Study of
B
!
l
and
B
!
l
decays and determination of
j
V
ub
j
P. del Amo Sanchez,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
M. Martinelli,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
M. Battaglia,
5
D. N. Brown,
5
B. Hooberman,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
5
T. Tanabe,
5
C. M. Hawkes,
6
N. Soni,
6
A. T. Watson,
6
H. Koch,
7
T. Schroeder,
7
D. J. Asgeirsson,
8
C. Hearty,
8
T. S. Mattison,
8
J. A. McKenna,
8
A. Khan,
9
A. Randle-Conde,
9
V. E. Blinov,
10
A. R. Buzykaev,
10
V. P. Druzhinin,
10
V. B. Golubev,
10
A. P. Onuchin,
10
S. I. Serednyakov,
10
Yu. I. Skovpen,
10
E. P. Solodov,
10
K. Yu. Todyshev,
10
A. N. Yushkov,
10
M. Bondioli,
11
S. Curry,
11
D. Kirkby,
11
A. J. Lankford,
11
M. Mandelkern,
11
E. C. Martin,
11
D. P. Stoker,
11
H. Atmacan,
12
J. W. Gary,
12
F. Liu,
12
O. Long,
12
G. M. Vitug,
12
Z. Yasin,
12
V. Sharma,
13
C. Campagnari,
14
T. M. Hong,
14
D. Kovalskyi,
14
J. D. Richman,
14
A. M. Eisner,
15
C. A. Heusch,
15
J. Kroseberg,
15
W. S. Lockman,
15
A. J. Martinez,
15
T. Schalk,
15
B. A. Schumm,
15
A. Seiden,
15
L. O. Winstrom,
15
C. H. Cheng,
16
D. A. Doll,
16
B. Echenard,
16
D. G. Hitlin,
16
P. Ongmongkolkul,
16
F. C. Porter,
16
A. Y. Rakitin,
16
R. Andreassen,
17
M. S. Dubrovin,
17
G. Mancinelli,
17
B. T. Meadows,
17
M. D. Sokoloff,
17
P. C. Bloom,
18
W. T. Ford,
18
A. Gaz,
18
J. F. Hirschauer,
18
M. Nagel,
18
U. Nauenberg,
18
J. G. Smith,
18
S. R. Wagner,
18
R. Ayad,
19,
*
W. H. Toki,
19
A. Hauke,
20
H. Jasper,
20
T. M. Karbach,
20
J. Merkel,
20
A. Petzold,
20
B. Spaan,
20
K. Wacker,
20
M. J. Kobel,
21
K. R. Schubert,
21
R. Schwierz,
21
D. Bernard,
22
M. Verderi,
22
P. J. Clark,
23
S. Playfer,
23
J. E. Watson,
23
M. Andreotti,
24a,24b
D. Bettoni,
24a
C. Bozzi,
24a
R. Calabrese,
24a,24b
A. Cecchi,
24a,24b
G. Cibinetto,
24a,24b
E. Fioravanti,
24a,24b
P. Franchini,
24a,24b
E. Luppi,
24a,24b
M. Munerato,
24a,24b
M. Negrini,
24a,24b
A. Petrella,
24a,24b
L. Piemontese,
24a
R. Baldini-Ferroli,
25
A. Calcaterra,
25
R. de Sangro,
25
G. Finocchiaro,
25
M. Nicolaci,
25
S. Pacetti,
25
P. Patteri,
25
I. M. Peruzzi,
25,
†
M. Piccolo,
25
M. Rama,
25
A. Zallo,
25
R. Contri,
26a,26b
E. Guido,
26a,26b
M. Lo Vetere,
26a,26b
M. R. Monge,
26a,26b
S. Passaggio,
26a
C. Patrignani,
26a,26b
E. Robutti,
26a
S. Tosi,
26a,26b
B. Bhuyan,
27
M. Morii,
28
A. Adametz,
29
J. Marks,
29
S. Schenk,
29
U. Uwer,
29
F. U. Bernlochner,
30
H. M. Lacker,
30
T. Lueck,
30
A. Volk,
30
P. D. Dauncey,
31
M. Tibbetts,
31
P. K. Behera,
32
U. Mallik,
32
C. Chen,
33
J. Cochran,
33
H. B. Crawley,
33
L. Dong,
33
W. T. Meyer,
33
S. Prell,
33
E. I. Rosenberg,
33
A. E. Rubin,
33
Y. Y. Gao,
34
A. V. Gritsan,
34
Z. J. Guo,
34
N. Arnaud,
35
M. Davier,
35
D. Derkach,
35
J. Firmino da Costa,
35
G. Grosdidier,
35
F. Le Diberder,
35
A. M. Lutz,
35
B. Malaescu,
35
A. Perez,
35
P. Roudeau,
35
M. H. Schune,
35
J. Serrano,
35
V. Sordini,
35,
‡
A. Stocchi,
35
L. Wang,
35
G. Wormser,
35
D. J. Lange,
36
D. M. Wright,
36
I. Bingham,
37
J. P. Burke,
37
C. A. Chavez,
37
J. P. Coleman,
37
J. R. Fry,
37
E. Gabathuler,
37
R. Gamet,
37
D. E. Hutchcroft,
37
D. J. Payne,
37
C. Touramanis,
37
A. J. Bevan,
38
F. Di Lodovico,
38
R. Sacco,
38
M. Sigamani,
38
G. Cowan,
39
S. Paramesvaran,
39
A. C. Wren,
39
D. N. Brown,
40
C. L. Davis,
40
A. G. Denig,
41
M. Fritsch,
41
W. Gradl,
41
A. Hafner,
41
K. E. Alwyn,
42
D. Bailey,
42
R. J. Barlow,
42
G. Jackson,
42
G. D. Lafferty,
42
T. J. West,
42
J. Anderson,
43
R. Cenci,
43
A. Jawahery,
43
D. A. Roberts,
43
G. Simi,
43
J. M. Tuggle,
43
C. Dallapiccola,
44
E. Salvati,
44
R. Cowan,
45
D. Dujmic,
45
P. H. Fisher,
45
G. Sciolla,
45
R. K. Yamamoto,
45
M. Zhao,
45
P. M. Patel,
46
S. H. Robertson,
46
M. Schram,
46
P. Biassoni,
47a,47b
A. Lazzaro,
47a,47b
V. Lombardo,
47a
F. Palombo,
47a,47b
S. Stracka,
47a,47b
L. Cremaldi,
48
R. Godang,
48,
x
R. Kroeger,
48
P. Sonnek,
48
D. J. Summers,
48
H. W. Zhao,
48
X. Nguyen,
49
M. Simard,
49
P. Taras,
49
G. De Nardo,
50a,50b
D. Monorchio,
50a,50b
G. Onorato,
50a,50b
C. Sciacca,
50a,50b
G. Raven,
51
H. L. Snoek,
51
C. P. Jessop,
52
K. J. Knoepfel,
52
J. M. LoSecco,
52
W. F. Wang,
52
L. A. Corwin,
53
K. Honscheid,
53
R. Kass,
53
J. P. Morris,
53
A. M. Rahimi,
53
N. L. Blount,
54
J. Brau,
54
R. Frey,
54
O. Igonkina,
54
J. A. Kolb,
54
R. Rahmat,
54
N. B. Sinev,
54
D. Strom,
54
J. Strube,
54
E. Torrence,
54
G. Castelli,
55a,55b
E. Feltresi,
55a,55b
N. Gagliardi,
55a,55b
M. Margoni,
55a,55b
M. Morandin,
55a
M. Posocco,
55a
M. Rotondo,
55a
F. Simonetto,
55a,55b
R. Stroili,
55a,55b
E. Ben-Haim,
56
G. R. Bonneaud,
56
H. Briand,
56
J. Chauveau,
56
O. Hamon,
56
Ph. Leruste,
56
G. Marchiori,
56
J. Ocariz,
56
J. Prendki,
56
S. Sitt,
56
M. Biasini,
57a,57b
E. Manoni,
57a,57b
C. Angelini,
58a,58b
G. Batignani,
58a,58b
S. Bettarini,
58a,58b
G. Calderini,
58a,58b,
k
M. Carpinelli,
58a,58b,
{
A. Cervelli,
58a,58b
F. Forti,
58a,58b
M. A. Giorgi,
58a,58b
A. Lusiani,
58a,58c
N. Neri,
58a,58b
E. Paoloni,
58a,58b
G. Rizzo,
58a,58b
J. J. Walsh,
58a
D. Lopes Pegna,
59
C. Lu,
59
J. Olsen,
59
A. J. S. Smith,
59
A. V. Telnov,
59
F. Anulli,
60a
E. Baracchini,
60a,60b
G. Cavoto,
60a
R. Faccini,
60a,60b
F. Ferrarotto,
60a
F. Ferroni,
60a,60b
M. Gaspero,
60a,60b
L. Li Gioi,
60a
M. A. Mazzoni,
60a
G. Piredda,
60a
F. Renga,
60a,60b
M. Ebert,
61
T. Hartmann,
61
T. Leddig,
61
H. Schro
̈
der,
61
R. Waldi,
61
T. Adye,
62
B. Franek,
62
E. O. Olaiya,
62
F. F. Wilson,
62
S. Emery,
63
G. Hamel de Monchenault,
63
G. Vasseur,
63
Ch. Ye
`
che,
