of 10
Search for the decay modes
D
0
!
e
þ
e

,
D
0
!

þ


, and
D
0
!
e



J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
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
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
D. J. Asgeirsson,
7
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov,
9
A. R. Buzykaev,
9
V. P. Druzhinin,
9
V. B. Golubev,
9
E. A. Kravchenko,
9
A. P. Onuchin,
9
S. I. Serednyakov,
9
Yu. I. Skovpen,
9
E. P. Solodov,
9
K. Yu. Todyshev,
9
A. N. Yushkov,
9
M. Bondioli,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
H. Atmacan,
11
J. W. Gary,
11
F. Liu,
11
O. Long,
11
E. Mullin,
11
G. M. Vitug,
11
C. Campagnari,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
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
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
B. Spaan,
18
K. R. Schubert,
19
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
P. J. Clark,
21
S. Playfer,
21
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a
E. Luppi,
22a,22b
M. Munerato,
22a,22b
L. Piemontese,
22a
V. Santoro,
22a
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
P. Patteri,
23
I. M. Peruzzi,
23,
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
B. Bhuyan,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. J. Edwards,
27
A. Adametz,
28
U. Uwer,
28
H. M. Lacker,
29
T. Lueck,
29
P. D. Dauncey,
30
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
P. Roudeau,
34
M. H. Schune,
34
A. Stocchi,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
K. Griessinger,
40
A. Hafner,
40
E. Prencipe,
40
R. J. Barlow,
41,
G. Jackson,
41
G. D. Lafferty,
41
E. Behn,
42
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
R. Cheaib,
45
D. Lindemann,
45
P. M. Patel,
45,
§
S. H. Robertson,
45
P. Biassoni,
46a,46b
N. Neri,
46a
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
k
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
M. Simard,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
M. Martinelli,
50
G. Raven,
50
C. P. Jessop,
51
J. M. LoSecco,
51
W. F. Wang,
51
K. Honscheid,
52
R. Kass,
52
J. Brau,
53
R. Frey,
53
N. B. Sinev,
53
D. Strom,
53
E. Torrence,
53
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
G. Simi,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
S. Akar,
55
E. Ben-Haim,
55
M. Bomben,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
S. Sitt,
55
M. Biasini,
56a,56b
E. Manoni,
56a,56b
S. Pacetti,
56a,56b
A. Rossi,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b
M. Carpinelli,
57a,57b,
{
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
B. Oberhof,
57a,57b
E. Paoloni,
57a,57b
A. Perez,
57a
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
C. Bu
̈
nger,
60
O. Gru
̈
nberg,
60
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60,
§
C. Voss,
60
R. Waldi,
60
T. Adye,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
J. F. Benitez,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
M. Ebert,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
P. Lewis,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
R. H. Schindler,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
J. Va’vra,
63
A. P. Wagner,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
C. C. Young,
63
V. Ziegler,
63
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
A. Randle-Conde,
65
S. J. Sekula,
65
M. Bellis,
66
P. R. Burchat,
66
T. S. Miyashita,
66
E. M. T. Puccio,
66
M. S. Alam,
67
J. A. Ernst,
67
R. Gorodeisky,
68
N. Guttman,
68
D. R. Peimer,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
J. L. Ritchie,
70
A. M. Ruland,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
S. Zambito,
72a,72b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
F. Martinez-Vidal,
74
A. Oyanguren,
74
H. Ahmed,
75
J. Albert,
75
Sw. Banerjee,
75
F. U. Bernlochner,
75
H. H. F. Choi,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
I. M. Nugent,
75
J. M. Roney,
75
R. J. Sobie,
75
N. Tasneem,
75
T. J. Gershon,
76
P. F. Harrison,
76
T. E. Latham,
76
H. R. Band,
77
S. Dasu,
77
Y. Pan,
77
R. Prepost,
77
and S. L. Wu
77
PHYSICAL REVIEW D
86,
032001 (2012)
1550-7998
=
2012
=
86(3)
=
032001(10)
032001-1
Ó
2012 American Physical Society
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
19
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
21
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
22b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711, USA
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstrasse 15, D-12489 Berlin, Germany
30
Imperial College London, London, SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Universite
́
Paris-Sud 11, Centre Scientifique d’Orsay,
B. P. 34, F-91898 Orsay Cedex, France
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London, E1 4NS, United Kingdom
38
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
40
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
41
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
46a
INFN Sezione di Milano, I-20133 Milano, Italy
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032001 (2012)
032001-2
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
55
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-56127 Pisa, Italy
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
58
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 26 June 2012; published 1 August 2012)
We present searches for the rare decay modes
D
0
!
e
þ
e

