of 25
Measurement of the
D
0
π
e
þ
ν
e
differential decay branching fraction as a
function of
q
2
and study of form factor parametrizations
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
M. J. Lee,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov,
9a,9b,9c
A. R. Buzykaev,
9a
V. P. Druzhinin,
9a,9b
V. B. Golubev,
9a,9b
E. A. Kravchenko,
9a,9b
A. P. Onuchin,
9a,9b,9c
S. I. Serednyakov,
9a,9b
Yu. I. Skovpen,
9a,9b
E. P. Solodov,
9a,9b
K. Yu. Todyshev,
9a,9b
A. J. Lankford,
10
M. Mandelkern,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
C. Campagnari,
12
M. Franco Sevilla,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
W. S. Lockman,
13
W. Panduro Vazquez,
13
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
T. S. Miyashita,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
M. Röhrken,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
B. G. Pushpawela,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17
,
W. H. Toki,
17
B. Spaan,
18
D. Bernard,
19
M. Verderi,
19
S. Playfer,
20
D. Bettoni,
21a
C. Bozzi,
21a
R. Calabrese,
21a,21b
G. Cibinetto,
21a,21b
E. Fioravanti,
21a,21b
I. Garzia,
21a,21b
E. Luppi,
21a,21b
L. Piemontese,
21a
V. Santoro,
21a
A. Calcaterra,
22
R. de Sangro,
22
G. Finocchiaro,
22
S. Martellotti,
22
P. Patteri,
22
I. M. Peruzzi,
22
,
M. Piccolo,
22
M. Rama,
22
A. Zallo,
22
R. Contri,
23a,23b
M. Lo Vetere,
23a,23b
M. R. Monge,
23a,23b
S. Passaggio,
23a
C. Patrignani,
23a,23b
E. Robutti,
23a
B. Bhuyan,
24
V. Prasad,
24
A. Adametz,
25
U. Uwer,
25
H. M. Lacker,
26
P. D. Dauncey,
27
U. Mallik,
28
C. Chen,
29
J. Cochran,
29
S. Prell,
29
H. Ahmed,
30
A. V. Gritsan,
31
N. Arnaud,
32
M. Davier,
32
D. Derkach,
32
G. Grosdidier,
32
F. Le Diberder,
32
A. M. Lutz,
32
B. Malaescu,
32
P. Roudeau,
32
A. Stocchi,
32
G. Wormser,
32
D. J. Lange,
33
D. M. Wright,
33
J. P. Coleman,
34
J. R. Fry,
34
E. Gabathuler,
34
D. E. Hutchcroft,
34
D. J. Payne,
34
C. Touramanis,
34
A. J. Bevan,
35
F. Di Lodovico,
35
R. Sacco,
35
G. Cowan,
36
J. Bougher,
37
D. N. Brown,
37
C. L. Davis,
37
A. G. Denig,
38
M. Fritsch,
38
W. Gradl,
38
K. Griessinger,
38
A. Hafner,
38
K. R. Schubert,
38
R. J. Barlow,
39
,
G. D. Lafferty,
39
R. Cenci,
40
B. Hamilton,
40
A. Jawahery,
40
D. A. Roberts,
40
R. Cowan,
41
G. Sciolla,
41
R. Cheaib,
42
P. M. Patel,
42
,*
S. H. Robertson,
42
N. Neri,
43a
F. Palombo,
43a,43b
L. Cremaldi,
44
R. Godang,
44
P. Sonnek,
44
D. J. Summers,
44
M. Simard,
45
P. Taras,
45
G. De Nardo,
46a,46b
G. Onorato,
46a,46b
C. Sciacca,
46a,46b
M. Martinelli,
47
G. Raven,
47
C. P. Jessop,
48
J. M. LoSecco,
48
K. Honscheid,
49
R. Kass,
49
E. Feltresi,
50a,50b
M. Margoni,
50a,50b
M. Morandin,
50a
M. Posocco,
50a
M. Rotondo,
50a
G. Simi,
50a,50b
F. Simonetto,
50a,50b
R. Stroili,
50a,50b
S. Akar,
51
E. Ben-Haim,
51
M. Bomben,
51
G. R. Bonneaud,
51
H. Briand,
51
G. Calderini,
51
J. Chauveau,
51
Ph. Leruste,
51
G. Marchiori,
51
J. Ocariz,
51
M. Biasini,
52a,52b
E. Manoni,
52a
S. Pacetti,
52a,52b
A. Rossi,
52a
C. Angelini,
53a,53b
G. Batignani,
53a,53b
S. Bettarini,
53a,53b
M. Carpinelli,
53a,53b
,**
G. Casarosa,
53a,53b
A. Cervelli,
53a,53b
M. Chrzaszcz,
53a
F. Forti,
53a,53b
M. A. Giorgi,
53a,53b
A. Lusiani,
53a,53c
B. Oberhof,
53a,53b
E. Paoloni,
53a,53b
A. Perez,
53a
G. Rizzo,
53a,53b
J. J. Walsh,
53a
D. Lopes Pegna,
54
J. Olsen,
54
A. J. S. Smith,
54
R. Faccini,
55a,55b
F. Ferrarotto,
55a
F. Ferroni,
55a,55b
M. Gaspero,
55a,55b
L. Li Gioi,
55a
A. Pilloni,
55a,55b
G. Piredda,
55a
C. Bünger,
56
S. Dittrich,
56
O. Grünberg,
56
M. Hess,
56
T. Leddig,
56
C. Voß,
56
R. Waldi,
56
T. Adye,
57
E. O. Olaiya,
57
F. F. Wilson,
57
S. Emery,
58
G. Vasseur,
58
F. Anulli,
59
,
††
D. Aston,
59
D. J. Bard,
59
C. Cartaro,
59
M. R. Convery,
59
J. Dorfan,
59
G. P. Dubois-Felsmann,
59
W. Dunwoodie,
59
M. Ebert,
59
R. C. Field,
59
B. G. Fulsom,
59
M. T. Graham,
59
C. Hast,
59
W. R. Innes,
59
P. Kim,
59
D. W. G. S. Leith,
59
P. Lewis,
59
D. Lindemann,
59
S. Luitz,
59
V. Luth,
59
H. L. Lynch,
59
D. B. MacFarlane,
59
D. R. Muller,
59
H. Neal,
59
M. Perl,
59
,*
T. Pulliam,
59
B. N. Ratcliff,
59
A. Roodman,
59
A. A. Salnikov,
59
R. H. Schindler,
59
A. Snyder,
59
D. Su,
59
M. K. Sullivan,
59
J. Va
vra,
59
W. J. Wisniewski,
59
H. W. Wulsin,
59
M. V. Purohit,
60
R. M. White,
60
,
‡‡
J. R. Wilson,
60
A. Randle-Conde,
61
S. J. Sekula,
61
M. Bellis,
62
P. R. Burchat,
62
E. M. T. Puccio,
62
M. S. Alam,
63
J. A. Ernst,
63
R. Gorodeisky,
64
N. Guttman,
64
D. R. Peimer,
64
A. Soffer,
64
S. M. Spanier,
65
J. L. Ritchie,
66
A. M. Ruland,
66
R. F. Schwitters,
66
B. C. Wray,
66
J. M. Izen,
67
X. C. Lou,
67
F. Bianchi,
68a,68b
F. De Mori,
68a,68b
A. Filippi,
68a
D. Gamba,
68a,68b
L. Lanceri,
69a,69b
L. Vitale,
69a,69b
F. Martinez-Vidal,
70
A. Oyanguren,
70
P. Villanueva-Perez,
70
J. Albert,
71
Sw. Banerjee,
71
A. Beaulieu,
71
F. U. Bernlochner,
71
H. H. F. Choi,
71
G. J. King,
71
R. Kowalewski,
71
M. J. Lewczuk,
71
T. Lueck,
71
I. M. Nugent,
71
J. M. Roney,
71
R. J. Sobie,
71
N. Tasneem,
71