63
M. Zito,
63
M. T. Allen,
64
D. Aston,
64
D. J. Bard,
64
R. Bartoldus,
64
J. F. Benitez,
64
C. Cartaro,
64
M. R. Convery,
64
J. C. Dingfelder,
64,
**
J. Dorfan,
64
G. P. Dubois-Felsmann,
64
W. Dunwoodie,
64
R. C. Field,
64
M. Franco Sevilla,
64
B. G. Fulsom,
64
A. M. Gabareen,
64
M. T. Graham,
64
P. Grenier,
64
C. Hast,
64
W. R. Innes,
64
M. H. Kelsey,
64
H. Kim,
64
P. Kim,
64
M. L. Kocian,
64
D. W. G. S. Leith,
64
S. Li,
64
B. Lindquist,
64
S. Luitz,
64
V. Luth,
64
H. L. Lynch,
64
D. B. MacFarlane,
64
H. Marsiske,
64
D. R. Muller,
64
H. Neal,
64
S. Nelson,
64
C. P. O’Grady,
64
I. Ofte,
64
M. Perl,
64
B. N. Ratcliff,
64
A. Roodman,
64
A. A. Salnikov,
64
V. Santoro,
64
R. H. Schindler,
64
PHYSICAL REVIEW D
83,
032007 (2011)
1550-7998
=
2011
=
83(3)
=
032007(45)
032007-1
Ó
2011 American Physical Society
J. Schwiening,
64
A. Snyder,
64
D. Su,
64
M. K. Sullivan,
64
K. Suzuki,
64
J. M. Thompson,
64
J. Va’vra,
64
A. P. Wagner,
64
M. Weaver,
64
C. A. West,
64
W. J. Wisniewski,
64
M. Wittgen,
64
D. H. Wright,
64
H. W. Wulsin,
64
A. K. Yarritu,
64
C. C. Young,
64
V. Ziegler,
64
X. R. Chen,
65
W. Park,
65
M. V. Purohit,
65
R. M. White,
65
J. R. Wilson,
65
S. J. Sekula,
66
M. Bellis,
67
P. R. Burchat,
67
A. J. Edwards,
67
T. S. Miyashita,
67
S. Ahmed,
68
M. S. Alam,
68
J. A. Ernst,
68
B. Pan,
68
M. A. Saeed,
68
S. B. Zain,
68
N. Guttman,
69
A. Soffer,
69
P. Lund,
70
S. M. Spanier,
70
R. Eckmann,
71
J. L. Ritchie,
71
A. M. Ruland,
71
C. J. Schilling,
71
R. F. Schwitters,
71
B. C. Wray,
71
J. M. Izen,
72
X. C. Lou,
72
F. Bianchi,
73a,73b
D. Gamba,
73a,73b
M. Pelliccioni,
73a,73b
M. Bomben,
74a,74b
G. Della Ricca,
74a,74b
L. Lanceri,
74a,74b
L. Vitale,
74a,74b
V. Azzolini,
75
N. Lopez-March,
75
F. Martinez-Vidal,
75
D. A. Milanes,
75
A. Oyanguren,
75
J. Albert,
76
Sw. Banerjee,
76
H. H. F. Choi,
76
K. Hamano,
76
G. J. King,
76
R. Kowalewski,
76
M. J. Lewczuk,
76
I. M. Nugent,
76
J. M. Roney,
76
R. J. Sobie,
76
T. J. Gershon,
77
P. F. Harrison,
77
J. Ilic,
77
T. E. Latham,
77
G. B. Mohanty,
77
E. M. T. Puccio,
77
H. R. Band,
78
X. Chen,
78
S. Dasu,
78
K. T. Flood,
78
Y. Pan,
78
R. Prepost,
78
C. O. Vuosalo,
78
and S. L. Wu
78
(
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
Facultat de Fisica, Departament ECM, Universitat de Barcelona, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
Institute of Physics, University of Bergen, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
University of Birmingham, Birmingham, B15 2TT, United Kingdom
7
Institut fu
̈
r Experimentalphysik, Ruhr Universita
̈
t Bochum, 1, D-44780 Bochum, Germany
8
University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada
9
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
10
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
11
University of California at Irvine, Irvine, California 92697, USA
12
University of California at Riverside, Riverside, California 92521, USA
13
University of California at San Diego, La Jolla, California 92093, USA
14
University of California at Santa Barbara, Santa Barbara, California 93106, USA
15
Institute for Particle Physics, University of California at Santa Cruz, Santa Cruz, California 95064, USA
16
California Institute of Technology, Pasadena, California 91125, USA
17
University of Cincinnati, Cincinnati, Ohio 45221, USA
18
University of Colorado, Boulder, Colorado 80309, USA
19
Colorado State University, Fort Collins, Colorado 80523, USA
20
Fakulta
̈
t Physik, Technische Universita
̈
t Dortmund, D-44221 Dortmund, Germany
21
Institut fu
̈
r Kern- und Teilchenphysik, Technische Universita
̈
t Dresden, D-01062 Dresden, Germany
22
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
23
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
24a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
24b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
25
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
26a
INFN Sezione di Genova, I-16146 Genova, Italy
26b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
27
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
28
Harvard University, Cambridge, Massachusetts 02138, USA
29
Physikalisches Institut, Universita
̈
t Heidelberg, Philosophenweg 12, D-69120 Heidelberg, Germany
30
Institut fu
̈
r Physik, Humboldt-Universita
̈
t zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
31
Imperial College London, London, SW7 2AZ, United Kingdom
32
University of Iowa, Iowa City, Iowa 52242, USA
33
Iowa State University, Ames, Iowa 50011-3160, USA
34
Johns Hopkins University, Baltimore, Maryland 21218, USA
35
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Centre Scientifique d’Orsay,
Universite
́
Paris-Sud 11, B. P. 34, F-91898 Orsay Cedex, France
36
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
37
University of Liverpool, Liverpool L69 7ZE, United Kingdom
38
Queen Mary, University of London, London, E1 4NS, United Kingdom
39
Royal Holloway and Bedford New College, University of London, Egham, Surrey TW20 0EX, United Kingdom
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032007 (2011)
032007-2
40
University of Louisville, Louisville, Kentucky 40292, USA
41
Institut fu
̈
r Kernphysik, Johannes Gutenberg-Universita
̈
t Mainz, D-55099 Mainz, Germany
42
University of Manchester, Manchester M13 9PL, United Kingdom
43
University of Maryland, College Park, Maryland 20742, USA
44
University of Massachusetts, Amherst, Massachusetts 01003, USA
45
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