,
D
0
!

þ


, and
D
0
!
e



in
continuum
e
þ
e

!
c

c
events recorded by the
BABAR
detector in a data sample that corresponds to
an integrated luminosity of
468 fb

1
. These decays are highly Glashow–Iliopoulos–Maiani suppressed
but may be enhanced in several extensions of the standard model. Our observed event yields are
consistent with the expected backgrounds. An excess is seen in the
D
0
!

þ


channel, although the
observed yield is consistent with an upward background fluctuation at the 5% level. Using the Feldman–
Cousins method, we set the following 90% confidence level intervals on the branching fractions:
B
ð
D
0
!
e
þ
e

Þ
<
1
:
7

10

7
,
B
ð
D
0
!

þ


Þ
within
½
0
:
6
;
8
:
1

10

7
, and
B
ð
D
0
!
e



Þ
<
3
:
3

10

7
.
DOI:
10.1103/PhysRevD.86.032001
PACS numbers: 13.20.Fc, 11.30.Hv, 12.15.Mm, 12.60.

i
I. INTRODUCTION
In the standard model (SM), the flavor-changing neutral
current decays
D
0
!
þ

are strongly suppressed by the
Glashow–Iliopoulos–Maiani mechanism. Long-distance
processes bring the predicted branching fractions up to
the order of
10

23
and
10

13
for
D
0
!
e
þ
e

and
D
0
!

þ


decays, respectively [
1
]. These predictions are well
below current experimental sensitivities. The lepton-flavor
violating decay
D
0
!
e



is forbidden in the SM.
Several extensions of the SM predict
D
0
!
þ

branch-
ing fractions that are enhanced by several orders of
*
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia.
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
Now at the University of Huddersfield, Huddersfield HD1
3DH, United Kingdom.
§
Deceased.
k
Now at University of South Alabama, Mobile, AL 36688,
USA.
{
Also with Universita
`
di Sassari, Sassari, Italy.
SEARCH FOR THE DECAY MODES
...
PHYSICAL REVIEW D
86,
032001 (2012)
032001-3
magnitude compared with the SM expectations [
1
]. The
connection between
D
0
!
þ

and
D
0
-

D
0
mixing in new
physics models has also been emphasized [
2
].
We search for
D
0
!
þ

decays using approximately
468 fb

1
of data produced by the PEP-II asymmetric-
energy
e
þ
e

collider [
3
] and recorded by the
BABAR
detector. The center-of-mass energy of the machine was
at, or 40 MeV below, the

ð
4
S
Þ
resonance for this data set.
The
BABAR
detector is described in detail elsewhere [
4
].
We give a brief summary of the main features below.
The trajectories and decay vertices of long-lived hadrons
are reconstructed with a 5-layer, double-sided silicon strip
detector (SVT) and a 40-layer drift chamber (DCH), which
are inside a 1.5 T solenoidal magnetic field. Specific
ionization (
dE=dx
) measurements are made by both the
SVT and the DCH. The velocities of charged particles are
inferred from the measured Cherenkov angle of radiation
emitted within fused silica bars, located outside the track-
ing volume and detected by an array of phototubes. The
dE=dx
and Cherenkov angle measurements are used in
particle identification. Photon and electron energy and
photon position are measured by a CsI(Tl) crystal calo-
rimeter (EMC). The steel of the flux return for the sole-
noidal magnet is instrumented with layers of either
resistive plate chambers or limited streamer tubes [
5
],
which are used to identify muons (IFR).
II. EVENT RECONSTRUCTION AND SELECTION
We form
D
0
candidates by combining pairs of oppositely
charged tracks and consider the following final states:
e
þ
e

,

þ


,
e



,

þ


,and
K


þ
. We use the measured
D
0
!

