of 8
Search for a Dark Photon in
e
þ
e
Collisions at
B
A
B
AR
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
M. Feng,
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
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
T. Hartmann,
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
PRL
113,
201801 (2014)
Selected for a
Viewpoint
in
Physics
PHYSICAL REVIEW LETTERS
week ending
14 NOVEMBER 2014
0031-9007
=
14
=
113(20)
=
201801(8)
201801-1
© 2014 American Physical Society
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
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
PRL
113,
201801 (2014)
PHYSICAL REVIEW LETTERS
week ending
14 NOVEMBER 2014
201801-2
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 12 June 2014; revised manuscript received 15 September 2014; published 10 November 2014)
Dark sectors charged under a new Abelian interaction have recently received much attention in the
context of dark matter models. These models introduce a light new mediator, the so-called dark photon (
A
0
),
connecting the dark sector to the standard model. We present a search for a dark photon in the reaction
e
þ
e
γ
A
0
,
A
0
e
þ
e
,
μ
þ
μ
using
514
fb
1
of data collected with the
BABAR
detector. We observe
no statistically significant deviations from the standard model predictions, and we set 90% confidence level
upper limits on the mixing strength between the photon and dark photon at the level of
10
4
10
3
for dark
photon masses in the range
0
.
02
10
.
2
GeV. We further constrain the range of the parameter space favored
by interpretations of the discrepancy between the calculated and measured anomalous magnetic moment
of the muon.
DOI:
10.1103/PhysRevLett.113.201801
PACS numbers: 13.66.Hk, 12.60.Cn, 14.80.-j, 95.35.+d
Dark sectors, which introduce new particles neutral
under the standard model (SM) gauge symmetries, arise
in many models of physics beyond the standard model
[1]
.
These particles would only interact feebly with ordinary
matter, and could easily have escaped detection in past
experimental searches. Besides gravity, a few renormaliz-
able interactions provide a portal into dark sectors. One
of the simplest realizations consists of a dark sector
charged under a new gauge group
U
ð
1
Þ
0
. The correspond-
ing gauge boson, dubbed the dark photon (
A
0
), couples to
the SM hypercharge via kinetic mixing
[2]
with a mixing
strength
ε
. This results in an effective interaction
ε
eA
0
μ
J
μ
EM
between the dark photon and the electromagnetic current
J
μ
EM
after electroweak symmetry breaking. This idea has
recently received much attention in the context of dark
matter models, where weakly interacting massive particles
(WIMPs) reside in a dark sector charged under a new
Abelian interaction
[3
5]
. Within this framework, dark
photons would mediate the annihilation of WIMPs into SM
fermions. To accommodate the recent anomalies observed
in cosmic rays
[6
8]
, the dark photon mass is constrained to
be in the MeV to GeV range.
Low-energy
e
þ
e
colliders offer an ideal environment to
probe low-mass dark sectors
[9,10]
. Dark photons could be
produced in association with a photon in
e
þ
e
collisions
and decay back to SM fermions if other dark sector states
are kinematically inaccessible. The dark photon width,
suppressed by a factor
ε
2
, is expected to be well below the
experimental resolution. Dark photons could therefore be
detected as narrow resonances in radiative
e
þ
e
γ
l
þ
l
(
l
¼
e;
μ
) events. No unambiguous signal for a dark photon
has been reported so far, and constraints have been set on
the mixing strength between the photon and dark photon as
a function of the dark photon mass
[11
22]
. Searches for an
additional low-mass, dark gauge boson
[23]
or dark Higgs
boson
[24]
have also yielded negative results.
PRL
113,
201801 (2014)
PHYSICAL REVIEW LETTERS
week ending
14 NOVEMBER 2014
201801-3
We report herein a search for dark photons in the
reaction
e
þ
e
γ
A
0
,
A
0
l
þ
l
(
l
¼
e;
μ
) with data
recorded by the
BABAR
detector
[25,26]
. This search is
based on
514
fb
1
of data collected mostly at the
Υ
ð
4
S
Þ
resonance, but also at the
Υ
ð
3
S
Þ
and
Υ
ð
2
S
Þ
peaks, as well
as data in the vicinity of these resonances
[27]
. We probe
dark photon masses in the range
0
.
02
<m
A
0
<
10
.
2
GeV
[28]
. To avoid experimental bias, we examine the data
only after finalizing the analysis strategy. About 5% of the
data set is used to optimize the selection criteria and
validate the fitting procedure, and is then discarded from
the final data sample.
Simulated signal events are generated by
MADGRAPH
[29]
for 35 different
A
0
mass hypotheses. The background
processes
e
þ
e
e
þ
e
ð
γ
Þ
and
e
þ
e
γγ
ð
γ
Þ
are simu-
lated using
BHWIDE
[30]
(see below), and
e
þ
e
μ
þ
μ
ð
γ
Þ
events are generated with
KK
[31]
. Resonance production
processes in initial state radiation,
e
þ
e
γ
X
½
X
¼
J=
ψ
;
ψ
ð
2
S
Þ
;
Υ
ð
1
S
Þ
;
Υ
ð
2
S
Þ
, are simulated using a structure
function technique
[32,33]
. The detector acceptance and
reconstruction efficiencies are determined using a
Monte Carlo (MC) simulation based on
GEANT
4
[34]
.
We select events containing two oppositely charged
tracks and a single photon having a center-of-mass
(c.m.) energy greater than 0.2 GeV. Additional low-energy
photons are allowed if their energies measured in the
laboratory frame do not exceed 0.2 GeV. At least one
track is required to be identified as an electron, or both
tracks as muons, by particle identification algorithms. The
cosine of the muon helicity angle, defined as the angle
between the muon and the c.m. frame in the
A
0
rest frame,
must be less than 0.95. To further suppress the contribution
from radiative Bhabha events, we also require the cosine
of the polar angle (the angle with respect to the electron
beam axis) of the positron in the c.m. frame to be larger
than
0
.
5
, and that of the electron to be less than 0.5. The
γ
l
þ
l
system is then fit, constraining the center-of-mass
energy of the candidate to be within the beam energy spread
and requiring the tracks to originate from the interaction
point to within its spread. Finally, we require the
χ
2
of the
fit to be less than 30 (for 8 degrees of freedom). These
criteria are chosen to maximize the signal significance over
a broad mass range.
A large contribution from converted photons produced
in
e
þ
e
γγ
,
γ
e
þ
e
events is still present at low
e
þ
e
invariant mass. A neural network is trained to further
reduce this background using the following variables:
the flight length of the
e
þ
e
pair in the plane transverse to
the beam, and the corresponding flight significance, the
electron helicity angle, the polar angle of the
e
þ
e
system,
and the angle between the photon and the plane formed
by the two tracks. We apply a requirement on the neural
network output that selects approximately 70% of the
signal in the low-mass region and rejects more than
99.7% of the photon conversions. The uncertainty
associated with this selection criterion, estimated from a
sample of
π
0
γ
e
þ
e
decays, is at the level of 2% at
m
A
0
20
MeV, and decreases rapidly to negligible levels
above
m
A
0
50
MeV.
The resulting dielectron and reduced dimuon mass
distributions are displayed in Fig.
1
, together with the
predictions of various simulated SM processes. The
reduced dimuon mass,
m
R
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
2
μμ
4
m
2
μ
q
, is easier to
model near threshold than the dimuon mass. The dielectron
(reduced dimuon) mass spectrum is dominated by radiative
Bhabha (dimuon) production, with smaller peaking con-
tributions from ISR production of
J=
ψ
;
ψ
ð
2
S
Þ
,
Υ
ð
1
S
Þ
, and
Υ
ð
2
S
Þ
resonances. The contribution from
φ
K
þ
K
,
where both kaons are misidentified as electrons or muons,
is found to be negligible. The mass distributions are
generally well described by the simulation, except in the
low
e
þ
e
mass region, where, as expected,
BHWIDE
fails
to reproduce events in which the two leptons are separated
by a small angle. Since the signal extraction procedure
5
10
6
10
Entries / 0.1 GeV
Data
-
e
+
e
γ
-
e
+
MC e
R
γ
-
e
+
MC e
(GeV)
ee
m
0246810
Data/MC
0.9
1
1.1
5
10
6
10
Entries / 0.1 GeV
Data
-
μ
+
μ
γ
-
e
+
MC e
R
γ
-
e
+
MC e
(GeV)
2
μ
- 4m
2
μ
μ
m
=
R
m
0246810
Data/MC
0.9
1
FIG. 1 (color online). Distribution of the final dielectron (top)
and reduced dimuon invariant masses (bottom), together with the
predictions of various simulated SM processes and ISR produc-
tion of
J=
ψ
,
ψ
ð
2
S
Þ
,
Υ
ð
1
S
Þ
, and
Υ
ð
2
S
Þ
resonances (collectively
labeled as
R
). The fit to the ratio between data and simulated
events is described in the text.
PRL
113,
201801 (2014)
PHYSICAL REVIEW LETTERS
week ending
14 NOVEMBER 2014
201801-4
does not depend on the background predictions, this
disagreement has little impact on the search.
The signal selection efficiency, typically 15% (35%)
for the dielectron (dimuon) channel, is determined from
Monte Carlo simulation. The difference is mostly due to
trigger efficiencies. For electrons, this is lowered in order
to suppress the rate of radiative Bhabha events. Correction
factors to the efficiency, which vary between 0.5% to 3%,
account for the effects of triggers, charged particle iden-
tification, and track and photon reconstruction. These are
assessed by fitting the ratios of the measured and simulated
e
þ
e
e
þ
e
γ
and
e
þ
e
μ
þ
μ
γ
differential mass dis-
tributions, as shown in Fig.
1
. For the dielectron channel,
we fit the ratio only in the region
m
e
þ
e
>
3
GeV, where
the simulation is expected to provide reliable predictions,
and extrapolate the corrections to the low-mass region. The
entire mass range is used for the dimuon final state. Half of
the corrections are propagated as systematic uncertainties
to cover statistical variations between neighboring mass
points and the uncertainty associated with the extrapolation
procedure.
The signal yield as a function of
m
A
0
is extracted by
performing a series of independent fits to the dielectron
and the reduced dimuon mass spectra for each beam
energy. The fits are performed in the range
0
.
02
<m
A
0
<
10
.
2
GeV (
0
.
212
<m
A
0
<
10
.
2
GeV) for the dielectron
(dimuon) sample taken near the
Υ
ð
4
S
Þ
resonance, and
up to 9.6 and 10.0 GeV for the data set collected near the
Υ
ð
2
S
Þ
and
Υ
ð
3
S
Þ
resonances, respectively
[28]
. We search
for a dark photon in varying mass steps that correspond to
approximately half of the dark photon mass resolution.
Each fit is performed over an interval at least 20 times
broader than the signal resolution at that mass, with the
constraint
m
e
þ
e
>
0
.
015
GeV for the dielectron channel.
For the purposes of determining the mass steps, the signal
resolution is estimated by Gaussian fits to several simulated
A
0
samples, and interpolated to all other masses. It varies
between 1.5 and 8 MeV. We sample a total of 5704 (5370)
mass hypotheses for the dielectron (dimuon) channel.
Example of fits can be found in the Supplemental
Material
[35]
. The bias in the fitted values is estimated
from a large ensemble of pseudoexperiments and found to
be negligible.
The likelihood function, described below, contains con-
tributions from signal, radiative dilepton background, and
peaking background where appropriate. The signal prob-
ability density function (PDF) is modeled directly from
the signal MC mass distribution using a nonparametric
kernel PDF, and interpolated between the known simulated
masses using an algorithm based on the cumulative mass
distributions
[36]
. An uncertainty of 5%
10% in this
procedure is assessed by taking the next to closest instead
of the closest simulated mass points to interpolate the
signal shape. Samples of simulated and reconstructed
e
þ
e
γ
J=
ψ
,
J=
ψ
l
þ
l
events indicate that the
simulation underestimates the signal width by 8% (4%)
for the dielectron (dimuon) channel. We assume that this
difference is independent of the dark photon mass, and we
increase the signal PDF width by the corresponding amount
for all mass hypotheses. We propagate half of these
correction factors as systematic uncertainties on the fitted
signal yields.
The radiative Bhabha background below 0.1 GeV is
described by a fourth-order polynomial, and elsewhere by a
third-order polynomial. The radiative dimuon background
is parametrized by a third-order polynomial, constrained
to pass through the origin for fits in the region below
0.05 GeV. Peaking contributions from the
J=
ψ
,
ψ
ð
2
S
Þ
,
Υ
ð
1
S
Þ
, and
Υ
ð
2
S
Þ
resonances for both final states are
included where appropriate. Their shapes are modeled as
Crystal Ball or Gaussian functions with parameters extrac-
ted from fits to the corresponding MC samples. Similarly
to the signal PDF, we increase their width by 8% (4%)
for the dielectron (dimuon) final states. The interference
between vector resonances with radiative dilepton produc-
tion is observed for the
ω
and
φ
mesons, and is fit with the
following empirical function:
f
ð
m
Þ¼ð
a
þ
bm
þ
cm
2
þ
dm
3
Þ