T. J. Gershon,
72
P. F. Harrison,
72
T. E. Latham,
72
H. R. Band,
73
S. Dasu,
73
Y. Pan,
73
R. Prepost,
73
and S. L. Wu
73
(
B
A
B
AR
Collaboration)
1
Laboratoire d
Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
PHYSICAL REVIEW D
91,
052022 (2015)
1550-7998
=
2015
=
91(5)
=
052022(25)
052022-1
© 2015 American Physical Society
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
9b
Novosibirsk State University, Novosibirsk 630090, Russia
9c
Novosibirsk State Technical University, Novosibirsk 630092, 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 Universität Dortmund, Fakultät Physik, D-44221 Dortmund, Germany
19
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
20
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
21a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
21b
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
23a
INFN Sezione di Genova, I-16146 Genova, Italy
23b
Dipartimento di Fisica, Università di Genova, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
25
Universität Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
26
Humboldt-Universität zu Berlin, Institut für Physik, D-12489 Berlin, Germany
27
Imperial College London, London, SW7 2AZ, United Kingdom
28
University of Iowa, Iowa City, Iowa 52242, USA
29
Iowa State University, Ames, Iowa 50011-3160, USA
30
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudia Arabia
31
Johns Hopkins University, Baltimore, Maryland 21218, USA
32
Laboratoire de l
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
Orsay, F-91898 Orsay Cedex, France
33
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
34
University of Liverpool, Liverpool L69 7ZE, United Kingdom
35
Queen Mary, University of London, London, E1 4NS, United Kingdom
36
University of London, Royal Holloway and Bedford New College,
Egham, Surrey TW20 0EX, United Kingdom
37
University of Louisville, Louisville, Kentucky 40292, USA
38
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
39
University of Manchester, Manchester M13 9PL, United Kingdom
40
University of Maryland, College Park, Maryland 20742, USA
41
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
42
McGill University, Montréal, Québec, Canada H3A 2T8
43a
INFN Sezione di Milano, I-20133 Milano, Italy
43b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
44
University of Mississippi, University, Mississippi 38677, USA
45
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
46a
INFN Sezione di Napoli, I-80126 Napoli, Italy
46b
Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
47
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, Netherlands
48
University of Notre Dame, Notre Dame, Indiana 46556, USA
49
Ohio State University, Columbus, Ohio 43210, USA
50a
INFN Sezione di Padova, I-35131 Padova, Italy
50b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
51
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS,
Université Pierre et Marie Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France
52a
INFN Sezione di Perugia, I-06123 Perugia, Italy
52b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
53a
INFN Sezione di Pisa, I-56127 Pisa, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
91,
052022 (2015)
052022-2
53b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
53c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
54
Princeton University, Princeton, New Jersey 08544, USA
55a
INFN Sezione di Roma, I-00185 Roma, Italy
55b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
56
Universität Rostock, D-18051 Rostock, Germany
57
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
58
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
59
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
60
University of South Carolina, Columbia, South Carolina 29208, USA
61
Southern Methodist University, Dallas, Texas 75275, USA
62
Stanford University, Stanford, California 94305-4060, USA
63
State University of New York, Albany, New York 12222, USA
64
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
65
University of Tennessee, Knoxville, Tennessee 37996, USA
66
University of Texas at Austin, Austin, Texas 78712, USA
67
University of Texas at Dallas, Richardson, Texas 75083, USA
68a
INFN Sezione di Torino, I-10125 Torino, Italy
68b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
69a
INFN Sezione di Trieste, I-34127 Trieste, Italy
69b
Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
70
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
71
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
72
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
73
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 22 December 2014; published 31 March 2015)
Based on a sample of 500 million
e
þ
e
c
̄
c
events recorded by the
BABAR
detector at c.m. energies
of close to 10.6 GeV, we report on a study of the decay
D
0
π
e
þ
ν
e
. We measure the ratio of branching
fractions,
R
D
¼
B
ð
D
0
π
e
þ
ν
e
Þ
=
B
ð
D
0
K
π
þ
Þ¼
0
.
0713