46
McGill University, Montre
́
al, Que
́
bec, H3A 2T8, Canada
47a
INFN Sezione di Milano, I-20133 Milano, Italy
47b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
48
University of Mississippi, Oxford, Mississippi 38677, USA
49
Physique des Particules, Universite
́
de Montre
́
al, Montre
́
al, Que
́
bec, H3C 3J7, Canada
50a
INFN Sezione di Napoli, I-80126 Napoli, Italy
50b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
51
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
52
University of Notre Dame, Notre Dame, Indiana 46556, USA
53
Ohio State University, Columbus, Ohio 43210, USA
54
University of Oregon, Eugene, Oregon 97403, USA
55a
INFN Sezione di Padova, I-35131 Padova, Italy
55b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
56
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
57a
INFN Sezione di Perugia, I-06100 Perugia, Italy
57b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
58a
INFN Sezione di Pisa, I-56127 Pisa, Italy
58b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
58c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
59
Princeton University, Princeton, New Jersey 08544, USA
60a
INFN Sezione di Roma, I-00185 Roma, Italy
60b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
61
Universita
̈
t Rostock, D-18051 Rostock, Germany
62
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
63
Centre de Saclay, CEA, Irfu, SPP, F-91191 Gif-sur-Yvette, France
64
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
65
University of South Carolina, Columbia, South Carolina 29208, USA
66
Southern Methodist University, Dallas, Texas 75275, USA
67
Stanford University, Stanford, California 94305-4060, USA
68
State University of New York, Albany, New York 12222, USA
69
School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel
70
University of Tennessee, Knoxville, Tennessee 37996, USA
71
University of Texas at Austin, Austin, Texas 78712, USA
72
University of Texas at Dallas, Richardson, Texas 75083, USA
73a
INFN Sezione di Torino, I-10125 Torino, Italy
73b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
74a
INFN Sezione di Trieste, I-34127 Trieste, Italy
74b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
75
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
76
University of Victoria, Victoria, British Columbia, V8W 3P6, Canada
77
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
78
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 18 May 2010; published 7 February 2011)
*
Present address: Temple University, Philadelphia, PA 19122, USA.
†
Also at Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
‡
Also at Universita
`
di Roma La Sapienza, I-00185 Roma, Italy.
x
Present address: University of South Alabama, Mobile, AL 36688, USA.
k
Also at 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.
{
Also at Universita
`
di Sassari, Sassari, Italy.
**
Present address: Physikalisches Institut, Universita
̈
t Bonn, Nußallee 12, 53115 Bonn, Germany.
STUDY OF
B
!
l
AND
...
PHYSICAL REVIEW D
83,
032007 (2011)
032007-3
We present an analysis of exclusive charmless semileptonic
B
-meson decays based on
377
10
6
B
B
pairs recorded with the
B
A
B
AR
detector at the
ð
4
S
Þ
resonance. We select four event samples correspond-
ing to the decay modes
B
0
!
‘
þ
,
B
þ
!
0
‘
þ
,
B
0
!
‘
þ
, and
B
þ
!
0
‘
þ
and find the
measured branching fractions to be consistent with isospin symmetry. Assuming isospin symmetry, we
combine the two
B
!
‘
samples, and similarly the two
B
!
‘
samples, and measure the branching
fractions
B
ð
B
0
!
‘
þ
Þ¼ð
1
:
41
0
:
05
0
:
07
Þ
10
4
and
B
ð
B
0
!
‘
þ
Þ¼ð
1
:
75
0
:
15
0
:
27
Þ
10
4
, where the errors are statistical and systematic. We compare the measured distribution in
q
2
, the momentum transfer squared, with predictions for the form factors from QCD calculations and
determine the Cabibbo-Kobayashi-Maskawa matrix element
j
V
ub
j
. Based on the measured partial
branching fraction for
B
!
‘
in the range
q
2
<
12 GeV
2
and the most recent QCD light-cone sum-
rule calculations, we obtain
j
V
ub
j¼ð
3
:
78
0
:
13
þ
0
:
55
0
:
40
Þ
10
3
, where the errors refer to the experimental
and theoretical uncertainties. From a simultaneous fit to the data over the full
q
2
range and the FNAL/
MILC lattice QCD results, we obtain
j
V
ub
j¼ð
2
:
95
0
:
31
Þ
10
3
from
B
!
‘
, where the error is the
combined experimental and theoretical uncertainty.
DOI:
10.1103/PhysRevD.83.032007
PACS numbers: 13.20.He, 12.15.Hh, 12.38.Qk, 14.40.Nd
I. INTRODUCTION
The elements of the Cabibbo-Kobayashi-Maskawa
(CKM) quark-mixing matrix are fundamental parameters
of the standard model (SM) of electroweak interactions.
With the increasingly precise measurements of decay-
time-dependent
CP
asymmetries in
B
-meson decays, in
particular
sin
ð
2
Þ
[
1
,
2
], improved measurements of the
magnitude of
V
ub
and
V
cb
will allow for more stringent
experimental tests of the SM mechanism for
CP
violation
[
3
]. This is best illustrated in terms of the unitarity triangle,
the graphical representation of one of the unitarity con-
ditions for the CKM matrix, for which the length of the side
that is opposite to the angle
is proportional to the ratio
j
V
ub
j
=
j
V
cb
j
. The best method to determine
j
V
ub
j
and
j
V
cb
j
is to measure semileptonic decay rates for
B
!
X
c
‘
and
B
!
X
u
‘
(
X
c
and
X
u
refer to hadronic states with or
without charm), which are proportional to
j
V
cb
j
2
and
j
V
ub
j
2
, respectively.
