of 23
Study of

B
!
X
u


decays in
B

B
events tagged by a fully reconstructed
B
-meson decay and determination of
j
V
ub
j
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
M. Martinelli,
3a,3b
D. A. Milanes,
3a
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
K. Tackmann,
5
H. Koch,
6
T. Schroeder,
6
D. J. Asgeirsson,
7
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
A. Khan,
8
V. E. Blinov,
9
A. R. Buzykaev,
9
V. P. Druzhinin,
9
V. B. Golubev,
9
E. A. Kravchenko,
9
A. P. Onuchin,
9
S. I. Serednyakov,
9
Yu. I. Skovpen,
9
E. P. Solodov,
9
K. Yu. Todyshev,
9
A. N. Yushkov,
9
M. Bondioli,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
D. P. Stoker,
10
H. Atmacan,
11
J. W. Gary,
11
F. Liu,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
T. Schalk,
13
B. A. Schumm,
13
A. Seiden,
13
C. H. Cheng,
14
D. A. Doll,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
M. S. Dubrovin,
15
Z. Huard,
15
B. T. Meadows,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
M. Nagel,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
B. Spaan,
18
M. J. Kobel,
19
K. R. Schubert,
19
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
P. J. Clark,
21
S. Playfer,
21
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
23
M. Munerato,
22a,22b
M. Negrini,
22a,22b
A. Petrella,
22a,22b
L. Piemontese,
22a
V. Santoro,
22a,22b
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
M. Nicolaci,
23
P. Patteri,
23
I. M. Peruzzi,
23,
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
B. Bhuyan,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. J. Edwards,
27
A. Adametz,
28
J. Marks,
28
U. Uwer,
28
F. U. Bernlochner,
29
M. Ebert,
29
H. M. Lacker,
29
T. Lueck,
29
P. D. Dauncey,
30
M. Tibbetts,
30
P. K. Behera,
31
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
E. I. Rosenberg,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
P. Roudeau,
34
M. H. Schune,
34
A. Stocchi,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
I. Bingham,
36
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
A. Hafner,
40
E. Prencipe,
40
K. E. Alwyn,
41
D. Bailey,
41
R. J. Barlow,
41,
G. Jackson,
41
G. D. Lafferty,
41
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
G. Simi,
42
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
D. Lindemann,
45
P. M. Patel,
45
S. H. Robertson,
45
M. Schram,
45
P. Biassoni,
46a,46b
A. Lazzaro,
46a,46b
V. Lombardo,
46a
N. Neri,
46a,46b
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
§
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
G. Raven,
50
H. L. Snoek,
50
C. P. Jessop,
51
K. J. Knoepfel,
51
J. M. LoSecco,
51
W. F. Wang,
51
K. Honscheid,
52
R. Kass,
52
J. Brau,
53
R. Frey,
53
N. B. Sinev,
53
D. Strom,
53
E. Torrence,
53
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
E. Ben-Haim,
55
M. Bomben,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
S. Sitt,
55
M. Biasini,
56a,56b
E. Manoni,
56a,56b
S. Pacetti,
56a,56b
A. Rossi,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b
M. Carpinelli,
57a,57b,
k
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
B. Oberhof,
57a,57b
E. Paoloni,
57a,57b
A. Perez,
57a
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
58
C. Lu,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
G. Cavoto,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
C. Bu
̈
nger,
60
O. Gru
̈
nberg,
60
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60
R. Waldi,
60
T. Adye,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
H. Kim,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
P. Lewis,
63
S. Li,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
I. Ofte,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
R. H. Schindler,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
J. Va’vra,
63
A. P. Wagner,
63
M. Weaver,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
A. K. Yarritu,
63
C. C. Young,
63
V. Ziegler,
63
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
A. Randle-Conde,
65
S. J. Sekula,
65
M. Bellis,
66
J. F. Benitez,
66
P. R. Burchat,
66
T. S. Miyashita,
66
M. S. Alam,
67
J. A. Ernst,
67
R. Gorodeisky,
68
N. Guttman,
68
D. R. Peimer,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
R. Eckmann,
70
J. L. Ritchie,
70
A. M. Ruland,
70
C. J. Schilling,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
PHYSICAL REVIEW D
86,
032004 (2012)
1550-7998
=
2012
=
86(3)
=
032004(23)
032004-1
Ó
2012 American Physical Society
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
V. Azzolini,
74
F. Martinez-Vidal,
74
A. Oyanguren,
74
H. Ahmed,
75
J. Albert,
75
Sw. Banerjee,
75
H. H. F. Choi,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
C. Lindsay,
75
I. M. Nugent,
75
J. M. Roney,
75
R. J. Sobie,
75
N. Tasneem,
75
T. J. Gershon,
76
P. F. Harrison,
76
T. E. Latham,
76
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
77
Y. Pan,
77
R. Prepost,
77
and S. L. Wu
77
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
19
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
21
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
22b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstrasse 15, D-12489 Berlin, Germany
30
Imperial College London, London, SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Universite
́
Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London, E1 4NS, United Kingdom
38
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
40
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
41
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
46a
INFN Sezione di Milano, I-20133 Milano, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032004 (2012)
032004-2
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
55
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-56127 Pisa, Italy
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
58
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 5 December 2011; published 7 August 2012)
We report measurements of partial branching fractions for inclusive charmless semileptonic
B
decays

B
!
X
u


and the determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix element
j
V
ub
j
. The
analysis is based on a sample of
467

