths (130
±
18 MeV
/c
2
and 93
±
14 MeV
/c
2
) measured
by
B
A
B
AR
[31], and have simulated these decays using the
form factor predictions [33]. Both
D
∗∗
and
D
(
)
may
contribute by their decays to
D
(
)
ππ
to
̄
B
D
(
)
ππℓ
̄
ν
decays. The decay rate for
D
1
Dππ
was measured
by Belle [29] and LHCb [30], LHCb also measured the
decay rate for
D
2
Dππ
. We account for contributions
from
̄
B
D
∗∗
e
̄
ν
,
̄
B
D
(
)
e
̄
ν
, and
̄
B
D
(
)
πe
̄
ν
decays to
̄
B
D
(
)
ππe
̄
ν
final states.
The main sources of secondary electrons are semilep-
tonic charm meson decays and
J/ψ
e
+
e
decays. The
J/ψ
momentum distribution was determined from this
data set and the MC simulation was adjusted to repro-
duce these measured spectra. The momentum spectra of
D
and
D
s
mesons produced in
B
B
decays were measured
earlier by
B
A
B
AR
[34] and the MC simulated spectra were
adjusted to reproduce these measurements.
8
V. CALCULATIONS OF
B
X
u
ℓν
DECAY RATE
While at the parton level the rate for
b
uℓν
decays
can be reliably calculated, the theoretical description of
inclusive semileptonic
B
X
u
ℓν
decays is more chal-
lenging. 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 back-
ground from the CKM-favored
B
X
c
ℓν
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 inclusion of additional perturbative and
non-perturbative effects. These calculations rely on HQE
and QCD factorization [35] and separate perturbative
and non-perturbative 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 [36, 37]. It is modeled us-
ing arbitrary functions for which low-order moments are
constrained by measurable parameters.
For the extraction of
|
V
ub
|
, we rely on ∆
B
(∆
p
), the par-
tial BF for
B
X
u
decays measured in the momen-
tum interval ∆
p
, and ∆
ζ
(∆
p
) = Γ
theory
×
f
u
(∆
p
)
/
|
V
ub
|
2
,
the theoretical predictions for partial decay rate normal-
ized by
|
V
ub
|
2
, measured in units of ps
1
:
|
V
ub
|
=
B
(∆
p
)
τ
b
ζ
(∆
p
)
.
(1)
Here
τ
b
= (1
.
580
±
0
.
005) ps is the average of the
B
0
and
B
+
lifetimes [2]. Γ
theory
is the total predicted decay rate
and
f
u
(∆
p
) refers to the fraction of the predicted decay
rate for the momentum interval ∆
p
.
In the following, we briefly describe four different the-
oretical methods to derive predictions for the partial and
total BFs. In the original work by De Fazio and Neu-
bert (DN) [19] and Kagan and Neubert [38] the deter-
mination of
|
V
ub
|
relies on the measurement of the elec-
tron spectrum for
B
X
u
and on the radiative de-
cays
B
X
s
γ
to derive the parameters of the lead-
ing SF. More comprehensive calculations were performed
by Bosch, Lange, Neubert, and Paz (BLNP) [39–45].
Calculations in the kinetic scheme were introduced by
Gambino, Giordano, Ossola, Uraltsev (GGOU) [46, 47].
BLNP and GGOU use
B
X
c
ℓν
and
B
X
s
γ
de-
cays to derive the parameters of the leading SF. Inclusive
spectra for
B
X
u
decays based on a calculation of
non-perturbative functions using Sudakov resummation
are presented in the dressed gluon exponentiation (DGE)
by Andersen and Gardi [48–51].
We assess individual contributions to the uncertainty
of the predictions of the decay rates by the different theo-
retical approaches. For this purpose, the authors of these
calculations have provided software to compute the dif-
ferential rates and to provide guidance for the assessment
of the uncertainties on the rate and thereby
|
V
ub
|
. We dif-
ferentiate uncertainties originating from the SF param-
eterization, including the sensitivity to
m
b
, the
b
-quark
mass, from the impact of the other purely theoretical un-
certainties. The uncertainty on
m
b
, the
b
-quark mass, has
a large impact. Weak annihilation could contribute sig-
nificantly at high momentum transfers (
q
2
). The impact
of weak annihilation is generally assumed to be asym-
metric, specifically, it is estimated to decrease
|
V
ub
|
by
O
(1
2)% [52].