There are two methods to extract these two CKM ele-
ments from
B
decays, one based on inclusive and the other
on exclusive semileptonic decays. Exclusive decays offer
better kinematic constraints and thus more effective back-
ground suppression than inclusive decays, but the lower
branching fractions result in lower event yields. Since the
experimental and theoretical techniques for these two ap-
proaches are different and largely independent, they can
provide important cross-checks of our understanding of the
theory and the measurements. An overview of the deter-
mination of
j
V
ub
j
using both approaches can be found in a
recent review [
4
].
In this paper, we present a study of four exclusive
charmless semileptonic decay modes,
B
0
!
‘
þ
,
B
þ
!
0
‘
þ
,
B
0
!
‘
þ
, and
B
þ
!
0
‘
þ
[
5
], and
a determination of
j
V
ub
j
. Here,
‘
refers to a charged lepton,
either
e
þ
or
þ
, and
refers to a neutrino, either
e
or
.
This analysis represents an update of an earlier measure-
ment [
6
] that was based on a significantly smaller data set.
For the current analysis, the signal yields and background
suppression have been improved and the systematic un-
certainties have been reduced through the use of improved
reconstruction and signal extraction methods, combined
with more detailed background studies.
The principal experimental challenge is the separation of
the
B
!
X
u
‘
from the dominant
B
!
X
c
‘
decays, for
which the inclusive branching fraction is a factor of 50
larger. Furthermore, the isolation of individual exclusive
charmless decays from all other
B
!
X
u
‘
decays is diffi-
cult, because the exclusive branching ratios are typically
only
10%
of
B
ð
B
!
X
u
‘
Þ¼ð
2
:
29
0
:
34
Þ
10
3
[
7
],
the inclusive branching fraction for charmless semileptonic
B
decays.
The reconstruction of signal decays in
e
þ
e
!
ð
4
S
Þ!
B
B
events requires the identification of three
types of particles, the hadronic state
X
u
producing one or
two charged and/or neutral final-state pions, the charged
lepton, and the neutrino. The presence of the neutrino is
inferred from the missing momentum and energy in the
whole event.
The event yields for each of the four signal decay modes
are extracted from a binned maximum-likelihood fit to the
three-dimensional distributions of the variables
m
ES
, the
energy-substituted
B
-meson mass,
E
, the difference be-
tween the reconstructed and the expected
B
-meson energy,
and
q
2
, the momentum transfer squared from the
B
meson
to the final-state hadron. The measured differential decay
rates in combination with recent form-factor (FF)
calculations are used to determine
j
V
ub
j
. By measuring
both
B
!
‘
and
B
!
‘
decays simultaneously, we
reduce the sensitivity to the cross feed between these two
decay modes and some of the background contributions.
The most promising decay mode for a precise determi-
nation of
j
V
ub
j
, both experimentally and theoretically, is
the
B
!
‘
decay, for which a number of measurements
exist. The first measurement of this type was performed by
the CLEO Collaboration [
8
]. In addition to the earlier
B
A
B
AR
measurement mentioned above [
6
], there is a
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032007 (2011)
032007-4
more recent
B
A
B
AR
measurement [
9
] in which somewhat
looser criteria on the neutrino selection were applied,
resulting in a larger signal sample but also substantially
higher backgrounds. These analyses also rely on the mea-
surement of the missing energy and momentum of the
whole event to reconstruct the neutrino, without explicitly
reconstructing the second
B
-meson decay in the event, but
are based on smaller data sets than the one presented here.
Recently, a number of measurements of both
B
!
‘
and
B
!
‘
decays were published, in which the
B
B
events
were tagged by a fully reconstructed hadronic or semi-
leptonic decay of the second
B
meson in the event [
10
,
11
].
These analyses have led to a simpler and more precise
reconstruction of the neutrino and very low backgrounds.
However, this is achieved at the expense of much smaller
signal samples, which limit the statistical precision of the
form-factor measurement.
II. FORM FACTORS
A. Overview
The advantage of charmless semileptonic decays over
charmless hadronic decays of the
B
meson is that the
leptonic and hadronic components of the matrix element
factorize. The hadronic matrix element is difficult to calcu-
late, since it must take into account physical mesons, rather
than free quarks. Therefore higher-order perturbative cor-
rections and nonperturbative long-distance hadronization
processes cannot be ignored. To overcome these difficulties,
a set of Lorentz-invariant form factors has been introduced
that give a global description of these QCD processes.
Avariety of theoretical predictions for these form factors
exists. They are based on QCD calculations, such as lattice
QCD and sum rules, in addition to quark models. We will
make use of a variety of these calculations to assess their
impact on the determination of
j
V
ub
j
from measurements
of the decay rates.
The
V
A
structure of the hadronic current is invoked,
along with the knowledge of the transformation properties
of the final-state meson, to formulate these form factors.
They are functions of
q
2
¼
m
2
W
, the mass squared of the
virtual
W
,
q
2
¼ð
P
‘
þ
P
Þ
2
¼ð
P
B
P
X
Þ
2
¼
M
2
B
þ
m
2
X
2
M
B
E
X
:
(1)
Here,
P
‘
and
P
refer to the four-momenta of the charged
lepton and the neutrino,
M
B
and
P
B
to the mass and the
four-momentum of the
B
meson, and
m
X
and
E
X
are the
mass and energy (in the
B
-meson rest frame) of the final-
state meson
X
u
.
We distinguish two main categories of exclusive semi-
leptonic decays: decays to pseudoscalar mesons,
B
!
‘
or
B
þ
!
‘
þ
, and decays to vector mesons,
B
!
‘
or
B
þ
!
!‘
þ
.
Figure
1
shows the phase space for
B
!
‘
and
B
!
‘
decays in terms of
q
2
and
E
‘
, the energy of the
charged lepton in the
B
-meson rest frame. The difference
between the distributions is due to the different spin struc-
ture of the decays.
B. Form factors
1.
B
decays to pseudoscalar mesons:
B
!
‘
For decays to a final-state pseudoscalar meson, the
hadronic matrix element is usually written in terms of
two form factors,
f
þ
ð
q
2
Þ
and
f
0
ð
q
2
Þ
[
12
,
13
],
h
ð
P
Þj
u
b
j
B
ð
P
B
Þi
¼
f
þ
ð
q
2
Þ
ð
P
B
þ
P
Þ
M
2
B
m
2
q
2
q
þ
f
0
ð
q
2
Þ
M
2
B
m
2
q
2
q
;
(2)
where
P
and
P
B
are the four-momenta of the final-state
pion and the parent
B
meson, and
m
and
M
B
are their
masses. This expression can be simplified for leptons with
small masses, such as electrons and muons, because in the
limit of
m
‘
M
B
the second term can be neglected. We
are left with a single form factor
f
þ
ð
q
2
Þ
, and the differen-
tial decay rate becomes
d
ð
B
0
!
‘
þ
Þ
dq
2
d
cos
W‘
¼j
V
ub
j
2
G
2
F
p
3
32
3
sin
2
W‘
j
f
þ
ð
q
2
Þj
2
;
(3)
where
p
is the momentum of the pion in the rest
frame of the
B
meson, and
q
2
varies from zero to
q
2
max
¼
ð
M
B
m
Þ
2
.