10
6

ð
4
S
Þ!
B

B
decays recorded with the
BABAR
detector at the
PEP-II
e
þ
e

storage rings. We select events in which the decay of one of the
B
mesons is fully
reconstructed and an electron or a muon signals the semileptonic decay of the other
B
meson. We measure
partial branching fractions

B
in several restricted regions of phase space and determine the CKM
element
j
V
ub
j
based on different QCD predictions. For decays with a charged lepton momentum
p

>
1
:
0 GeV
in the
B
meson rest frame, we obtain

B
¼ð
1
:
80

0
:
13
stat

0
:
15
sys

0
:
02
theo
Þ
10

3
from a
fit to the two-dimensional
M
X

q
2
distribution. Here,
M
X
refers to the invariant mass of the final state
hadron
X
and
q
2
is the invariant mass squared of the charged lepton and neutrino. From this measurement
*
Now at Temple University, Philadelphia, PA 19122, USA.
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
Now at the University of Huddersfield, Huddersfield HD1 3DH, United Kingdom.
§
Now at University of South Alabama, Mobile, AL 36688, USA.
k
Also with Universita
`
di Sassari, Sassari, Italy.
STUDY OF

B
!
X
u


DECAYS
...
PHYSICAL REVIEW D
86,
032004 (2012)
032004-3
we extract
j
V
ub
j¼ð
4
:
33

0
:
24
exp

0
:
15
theo
Þ
10

3
as the arithmetic average of four results obtained
from four different QCD predictions of the partial rate. We separately determine partial branching
fractions for

B
0
and
B

decays and derive a limit on the isospin breaking in

B
!
X
u


decays.
DOI:
10.1103/PhysRevD.86.032004
PACS numbers: 13.20.He, 12.15.Hh, 12.38.Qk, 14.40.Nd
I. INTRODUCTION
A principal physics goal of the
BABAR
experiment is to
establish
CP
violation in
B
meson decays and to test
whether the observed effects are consistent with the stan-
dard model (SM) expectations. In the SM,
CP
-violating
effects result from an irreducible phase in the Cabibbo–
Kobayashi–Maskawa (CKM) quark-mixing matrix [
1
,
2
].
Precise determinations of the magnitude of the matrix
element
j
V
ub
j
will permit more stringent tests of the SM
mechanism for
CP
violation. This is best illustrated in
terms of the unitarity triangle [
3
], the graphical represen-
tation of one of the unitarity conditions of the CKM matrix,
for which the side opposite to the angle

is proportional to
the ratio
j
V
ub
j
=
j
V
cb
j
. The best way to determine
j
V
ub
j
is to
measure the decay rate for

B
!
X
u


(here
X
refers to a
hadronic final state and the index
c
or
u
indicates whether
this state carries charm or not), which is proportional
to
j
V
ub
j
2
.
There are two approaches to these measurements, based
on either inclusive or exclusive measurements of semi-
leptonic decays. The experimental uncertainties on the
methods are largely independent, and the extraction of
j
V
ub
j
from the measured branching fractions relies on
different sets of calculations of the hadronic contributions
to the matrix element. For quite some time, the results of
measurements of
j
V
ub
j
from inclusive and exclusive decays
have been only marginally consistent [
4
,
5
]. Global fits
[
6
,
7
] testing the compatibility of the measured angles and
sides with the unitarity triangle of the CKM matrix reveal
small differences that might indicate potential deviations
from SM expectations. Therefore, it is important to per-
form redundant and improved measurements, employing
different experimental techniques and a variety of theoreti-
cal calculations, to better assess the accuracy of the theo-
retical and experimental uncertainties.
Although inclusive branching fractions exceed those of
individual exclusive decays by an order of magnitude, the
most challenging task for inclusive measurements is the
discrimination between the rare charmless signal and
the much more abundant decays involving charmed
mesons. To improve the signal-to-background ratio, the
events are restricted to selected regions of phase space.
Unfortunately these restrictions lead to difficulties in cal-
culating partial branching fractions. They impact the con-
vergence of heavy quark expansions (HQE) [
8
,
9
], enhance
perturbative and nonperturbative QCD corrections, and
thus lead to significantly larger theoretical uncertainties
in the determination of
j
V
ub
j
.
We report herein measurements of partial branching
fractions (

B
) for inclusive charmless semileptonic
B
meson decays,

B
!
X
u


[
10
]. This analysis extends the
event selection and methods employed previously by
BABAR
to a larger data set [
11
]. We tag

ð
4
S
Þ!
B

B
events with a fully reconstructed hadronic decay of one
of the
B
mesons (
B
reco
). This technique results in a low
event selection efficiency, but it uniquely determines the
momentum and charge of both
B
mesons in the event,
reducing backgrounds significantly. For charged
B
mesons
it also determines their flavor. The semileptonic decay of
the second
B
meson (
B
recoil
) is identified by the presence of
an electron or a muon and its kinematics are constrained
such that the undetectable neutrino can be identified from
the missing momentum and energy of the rest of the event.
However, undetected and poorly reconstructed charged
particles or photons lead to large backgrounds from the
dominant

B
!
X
c


decays, and they distort the kinemat-
ics, e.g., the hadronic mass
M
X
and the leptonic mass
squared
q
2
.
For the
B
reco
sample, the two dominant background
sources are non-
B

B
events from continuum processes,
e
þ
e

!
q

q
ð

Þ
with
q
¼
u
,
d
,
s
,or
c
, and combinatorial
B

B
background. The sum of these two backgrounds is esti-
mated from the distribution of the beam energy-substituted
mass
m
ES
, which takes the following form in the laboratory
frame:
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s=
2
þ
~
p
B