0
.
0017
stat

0
.
0024
syst
, and use the
present world average for
B
ð
D
0
K
π
þ
Þ
to obtain
B
ð
D
0
π
e
þ
ν
e
Þ¼ð
2
.
770

0
.
068
stat

0
.
092
syst

0
.
037
ext
Þ
×
10
3
where the third error accounts for the uncertainty on the branching fraction for the
reference channel. The measured dependence of the differential branching fraction on
q
2
, the four-
momentum transfer squared between the
D
and the
π
meson, is compared to various theoretical predictions
for the hadronic form factor,
f
π
þ
;D
ð
q
2
Þ
, and the normalization
j
V
cd
j
×
f
π
þ
;D
ð
q
2
¼
0
Þ¼
0
.
1374

0
.
0038
stat

0
.
0022
syst

0
.
0009
ext
. is extracted from a fit to data. Using the most recent LQCD prediction
of
f
π
þ
;D
ð
q
2
¼
0
Þ¼
0
.
666

0
.
029
, we obtain
j
V
cd
0
.
206

0
.
007
exp

0
.
009
LQCD
. Assuming, instead,
j
V
cd
j¼j
V
us
0
.
2252

0
.
0009
, we obtain
f
π
þ
;D
ð
q
2
¼
0
Þ¼
0
.
610

0
.
020
exp

0
.
005
ext
. The
q
2
dependence of
f
π
þ
;D
ð
q
2
Þ
is compared to a variety of multipole parametrizations. This information is
applied to
B
0
π
e
þ
ν
e
decays and, combined with an earlier
B
0
π
e
þ
ν
e
measurement by
BABAR
,
is used to derive estimates of
j
V
ub
j
.
DOI:
10.1103/PhysRevD.91.052022
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh
I. INTRODUCTION
Precision measurements of the elements of the Cabibbo-
Kobayashi-Maskawa (CKM) quark-mixing matrix rely
primarily on decay rate measurements of either nuclear
β
decay, or leptonic and semileptonic decays of
π
,
K
,
D
,
and
B
mesons. The rates for exclusive semileptonic decays
of mesons are proportional to the square of the product
of the specific CKM element and form factors which
are introduced to account for hadronization effects.
Various Lorentz invariant form factor calculations, models,
and parametrizations have been developed to describe
these perturbative and nonperturbative QCD processes.
*
Deceased.
Present address: University of Tabuk, Tabuk 71491, Saudi
Arabia.
Also at Università di Perugia, Dipartimento di Fisica, I-06123
Perugia, Italy.
§
Present address: Laboratoire de Physique Nucléaire et de
Hautes Energies, IN2P3/CNRS, F-75252 Paris, France.
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
**
Also at Università di Sassari, I-07100 Sassari, Italy.
††
Also at INFN Sezione di Roma, I-00185 Roma, Italy.
‡‡
Present address: Universidad Técnica Federico Santa Maria,
2390123 Valparaiso, Chile.
MEASUREMENT OF THE
D
0
π
e
þ
ν
e
...
PHYSICAL REVIEW D
91,
052022 (2015)
052022-3
Theoretical uncertainties in these form factor predictions
significantly impact the extraction of the CKM elements
from semileptonic decays, in particular
j
V
ub
j
.
In the following, we present a measurement of the
q
2
dependence of the Cabibbo-suppressed semileptonic
D
0
π
e
þ
ν
e
decay rate, where
q
2
¼ð
P
D
P
π
Þ
2
refers to the
four-momentum transfer squared between initial and final
state meson. Charge conjugate states are implied through-
out the document. This analysis exploits the large produc-
tion of charm mesons via the process
e
þ
e
c
̄
c
and
identifies
D
0
from the decay
D
D
0
π
þ
. The momen-
tum of the signal
D
0
is derived from all particles recon-
structed in the event. A very similar method was
successfully employed in the
BABAR
analysis of the
Cabibbo-favored
D
0
K
e
þ
ν
e
[1]
decay. The validity
of this procedure is examined and the associated systematic
uncertainties reduced by analyzing in parallel the two-body
decay
D
0
K
π
þ
. From the ratio of branching fractions,
R
D
¼
B
ð
D
0
π
e
þ
ν
e
Þ
=
B
ð
D
0
K
π
þ
Þ
, we derive the
absolute value of the
D
0
π
e
þ
ν
e
branching fraction,
using the world average for the branching fraction for the
normalization,
B
ð
D
0
K
π
þ
Þ
.
The
D
0
π
e
þ
ν
e
decay rate is proportional to the square
of the product
j
V
cd
j
×
f
π
þ
;D
ð
q
2
Þ
which can be extracted from
the measured distribution.
f
π
þ
;D
ð
q
2
Þ
is the corresponding
hadronic form factor and is defined in Sec.
II B
. Using the
LQCD prediction for the form factor normalization
f
π
þ
;D
ð
q
2
¼
0
Þ
, we extract
j
V
cd
j
. Alternatively, using the
most precise determination of
j
V
us
0
.
2252

0
.
0009
from kaon decays
[2]
, and the Wolfenstein parametrization
of the CKM matrix, neglecting terms of order
λ
5
,
j
V
cd
j¼j
V
us
λ
, we determine the hadronic form factor,
its normalization, and
q
2
dependence. We compare the
measurements with predictions of QCD calculations and
various form factor parametrizations. Furthermore, we
follow a procedure suggested by theorists
[3]
to use the
information extracted in terms of certain form factor para-
metrizations for
D
0
π
e
þ
ν
e
decays and adapt them to
B
0
π
e
þ
ν
e
decays
[3]
to arrive at estimates for
j
V
ub
j
.
Measurements of
D
0
K
e
þ
ν
e
and
D
0
π
e
þ
ν
e
decays were first published by the CLEO
[4]
, FOCUS
[5]
, and Belle
[6]
Collaborations, and more recently by
the CLEO-c
[7,8]
Collaboration, exploiting the very large
sample of tagged events recorded at the
ψ
ð
3770
Þ
reso-
nance. Operating in the same energy region, the BESIII
Collaboration
[9]
has also distributed preliminary results in
summer 2014.
II. DECAY RATE AND FORM FACTORS
A. Differential decay rate
The decay amplitude for semileptonic
D
decays to a final-
state pseudoscalar meson can be written in terms of vector
and scalar form factors,
f
þ
;D
ð
q
2
Þ
and
f
0
;D
ð
q
2
Þ
[10
12]
,
h
π
ð
P
π
Þj
̄
d
γ
μ
c
j
D
ð
P
D
Þi
¼
f
π
þ
;D
ð
q
2
Þ