1
Q
m
ω
=
φ
Γ
s
m
2
ω
=
φ
im
ω
=
φ
Γ




2
;
where
m
ω
=
φ
(
Γ
) denotes the mass (width) of the resonance,
Q
the resonant fraction, and
a
,
b
,
c
,
d
are free parameters.
We fix the masses and widths to their nominal values
[37]
,
and let their fractions float. We exclude the resonant
regions from the search, vetoing ranges of

30
MeV
around the nominal mass of the
ω
and
φ
resonances, and

50
MeV around the
J=
ψ
,
ψ
ð
2
S
Þ
,and
Υ
ð
1
S;
2
S
Þ
reso-
nances (approximately

5
σ
R
,where
σ
R
denotes the
experimental resolution of the resonances). An alternative
signal extraction fit, using parametric PDFs for signal
[21]
and a different background parametrization, has been
performed for the
μ
þ
μ
channel. The results of both
methods are statistically consistent with each other. The
uncertainty on the background modeling is estimated
by using an alternative description of the radiative
Bhabha and dimuon contributions based on a second- or
fourth-order polynomial, depending on the mass hypoth-
esis. This uncertainty is almost as large as the statistical
uncertainty near the dielectron threshold, and can be as
large as 50% of the statistical uncertainty in the vicinity
of the
Υ
ð
1
S;
2
S
Þ
resonances. Outside these regions, the
uncertainty varies from a few percent at low masses to
20%
of the statistical uncertainty in the high-mass region.
In addition, we propagate half of the corrections applied
to the signal width, as well as the uncertainties on the
ω
and
φ
masses and widths, as systematic uncertainties on
the fitted signal yields.
The
e
þ
e
γ
A
0
,
A
0
e
þ
e
and
e
þ
e
γ
A
0
,
A
0
μ
þ
μ
cross sections as a function of the dark photon mass are
PRL
113,
201801 (2014)
PHYSICAL REVIEW LETTERS
week ending
14 NOVEMBER 2014
201801-5