A. DN calculations
While the calculations by BLNP are to supersede the
earlier work by DN, we use DN predictions for compar-
isons with previous measurements based on these predic-
tions and also for comparisons with other calculations.
The early DN calculations [19] predict the differen-
tial spectrum with
O
(
α
s
) corrections to leading order
in HQE. This approach is based on a parameteriza-
tion of the leading-power non-perturbative SF. The long-
distance interaction is described by a single light cone
distribution. In the region close to phase-space bound-
aries these non-perturbative corrections to the spectrum
are large. The prediction for the decay distribution is
obtained by a convolution of the parton model spec-
trum with the SF. The SF is described by two pa-
rameters
̄
Λ
SF
=
M
B
m
b
and
λ
SF
1
which were de-
termined from the measured photon energy moments
in
B
X
s
γ
decays [38]. We use
B
A
B
AR
measure-
ments [53] of the SF parameters,
m
SF
b
= (4
.
79
+0
.
06
0
.
10
) GeV
and
λ
SF
1
=
0
.
24
+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 ∆
ζ
(∆
p
), we rely on the DN
predictions for
f
u
(∆
p
), the fractions of
B
X
u
decays
in the interval ∆
p
, and an independent prediction for the
normalized total decay rate
ζ
= (65
.
7
+2
.
4
2
.
7
) ps
1
[49] (the
current value of
m
MS
b
= (4
.
18
±
0
.
03) GeV [2] is used to
calculate
ζ
). Earlier determinations of
ζ
can be found in
[52, 55–60].
The uncertainty on
|
V
ub
|
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
|
V
ub
|
is about 2
.
1% (for
p
e
>
0
.
8 GeV
/c
).
9
B. BLNP predictions
The BLNP calculations incorporate all known pertur-
bative and power corrections and interpolation between
the HQE and SF regions [39–41]. The differential and
partially integrated spectra for the inclusive
B
X
u
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. Formu-
lae for the triple differential rate of
B
X
u
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 deter-
mined by fits to moments of the hadron mass and lep-
ton energy spectra from inclusive
B
X
c
ℓν
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
(3 GeV) = 0
.
998
±
0
.
029 GeV
/c
2
. These parameters
are translated from the kinetic to the SF mass scheme
[43].
The impact of the uncertainties in these SFs are esti-
mated by varying the scale parameters
μ
i
and choices of
different subleading SF. The next-to-next-to-leading or-
der (NNLO) corrections were studied in detail [45]. In
extractions of
|
V
ub
|
, the choice
μ
i
= 1
.
5 GeV introduces
for the NNLO corrections significant shifts to lower val-
ues 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
im-
pact the agreement between the NLO and NNLO results.
We adopt the authors’ recommendation and use values
μ
i
= 2
.
0 GeV and
μ
h
= 4
.
25 GeV, as the default. The
results obtained in the SF mass scheme with the
m
c
con-
straint and
μ
i
= 2
.
0 GeV are
m
SF
b
= (4
.
561
±
0
.
023) GeV
and
μ
2 SF
π
= (0
.
149
±
0
.
040) GeV
2
[54]. The 1
σ
contours
for different choices of these parameters are presented in
Fig. 3.
In the BLNP framework, the extraction of
|
V
ub
|
is
based on the predicted partial rate
ζ
(∆
p
) [44] for
B
X
u
decays and the measurement of ∆
B
. The predic-
tions for total decay rate are:
ζ
= (73
.
5
±
1
.
9
SF
+5
.
5
4
.
9 theory
) ps
1
(2)
m
c
constraint,
μ
i
= 2
.
0 GeV
,
ζ
= (70
.
4
±
1
.
9
SF
+6
.
4
5
.
2 theory
) ps
1
(3)
m
c
constraint,
μ
i
= 1
.
5 GeV
,
ζ
= (74
.
5
±
2
.
7
SF
+5
.
5
4
.
9 theory
) ps
1
(4)
X
s
γ
constraint,
μ
i
= 2
.