The decay rate depends on the third power of the pion
momentum, suppressing the rate at high
q
2
. The rate also
depends on
sin
2
W‘
, where
W‘
is the angle of the charged-
lepton momentum in the
W
rest frame with respect to the
direction of the
W
boost from the
B
rest frame. The
combination of these two factors leads to a lepton-
momentum spectrum that is peaked well below the kine-
matic limit (see Fig.
1
).
2.
B
decays to vector mesons:
B
!
‘
For decays with a vector meson in the final state, the
polarization vector
of the vector meson plays an impor-
tant role. The hadronic current is written in terms of four
FIG. 1 (color). Simulated distributions of
q
2
versus
E
‘
for
(a)
B
!
‘
and (b)
B
!
‘
decays.
E
‘
is the lepton energy
in the
B
-meson rest frame.
STUDY OF
B
!
l
AND
...
PHYSICAL REVIEW D
83,
032007 (2011)
032007-5
form factors, of which only three (
A
i
with
i
¼
0
;
1
;
2
) are
independent [
12
,
13
],
h
ð
P
;
Þj
V
A
j
B
ð
P
B
Þi ¼
2
iV
ð
q
2
Þ
M
B
þ
m
P
P
B
ð
M
B
þ
m
Þ
A
1
ð
q
2
Þ
þ
A
2
ð
q
2
Þ
M
B
þ
m
P
B
ð
P
B
þ
P
Þ
þ
2
m
P
B
q
2
q
½
A
3
ð
q
2
Þ
A
0
ð
q
2
Þ
;
(4)
where
m
and
P
refer to the vector-meson mass and four-
momentum. Again, a simplification can be made for low-
mass charged leptons. The term with
q
can be neglected,
so there are effectively only three form factors for electrons
and muons: the axial-vector form factors,
A
1
ð
q
2
Þ
and
A
2
ð
q
2
Þ
, and the vector form factor,
V
ð
q
2
Þ
. Instead of using
these form factors, the full differential decay rate is usually
expressed in terms of the helicity amplitudes correspond-
ing to the three helicity states of the
meson,
H
ð
q
2
Þ¼ð
M
B
þ
m
Þ
A
1
ð
q
2
Þ
2
M
B
p
ð
M
B
þ
m
Þ
2
V
ð
q
2
Þ
;
H
0
ð
q
2
Þ¼
M
B
þ
m
2
m
ffiffiffiffiffi
q
2
p
ð
M
2
B
m
2
q
2
Þ
A
1
ð
q
2
Þ
4
M
2
B
p
2
ð
M
B
þ
m
Þ
2
A
2
ð
q
2
Þ
;
(5)
where
p
is the momentum of the final-state
meson in the
B
rest frame. While
A
1
dominates the three helicity ampli-
tudes,
A
2
contributes only to
H
0
, and
V
contributes only
to
H
.
Thus, the differential decay rate can be written as
d
ð
B
!
‘
Þ
dq
2
d
cos
W‘
¼j
V
ub
j
2
G
2
F
p
q
2
128
3
M
2
B
sin
2
W‘
j
H
0
j
2
þð
1
cos
W‘
Þ
2
j
H
þ
j
2
2
þð
1
þ
cos
W‘
Þ
2
j
H
j
2
2
:
(6)
The
V
A
nature of the charged weak current leads to a
dominant contribution from
H
and a distribution of
events characterized by a forward peak in
cos
W‘
and
high lepton momenta (see Fig.
1
).
C. Form-factor calculations and models
The
q
2
dependence of the form factors can be extracted
from the data. Since the differential decay rates are pro-
portional to the product of
j
V
ub
j
2
and the form-factor
terms, we need at least one point in
q
2
at which the form
factor is predicted in order to extract
j
V
ub
j
from the mea-
sured branching fractions.
Currently, predictions of form factors are based on
(i) quark-model calculations, the Isgur-Scora-
Grinstein-Wise model (ISGW2) [
14
],
(ii) QCD light-cone sum rules (LCSR) [
15
–
19
],
(iii) lattice QCD calculations (LQCD) [
20
–
23
].
These calculations will also be used to simulate the kine-
matics of the signal decay modes and thus might impact the
detection efficiency, and thereby the branching-fraction
measurement. The two QCD calculations result in predic-
tions for different regions of phase space. The lattice
calculations are only available in the high-
q
2
region, while
LCSR provide information near
q
2
¼
0
. Interpolations
between these two regions can be constrained by unitarity
and analyticity requirements [
24
,
25
].
Figure
2
shows the
q
2
distributions for
B
!
‘
and
B
!
‘
decays for various form-factor calculations. The
uncertainties in these predictions are not indicated. For
B
!
‘
decays, they are largest at low
q
2
for LQCD
predictions and largest at high
q
2
for LCSR calculations.
Estimates of the uncertainties of the calculations are cur-
rently not available for
B
!
‘
decays.
The ISGW2 [
14
] is a constituent quark model with
relativistic corrections. Predictions extend over the full
q
2
range; they are normalized at
q
2
q
2
max
. The form
factors are parameterized as
f
þ
ð
q
2
Þ¼
f
ð
q
2
max
Þ
1
þ
1
6
N
2
ð
q
2
max
q
2
Þ
N
;
(7)
where
is the charge radius of the final-state meson and
N
¼
2
(
N
¼
3
) for decays to pseudoscalar (vector) me-
sons. The uncertainties of the predictions by this model are
difficult to quantify.
QCD light-cone sum-rule calculations are nonperturba-
tive and combine the idea of QCD sum rules with twist
expansions performed to
O
ð
s
Þ
. These calculations pro-
vide estimates of various form factors at low to intermedi-
ate
q
2
, for both pseudoscalar and vector decays. The
)
2
(GeV
2
q
0
5
10
15
20
25
)
-1
s
-2
(GeV
-2
|
ub
|V
2
/dq
Γ
d
0
0.2
0.4
0.6
12
10
×
LCSR 1
LCSR 2
HPQCD
ISGW2
)
2
(GeV
2
q
0
5
10
15
20
)
-1
s
-2
(GeV
-2
|
ub
|V
2
/dq
Γ
d
0
0.2
0.4
0.6
0.8
1
1.2
12
10
×
LCSR
ISGW2
FIG. 2 (color).
q
2
distributions for
B
!
‘
(left) and
B
!
‘
(right) decays, based on form-factor predictions from the
ISGW2 model [
14
], LCSR calculations (LCSR 1 [
15
] and LCSR
2[
19
] for
B
!
‘
and LCSR [
17
] for
B
!
‘
), and the
HPQCD [
23
] lattice calculation. The extrapolations of the QCD
predictions to the full
q
2
range are marked as dashed lines.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032007 (2011)
032007-6
overall normalization is predicted at low
q
2
with typical
uncertainties of
10
–
13%
[
15
,
17
].
Lattice QCD calculations can potentially provide heavy-
to-light-quark form factors from first principles.
Unquenched lattice calculations, in which quark-loop ef-
fects in the QCD vacuum are incorporated, are now avail-
able for the
B
!