þ


yield and the known
D
0
!

þ


branching
fraction to normalize our
D
0
!
þ

branching fractions.
We also use the
D
0
!

þ


candidates, as well as the
D
0
!
K


þ
candidates, to measure the probability of
misidentifying a

as either a

or an
e
.Combinatorial
background is reduced by requiring that the
D
0
candidate
originate from the decay
D

ð
2010
Þ
þ
!
D
0

þ
[
6
]. We
select
D
0
candidates produced in continuum
e
þ
e

!
c

c
events by requiring that the momentum of the
D
0
candidate
be above 2.4 GeV in the center-of-mass (CM) frame, which
is close to the kinematic limit for
B
!
D


,
D
!
D
0

þ
.
This reduces the combinatorial background from
e
þ
e

!
B

B
events.
Backgrounds are estimated directly from data control
samples. Signal
D
0
candidates with a reconstructed
D
0
mass above 1.9 GeV consist of random combinations of
tracks. We use a sideband region above the signal region in
the
D
0
mass ([1.90, 2.05] GeV) in a wide

m

m
ð
D
0

þ
Þ
m
ð
D
0
Þ
window ([0.141, 0.149] GeV) to
estimate the amount of combinatorial background. The
D
0
and

m
mass resolutions, measured in the
D
0
!

þ


sample, are 8.1 MeVand 0.2 MeV, respectively. We estimate
the number of
D
0
!

þ


background events selected
as
D
0
!
þ

candidates by scaling the observed
D
0
!

þ


yield, with no particle identification criteria
applied, by the product of pion misidentification probabil-
ities and a misidentification correlation factor
G
.Themis-
identification correlation factor
G
is estimated with the
D
0
!
K


þ
data control sample.
The tracks for the
D
0
candidates must have momenta
greater than 0.1 GeV and have at least six hits in the SVT.
The slow pion track from the
D
!
D
0

þ
decay must
have at least 12 position measurements in the DCH. A fit of
the
D
!
D
0

þ
;
D
0
!
t
þ
t

decay chain is performed
where the
D
0
tracks (
t
) are constrained to come from a
common vertex and the
D
0
and slow pion are constrained
to form a common vertex within the beam interaction
region. The

2
probabilities of the
D
0
and
D

vertices
from this fit must be at least 1%. The reconstructed
D
0
mass
m
ð
D
0
Þ
must be within [1.65, 2.05] GeV and the
mass difference

m
must be within [0.141, 0.149] GeV.
We subtract a data–Monte Carlo difference of
0
:
91

0
:
06 MeV
, measured in the
D
0
!

þ


sample, from
the reconstructed
D
0
mass in the simulation.
We use an error-correcting output code (ECOC) algo-
rithm [
7
] with 36 input variables to identify electrons and
pions. The ECOC combines multiple bootstrap aggregated
[
8
] decision tree [
9
] binary classifiers trained to separate
e
,

,
K
,and
p
. The most important inputs for electron iden-
tification are the EMC energy divided by the track momen-
tum, several EMC shower shape variables, and the deviation
from the expected value divided by the measurement uncer-
tainty for the Cherenkov angle and
dE=dx
for the
e
,