~
p
beams
Þ
2
=E
2
beams

~
p
2
B
q
.Here
~
p
B
refers to the momentum of the
B
reco
candidate derived
from the measured momenta of its decay products,
P
beams
¼ð
E
beams
;
~
p
beams
Þ
to the four-momentum of the
colliding beam particles, and
ffiffiffi
s
p
to the total energy in
the

ð
4
S
Þ
frame. For correctly reconstructed
B
reco
decays,
the distribution peaks at the
B
meson mass, and the width
of the peak is determined by the energy spread of the
colliding beams. The size of the underlying background is
determined from a fit to the
m
ES
distribution.
We minimize experimental systematic uncertainties, by
measuring the yield for selected charmless semileptonic
decays relative to the total yield of semileptonic decays

B
!
X‘


, after subtracting combinatorial backgrounds of
the
B
reco
selection from both samples.
In order to reduce the overall uncertainties, measure-
ment of the signal

B
!
X
u


decays is restricted to regions
of phase space where the background from the dominant

B
!
X
c


decays is suppressed and theoretical uncertain-
ties can be reliably assessed. Specifically, signal events
tend to have higher charged lepton momenta in the
B
-meson rest frame (
p

), lower
M
X
, higher
q
2
, and smaller
values of the light-cone momentum
P
þ
¼
E
X
j
~
p
X
j
,
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032004 (2012)
032004-4
where
E
X
and
~
p
X
are energy and momentum of the had-
ronic system
X
in the
B
meson rest frame.
The observation of charged leptons with momenta ex-
ceeding the kinematic limit for

B
!
X
c


presented first
evidence for charmless semileptonic decays. This was
followed by a series of measurements close to this kine-
matic limit [
12
16
]. Although the signal-to-background
ratio for this small region of phase space is favorable, the
theoretical uncertainties are large and difficult to quantify.
Since then, efforts have been made to select larger phase
space regions, thereby reducing the theoretical uncertain-
ties. The Belle Collaboration has recently published an
analysis that covers about 88% of the signal phase space
[
17
], similar to one of the studies detailed in this article.
We extract
j
V
ub
j
from the partial branching fractions
relying on four different QCD calculations of the partial
decay rate in several phase space regions: BLNP by Bosch,
Lange, Neubert, and Paz [
18
20
]; DGE, the dressed gluon
exponentiation by Andersen and Gardi [
21
,
22
]; ADFR by
Aglietti, Di Lodovico, Ferrera, and Ricciardi [
23
,
24
]; and
GGOU by Gambino, Giordano, Ossola, and Uraltsev [
25
].
These calculations differ significantly in their treatment of
perturbative corrections and the parametrization of non-
perturbative effects that become important for the different
restrictions in phase space.
This measurement of
j
V
ub
j
is based on combined
samples of charged and neutral
B
mesons. In addition,
we present measurements of the partial decay rates for

B
0
and
B

decays separately. The observed rates are found
to be equal within uncertainties. We use this observation
to set a limit on weak annihilation (WA), the process
b

u
!



, which is not included in the QCD calculation
of the

B
!
X‘


decay rates. Since final state hadrons
originate from soft gluon emission, WA is expected to
contribute to the decay rate at large values of
q
2
[
26
29
].
The outline of this paper is as follows: a brief overview
of the
BABAR
detector, particle reconstruction, and the
data and Monte Carlo (MC) samples is given in Sec.
II
,
followed in Sec.
III
by a description of the event recon-
struction and selection of the two event samples, the
charmless semileptonic signal sample, and the inclusive
semileptonic sample that serves as normalization. The
measurement of the partial branching fractions and their
systematic uncertainties are presented in Secs.
IV
and
V
.
The extraction of
j
V
ub
j
based on four sets of QCD calcu-
lations for seven selected regions of phase space is pre-
sented in Sec.
VI
, followed by the conclusions in Sec.
VII
.
II. DATA SAMPLE, DETECTOR,
AND SIMULATION
A. Data sample
The data used in this analysis were recorded with the
BABAR
detector at the PEP-II asymmetric energy
e
þ
e

collider operating at the

ð
4
S
Þ
resonance. The total data
sample, corresponding to an integrated luminosity of
426 fb

1
and containing
467

10
6

ð
4
S
Þ!
B

B
events,
was analyzed.
B. The
BABAR
detector
The
BABAR
detector and the general event reconstruc-
tion are described in detail elsewhere [
30
,
31
]. For this
analysis, the most important detector features are the
charged-particle tracking, photon reconstruction, and par-
ticle identification. The momenta and angles of charged
particles are measured in a tracking system consisting of a
five-layer silicon vertex tracker (SVT) and a 40-layer,
small-cell drift chamber (DCH). Charged particles of dif-
ferent masses are distinguished by their ionization energy
loss in the tracking devices and by the DIRC, a ring-
imaging detector of internally reflected Cherenkov radia-
tion. A finely segmented electromagnetic calorimeter
(EMC) consisting of 6580 CsI(Tl) crystals measures the
energy and position of showers generated by electrons and
photons. The EMC is surrounded by a thin superconduct-
ing solenoid providing a 1.5 T magnetic field and by a steel
flux return with a hexagonal barrel section and two end
caps. The segmented flux return (IFR) is instrumented with
multiple layers of resistive plate chambers and limited
streamer tubes to identify muons and to a lesser degree
K
L
.
C. Single particle reconstruction
In order to reject misidentified and background tracks
that do not originate from the interaction point, we require
the radial and longitudinal impact parameters to be
r
0
<
1
:
5cm
and
j
z
0
j
<
10 cm
. For secondary tracks from
K
S
!