ð
P
D
þ
P
π
Þ
μ
m
2
D
m
2
π
q
2
q
μ

þ
f
π
0
;D
ð
q
2
Þ
m
2
D
m
2
π
q
2
q
μ
;
ð
1
Þ
where
P
π
and
P
D
refer to the four-momenta of the final state
pionand theparent
D
meson,and
m
π
and
m
D
to their masses.
The four-momenta of the final state antielectron and
neutrino are denoted with
P
e
and
P
ν
e
, respectively. The
constraint
f
π
þ
;D
ð
0
Þ¼
f
π
0
;D
ð
0
Þ
avoids a singularity at
q
2
¼
0
.
This expression can be simplified for electrons, because in
the limit of
m
e
m
D
the second and third terms can be
neglected. We are left with a single form factor
f
þ
;D
ð
q
2
Þ
and
the differential decay rate becomes
d
Γ
dq
2
d
cos
θ
e
¼
G
2
F
32
π
3
ðj
V
cd
j
×
j
f
π
þ
;D
ð
q
2
ÞjÞ
2
p

3
π
ð
q
2
Þ
sin
2
θ
e
:
ð
2
Þ
Since the
D
0
and the
π
have zero spin, only the helicity
zero component of the virtual
W
contributes. The decay rate
depends on the third power of
p

π
, the pion momentum in
the
D
0
rest frame. The rate also depends on sin
2
θ
e
, where
θ
e
is the angle of the positron in the
e
þ
ν
e
rest frame with
respect to the direction of the pion in the
D
0
rest frame.
The variation of the rate with
q
2
depends on the decay
dynamics and needs to be determined experimentally. The
form factor normalization requires knowledge of the CKM
element
j
V
cd
j
.
For various form factor parametrizations, in particular in
terms of pole contributions,
D
0
π
e
þ
ν
e
decays are of
particular interest because the contribution from the lowest
mass pole to
f
π
þ
;D
ð
q
2
Þ
can be determined using additional
information (for instance, the value of the
D
intrinsic
width), thereby gaining sensitivity to contributions from
singularities due to higher mass states.
It has been suggested
[13]
that precise knowledge of the
form factors in
D
0
π
e
þ
ν
e
decays could be used to
determine
f
π
þ
;B
ð
q
2
Þ
in the high
q
2
region for the
B
0
π
e
þ
ν
e
decays, and thereby improve the extraction of
j
V
ub
j
. For this application, the
D
0
π
e
þ
ν
e
measure-
ments are extrapolated to larger values of
q
2
to overlap with
the
B
0
π
e
þ
ν
e
physical region. Two approaches are
proposed. One is based on lattice QCD (LQCD) calcu-
lations of the ratio
f
π
þ
;B
ð
q
2
Þ
=f
π
þ
;D
ð
q
2
Þ
and measurements of
the differential rates for
D
0
π
e
þ
ν
e
and
B
0
π
e
þ
ν
e
decays. This method relies on the assumption that LQCD
can predict the form factor ratio with higher accuracy than
individual form factors. The second approach relies on
measured contributions of individual resonances to the
D
form factor
f
π
þ
;D
ð
q
2
Þ
and scaling laws that relate this
J. P. LEES
et al.
PHYSICAL REVIEW D
91,
052022 (2015)
052022-4
information to the
B
form factor
f
π
þ
;B
ð
q
2
Þ
in order to extract
a value of
j
V
ub
j
. The assumptions in this approach are
described in
[3,14]
.
B. The
f
π
þ
;
D
ð
q
2
Þ
hadronic form factor
The most general expression for the form factor
f
π
þ
;D
ð
q
2
Þ
satisfies the dispersion relation,
f
π
þ
;D
ð
q
2
Þ¼
1
π
Z
ð
m
D
þ
m
π
Þ
2
dt
I
m
ð
f
π
þ
;D
ð
t
ÞÞ
t
q
2
i
ε
;
ð
3
Þ
Singularities of
f
π
þ
;D
ð
t
Þ
in the complex
t
-plane originate
from the interaction of the
c
and
d
quarks resulting in a
series of charm vector states of different masses with
J
P
¼
1
. The kinematic threshold is at
t
þ
¼ð
m
D
þ
m
π
Þ
2
.
In practice this series of poles is truncated: one, two or
three poles are considered. The lowest pole, the
D
is
located just above threshold and its contribution can be
isolated because of its narrow width, of the order
0
.
1
MeV
=c
2
. The next pole (denoted
D
0
1
in the following)
has a mass of
ð
2610

4
Þ
MeV
=c
2
and width of
ð
93

14
Þ
MeV
=c
2
and corresponds to the first radial vector
excitation
[15]
. The LHCb Collaboration
[16]
has mea-
sured somewhat different values of
ð
2649

5
Þ
MeV
=c
2
-
and
ð
140

25
Þ
MeV
=c
2
for the mass and width of this
state. However, considering other sources of uncertainties,
these differences have very little impact on the present
analysis. Since hadronic singularities (poles and cuts) are
above the physical region, it is expected that
f
π
þ
;D
ð
q
2
Þ
is a
monotonically rising function of
q
2
.
Inthe following,wediscussvarioustheoretical approaches
and their parametrizations which are used to describe the
q
2
dependence of the
D
meson form factor
f
π
þ
;D
ð
q
2
Þ
.
1. Dispersive approach with constraints
Several constraints have to be satisfied by the dispersion
relations for the form factor
[14]
. Using
H
to denote a
heavy
D
or
B
meson, the integral in Eq.
(3)
can be
expressed in terms of three contributions:
(i) the
H

pole contribution, which is dominant;
(ii) the sum of radially excited,
J
P
¼
1
, resonances
noted
H
0
i
;
(iii) the contribution from the
H
π
continuum.
f
π
þ
;H
ð
q
2
Þ¼
Res
ð
f
π
þ
;H
Þ
H

m
2
H

q
2
þ
X
i
Res
ð
f
π
þ
;H
Þ
H
0
i
m
2
H
0
i
q
2
þ
1
π
Z
Λ
2
t
þ
dt
I
m
ð
f
π
;
cont
þ
;H
ð
t
ÞÞ
t
q
2
i
ε
:
ð
4
Þ
In this expression, the quantities Res
ð
f
π
þ
;H
Þ
H
ð0Þ
ð
i
Þ
are the
residues for the different vector resonances
H
ð0Þ
ð
i
Þ
.
The integral over the continuum is evaluated between
the threshold and the first radial excited state (
Λ
m
H
0
1
).
Contributions from orbital excitations are expected to be
small
[14]
.
The residue which defines the contribution of the
H

resonance can be expressed in terms of the meson decay
constant
f
H

, and
g
H

H
π
, the coupling to the
H
π
final state,
Res
ð
f
π
þ
;H
Þ
H

¼
1
2
m
H


f
H

f
H

f
H
g
H

H
π
:
ð
5
Þ
Similar expressions can be derived for the higher mass
states
H
0
i
. The expected values for the residues at the first
two poles are given in Appendix
A
.
Using the behavior of the form factor at very large values
of
q
2
, a constraint (commonly referred to as superconver-
gence condition) is obtained on the residues
[14]
,
Res
ð
f
π
þ
;H
Þ
H