,
K
,
and
p
hypotheses. For tracks with momentum greater than
0.5 GeV, the electron identification has an efficiency of 95%
for electrons and a pion misidentification probability of less
than 0.2%. Neutral clusters in the EMC that are consistent
with bremsstrahlung radiation are used to correct the mo-
mentum and energy of electron candidates. The efficiency of
the pion identification is above 90% for pions, with a kaon
misidentification probability below 10%.
Muons are identified using a bootstrap aggregated deci-
sion tree algorithm with 30 input variables. Of these, the
most important are the number and positions of the hits in
the IFR, the difference between the measured and expected
DCH
dE=dx
for the muon hypothesis, and the energy
deposited in the EMC. For tracks with momentum greater
than 1 GeV, the muon identification has an efficiency of
about 60% for muons, with a pion misidentification proba-
bility of between 0.5% and 1.5%.
The reconstruction efficiencies for the different channels
after the above particle identification requirements are
about 18% for
e
þ
e

, 9% for

þ


, 13% for
e



, and
26% for

þ


. The background candidates that remain
are either random combinations of two leptons (combina-
torial background) or
D
0
!

þ


decays where both
pions pass the lepton identification criteria (peaking back-
ground). The
D
0
!

þ


background is most important
for the
D
0
!

þ


channel.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032001 (2012)
032001-4
Figure
1
shows the reconstructed invariant mass
distributions from Monte Carlo (MC) simulated samples
for the three
D
0
!
þ

signal channels. Also shown
are the distributions from
D
0
!

þ


reconstructed as
D
0
!
þ

and
D
0
!
K


þ
reconstructed as
D
0
!
þ

for each signal channel. The overlap between the
D
0
!
þ

and
D
0
!

þ


distributions is largest
for the
D
0
!

þ


channel, while the
D
0
!
þ

and
D
0
!
K


þ
distributions are well separated.
The combinatorial background originates mostly from
events with two semileptonic
B
and/or
D
decays. The
sample of events selected by the above criteria are domi-
nantly from
e
þ
e

!
B

B
events, rather than events from
the
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
) continuum. We use a linear
combination (Fisher discriminant [
10
]) of the following
five variables to reduce the combinatorial
B

B
background:
(i) The measured
D
0
flight length divided by its
uncertainty.
(ii) The value of
j
cos

hel
j
, where

hel
is defined as the
angle between the momentum of the positively
charged
D
0
daughter and the boost direction from
the lab frame to the
D
0
rest frame, all in the
D
0
rest
frame.
(iii) The missing transverse momentum with respect to
the beam axis.
(iv) The ratio of the second and zeroth Fox–Wolfram
moments [
11
].
(v) The
D
0
momentum in the CM frame.
The flight length for the combinatorial background is
symmetric about zero, while the signal has an exponential
distribution. The
j
cos

hel
j
distribution is uniform for the
signal but peaks at zero for the combinatorial
B

B
back-
ground. The neutrinos from the semileptonic decays in
B

B
background events create missing transverse momentum,
while there is none for signal events. The ratio of Fox–
Wolfram moments uses general event-shape information to
separate
B

B
and continuum
q

q
events. Finally, the signal
has a broad
D
0
CM momentum spectrum that peaks at
about 3 GeV, while the combinatorial background peaks at
the minimum allowed value of 2.4 GeV.
Figure
2
shows distributions of the Fisher discriminant
(
F
) for samples of
B

B
MC,
D
0
!

þ


signal MC, and
continuum background MC. The separation between signal
and
B

B
background distributions is large, while the signal
and continuum background distributions are similar. For
example, requiring
F
to be greater than 0 removes about
90% of the
B

B
background while keeping 85% of the
signal. The minimum
F
value is optimized for each signal
channel as described below.
We use the
j
cos

hel
j
variable directly to remove the
continuum combinatorial background. Figure
3
shows
distributions of
j
cos

hel
j
before making a minimum
F
requirement, for
B

B
background, continuum background,
and signal. The dropoff for
j
cos

hel
j
near 1.0 in the
signal distributions is caused by the selection and particle
identification requirements. The
B