þ


decays, no restrictions on the impact parame-
ter are imposed. The efficiency for the reconstruction of
charged particles inside the fiducial volume for SVT, DCH,
and EMC, defined by the polar angle in the laboratory
frame,
0
:
410
<
lab
<
2
:
54 rad
, exceeds 96% and is well
reproduced by MC simulation.
Electromagnetic showers are detected in the EMC as
clusters of energy depositions. Photons are required not to
be matched to a charged track extrapolated to the position
of the shower maximum in the EMC. To suppress photons
from beam-related background, we only retain photons
with energies larger than 50 MeV. Clusters created by
neutral hadrons (
K
L
or neutrons) interacting in the EMC
are distinguished from photons by their shower shape.
Electrons are primarily separated from charged hadrons
on the basis of the ratio of the energy deposited in the EMC
to the track momentum. This quantity should be close to 1
for electrons since they deposit all their energy in the
calorimeter. Most other charged tracks are minimum
ionizing, unless they shower in the EMC crystals.
Muons are identified by a neural network that combines
information from the IFR with the measured track momen-
tum and the energy deposition in the EMC.
The average electron efficiency for laboratory momenta
above 0.5 GeV is 93%, largely independent of momentum.
STUDY OF

B
!
X
u


DECAYS
...
PHYSICAL REVIEW D
86,
032004 (2012)
032004-5
The average hadron misidentification rate is less than 0.2%.
Within the polar-angle acceptance, the average muon effi-
ciency rises with laboratory momentum and reaches a
plateau of about 70% above 1.4 GeV. The muon efficiency
varies between 50% and 80% as a function of the polar
angle. The average hadron misidentification rate is about
1.5%, varying by about 0.5% as a function of momentum
and polar angle.
Charged kaons are selected on the basis of information
from the DIRC, DCH, and SVT. The efficiency is higher
than 80% over most of the momentum range and varies
with the polar angle. The probability of a pion to be
misidentified as a kaon is close to 2%, varying by about
1% as a function of momentum and polar angle.
Neutral pions are reconstructed from pairs of photon
candidates that are detected in the EMC and are assumed
to originate from the primary vertex. Photon pairs having
an invariant mass within 17.5 MeV (corresponding to
2
:
5

) of the nominal

0
mass are considered

0
candi-
dates. The overall detection efficiency, including solid
angle restrictions, varies between 55% and 65% for

0
energies in the range of 0.2 to 2.5 GeV.
K
0
S
!

þ


decays are reconstructed as pairs of tracks
of opposite charge with a common vertex displaced from
the interaction point. The invariant mass of the pair is
required to be in the range
490
<m

þ


<
505 MeV
.
D. Monte Carlo simulation
We use MC techniques to simulate the response of the
BABAR
detector [
32
] and the particle production and de-
cays [
33
], to optimize selection criteria, and to determine
signal efficiencies and background distributions. The
agreement of the simulated distributions with those in
data has been verified with control samples, as shown in
Sec.
IV D
; the impact of the inaccuracies of the simulation
is estimated in Sec.
V
.
The size of the simulated sample of generic
B

B
events
exceeds the
B

B
data sample by about a factor of 3. This
sample includes the common

B
!
X
c


decays. MC
samples for inclusive and exclusive

B
!
X
u


decays
exceed the size of the data samples by factors of 15 or
more.
Charmless semileptonic

B
!
X
u


decays are simu-
lated as a combination of resonant three-body decays
with
X
u
¼

,

,

0
,

,
!
, and decays to nonresonant
hadronic final states
X
u
. The branching ratios assumed
for the various resonant decays are detailed in Table
I
.
Exclusive charmless semileptonic decays are simulated
using a number of different parametrizations: for

B
!
‘


decays we use a single-pole ansatz [
35
] for the
q
2
dependence of the form factor with a single parameter
measured by
BABAR
[
36
]; for decays to pseudoscalar
mesons

and

0
and vector mesons

and
!
we use
form factor parametrizations based on light-cone sum cal-
culations [
37
,
38
].
The simulation of the inclusive charmless semileptonic
B
decays to hadronic states with masses larger than
2
m

is
based on a prescription by De Fazio and Neubert (DFN)
[
39
] for the triple-differential decay rate,
d
3

=dq
2
dE
ds
H
(
E
refers to the energy of the charged lepton and
s
H
¼
M
2
X
) with QCD corrections up to
O
ð
s
Þ
. The motion
of the
b
quark inside the
B
meson is incorporated in the
DFN formalism by convolving the parton-level triple-
differential decay rate with a nonperturbative shape
function (SF). This SF describes the distribution of the
momentum
k
þ
of the
b
quark inside the
B
meson. The
two free parameters of the SF are


SF
and
1
SF
. The first
relates the
B
meson mass
m
B
to the
b
quark mass,
m
SF
b
¼
m
B



SF
, and
1
SF
is the average momentum squared of
the
b
quark. The SF parametrization is of the form
F
ð
k
þ
Þ¼
N
ð
1

x
Þ
a
e
ð
1
þ
a
Þ
x
, where
x
¼
k
þ
=


SF

1
and
a
¼
3
ð


SF
Þ
2
=
1
SF

1
. The first three moments
A
i
of
the SF must satisfy the following relations:
A
0
¼
1
,
A
1
¼
0
,
and
A
2
¼
1
SF
=
3
.
The nonresonant hadronic state
X
u
is simulated with a
continuous invariant mass spectrum according to the DFN
prescription. The fragmentation of the
X
u
system into final
state hadrons is performed by
JETSET
[
40
]. The resonant
and nonresonant components are combined such that the
sum of their branching fractions is equal to the measured
branching fraction for inclusive

B
!
X
u


decays [
34
],
and the spectra agree with the DFN prediction. In order to
obtain predictions for different values of


SF
and
1
SF
, the
generated events are reweighted.
We estimate the shape of background distributions by
using simulations of the process
e
þ
e

!