þ
X
i
Res
ð
f
π
þ
;H
Þ
H
ð0Þ
i
þ
c
H
0
;
ð
6
Þ
which can be compared to measurements;
c
H
denotes the
contribution from continuum.
2. Multipole parametrizations
Limiting the contributions to three poles, the following
expression is obtained,
f
π
þ
;D
ð
q
2
Þ¼
f
π
þ
;D
ð
0
Þ
1
c
2
c
3

1
1
q
2
m
2
D

X
3
i
¼
2
c
i
1
q
2
m
2
D
0
i

:
ð
7
Þ
The coefficients
c
i
are related to the residues introduced
previously through the following expression,
c
i
¼
ð
m
2
D

=m
2
D
0
i
Þ
×
ð
Res
ð
f
π
þ
;D
Þ
D
ð0Þ
i
=
Res
ð
f
π
þ
;D
Þ
D

Þ
.
The variation with
q
2
of each component is determined
by the pole masses. In addition to the
D

pole, we fix the
mass of the first radial excitation at
2
.
61
GeV
=c
2
[15]
.For
the higher radial excitation we either use a fixed value of
3
.
1
GeV
=c
2
[17]
(fixed three-pole ansatz) or an effective
pole mass corresponding to the sum of contributions from
all poles at higher masses (effective three-pole ansatz).
Values expected for the residues at the
D

[Eq.
(A1)
] and at
the
D
0
1
[Eq.
(A3)
] can be used as constraints. In the fixed
three-pole ansatz, the constraint on the value of the residue
at the
D
0
1
pole is used. In the effective three-pole ansatz,
constraints at the two poles are used and the value of the
residue at the effective pole is given by the superconver-
gence condition [Eq.
(6)
]. These constraints are entered in
the likelihood function by including Gaussian distributions
centered at the expected values with standard deviations
equal to the corresponding expected uncertainties.
Given the fact that the hadronic form factor is dominated
by the
D

pole, other contributions can be accounted for
MEASUREMENT OF THE
D
0
π
e
þ
ν
e
...
PHYSICAL REVIEW D
91,
052022 (2015)
052022-5
by an effective pole at higher mass, resulting in a two-pole
ansatz
[18]
,
f
π
þ
;D
ð
q
2
Þ¼
f
π
þ
;D
ð
0
Þ
1
δ
pole
q
2
m
2
D


1
q
2
m
2
D


1
β
pole
q
2
m
2
D


;
ð
8
Þ
where
f
π
þ
;D
ð
0
Þ
,
δ
pole
and
β
pole
are free parameters that are
extracted by a fit to data. In the present analysis, the
expected value of the residue at the
D

pole is used as a
constraint in the fits.
If, in addition, the form factors
f
π
þ
;D
and
f
π
0
;D
meet
certain conditions, expected to be valid at large recoil in
the heavy quark limit
[18]
, then the ansatz can be further
simplified,
f
π
þ
;D
ð
q
2
Þ¼
f
π
þ
;D
ð
0
Þ

1
q
2
m
2
D


1
α
pole
q
2
m
2
D


;
ð
9
Þ
with two free parameters
f
π
þ
;D
ð
0
Þ
and
α
pole
. This modified-
pole ansatz can be further simplified,
f
π
þ
;D
ð
q
2
Þ¼
f
π
þ
;D
ð
0
Þ
1
q
2
m
2
pole
;
ð
10
Þ
where
m
pole
is the single free parameter. Of course, such an
effective pole mass has no clear interpretation and the
proposed
q
2
variation does not comply with constraints
from QCD. The obtained pole-mass value may nonetheless
be useful for comparisons with results from different
experiments.
3. z expansion
The
z
expansion is a model-independent parametrization
which is based on general properties of analyticity, unitarity
and crossing symmetries. Except for physical poles and
thresholds, form factors are analytic functions of
q
2
, and
can be expressed as a convergent power series, given a
change of variables
[19
24]
of the following form,
z
ð
t; t
0
Þ¼
ffiffiffiffiffiffiffiffiffiffiffiffi
t
þ
t
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
t
þ
t
0
p
ffiffiffiffiffiffiffiffiffiffiffiffi
t
þ
t
p
þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
t
þ
t
0
p
;
ð
11
Þ
where
t
0
¼
t
þ
ð
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
t
=t
þ
p
Þ
with
t
¼
q
2
max
¼ð
m
D
m
π
Þ
2
2
.
98
GeV
2
. This transformation maps the kin-
ematic region for the semileptonic decay (
0
<q
2
<t
)
onto a real segment extending over the range
j
z
j
max
¼
0
.
167
. More details on this parametrization are
given in Appendix
B
.
In terms of the variable
z
, the form factor, consistent with
constraints from QCD, takes the form
f
π
þ
;D
ð
t
Þ¼
1
P
ð
t
Þ
Φ
ð
t; t
0
Þ
X
k
¼
0
a
k
ð
t
0
Þ
z
k
ð
t; t
0
Þ
;
ð
12
Þ
where
P
ð
t
Þ¼
1
and
Φ
ð
t; t
0
Þ
is an arbitrary analytical
function for which the
standard
choice is given in
Appendix
B
. The
z
expansion provides a parametrization
within the physical region and is well suited for fits to
data and converges readily. The commonly used param-
eters are defined as
r
k
¼
a
k
=a
0
for
k
¼
1
;
2
,andthe
overall normalization of the expansion is chosen to
be
j
V
cd
j
×
f
π
þ
;D
ð
0
Þ
.
The
z
expansion has some disadvantages in comparison
to phenomenological approaches
[25]
. Specifically, there is
no simple interpretation of the coefficients
a
k
ð
t
0
Þ
. The
contribution from the first pole (
D
) is difficult to obtain
because it requires extrapolation beyond the physical
region while the other coefficients are only weakly con-
strained by the available data.
4. ISGW2 quark model
For completeness, we also list ISGW2
[26]
, a constituent
quark model with relativistic corrections. Predictions are
normalized at
q
2
max
¼
t
. The form factor is parametrized as
f
π
þ
;D
ð
q
2
Þ¼
f
ð
q
2
max
Þ