B
background peaks
near zero, while the continuum background peaks sharply
near one.
The selection criteria for each signal channel were
chosen to give the lowest expected signal branching
), GeV
0
m(D
1.8
1.85
1.9
Arbitrary units / 4 MeV
0
0.1
0.2
-
e
+
e
0
D
), GeV
0
m(D
1.8
1.85
1.9
Arbitrary units / 4 MeV
0
0.1
0.2
-
μ
+
μ
0
D
), GeV
0
m(D
1.8
1.85
1.9
Arbitrary units / 4 MeV
0
0.1
0.2
-+
μ
+-
e
0
D
m, GeV
0.142
0.144
0.146
0.148
Arbitrary units / 0.2 MeV
0
0.1
0.2
0.3
0.4
-
e
+
e
0
D
m, GeV
0.142
0.144
0.146
0.148
Arbitrary units / 0.2 MeV
0
0.1
0.2
0.3
0.4
-
μ
+
μ
0
D
m, GeV
0.142
0.144
0.146
0.148
Arbitrary units / 0.2 MeV
0
0.1
0.2
0.3
0.4
-+
μ
+-
e
0
D
FIG. 1 (color online). Reconstructed
D
0
mass (left) and

m
(right) for the three signal channels:
D
0
!
e
þ
e

(top),
D
0
!

þ


(middle), and
D
0
!
e



(bottom). The solid
(black) histogram is the signal MC sample, the dashed (blue)
histogram is the
D
0
!

þ


MC sample reconstructed as
D
0
!
þ

, and the dotted (red) histogram is the
D
0
!
K


þ
MC sample reconstructed as
D
0
!
þ

. The
D
0
!
þ

and
D
0
!

þ


distributions have been normalized to
unit area. The
D
0
!
K


þ
normalization is arbitrary.
Fisher Discriminant
2
0
2
-
Arbitrary Units / 0.125
0
0.05
0.1
0.15
FIG. 2 (color online). Fisher discriminant,
F
, distributions for
the
B

B
MC sample (dashed blue line), the
D
0
!

þ


signal
MC sample (solid black line), and the continuum MC sample
(dotted red line). The
F
distributions for
D
0
!
e
þ
e

and
D
0
!
e



are similar to those of
D
0
!

þ


.
SEARCH FOR THE DECAY MODES
...
PHYSICAL REVIEW D
86,
032001 (2012)
032001-5
fraction upper limit for the null hypothesis (a true branching
fraction of zero) using the MC samples. The Fisher dis-
criminant coefficients were determined before applying the
j
cos

hel
j
,
D
0
mass, and

m
requirements. We then tested a
total of 2700 configurations of
j
cos

hel
j
,
F
,
D
0
mass, and

m
criteria. Table
I
summarizes the resulting best values
for the maximum
j
cos

hel
j
, minimum
F
,
m
ð
D
0
Þ
signal
window, and

m
interval.
After the selection criteria in Table
I
were determined,
the data yields in the sideband region were compared to
the expectations from Monte Carlo samples. The
D
0
!

þ


and
D
0
!
e



data yields were consistent with
the expectations from the Monte Carlo samples. However,
the
D
0
!
e
þ
e

sideband yield showed a substantial ex-
cess of events; 90 events were observed when
5
:
5

1
:
6
were expected.
The excess of data sideband events over the expected
background from Monte Carlo samples was investigated
and found to have several distinct features: low track
multiplicity, event-shape characteristics that are similar
to continuum events, tracks consistent with electrons
produced in photon conversions, low
D
0
daughter track
momenta, and undetected energy along the beam axis.
We found that such events result from hard initial state
radiation events or two-photon interaction processes that
are not simulated in the continuum MC samples used in the
analysis. The following selection criteria were added in
order to remove such background contributions:
(i) Events must have at least five tracks for the
D
0
!
e
þ
e

channel and at least four tracks for the
D
0
!

þ


and
D
0
!
e



channels.
(ii) Events can have at most three electron candidates.
(iii) The longitudinal boost of the event, reconstructed
from all tracks and neutral clusters, along the high-
energy beam direction
p
z
=E
in the CM frame must
be greater than

0
:
5
for all three
D
0
!
þ

channels.
(iv) For
D
0
!