ð
4
S
Þ!
B

B
with the
B
mesons decaying according to measured
branching fractions [
34
].
For the simulation of the dominant background from

B
!
X
c


decays, we have chosen a variety of differ-
ent form factor parametrizations. For

B
!
D‘


and

B
!
D



decays we use parametrizations [
41
] based on
heavy quark effective theory [
42
45
]. In the limit of neg-
ligible charged lepton masses, decays to pseudoscalar
mesons are described by a single form factor for which
the
q
2
dependence is expressed in terms of a slope parame-
ter

2
D
. We use the world average

2
D
¼
1
:
19

0
:
06
[
46
],
updated with recent precise measurements by the
BABAR
Collaboration [
47
,
48
]. Decays to vector mesons are
TABLE I. Branching fractions and their uncertainties [
34
] for
exclusive

B
!
X
u


decays.
Mode
B
ð

B
0
!
X
u


Þ
B
ð
B

!
X
u


Þ

B
!
‘


ð
136

7
Þ
10

6
ð
77

12
Þ
10

6

B
!
‘


ð
64

20
Þ
10

6

B
!
‘


ð
247

33
Þ
10

6
ð
128

18
Þ
10

6

B
!
!‘


ð
115

17
Þ
10

6

B
!

0


ð
17

22
Þ
10

6
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032004 (2012)
032004-6
described by three form factors, of which the axial vector
form factor dominates. In the limit of heavy quark sym-
metry, their
q
2
dependence can be described by three
parameters for which we use the most precise
BABAR
measurements [
47
,
49
]:

2
D

¼
1
:
20

0
:
04
[
47
,
49
],
R
1
¼
1
:
429

0
:
074
, and
R
2
¼
0
:
827

0
:
044
[
49
]. For the
simulation of semileptonic decays to the four
L
¼
1
charm
states, commonly referred to as
D

resonances, we use
calculations of form factors by Leibovich, Ligeti, Stewart,
and Wise [
50
]. We have adopted the prescription by Goity
and Roberts [
51
] for nonresonant

B
!
D
ðÞ
X‘


decays.
III. EVENT RECONSTRUCTION
AND SIGNAL EXTRACTION
A. Reconstruction of hadronic
B
decays
tagging
B

B
events

ð
4
S
Þ!
B

B
events are tagged by the hadronic decays
of one of the
B
mesons based on a semiexclusive algorithm
that was employed in an earlier analysis [
11
]. We look for
decays of the type
B
reco
!
D
ðÞ
Y

, where
D
ðÞ
is a
charmed meson (
D
0
,
D
þ
,
D

0
,or
D

) and
Y
is a charged
state decaying into at most five charged hadrons (pions or
kaons), plus at most two neutral mesons (
K
0
S
or

0
). The
following decay modes of
D
mesons are reconstructed:
D
0
!
K


þ
,
K


þ

0
,
K


þ



þ
,
K
0
S

þ


and
D
þ
!
K


þ

þ
,
K


þ

þ

0
,
K
0
S

þ
,
K
0
S

þ

þ


,
K
0
S

þ

0
with
K
0
S
!

þ


.
D

mesons are identified by
their decays,
D
!
D
0

þ
,
D
þ

0
and
D

0
!
D
0

0
,
D
0

. Pions and photons from
D

decays are of low energy,
and therefore the mass difference

M
¼
m
ð
D
Þ
m
ð
D
Þ
serves as an excellent discriminator for these decays.
Of the 1113
B
reco
decay chains that we consider,
we retain only the 342 ones with a signal purity
P
¼
S=
ð
S
þ
B
Þ
>
20%
, where
S
and
B
, derived from MC
samples, denote the signal and background yields. The
kinematic consistency of the
B
reco
candidates with
B
me-
son decays is checked using
m
ES
and the energy difference,

E
¼ð
P
B

P
beams

s=
2
Þ
=
ffiffiffi
s
p
. We restrict the
B
reco
mass
to
m
ES
>
5
:
22 GeV
and require

E
¼
0 GeV
within
approximately 3 standard deviations, where the

E
reso-
lution depends on the decay chain. If an event contains
more than one
B
reco
candidate, the decay chain with the
highest
2
probability is chosen. For this purpose we define
2
total
¼
2
vertex
þ
M
D
ðÞ
reco

M
D
ðÞ

D
ðÞ
reco
!
2
þ

E


E
!
2
:
(1)
Here the first term is taken from a vertex fit for tracks from
B
reco
decays, the second relates reconstructed and nominal
masses [
34
],
M
D
ðÞ
reco
and
M
D
ðÞ
, of the charm mesons
(
D
0
,
D
þ
,
D

0
,or
D

), with the resolution

D
ðÞ
reco
, and the
third term checks the energy balance

E
compared to its
resolution


E
. The number of degrees of freedom is
therefore defined as
N
dof
¼
N
dof
vertex
þ
2
. The resulting
overall tagging efficiency is 0.3% for
B
0