‘
form factors from the Fermilab/
MILC [
22
] and the HPQCD [
23
] Collaborations. Both
calculations account for three dynamical quark flavors,
the mass-degenerate
u
and
d
quarks and a heavier
s
quark,
but they differ in the way the
b
quark is simulated.
Predictions for
f
0
ð
q
2
Þ
and
f
þ
ð
q
2
Þ
are shown in Fig.
3
.
The two lattice calculations agree within the stated uncer-
tainties, which are significantly smaller than those of ear-
lier quenched approximations.
D. Form-factor parametrizations
Neither the lattice nor the LCSR QCD calculations
predict the form factors over the full
q
2
range. Lattice
calculations are restricted to small hadron momenta, i.e.,
to
q
2
q
2
max
=
2
, while LCSR work best at small
q
2
. If the
q
2
spectrum is well measured, the shape of the form factors
can be constrained, and the QCD calculations provide the
normalization necessary to determine
j
V
ub
j
.
A number of parametrizations of the pseudoscalar
form factor
f
þ
ð
q
2
Þ
are available in the literature. The
following four parametrizations are commonly used. All
of them include at least one pole term at
q
2
¼
m
2
B
, with
m
B
¼
5
:
325 GeV
<M
B
þ
m
.
(1) Becirevic-Kaidalov (BK) [
26
]:
f
þ
ð
q
2
Þ¼
f
þ
ð
0
Þ
ð
1
q
2
=m
2
B
Þð
1
BK
q
2
=m
2
B
Þ
;
(8)
f
0
ð
q
2
Þ¼
f
0
ð
0
Þ
1
1
BK
q
2
=m
2
B
;
(9)
where
f
þ
ð
0
Þ
and
f
0
ð
0
Þ
set the normalizations, and
BK
and
BK
define the shapes. The BK parametri-
zation has been applied in fits to the HPQCD lattice
predictions for form factors, with the constraint
f
þ
ð
0
Þ¼
f
0
ð
0
Þ
.
(2) Ball-Zwicky (BZ) [
15
,
16
]:
f
þ
ð
q
2
Þ¼
f
þ
ð
0
Þ
2
4
1
1
q
2
=m
2
B
þ
r
BZ
q
2
=m
2
B
ð
1
q
2
=m
2
B
Þð
1
BZ
q
2
=m
2
B
Þ
3
5
;
(10)
where
f
þ
ð
0
Þ
is the normalization, and
BZ
and
r
BZ
determine the shape. This is an extension of the BK
ansatz, related by the simplification
BK
¼
BZ
¼
r
BZ
. This ansatz was used to extend the LCSR
predictions to higher
q
2
, as shown in Fig.
3
.
(3) Boyd, Grinstein, Lebed (BGL) [
24
,
25
]:
f
þ
ð
q
2
Þ¼
1
P
ð
q
2
Þ
ð
q
2
;q
2
0
Þ
X
k
max
k
¼
0
a
k
ð
q
2
0
Þ½
z
ð
q
2
;q
2
0
Þ
k
;
(11)
z
ð
q
2
;q
2
0
Þ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
2
þ
q
2
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
2
þ
q
2
0
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
2
þ
q
2
q
þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
2
þ
q
2
0
q
;
(12)
where
m
¼
M
B
m
and
q
2
0
is a free parameter
[
27
]. The so-called Blaschke factor
P
ð
q
2
Þ¼
z
ð
q
2
;m
2
B
Þ
accounts for the pole at
q
2
¼
m
2
B
, and
ð
q
2
;q
2
0
Þ
is an arbitrary analytic function [
28
]
whose choice only affects the particular values of
the series coefficients
a
k
. In this expansion in the
variable
z
, the shape is given by the values of
a
k
,
with truncation at
k
max
¼
2
or 3. The expansion
parameters are constrained by unitarity,
P
k
a
2
k
1
.
Becher and Hill [
25
] have pointed out that, due to
the large
b
-quark mass, this bound is far from being
saturated. Assuming that the ratio
=m
b
is less than
0.1, the heavy-quark bound is approximately 30
times more constraining than the bound from uni-
tarity alone,
P
k
a
2
k
ð
=m
b
Þ
3
0
:
001
. For more
details, we refer to the literature [
24
,
25
].
)
2
(GeV
2
q
0
5
10
15
20
25
+,0
f
0
2
4
6
8
10
HPQCD
FNAL/MILC
LCSR
0
f
+
f
FIG. 3 (color online). Predictions of the form factors
f
þ
and
f
0
for
B
!
‘
decays based on unquenched LQCD calcula-
tions by the FNAL/MILC [
22
] and HPQCD [
23
] Collaborations
(data points with combined statistical and systematic errors) and
LCSR calculations [
15
] (solid black lines). The dashed lines
indicate the extrapolations of the LCSR predictions to
q
2
>
16 GeV
2
.
STUDY OF
B
!
l
AND
...
PHYSICAL REVIEW D
83,
032007 (2011)
032007-7
(4) Bourrely, Caprini, Lellouch (BCL) [
29
]:
f
þ
ð
q
2
Þ¼
1
1
q
2
=m
2
B
X
k
max
k
¼
0
b
k
ð
q
2
0
Þ
½
z
ð
q
2
;q
2
0
Þ
k
ð
1
Þ
k
k
max
1
k
k
max
þ
1
½
z
ð
q
2
;q
2
0
Þ
k
max
þ
1
;
(13)
where the variable
z
is defined as in Eq. (
12
) with free
parameter
q
2
0
[
27
]. In this expansion, the shape is
given by the values of
b
k
, with truncation at
k
max
¼
2
or 3. The BCL parametrization exhibits the QCD
scaling behavior
f
þ
ð
q
2
Þ/
1
=q
2
at large
q
2
.
The BK and BZ parametrizations are intuitive and have
few free parameters. Fits to the previous
B
A
B
AR
form-factor
measurements using these parametrizations have shown
that they describe the data quite well [
9
]. The BGL and
BCL parametrizations are based on fundamental theoreti-
cal concepts like analyticity and unitarity. The
z
expansion
avoids
ad hoc
assumptions about the number of poles and
pole masses, and it can be adapted to the precision of the
data.
III. DATA SAMPLE, DETECTOR,
AND SIMULATION
A. Data sample
The data used in this analysis were recorded with the
B
A
B
AR
detector at the PEP-II energy-asymmetric
e
þ
e
collider operating at the
ð
4
S
Þ
resonance. A sample of
377
10
6
ð
4
S
Þ!
B
B
events, corresponding to an inte-
grated luminosity of
349 fb
1
, was collected. An addi-
tional sample of
35
:
1fb
1
was recorded at a center-of-
mass (c.m.) energy approximately 40 MeV below the
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
contributions from the data collected
at the
ð
4
S
Þ
resonance. The principal source of these
hadronic non-
B
B
events is
e
þ
e
annihilation in the con-
tinuum to
q
q
pairs, where
q
¼
u; d; s; c
refers to quarks.
The relative normalization of the off-resonance and on-
resonance data samples is derived from luminosity mea-
surements, which are based on the number of detected
þ
pairs and the QED cross section for
e
þ
e
!