1
þ
1
12
α
I
ð
q
2
max
q
2
Þ

2
;
ð
13
Þ
where
α
I
¼
ξ
2
=
12
and
ξ
is the charge radius of the final-
state meson. The uncertainties of the predictions are
difficult to quantify.
5. Summary of form factor parametrizations
The different parametrizations of
f
π
þ
;D
ð
q
2
Þ
considered in
this analysis are listed in Table
I
, along with the parameters
and constraints considered.
C. Comparison of
f
π
þ
;
D
ð
q
2
Þ
and
f
π
þ
;
B
ð
q
2
Þ
Form factor studies for
D
0
π
e
þ
ν
e
decays are of
particular interest because LQCD calculations are expected
to result in predictions for the ratio of hadronic form factors
for
B
and
D
mesons with a better accuracy than for the form
factors of the individual mesons.
Two independent approaches to predict
f
π
þ
;B
ð
q
2
Þ
based
on
f
π
þ
;D
ð
q
2
Þ
are considered (see Sec.
VII
):
(i) Fits to
f
π
þ
;D
ð
q
2
Þ
according to the fixed three-pole
ansatz as specified in Eq.
(7)
areusedtoestimatethe
variation of
B
ð
B
0
π
e
þ
ν
e
Þ
as a function of the
pion energy, under the assumption that the ratio of
the hadronic form factors in
B
and
D
decays is largely
insensitive to the energy of the final state pion.
(ii) The effective three-pole ansatz given in Eq
(33)
is
used, obtaining the value of the residue at the
B

J. P. LEES
et al.
PHYSICAL REVIEW D
91,
052022 (2015)
052022-6
pole from LQCD and imposing the superconver-
gence condition.
Though estimates for the form factor ratios are not yet
available, we discuss some aspects in Appendix
C
which
indicate that this approach may be promising in the future
for larger data samples.
III. THE
BABAR
DETECTOR AND DATA SETS
A. Detector
A detailed description of the
BABAR
detector and
the algorithms used for charged and neutral particle
reconstruction and identification is provided elsewhere
[27,28]
. Charged particles are reconstructed by matching
hits in the 5-layer silicon vertex tracker (SVT) with track
elements in the 40-layer drift chamber (DCH), filled with a
gas mixture of helium and isobutane. Particles of low
transverse momentum with an insufficient number of DCH
hits are reconstructed in the SVT. Charged hadron iden-
tification is performed combining the measured ionization
losses in the SVT and in the DCH with the information
from the Cherenkov detector (DIRC). Electrons are iden-
tified by the ratio of the track momentum to the associated
energy in the CsI(Tl) electromagnetic calorimeter (EMC),
the transverse profile of the shower, the ionization loss in
the DCH, and the Cherenkov angle in the DIRC. Photon
energies are measured in the EMC.
B. Data and MC samples
The data used in this analysis were recorded with the
BABAR
detector at the PEP-II energy-asymmetric
e
þ
e
collider. The results presented here were obtained using
e
þ
e
c
̄
c
events from a sample with a total integrated
luminosity of
347
.
2
fb
1
[29]
, collected at the
Υ
ð
4
S
Þ
resonance (on-peak data) at 10.58 GeV center-of-mass
(c.m.) energy. An additional sample of
36
.
6
fb
1
was
recorded 40 MeV below (off-peak data), just below the
threshold for
B
̄
B
production.
The normalization of off-peak and on-peak data samples
is derived from luminosity measurements, which are based
on the number of detected
μ
þ
μ
pairs and the QED cross
section for
e
þ
e
μ
þ
μ
ð
γ
Þ
production.
At 10.6 GeV c.m. energy, the nonresonant cross section
for
e
þ
e
q
̄
q
with
q
¼ð
u; d; s; c
Þ
(referred to as con-
tinuum) is 3.4 nb, compared to the
Υ
ð
4
S
Þ
peak cross
section of 1.05 nb. We use Monte Carlo (MC) techniques
[30]
to simulate the production and decay of
B
̄
B
and
q
̄
q
pairs and the detector response
[31]
. The quark fragmen-
tation in continuum events is simulated using JETSET
[32]
.
The MC simulations include radiative effects, such as
bremsstrahlung in the detector material and initial-state
and final-state radiation
[33]
.
The size of the MC event samples for
Υ
ð
4
S
Þ
decays,
c
̄
c
pairs, and light quark pairs from continuum exceed the data
samples by factors of 3.3, 1.7 and 1.1, respectively. These
simulated samples are primarily used to study the back-
ground composition and suppression. Dedicated samples of
nine times the size of the data sample of pure signal events;
i.e.,
c
̄
c
events with
D
D
0
π
þ
s
decay, followed by the
signal
D
0
π
e
þ
ν
e
decay, were generated and used to
account for efficiencies and resolution effects. These
samples were generated using the modified pole para-
metrization for
f
þ
;D
ð
q
2
Þ
with
α
π
pole
¼
0
.
44
as defined
in Eq.
(9)
.
The MC distributions are normalized to the data lumi-
nosity, using the following cross sections: 1.3 nb for
c
̄
c
,
0.525 nb for
B
þ
B
and
B
0
̄
B
0
and 2.09 nb for light
u
̄
u
,
d
̄
d
,
s
̄
s
quark pairs.
IV. SIGNAL RECONSTRUCTION
We reconstruct signal
D
0
π
e
þ
ν
e
ð
γ
Þ
decays, in events
produced in
e
þ
e
annihilation to
c
̄
c
, with the
D
0
origi-
nating from a
D
D
0
π
þ
s
decay. The decay channel
includes photons from final state radiation.
TABLE I. Overview of
f
π
þ
;D
ð
q
2
Þ
parametrizations. In the fixed three-pole ansatz, the value expected for
Res
ð
f
π
þ
;D
Þ
D
0
1
[Eq.
(A3)
] is used as a constraint whereas in the effective three-pole ansatz the values expected for the
residues at the
D