B
0
and 0.5% for
B
þ
B

events.
B. Selection of inclusive

B
!
X‘


decays
In order to minimize systematic uncertainties, we mea-
sure the yield of selected charmless semileptonic decays in
a specific kinematic region normalized to the total yield of
semileptonic

B
!
X‘


decays. Both semileptonic decays,
the charmless and the normalization modes, are identified
by at least one charged lepton in events that are tagged by a
B
reco
decay. Both samples are background-subtracted and
corrected for efficiency. Using this normalization, the sys-
tematic uncertainties on the
B
reco
reconstruction and the
charged lepton detection cancel in the ratio or are elimi-
nated to a large degree.
The selection criteria for the charmless and the total
semileptonic samples are chosen to minimize the statistical
uncertainty of the measurement as estimated from a sample
of fully simulated MC events that includes both signal and
background processes.
A restriction on the momentum of the electron or muon
is applied to suppress backgrounds from secondary charm
or

decays, photon conversions, and misidentified had-
rons. This is applied to
p

, the lepton momentum in the rest
frame of the recoiling
B
meson, which is accessible since
the momenta of the

ð
4
S
Þ
and the reconstructed
B
are
known. This transformation is important because theoreti-
cal calculations refer to variables that are Lorentz invariant
or measured in the rest frame of the decaying
B
meson. We
require
p

to be greater than 1 GeV, for which about 90%
of the signal is retained.
For electrons and muons the angular acceptance is de-
fined as
0
:
450
<<
2
:
473 rad
, where

refers to the polar
angle relative to the electron beam in the laboratory frame.
This requirement excludes regions where charged-particle
tracking and identification are not efficient. We suppress
muons from
J=
c
decays by rejecting the event if a muon
candidate paired with any other charged track of opposite
charge (and not part of
B
reco
) results in an invariant mass of
the pair that is consistent with the
J=
c
mass. A similar
requirement is not imposed on electron candidates,
because of the poor resolution of the corresponding
J=
c
peak.
We also reject events if the electron candidate paired
with any other charged track of opposite charge is consis-
tent with a

!
e
þ
e

conversion.
A variety of processes contributes to the inclusive semi-
leptonic event samples, i.e. candidates selected by a
B
reco
decay and the presence of a high momentum lepton. In
addition to true semileptonic decays tagged by a correctly
reconstructed
B
reco
, we consider the following classes of
backgrounds:
(i)
Combinatorial background:
the
B
reco
is not correctly
reconstructed. This background originates from
B

B
or continuum
e
þ
e

!
q

q
ð

Þ
events. In order to
STUDY OF

B
!
X
u


DECAYS
...
PHYSICAL REVIEW D
86,
032004 (2012)
032004-7
subtract this background, the yield of true
B
reco
decays is determined from an unbinned maximum-
likelihood fit to the
m
ES
distribution (Sec.
III D
).
(ii)
Cascade background:
the lepton does not originate
from a semileptonic
B
decay, but from secondary
decays, for instance, from
D
mesons, including
D
s
!

, or residual
J=
c
background.
(iii)
background:
electrons or muons originate from
prompt
leptons, primarily from

B
!
X


decays.
(iv)
Fake leptons:
hadrons are misidentified as leptons,
primarily muons.
The last three sources of background are combined and in
the following are referred to as ‘‘other’’ background.
C. Selection of inclusive

B
!
X
u


decays
A large fraction of

B
!
X
c


decays is expected to have
a second lepton from cascade decays of the charm parti-
cles. In contrast, in

B
!
X
u


decays secondary leptons
are very rare. Therefore, we enhance signal events
by selecting events with only one charged lepton having
p

>
1 GeV
.
In semileptonic
B
meson decays, the charge of the
primary lepton is equal to the sign of the charge of the
b
quark. Thus for
B
þ
B

events in which the
B
reco
and the
lepton originate from different
B
decays in the event, we
impose the requirement
Q
b
Q
<
0
, where
Q
b
is the charge
of the
b
quark of the
B
reco
and
Q
is the charge of the
lepton. For
B
0

B
0
events this condition does not strictly
hold because of flavor mixing. Thus, to avoid a loss in
efficiency, this requirement is not imposed. The hadronic
state
X
u
in charmless semileptonic decays is reconstructed
from all particles that are not associated with the
B
reco
candidate or the charged lepton. The measured four-
momentum
P
X
is defined as
P
X
¼
X
N
trk
i
¼
1
P
trk
i
þ
X
N

i
¼
1
P

i
;
(2)
where the summation extends over the four-vectors of the
charged particles and photon candidates. From this four-
vector, other kinematic variables,
M
2
X
¼
P
2
X
¼
E
2
X

p
2
X
,
q
2
¼
P
B
reco

P
X
(
P
B
reco
being the
B
reco
four-momentum),
and
P
þ
, can be calculated. The loss of one or more charged
or neutral particles or the addition of tracks or single
electrons from photon conversions degrade the reconstruc-
tion of
X
u
and the resolution of the measurement of any
related kinematic variables. In order to reduce the impact
of missing charged particles and the effect of single elec-
trons from

!
e
þ
e

conversions, we impose charge
conservation on the whole event,
Q
tot
¼
Q
B
reco
þ
Q
X
þ
Q
¼
0
. This requirement rejects a larger fraction of

B
!
X
c


events because of their higher charged multi-
plicity and the presence of very low momentum charged
pions from
D