þ


and
D
0
!
e



candidates, the
pion track from the
D
decay and the leptons must
be inconsistent with originating from a photon
conversion.
The signal efficiencies for the
D
0
!
e
þ
e

,
D
0
!

þ


,
and
D
0
!
e



channels for these additional criteria are
91.4%, 99.3%, and 96.8%, respectively. The
D
0
!
e
þ
e

sideband yield in the data with these criteria applied is
reduced to eight events where
4
:
5

1
:
3
are expected,
based on the Monte Carlo samples.
A. Peaking
D
0
!

þ


background estimation
The amount of
D
0
!

þ


peaking background within
the
m
ð
D
0
Þ
signal window is estimated from data and
calculated separately for each
D
0
!
þ

channel using
N
BG

¼

X
i
N
NP
;i
h
p
þ
f;i
ih
p

f;i
i



m
ð
D
0
Þ

G;
(1)
where the sum
i
is over the six data-taking periods,
N
NP
;i
is
the number of
D
0
!

þ


events that pass all of the
D
0
!
þ

selection criteria except for the lepton identi-
fication and
m
ð
D
0
Þ
signal window requirements,
h
p
þ
f;i
i
h
p

f;i
i
is the product of the average probability that the

þ
)|
hel
θ
|cos(
00.5 1
Candidates / 0.025
0
10
20
30
B background
Continuum
-
e
+
e
0
D
)|
hel
θ
|cos(
00.5 1
Candidates / 0.025
0
5000
Signal MC
-
e
+
e
0
D
)|
hel
θ
|cos(
00.5 1
Candidates / 0.025
0
10
20
B background
Continuum
-
μ
+
μ
0
D
)|
hel
θ
|cos(
00.5 1
Candidates / 0.025
0
2000
4000
Signal MC
-
μ
+
μ
0
D
)|
hel
θ
|cos(
00.5 1
Candidates / 0.025
0
20
40
B background
Continuum
-+
μ
+-
e
0
D
)|
hel
θ
|cos(
00.5 1
Candidates / 0.025
0
2000
4000
6000
Signal MC
-+
μ
+-
e
0
D
FIG. 3 (color online). Distributions of
j
cos
ð

hel
Þj
for the three signal channels:
D
0
!
e
þ
e

(left),
D
0
!

þ


(center), and
D
0
!
e



(right). The top distributions show Monte Carlo distributions for the combinatorial
B

B
(dashed blue lines) and continuum
(dotted red lines) backgrounds. The bottom distributions show the signal Monte Carlo samples with arbitrary normalization.
TABLE I. Selection criteria for the three
D
0
!
þ

signal
decay modes. The parameter in the last row is defined as


m


m


m
0
, where

m
0
is the nominal
D

D
0
mass differ-
ence [
12
].
Parameter
e
þ
e


þ


e



j
cos

hel
j
<
0
:
85
<
0
:
90
<
0
:
85
F
>
0
:
00
>

0
:
25
>
0
:
00
m
ð
D
0
Þ
(GeV) [1.815, 1.890] [1.855, 1.890] [1.845, 1.890]
j


m
j
(MeV)
<
0
:
5
<
0
:
5
<
0
:
4
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032001 (2012)
032001-6
and the


pass the lepton identification criteria,

m
ð
D
0
Þ
is
the efficiency for
D
0
!

þ


background to satisfy the
m
ð
D
0
Þ
signal window requirement, and
G
takes into ac-
count a positive correlation in the probability that the

þ
and the


pass the muon identification criteria. The value
of
h
p
þ
f;i
i
(
h
p

f;i
i
) is measured using the ratio of the
D
0
!

þ


yield requiring that the

þ
(


) satisfy the lepton
identification requirements to the
D
0
!

þ


yield with
no lepton identification requirements applied. The
h
p
þ
f;i
i
and
h
p

f;i
i
are measured separately for each of the six major
data-taking periods due to the changing IFR performance
with time. The values of
h
p
þ
f;i
i
and
h
p

f;i
i
vary between
0.5% and 1.5%. The probability that the

þ
and


both
pass the muon identification criteria is enhanced when the
two tracks curve toward each other, instead of away from
each other, in the plane perpendicular to the beam axis. We
use
G
¼
1
:
19

0
:
05
for the
D
0
!