[Eq.
(A1)
] and
D
0
1
[Eq.
(A3)
] poles are used as constraints and the value of the residue at the
effective pole is given by the superconvergence condition [Eq.
(6)
]. In the two poles ansatz, the value expected for
the residue at the
D

pole [Eq.
(A1)
] is used as constraint. These constraints are entered in fits assuming that their
expected values have Gaussian distributions.
Ansatz
Parameters
Constraints
z
expansion
[19]
a
0
;r
k
¼
a
k
=a
0
Effective three-pole
Res
ð
f
π
þ
;D
Þ
D

;
Res
ð
f
π
þ
;D
Þ
D
0
1
;m
pole
3
Res
ð
f
π
þ
;D
Þ
D

;
Res
ð
f
π
þ
;D
Þ
D
0
1
Fixed three-pole
f
þ
;D
ð
0
Þ
;c
2
;c
3
Res
ð
f
π
þ
;D
Þ
D
0
1
Two poles
[18]
f
þ
;D
ð
0
Þ
;
β
pole
;
δ
pole
Res
ð
f
π
þ
;D
Þ
D

Modified pole
[18]
f
þ
;D
ð
0
Þ
;
α
pole
Simple pole
f
þ
;D
ð
0
Þ
;m
pole
ISGW2
[26]
f
þ
;D
ð
t
Þ
;
α
I
MEASUREMENT OF THE
D
0
π
e
þ
ν
e
...
PHYSICAL REVIEW D
91,
052022 (2015)
052022-7
In parallel, we reconstruct the reference sample of
D
0
K
π
þ
ð
γ
Þ
decays, with the
D
0
also originating from a
D
decay. This sample has the same number of final state
particles, except for the undetected neutrino. The data
reference sample combined with the corresponding MC
sample is critical for tuning details of the
c
quark
fragmentation and the kinematics of particles accompany-
ing the
D
. Both data and MC reference samples are also
used to study the reconstruction of the missing neutrino.
This analysis follows very closely the measurement of
D
0
K
e
þ
ν
e
decays in
[1]
. The main differences in the
selection are tighter identification criteria on the pion
candidate, a veto against kaons, and the use of sideband
regions in the
Δ
ð
m
Þ¼
m
ð
D
0
π
þ
s
Þ
m
ð
D
0
Þ
mass distribu-
tion to assess the different combinatorial and peaking
background contributions.
In the following, we present the principal features of this
analysis, emphasizing those that differ from the previous
analysis.
A. Signal selection
This analysis exploits the two-jet topology of
e
þ
e
c
̄
c
events, generated by the largely independent, hard frag-
mentation of the two c-quarks. We divide the event into two
hemispheres. For this purpose, all charged and neutral
particle momenta are measured in the c.m. system, and a
common thrust axis is determined. The plane which crosses
the interaction point and is perpendicular to the thrust axis
defines the two hemispheres. To improve the event contain-
ment, only events with a polar angle of the thrust axis in the
range
j
cos
ð
θ
thrust
Þj
<
0
.
6
are retained.
In each hemisphere, we search for a positron and pion of
opposite charge, and require that the positron (or electron
for the charge conjugate
̄
D
0
decays) has a minimum c.m.
momentum of
0
.
5
GeV
=c
. The combinatorial background
level is higher in this analysis than in the
D
0
K
e
þ
ν
e
analysis because the Cabibbo-suppressed decay results in a
final-state charged pion in place of a charged kaon. To
reduce the contamination from
D
0
K
e
þ
ν
e
decays, two
cases are considered. To avoid the presence of a charged
kaon as pion candidate the particle identification criterion
(tight identification) is chosen to limit the kaon misidenti-
fication as a pion to 0.4%. If the charged kaon is not the
pion candidate, a different criterion (loose identification) is
chosen to veto kaons accompanying the
D
0
candidate. In
this case, kaon candidates are identified by the condition
L
K
=
ð
L
K
þ
L
π
Þ
>
0
.
82
, where
L
K
and
L
π
correspond to the
likelihoods for the kaon and pion hypotheses, respectively.
This selection has an efficiency of 90% for real kaons
whereas pions have a probability to be signed as kaons
varying between 2.5% at
2
GeV
=c
and 15% at
5
GeV
=c
.
The
ν
e
momentum is unmeasured and two kinematic fits
are performed, imposing in turn the
D
0
and
D
mass
constraint. First, the
D
0
direction and the neutrino energy
are estimated from all particles measured in the event.
The
D
0
direction is taken to be opposite to the sum of the
momenta of all reconstructed particles in the event, except
for the pion and the positron associated with the signal
candidate. The neutrino energy is estimated as the differ-
ence between the total energy of the hemisphere and the
sum of the energies of all reconstructed particles in this
hemisphere. A correction, which depends on the value of
the missing energy measured in the opposite hemisphere, is
applied to account for the presence of missing energy due
to particles escaping detection, even in the absence of a
neutrino from the
D
0
decay. The energy in each hemisphere
is defined using the measured hemisphere masses and the
total event energy. The
D
0
candidate is retained if the
χ
2
probability,
P
ð
χ
2
Þ
, of the first kinematic fit exceeds
10
2
.
Detector performance for the reconstruction of the
D
0
momentum and energy are derived from the
D
0
K
π
þ
reference sample. Corrections are applied to account for
observed differences between data and simulation.
Each
D
0
candidate is combined with a low-momentum
charged pion
π
þ
s
of the same charge as the lepton, in
the same hemisphere. The mass difference
Δ
ð
m
Þ¼
m
ð
D
0
π
þ
s
Þ
m
ð
D
0
Þ
is measured using the invariant mass
of this system. We define a signal region as
Δ
ð
m
Þ
<
0
.
155
GeV
=c
2
, and two sidebands as
0
.
155
<
Δ
ð
m
Þ
<
0
.
20
GeV
=c
2
and
Δ
ð
m
Þ
>
0
.
20
GeV
=c
2
.
The second kinematic fit constrains the invariant mass of
the candidate
π
e
þ
ν
e
π
þ
s
to fixed values. For events in the
signal region, the
D
mass is used whereas in sidebands
several values differing by
0
.
02
GeV
=c
2
are taken. A
requirement that
P
ð
χ
2
Þ
>
0
.
01
leads to a reduction of