!
D
0


soft
decays that have low detection
efficiency.
In

B
!
X‘


decays, where the state
X
decays hadroni-
cally, the only undetected particle is a neutrino. The
neutrino four-momentum
P

can be estimated from the
missing momentum four-vector
P
miss
¼
P

ð
4
S
Þ

P
B
reco

P
X

P
. For correctly reconstructed events with a single
semileptonic decay, the missing mass squared,
MM
2
¼
P
2
miss
, is consistent with zero. Failure to detect one or
more particles in the event creates a tail at large positive
values; thus
MM
2
is used as a measure of the quality of the
event reconstruction. Though
MM
2
is Lorentz invariant,
the missing momentum is usually measured in the labora-
tory frame, because this avoids the additional uncertainty
related to the transformation into the c.m. frame. We
require
MM
2
to be less than
0
:
5 GeV
2
. Because of the
higher probability for additional unreconstructed neutral
particles, a neutrino, or
K
L
, the
MM
2
distribution is
broader for

B
!
X
c


decays, and this restriction sup-
presses this background more than signal events.
In addition, we suppress the

B
!
D



background by
exploiting the small
Q
value of the
D

!
D
soft
decays,
which result in a very low momentum pion. For energetic
D

mesons, the momenta
p

soft
and
p
D
are almost collinear,
and we can approximate the
D

direction by the

soft
direction and estimate the
D

energy by a simple approxi-
mation based on the
E

soft
,
E
D


m
D


E

soft
=
145 MeV
.
Using the measured
B
reco
and charged lepton momenta,
and the four-momentum of the
D

derived from any
pion with c.m. momentum below 200 MeV, we estimate
the neutrino mass for a potential

B
!
D



decay
as
MM
2
veto
¼ð
P
B

P
D


P
Þ
2
. For true

B
!
D



de-
cays, this distribution peaks at zero. Thus, we veto
D

decays to low momentum charged or neutral pions
by requiring, respectively,
MM
2
veto
ð

þ
soft
Þ
<

3 GeV
2
or
MM
2
veto
ð

0
soft
Þ
<

2 GeV
2
. This is achieved without ex-
plicit reconstruction of the
D
meson decays, and thus
avoids large losses in rejection power for this veto.
We reduce

B
!
D



background by vetoing events
with a charged or neutral kaon (
K
0
S
!

þ


) that origi-
nate primarily from the decays of charm particles.
A summary of the impact of the signal selection criteria
on the high-energy lepton sample, for the signal, semi-
leptonic, and nonsemileptonic background samples is pre-
sented in Table
II
, in terms of cumulative selection
efficiencies. Figure
1
shows the kinematic variables that
appear in Table
II
for different event categories.
Combinatorial background is not included; it is subtracted
based on fits to the
m
ES
distributions, as described in
Sec.
III D
. The overall efficiency for selecting charmless
semileptonic decays in the sample of tagged events with a
charged lepton is 33.8%; the background reduction is
97.8% for

B
!
X
c


and 95.3% for ‘‘other.’’
The resolution functions determined from MC simula-
tion of signal events passing the selection requirements are
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032004 (2012)
032004-8
shown in Fig.
2
for the variables
M
X
,
q
2
, and
P
þ
. Each of
these distributions has a narrow core containing 30%, 50%,
and 30% of the

B
!
X
u


events, with widths of 25 MeV,
250 MeV
2
, and 10 MeV, respectively. The remaining
events have a considerably poorer resolution, primarily
because of lost secondary particles from the decay of the
hadronic
X
u
.
On the basis of the kaon and the
D

veto, two data
samples are defined:
(i)
signal-enriched:
events that pass the vetoes; this
sample is used to extract the signal;
(ii)
signal-depleted:
events rejected by at least one
veto; they are used as the control sample to check
the agreement between data and simulated
backgrounds, including the poorly understood

B
!
D



decays.
D. Subtraction of combinatorial background
The subtraction of the combinatorial background of the
B
reco
tag for the signal and normalization samples relies on
unbinned maximum-likelihood fits to the
m
ES
distribu-
tions. For signal decays the goal is to extract the distribu-
tions in the kinematic variables
p

,
M
X
,
q
2
, and
P
þ
.
Because the shapes and relative yields of the signal and
background contributions depend on the values of these
kinematic variables, the continuum and combinatorial
background subtraction is performed separately for sub-
samples corresponding to events in bins of these variables.
This results in more accurate spectra than a single fit to the
full sample of events in each selected region of phase
space.
TABLE II. Comparison of the cumulative selection efficien-
cies for samples of signal

B
!
X
u


decays and

B
!
X
c


and
‘‘other’’ backgrounds. The efficiencies are relative to the sample
of
B
reco
-tagged events with a charged lepton.
Selection

B
!
X
u



B
!
X
c


Other
Only one lepton
99.3%
98.1%
95.8%
Total charge
Q
¼
0
65.5%
52.9%
49.1%
MM
2
44.2%
17.8%
17.8%
D