þ
production, adjusted for the small difference in
c.m. energy. The systematic error on the relative normal-
ization is estimated to be
0
:
25%
.
B.
B
A
B
AR
detector
The
B
A
B
AR
detector and event reconstruction are de-
scribed in detail elsewhere [
30
,
31
]. 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 drift chamber (DCH) filled with a
helium-isobutane gas mixture. Charged particles of differ-
ent masses are distinguished by their ionization energy loss
in the tracking devices and by a ring-imaging Cerenkov
detector (DIRC). Electromagnetic showers from electrons
and photons are measured in a finely segmented CsI(Tl)
calorimeter (EMC). These detector components are em-
bedded in the 1.5-T magnetic field of the solenoid. The
magnet flux return steel is segmented and instrumented
(IFR) with planar resistive plate chambers and limited
streamer tubes, which detect particles penetrating the mag-
net coil and steel.
The efficiency for the reconstruction of charged particles
inside the fiducial volume of the tracking system exceeds
96%
and is well reproduced by Monte Carlo (MC) simu-
lation. An effort has been made to minimize fake charged
tracks, caused by multiple counting of a single low-energy
track curling in the DCH, split tracks, or background-
generated tracks. The average uncertainty in the track-
reconstruction efficiency is estimated to range from
0
:
25%
to
0
:
5%
per track.
To remove beam-generated background and noise in the
EMC, photon candidates are required to have an energy of
more than 50 MeV and a shower shape that is consistent
with an electromagnatic shower. The photon efficiency and
its uncertainty are evaluated by comparing
!
to
!
samples and by studying
e
þ
e
!
þ
ð
Þ
events.
Electron candidates are selected on the basis of the ratio
of the energy detected in the EMC and the track momen-
tum, the EMC shower shape, the energy loss in the SVT
and DCH, and the angle of the Cerenkov photons recon-
structed in the DIRC. The energy of electrons is corrected
for bremsstrahlung detected as photons emitted close to the
electron direction. Muons are identified by using a neural
network that combines the information from the IFR with
the measured track momentum and the energy deposition
in the EMC.
The electron and muon identification efficiencies and the
probabilities to misidentify a pion, kaon, or proton as an
electron or muon are measured as a function of the labo-
ratory momentum and angles using high-purity samples of
particles selected from data. These measurements are per-
formed separately for positive and negative leptons. For the
determination of misidentification probabilities, knowl-
edge of the inclusive momentum spectra of positive and
negative hadrons and the measured fractions of pions,
kaons, and protons and their misidentification rates is used.
Within the acceptance of the SVT, DCH, and EMC
defined by the polar angle in the laboratory frame,
0
:
72
<
cos
lab
<
0
:
92
, the average electron efficiency
for laboratory momenta above 0.5 GeV is
93%
, largely
independent of momentum. The average hadron misiden-
tification rate is less than
0
:
2%
. Within the same polar-
angle acceptance, the average muon efficiency rises with
laboratory momentum to reach a plateau of about
70%
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032007 (2011)
032007-8
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
2
:
5%
, 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 assumed to
originate from the primary vertex. Photon pairs with an
invariant mass within 17.5 MeVof the nominal
0
mass are
considered
0
candidates. 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.
C. Monte Carlo simulation
We assume that the
ð
4
S
Þ
resonance decays exclusively
to
B
B
pairs [
32
] and that the nonresonant cross section for
e
þ
e
!
q
q
is 3.4 nb, compared to the
ð
4
S
Þ
peak cross
section of 1.05 nb. We use MC techniques [
33
] to simulate
the production and decay of
B
B
and
q
q
pairs and the
detector response [
34
] to estimate signal and background
efficiencies and to extract the expected signal and back-
ground distributions. The size of the simulated sample of
generic
B
B
events exceeds the
B
B
data sample by about a
factor of 3, while the MC samples for inclusive and ex-
clusive
B
!
X
u
‘
decays exceed the data samples by
factors of 15 or larger. The MC sample for
q
q
events is
comparable in size to the
q
q
data sample recorded at the
ð
4
S
Þ
resonance.
Information extracted from studies of selected data con-
trol samples on efficiencies and resolution is used to im-
prove the accuracy of the simulation. Specifically,
comparisons of data with the MC simulations reveal small
differences in the tracking efficiencies and calorimeter
resolution. We apply corrections to account for these dif-
ferences. The MC simulations include radiative effects
such as bremsstrahlung in the detector material and
initial-state and final-state radiation [
35
]. Adjustments
are made to take into account the small variations of the
beam energies over time.
For this analysis, no attempt is made to reconstruct
K
0
L
interacting in the EMC or IFR. Since a
K
0
L
deposits only a
small fraction of its energy in the EMC,
K
0
L
production can
have a significant impact on the energy and momentum
balance of the whole event, and thereby the neutrino re-
construction. It is therefore important to verify that the
production rate of neutral kaons and their interactions in
the detector are well reproduced.
From detailed studies of large data and MC samples of
D
0
!
K
0
L
þ
and
D
0
!
K
0
S
þ
decays, corrections
to the simulation of the
K
0
L
detection efficiency and energy
deposition in the EMC are determined. The MC simulation
reproduces the efficiencies well for
K
0
L
laboratory mo-
menta above 0.7 GeV. At lower momenta, the difference
between MC and data increases significantly; in this range,
the MC efficiencies are reduced by randomly eliminating
a fraction of the associated EMC showers. The energy
deposited by
K
0
L
in the EMC is significantly underesti-
mated by the simulation for momenta up to 1.5 GeV. At
higher momenta, the differences decrease. Thus, the simu-
lated energies are scaled by factors varying between 1.20
and 1.05 as a function of momentum. Furthermore, assum-
ing equal inclusive production rates for
K
0
L
and
K
0
S
,we
verify the production rate as a function of momentum, by
comparing data and MC-simulated
K
0
S
momentum spectra.
We observe differences at small momenta; below 0.4 GeV,
the data rate is lower by as much as
22
7%
, compared to
the MC simulation. To account for this difference, we
reduce the rate of low-momentum
K
0
L
in the simulation
by randomly transforming the excess
K
0
L
into a fake pho-
ton, i.e., we replace the energy deposited in the EMC by the
total
K
0
L
energy and set the mass to zero. Thus, we correct
the overall energy imbalance created by the excess in
K
0
L
production.
For reference, the values of the branching fractions,
lifetimes, and parameters most relevant to the MC simula-
tion are presented in Tables
I
and
II
.
The simulation of inclusive charmless semileptonic de-
cays
B
!
X
u
‘
is based on predictions of a heavy-quark
expansion (HQE) (valid to
O
ð
s
Þ
[
40
]) for the differential
decay rates. This calculation produces a smooth hadronic
TABLE I. Branching fractions and their errors for the semi-
leptonic
B
decays used in this analysis.
Decay
Unit
B
0
B
Reference
B
!
‘
10
4
0
:
40
0
:
09
[
36
]
B
!
0
‘
10
4
0
:
21
0
:
21
[
36
]
B
!
!‘
10
4
1
:
15
0
:
16
[
36
]
B
!
X
u
‘
10
3
2
:
25
0
:
22 2
:
41
0
:
22
[
7
]
B
!