combinatorial background. With this procedure, large
samples of sideband events are kept.
B. Background rejection
Background events arise from
Υ
ð
4
S
Þ
B
̄
B
decays and
e
þ
e
q
̄
q
continuum events. These backgrounds are
significantly reduced by multivariate analyses employing
two Fisher discriminants.
To reduce the
B
̄
B
background, a Fisher discriminant
F
b
̄
b
is defined based on three variables exploiting the difference
in topology of
B
̄
B
events and
c
̄
c
continuum:
(i)
R
2
, the ratio between the second- and zeroth-order
Fox-Wolfram moments
[34]
;
(ii) the total multiplicity of the detected charged and
neutral particles;
(iii) the momentum of the
π
þ
s
from the
D
D
0
π
þ
s
decay.
The particle distribution in
Υ
ð
4
S
Þ
events tends to be
isotropic because the
B
mesons are produced near thresh-
old, while the particle distribution in
c
̄
c
events is jet-like
due to the hard fragmentation of the high-momentum
c
quarks. For the same reason, the
D
momenta in
Υ
ð
4
S
Þ
decays are lower than in
c
̄
c
events. The three variables are
J. P. LEES
et al.
PHYSICAL REVIEW D
91,
052022 (2015)
052022-8
combined linearly in a Fisher discriminant. Only events
with
F
b
̄
b
>
1
.
2
are retained.
Because few electrons are produced in light-quark
fragmentation and lower mass particle decays, the back-
ground from the continuum arises primarily from the
decay of charmed particles in
c
̄
c
events. Furthermore,
the hard fragmentation function of
c
quarks results in
charm particles and in their decay products with higher
average energies and smaller angular spread (relative to the
thrust axis or to the
D
direction) compared with other
particles in the hemisphere. These other particles are
referred to as
spectators,
and the spectator with highest
momentum is referred to as the
leading
particle. To
reduce background from
c
̄
c
events, a Fisher discriminant
F
c
̄
c
is defined based on the same variables used in the
earlier
D
0
K
e
þ
ν
e
measurement:
(i) the
D
momentum;
(ii) the invariant mass of spectators;
(iii) the direction of the sum of the momenta of the
spectators relative to the thrust axis;
(iv) the magnitude of the momentum of the leading
spectator;
(v) the direction of the leading spectator relative to the
D
0
direction;
(vi) the direction of the leading spectator relative to the
thrust axis;
(vii) the direction of the lepton relative to the pion
direction, in the
ð
e
þ
;
ν
e
Þ
rest frame;
(viii) the charged lepton momentum (
p
e
) in the c.m.
frame.
The first six variables are sensitive to the properties of
c
quark hadronization whereas the last two are related to the
decay characteristics of the signal decay. In the following,
the combination of the first six variables is referred to as
F
c
̄
c
2
. All eight variable are combined linearly into the
Fisher discriminant
F
c
̄
c
. Only events with
F
c
̄
c
>
0
.
6
are
retained. Other selection requirements on
F
b
̄
b
and
F
c
̄
c
have
been studied and we have used those which correspond to
the smaller systematic uncertainty for a similar total error
on fitted quantities. Figure
1
shows the distribution of the
two Fisher discriminants for the signal and background
samples.
Figure
2
shows the mass difference
Δ
ð
m
Þ
for events
passing all selection criteria described above, after the
sequential background suppression by the two kinematic
fits. The distributions show the expected narrow enhance-
ment for the signal at low
Δ
ð
m
Þ
, and the suppression of
the background, primarily combinatorial in nature, by the
second kinematic fit. To perform detailed studies of the
peaking and the nonpeaking backgrounds, we use the two
sidebands shown in the figure.
The remaining background from
c
̄
c
-events can be
divided into a peaking component at low
Δ
ð
m
Þ
and a
nonpeaking component extending to higher values of
Δ
ð
m
Þ
. In the signal region, the latter component amounts
to 23% of the charm background. Peaking background
events are from real
D
decays in which the slow
π
þ
s
is
included in the candidate track combination. Backgrounds
from
e
þ
e
annihilations into light
d
̄
d
,
u
̄
u
,
s
̄
s
pairs,
τ
þ
τ
pairs and
B
̄
B
events are nonpeaking components.
To improve the background simulation, simulated back-
ground distributions are corrected for observed differences
between data and MC simulations for sideband events.
Most important among them is the two-dimensional dis-
tribution of the
π
þ
momentum versus the missing energy in
the signal hemisphere. These last corrections are discussed
in Sec.
VD
. As a result, the measured
Δ
ð
m
Þ
distribution is
well reproduced by the simulation and the systematic
uncertainties in the signal yields are significantly reduced
(for further details, see Sec.
V
).
The fraction of signal events is determined by the excess of
events above the sum of the corrected background distribu-
tions in the
Δ
ð
m
Þ
distribution. Figure
3
shows the
q
2
¼
ð
p
D
p
π
Þ
2
distribution for events selected in the signal
region. There are 9,926 signal candidates containing an
estimated number of 4,623 background events. The selection
bb
_
F
-4
-3
-2
-1
0
1
2
3
4
5
Normalized events
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Signal
Background
cc
_
F
-3
-2
-1
0
1
2
3
Normalized events
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Signal
Background
FIG. 1 (color online). Distributions of the Fisher discriminants. Left:
F
b
̄
b
for signal and
B
̄
B
events. Right:
F
c
̄
c
for signal and other
c
̄
c
events. The vertical lines indicate the selection requirements:
F
b
̄
b
>
1
.
2
and
F
c
̄
c
>
0
.
6
.
MEASUREMENT OF THE
D
0
π
e
þ
ν
e
...
PHYSICAL REVIEW D
91,
052022 (2015)
052022-9