ð

þ
s
Þ
veto
40.6%
9.9%
14.4%
D



ð

0
s
Þ
veto
34.8%
6.3%
9.1%
Kaon veto
33.8%
2.2%
4.7%
Number of leptons
01234
Entries / bin
-5
10
-4
10
-3
10
-2
10
-1
10
1
To t a l C h a r g e
-4
-3
-2
-1
0
1
2
3
4
Entries / bin
0
0.2
0.4
0.6
)
2
(GeV
2
MM
-5
0
5
10
15
2
Entries / 0.5 GeV
-3
10
-2
10
-1
10
)
2
) (GeV
soft
+
π
(
veto
2
MM
-100
-80
-60
-40
-20
0
2
Entries / GeV
-3
10
-2
10
-1
10
)
2
) (GeV
soft
0
π
(
veto
2
MM
-40
-30
-20
-10
0
10
2
Entries / GeV
-4
10
-3
10
-2
10
-1
10
Number of Kaons
012345
Entries / bin
-3
10
-2
10
-1
10
1
FIG. 1. MC distribution of the kinematic variables for which we apply restrictions sequentially as listed in Table
II
, for

B
!
X
u


(solid line),

B
!
X
c


(dashed line), and ‘‘other’’ component (dotted line). All distributions are normalized to unity, and selection
criteria have been applied cumulatively, except those affecting directly the variable shown. The arrows indicate the selection
requirement for a specific variable, as described in Sec.
III C
.
STUDY OF

B
!
X
u


DECAYS
...
PHYSICAL REVIEW D
86,
032004 (2012)
032004-9
For the normalization sample, the fit is performed for the
full event sample, separately for

B
0
and
B

tags.
The
m
ES
distribution for the combinatorial
B
reco
back-
ground can be described by an ARGUS function [
52
],
f
bkg
ð
m
Þ¼
N
bkg
m
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1

m
2
p
e

ð
1

m
2
Þ
;
(3)
where
m
¼
m
ES
=m
max
ES
and
m
max
ES
is the end point of the
m
ES
distribution that depends on the beam energy, and
deter-
mines the shape of the function.
N
bkg
refers to the total
number of background events in the distribution.
For signal events, the
m
ES
distribution resembles a reso-
lution function peaking at the
B
meson mass with a slight
tail to lower masses. Usually the peak of the
m
ES
distribu-
tion is empirically described by a crystal ball function [
53
],
but this ansatz turned out to be inadequate for this data set
because the
B
reco
sample is composed of many individual
decay modes with different resolutions. We therefore fol-
low an approach previously used in
BABAR
data [
54
]
and build a more general function, using a Gaussian func-
tion,
f
g
ð
x
Þ¼
e

x
2
=
2
, and the derivative of
tanh
x
,
f
t
ð
x
Þ¼
e

x
=
ð
1
þ
e

x
Þ
, to arrive at
f
sig
ð

Þ¼
8
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
:
C
2
ð
C
3


Þ
n
if

<
C
1

L
f
t



L

if


<
0
r

1
f
t



1

þ
1

r

2
f
g



2

if


0
:
(4)
Here

¼
m
ES


m
ES
, where

m
ES
is the maximum of the
m
ES
distribution.
C
1
,
C
2
, and
C
3
are functions of the
parameters

m
ES
,
r
,

1
,

2
,

L
,
, and
n
, which ensure
the continuity of
f
sig
.
Given the very large number of parameters, we first per-
form a fit to samples covering the full kinematic range and
determine all parameters describing
f
sig
and the ARGUS
function. We then repeat the fit for events in each bin of the
kinematic variables, with only the relative normalization of
the signal and background, and the shape parameter
of the
ARGUS function as free parameters. Figure
3
shows the
m
ES
distribution for the inclusive semileptonic sample, separately
for charged and neutral
B
mesons.
Finally, we correct for the contamination from cascade
background in the number of neutral
B
mesons, due to the
effect of
B
0


B
0
mixing, in each bin of the kinematic
variables. We distinguish neutral
B
decays with right- and
wrong-sign leptons, based on the flavor of the
B
reco
decay.
The contribution from cascade decays is subtracted by
computing the number of neutral
B
mesons
N
B
0
as
N
B
0
¼
1

d
1

2
d
N
B
0
rs

d
1

2
d
N
B
0
ws
;
(5)
where
N
B
0
rs
and
N
B
0
ws
are the number of neutral
B
mesons
with right and wrong sign of the charge of the accompany-
ing lepton, and
d
¼
0
:
188

0
:
002
[
34
] is the
B
0


B
0
mixing parameter.
The performance of the
m
ES
fit has been verified using
MC simulated distributions. We split the full sample in two
parts. One part, containing one-third of the events, is
treated as data and is similar in size to the total data sample.
(GeV)
X
M
-0.6 -0.4 -0.2
0
0.2 0.4 0.6
Entries / 32 MeV
0
50
100
150
200
250
300
350
)
2
(GeV
2
q
-3
-2
-1
0
1
2
3
2
Entries / 120 MeV
0
20
40
60
80
100
120
140
160
180
200
220
(GeV)
+
P
-0.4
-0.2
0
0.2
0.4
Entries / 14 MeV
0
50
100
150
200
250
300
350
FIG. 2. Resolution for MC simulated for signal

B
!
X
u


events passing all event selection criteria, (left)
M
X
reco

M
X
true
, (center)
q
2
reco

q
2
true
, and (right)
P
þ
;
reco

P
þ
;
true
. The curve shows a fit result for the sum of two Gaussian functions.
5.22
5.24
5.26
5.28
Entries / 0.5 MeV
0
5000
10000
(GeV)
ES
m
5.245.265.28
FIG. 3. The
m
ES
distribution for the inclusive semileptonic
sample, for fully reconstructed hadronic decays of
B

(left)
and

B
0
mesons (right). The solid line shows the result of the
maximum-likelihood fit to signal and combinatorial back-
grounds; the dashed line indicates the shape of the background
described by an ARGUS function.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032004 (2012)
032004-10