D‘
10
2
2
:
17
0
:
08 2
:
32
0
:
09
[
36
,
37
]
B
!
D
‘
10
2
5
:
11
0
:
19 5
:
48
0
:
27
[
36
,
37
]
B
!
D
1
‘
10
2
0
:
69
0
:
14 0
:
77
0
:
15
[
36
,
37
]
B
!
D
2
‘
10
2
0
:
56
0
:
11 0
:
59
0
:
12
[
36
,
37
]
B
!
D
0
‘
10
2
0
:
81
0
:
24 0
:
88
0
:
26
[
36
,
37
]
B
!
D
0
1
‘
10
2
0
:
76
0
:
22 0
:
82
0
:
25
[
36
,
37
]
TABLE II. Values of parameters used in the MC simulation:
form factors for
B
!
D‘
and
B
!
D
‘
decays, based on the
parametrization of Caprini, Lellouch, and Neubert [
38
], the
B
0
lifetime, the
B
0
to
B
þ
lifetime ratio, and relative branching
fraction at the
ð
4
S
Þ
resonance.
Parameter
Value
Reference
B
!
D‘
FF
2
D
1
:
18
0
:
04
0
:
04
[
44
,
45
]
B
!
D
‘
FF
2
D
1
:
191
0
:
048
0
:
028
[
39
]
B
!
D
‘
FF
R
1
1
:
429
0
:
061
0
:
044
[
39
]
B
!
D
‘
FF
R
2
0
:
827
0
:
038
0
:
022
[
39
]
B
0
lifetime
0
(ps)
1
:
530
0
:
009
[
7
]
B
lifetime ratio
þ
=
0
1
:
071
0
:
009
[
7
]
ð
4
S
Þ
ratio
f
þ
=f
00
1
:
065
0
:
026
[
36
]
STUDY OF
B
!
l
AND
...
PHYSICAL REVIEW D
83,
032007 (2011)
032007-9
mass spectrum. The hadronization of
X
u
with masses
above
2
m
is performed by JETSET [
41
]. To describe
the dynamics of the
b
quark inside the
B
meson, we use
HQE parameters extracted from global fits to moments of
inclusive lepton-energy and hadron-mass distributions in
B
!
X
c
‘
decays and moments of inclusive photon-
energy distributions in
B
!
X
s
decays [
42
]. The specific
values of the HQE parameters in the shape-function
scheme are
m
b
¼
4
:
631
0
:
034 GeV
and
2
¼
0
:
184
0
:
36 GeV
2
; they have a correlation of
¼
0
:
27
.
Samples of exclusive semileptonic decays involving low-
mass charmless mesons (
,
,
!
,
,
0
) are simulated
separately and then combined with samples of decays to
nonresonant and higher-mass resonant states, so that the
cumulative distributions of the hadron mass, the momen-
tum transfer squared, and the lepton momentum reproduce
the HQE predictions. The generated distributions are re-
weighted to accommodate variations due to specific
choices of the parameters for the inclusive and exclusive
decays. The overall normalization is adjusted to reproduce
the measured inclusive
B
!
X
u
‘
branching fraction.
For the generation of decays involving charmless pseu-
doscalar mesons, we choose two approaches. For the signal
decay
B
!
‘
, we use the ansatz by Becirevic and
Kaidalov [
26
] for the
q
2
dependence, with the single
parameter
BK
set to the value determined in a previous
B
A
B
AR
analysis [
9
]of
B
!
‘
decays,
BK
¼
0
:
52
0
:
06
. For decays to
and
0
, we use the form-
factor parametrization of Ball and Zwicky with specific
values reported in [
18
].
Decays involving charmless vector mesons (
; !
) are
generated based on form factors determined from LCSR by
Ball, Braun, and Zwicky [
17
]. We use the parametrization
proposed by the authors to describe the
q
2
dependence of
the form factors in terms of a modified pole ansatz using up
to three independent parameters
r
1
,
r
2
, and
m
fit
. Table
III
shows the suggested values for these parameters.
m
fit
refers
to an effective pole mass that accounts for contributions
from higher-mass
B
mesons with
J
P
¼
1
, and
r
1
and
r
2
give the relative scale of the two pole terms.
For the simulation of the dominant
B
!
X
c
‘
decays,
we have chosen a variety of models. For
B
!
D‘
and
B
!
D
‘
decays, we use parametrizations [
38
,
43
] of the
form factors based on heavy quark effective theory
(HQET). In the limit of negligible lepton masses, decays
to pseudoscalar mesons are described by a single
form factor for which the
q
2
dependence is given by a
slope parameter. We use the world average [
36
], updated
for recent precise measurements by the
B
A
B
AR
Collaboration [
44
,
45
]. Decays to vector mesons are de-
scribed 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:
2
D
,
R
1
, and
R
2
. We use the most precise
B
A
B
AR
measurement [
39
] of these parameters.
For the generation of the semileptonic decays to
D
resonances (four
L
¼
1
states), we use the ISGW2 [
14
]
model. At present, the sum of the branching fractions for
these four decay modes is measured to be
1
:
7%
, but so far
only the decays
D
!
D
and
D
!
D
have been
reconstructed, while the total individual branching frac-
tions for these four states remain unknown. Since the
measured inclusive branching fraction for
B
!
X
c
‘
ex-
ceeds the sum of the measured branching fractions of all
exclusive semileptonic decays by about
1
:
0%
, and since
nonresonant
B
!
D
ðÞ
‘
decays have not been observed
[
37
], we assume that the missing decays are due to
B
!
D
‘
, involving hadronic decays of the
D
mesons that
have not yet been measured. To account for the observed
deficit, we increase the
B
!
D
‘
branching fractions by
60%
and inflate the errors by a factor of 3.
IV. EVENT RECONSTRUCTION
AND CANDIDATE SELECTION
In the following, we describe the selection and kine-
matic reconstruction of signal candidates, the definition of
the various background classes, and the application of
neural networks to suppress these backgrounds.
A. Signal-candidate selection
Signal candidates are selected from events having
at least four charged tracks. The reconstruction of the
four signal decay modes,
B
0
!
‘
þ
,
B
þ
!
0
‘
þ
,
B
0
!
‘
þ
, and
B
þ
!
0
‘
þ
, requires the identifica-
tion of a charged lepton, the reconstruction of the hadronic
state consisting of one or more charged or neutral pions,
and the reconstruction of the neutrino from the missing
energy and missing momentum of the whole event.
TABLE III. Parametrization of the LCSR form-factor calculations [
15
,
17
] for decays to pseudoscalar mesons
and
0
(
f
þ
) and
vector mesons
and
!
(
A
1
;A
2
;V
).
Form factor
f
þ
A
1
A
2
V
A
!
1
A
!
2
V
!
F
ð
0
Þ
0.273
0.242
0.221
0.323
0.219
0.198
0.293
r
1
0.122
0.009
1.045
0.006
1.006
r
2
0.155
0.240
0.212
0
:
721
0.217
0.192
0
:
713
m
2
fit
ð
GeV
2
Þ
31.46
37.51
40.82
38.34
37.01
41.24
37.45
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032007 (2011)
032007-10