þ


channel and
G
¼
1
for the
D
0
!
e
þ
e

and
D
0
!
e



channels.
The
G
factor is measured using a high-statistics
D
0
!
K


þ
sample where the
K
is required to have a signature
in the IFR that matches that of a

, which passes the

identification criteria. This is in good agreement with the
MC estimate of the
G
factor value,
1
:
20

0
:
10
.
B. Combinatorial background estimation
The combinatorial background is estimated by using the
number of observed events in a sideband region and the
expected ratio of events
R
cb
in the signal and sideband
regions, determined from MC simulation. The sideband is
above the signal region in the
D
0
mass ([1.90, 2.05] GeV)
in a wide

m
window ([0.141, 0.149] GeV). We fit the
D
0
mass and

m
projections of the combinatorial background
MC using second-order polynomials. A two-dimensional
probability density function (PDF) is formed by multiply-
ing the one-dimensional PDFs, assuming the variables are
uncorrelated. The combinatorial background signal-to-
sideband ratio
R
cb
is then computed from the ratio of the
integrals of the two-dimensional PDF.
III. RESULTS
The distribution of

m
vs
D
0
mass as well as projections
of

m
and the
D
0
mass for the data events for the three
signal channels are shown in Fig.
4
. Peaks from
D
0
!
K


þ
and
D
0
!

þ


are visible at 1.77 GeV and
1.85 GeV in the
D
0
mass distribution for
D
0
!

þ


candidates. We observe 1, 8, and 2 events in the
D
0
!
e
þ
e

,
D
0
!

þ


, and
D
0
!
e



signal regions,
respectively.
A.
D
0
!
þ

branching fractions
The yield of
D
0
!

þ


decays in the

control
sample, selected with the same
F
and
j
cos

hel
j
criteria
for each
D
0
!
þ

signal mode (see Table
I
), is used to
normalize the
D
0
!
þ

signal branching fraction. For
each
D
0
!
þ

signal channel, the
D
0
!

þ


yield
N
fit

is determined by fitting the
D
0
mass spectrum of the
D
0
!

þ


control sample in the range [1.7, 2.0] GeV.
The fit has three components:
D
0
!

þ


,
D
0
!
K


þ
,
and combinatorial background. The PDF for the
D
0
!

þ


component is the sum of a Crystal Ball function
and two Gaussians. The Crystal Ball function is a Gaussian
modified to have an extended, power-law tail on the low
side [
13
]. The PDF for the
D
0
!
K


þ
component is the
sum of a Crystal Ball function and an exponential function.
The combinatorial background PDF is an exponential
function.
The
D
0
!
þ

branching fraction is given by
B
‘‘
¼

N
‘‘
N
fit





‘‘

B

¼
S
‘‘

N
‘‘
;
(2)
where
N
‘‘
is the number of
D
0
!
þ

signal candidates,
N
fit

is the number of
D
0
!

þ


candidates from the fit,


and

‘‘
are the efficiencies for the corresponding
decay modes,
B

¼ð
1
:
400

0
:
026
Þ
10

3
is the
D
0
!

þ


branching fraction [
12
], and
S
‘‘
is defined by
S
‘‘

B

N
fit




‘‘
:
(3)
The expected observed number of events in the signal
region is given by
N
obs
¼
B
‘‘
=S
‘‘
þ
N
BG
:
(4)
The uncertainties on
S
‘‘
and
N
BG
are incorporated into a
likelihood function by convolving a Poisson PDF in
N
obs
with Gaussian PDFs in
S
‘‘
and
N
BG
. We determine
90% confidence level intervals using the likelihood ratio
ordering principle of Feldman and Cousins [
14
] to con-
struct the confidence belts. The estimated branching frac-
tions and 1 standard deviation uncertainties are determined
from the values of
B
‘‘
that maximize the likelihood and
give a change of 0.5 in the log likelihood relative to the
maximum, respectively.
B. Systematic uncertainties
Table
II
summarizes the systematic uncertainties.
Several of the uncertainties in