0 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
π
μ
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
π
μ
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
+
X
s
γ
data (
μ
i
= 1
.
5 GeV,
μ
=
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 t
o
X
c
+
X
s
γ
data with
μ
i
= 2
.
0 GeV,
μ
=
μ
i
(dash-dotted line,
open square). The previous
B
A
B
AR
endpoint analysis [8] was
based on a
X
s
+
X
c
fit (long dashed line, open circle). The
contours represent ∆
χ
2
= 1.
ζ
= (71
.
4
±
2
.
7
SF
+6
.
5
5
.
3 theory
) ps
1
(5)
X
s
γ
constraint,
μ
i
= 1
.
5 GeV
.
The estimated SF uncertainty and total theoretical un-
certainty on
|
V
ub
|
are about 5
.
0% and 3
.
6%, respectively
(for
p
e
>
0
.
8 GeV
/c
).
C. GGOU predictions
The GGOU calculations [46, 47] of the triple dif-
ferential decay rate include all perturbative and non-
perturbative effects through
O
(
α
2
s
β
0
) and
O
(1
/m
3
b
). The
Fermi motion is parameterized 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 cut-off at
μ
= 1 GeV.
The SF parameters are determined by fits to mo-
ments of the hadron mass and lepton energy spectra
10
from inclusive
B
X
c
ℓν
decays, and either includ-
ing photon energy moments in
B
X
s
γ
decays or by
applying a constraint on the
c
quark mass. The re-
sults obtained in the kinetic scheme with the
m
c
con-
straint are
m
kin
b
(1
.
0 GeV) = (4
.
560
±
0
.
023) GeV and
μ
2 kin
π
(1
.
0 GeV) = (0
.
453
±
0
.
036) GeV
2
[54]. The 1
σ
con-
tours for the resulting SF parameters are presented in
Fig. 3.
The uncertainties are estimated as prescribed in [47].
To estimate the uncertainties of the higher order pertur-
bative 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 perturba-
tive and non-perturbative calculations. The uncertainty
due to weak annihilation is assumed to be asymmetric,
i.e.
, it tends to decrease
|
V
ub
|
. The uncertainty in the
modeling of the tail of the
q
2
distribution is estimated
by comparing two different assumptions for the range
(8
.
5
13
.
5) GeV
2
.
The extraction of
|
V
ub
|
is based on the measured par-
tial BF ∆
B
(∆
p
), and the GGOU prediction for the par-
tial normalized rate
ζ
(∆
p
). The predictions for the total
decay rate are,
ζ
= (67
.
2
±
1
.
6
SF
+2
.
5
1
.
3 theory
) ps
1
(6)
m
c
constraint,
ζ
= (67
.
9
±
2
.
3
SF
+2
.
8
5
.
1 theory
) ps
1
(7)
X
s
γ
constraint.
The estimated uncertainties on
|
V
ub
|
for the SF and the
total theoretical uncertainty are about 4
.
1% and 2
.
0%,
respectively (for
p
e
>
0
.
8 GeV/c).
D. DGE predictions
The Dressed Gluon Exponentiation (DGE) [48] is a
general formalism for inclusive distributions near the
kinematic boundaries. In this approach, the on-shell cal-
culation, converted to hadronic variables, is directly used
as an approximation to the decay spectrum without the
use of a leading-power non-perturbative function. The
perturbative expansion includes NNLO resummation in
momentum space as well as full
O
(
α
s
) and
O
(
α
2
s
β
0
) cor-
rections. The triple differential rate of
B
X
u
was
calculated [49, 51]. The DGE calculations rely on the
MS
renormalization scheme.
Based on the prescriptions by the authors [51], we
have estimated the uncertainties in these calculations and
their impact on
|
V
ub
|
. The theoretical uncertainty is ob-
tained by accounting for the uncertainty in
α
s
= 0
.
1184
±
0
.
0007 and
m
MS
b
= (4
.
18
±
0
.
03) GeV [2]. The renormal-
ization scale factor
μ/m
b
=1.0 is varied between 0.5 and
2.0, and the default values of (
C
3
/
2
,f
pv
) = (1
.
0
,
0
.