=
‘‘
cancel, including
tracking efficiency for the
D
0
daughters, slow pion effi-
ciency, and the efficiencies of the
F
and
D
0
momentum
requirements. The uncertainty on


=
‘‘
due to particle
identification is 4%. Bremsstrahlung creates a low-side tail
in the
D
0
mass distributions for the
D
0
!
e
þ
e

and
D
0
!
e



decay modes. The uncertainty

‘‘
due to the mod-
eling of this tail is 3% for
D
0
!
e
þ
e

and 2% for
D
0
!
e



. The Crystal Ball shape parameters that describe the
low-side tail of the
D
0
mass distribution were varied,
leading to an uncertainty of 1.1% to 1.3% on
N
fit

.We
use the world average for the
D
0
!

þ


branching
fraction [
12
], which has an uncertainty of 1.9%. We
SEARCH FOR THE DECAY MODES
...
PHYSICAL REVIEW D
86,
032001 (2012)
032001-7
mass, GeV
0
D
1.7
1.8
1.9
2
m, GeV
0.142
0.144
0.146
0.148
-
e
+
e
0
D
mass, GeV
0
D
1.7
1.8
1.9
2
m, GeV
0.142
0.144
0.146
0.148
-
μ
+
μ
0
D
mass, GeV
0
D
1.7
1.8
1.9
2
m, GeV
0.142
0.144
0.146
0.148
-+
μ
+-
e
0
D
mass, GeV
0
D
1.7
1.8
1.9
2
Candidates / 15 MeV
0
2
4
-
e
+
e
0
D
mass, GeV
0
D
1.7
1.8
1.9
2
Candidates / 17.5 MeV
0
10
20
-
μ
+
μ
0
D
mass, GeV
0
D
1.7
1.8
1.9
2
Candidates / 15 MeV
0
2
4
6
-+
μ
+-
e
0
D
m, GeV
0.142
0.144
0.146
0.148
Candidates / 0.33 MeV
0
2
4
-
e
+
e
0
D
m, GeV
0.142
0.144
0.146
0.148
Candidates / 0.33 MeV
0
5
10
15
-
μ
+
μ
0
D
m, GeV
0.142
0.144
0.146
0.148
Candidates / 0.27 MeV
0
5
-+
μ
+-
e
0
D
FIG. 4 (color online). Data distributions of

m
vs the reconstructed
D
0
mass (top row), projections of the
D
0
mass (middle row), and

m
(bottom row). The columns contain the distributions for the
D
0
!
e
þ
e

(left),
D
0
!

þ


(center), and
D
0
!
e



(right)
decay modes. The shaded
D
0
mass (

m
) distributions represent the subset of events that fall in the

m
(
D
0
mass) signal window. In the
top row, the dotted (black) box indicates the signal region and the dashed (red) box indicates the sideband region. In the middle and
bottom rows, the vertical dotted black lines indicate the boundaries of the signal region.
TABLE II. Systematic uncertainties. The uncertainty on
S
‘‘
results from the uncertainties on


=
‘‘
,
N
fit

, and
B

added in quadrature. The systematic uncertainty on the overall
background
N
BG
is obtained from the uncertainties on
N
BG

and
N
cb
added in quadrature.
D
0
!
e
þ
e

D
0
!

þ


D
0
!
e





=
‘‘
, particle ID
4%
4%
4%


=
‘‘
, bremsstrahlung
3%
-
2%
N
fit

1.2%
1.3%
1.1%
B

1.9%
1.9%
1.9%
S
‘‘
5.4%
4.6%
5.0%
N
BG

11% (0.004 events) 16% (0.43 events)
5%
N
cb
,
R
cb
36% (0.35 events)
20% (0.25 events) 19% (0.20 events)
N
BG
0.35 events
0.50 events
0.20 events
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032001 (2012)
032001-8