0) are
changed to (
C
3
/
2
,f
pv
) = (6
.
2
,
0
.
4) to assess the uncer-
tainties in the non-perturbative effects.
DGE predict the shape of differential electron spec-
trum, but do not provide a normalization. Thus we
rely on the DGE predictions for
f
u
(∆
p
), the fraction
of
B
X
u
decays in the interval ∆
p
, and an inde-
pendent prediction for the normalized total decay rate,
ζ
= (65
.
7
+2
.
4
2
.
7
) ps
1
[49] to derive ∆
ζ
(∆
p
) (the current
value of
m
MS
b
= (4
.
18
±
0
.
03) GeV [2] is used to calculate
ζ
).
The estimated total theoretical uncertainty on
|
V
ub
|
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 po-
lar 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, including
τ
+
τ
pair production and
e
+
e
q
̄
q
(
γ
) 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 de-
cay
J/ψ
e
+
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
+
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 high-
est 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:
R
2
, the ratio of the second to the zeroth Fox-
Wolfram moments [61], calculated from all detected
particles in the event (Fig. 4(a)).
11
l
2
=
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)).
cos
θ
e
roe
, the cosine of the angle between the elec-
tron 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
and
20% non-
B
B
events.
The positive output corresponds the selection with max-
imum significance level.
This selection results in an efficiency of 50
60% for
B
X
u
decays; the dependence on the electron mo-
mentum is shown in Fig. 6.
B. Background Subtraction
The selected sample of events from the on-resonance
data contains considerable background from
B
B
events
and non-
B
B
events. The
B
B
background is dominated
by primary electrons from semileptonic
B
decays and sec-
ondary electrons from decays of charm mesons and
J/ψ
mesons. Hadronic
B
decays contribute mostly via the
misidentification of charged particles. Non-
B
B
events
originate from
e
+
e
q
q
(
γ
) annihilation and lepton
pair production, especially
e
+
e
τ
+
τ
.
1. Non-
B
B
Background
To determine the momentum-dependent shape of the
non-
B
B
background, we perform a binned
χ
2
fit to
the off-resonance data in the momentum interval 0.8 to
3.5 GeV
/c
, combined with on-resonance data in the mo-
mentum interval 2.8 to 3.5 GeV
/c
,
i.e.,
above the end-
point for electrons from
B
decays. Since the c.m. energy
for the off-resonance data is 0
.
4% lower than for the on-
resonance data, we scale the electron momenta for the
off-resonance data by the ratio of the c.m. energies.
The relative normalization for the two data samples
[15, 16] is
r
(0)
L
=
s
OFF
s
ON
L
ON
dt
L
OFF
dt
= 9
.
560
±
0
.
003
stat
±
0
.
006
syst
,
where
s
and
Ldt
refer to the c.m. energy squared and
integrated luminosity of the on- and off-resonance data.
The statistical uncertainty of
r
L
of 0
.
03% is based on the
number of detected
μ
+
μ
pairs used for the measurement
of the integrated luminosity; the relative systematic un-
certainty on the ratio is estimated to be 0
.
06%.
The binned
χ
2
for the fit to the electron spectrum for
selected non-
B
B
events is defined as,
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Number of Events
500
1000
1500
2000
2500
3000
3500
3
10
×
(a)
2
R
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Ratio
0.96
0.98
1
1.02
1.04
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of Events
500
1000
1500
2000
2500
3000
3500
4000
4500
3
10
×
(b)
2
l
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ratio
0.96
0.98
1
1.02
1.04
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of Events
1000
2000
3000
4000
5000
3
10
×
(c)
e-roe
θ
cos
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ratio
0.96
0.98
1
1.02
1.04
FIG. 4: The number of events before the NN selection, as
a function of (a)
R
2
, (b)
l
2
, (c)
cosθ
e
roe
: on-resonance data
(triangles), the sum of simulated
B
B
events and off-resonance
data (solid histogram), MC simulated
B
B
events (dashed
histogram), and off-resonance data (dotted histogram). For
comparison, the distributions for
B
B
events with a signal
B
X
u
decay (dash-dotted histogram), are shown (scaled
by a factor of 50). Ratio = (
B
B
(MC) + off-resonance)/on-
resonance.