B
A
B
AR
-PUB-14/002
SLAC-PUB-15979
arXiv:1406.2980 [hep-ex]
Search for a dark photon in
e
+
e
−
collisions at
B
A
B
AR
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano
ab
,
3
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
abc
,
9
A. R. Buzykaev
a
,
9
V. P. Druzhinin
ab
,
9
V. B. Golubev
ab
,
9
E. A. Kravchenko
ab
,
9
A. P. Onuchin
abc
,
9
S. I. Serednyakov
ab
,
9
Yu. I. Skovpen
ab
,
9
E. P. Solodov
ab
,
9
K. Yu. Todyshev
ab
,
9
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
a
,
21
C. Bozzi
a
,
21
R. Calabrese
ab
,
21
G. Cibinetto
ab
,
21
E. Fioravanti
ab
,
21
I. Garzia
ab
,
21
E. Luppi
ab
,
21
L. Piemontese
a
,
21
V. Santoro
a
,
21
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
ab
,
23
M. Lo Vetere
ab
,
23
M. R. Monge
ab
,
23
S. Passaggio
a
,
23
C. Patrignani
ab
,
23
E. Robutti
a
,
23
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
a
,
43
F. Palombo
ab
,
43
L. Cremaldi,
44
R. Godang,
44,
∗∗
P. Sonnek,
44
D. J. Summers,
44
M. Simard,
45
P. Taras,
45
G. De Nardo
ab
,
46
G. Onorato
ab
,
46
C. Sciacca
ab
,
46
M. Martinelli,
47
G. Raven,
47
C. P. Jessop,
48
J. M. LoSecco,
48
K. Honscheid,
49
R. Kass,
49
E. Feltresi
ab
,
50
M. Margoni
ab
,
50
M. Morandin
a
,
50
M. Posocco
a
,
50
M. Rotondo
a
,
50
G. Simi
ab
,
50
F. Simonetto
ab
,
50
R. Stroili
ab
,
50
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
ab
,
52
E. Manoni
a
,
52
S. Pacetti
ab
,
52
A. Rossi
a
,
52
C. Angelini
ab
,
53
G. Batignani
ab
,
53
S. Bettarini
ab
,
53
M. Carpinelli
ab
,
53,
††
G. Casarosa
ab
,
53
A. Cervelli
ab
,
53
M. Chrzaszcz
a
,
53
F. Forti
ab
,
53
M. A. Giorgi
ab
,
53
A. Lusiani
ac
,
53
B. Oberhof
ab
,
53
E. Paoloni
ab
,
53
A. Perez
a
,
53
G. Rizzo
ab
,
53
J. J. Walsh
a
,
53
D. Lopes Pegna,
54
J. Olsen,
54
A. J. S. Smith,
54
R. Faccini
ab
,
55
F. Ferrarotto
a
,
55
F. Ferroni
ab
,
55
M. Gaspero
ab
,
55
L. Li Gioi
a
,
55
A. Pilloni
ab
,
55
G. Piredda
a
,
55
C. B ̈unger,
56
S. Dittrich,
56
O. Gr ̈unberg,
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
ab
,
68
F. De Mori
ab
,
68
A. Filippi
a
,
68
D. Gamba
ab
,
68
L. Lanceri
ab
,
69
L. Vitale
ab
,
69
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
arXiv:1406.2980v2 [hep-ex] 18 Sep 2014
(The
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, 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 Universit ̈at Bochum, Institut f ̈ur 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 SB RAS, Novosibirsk 630090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 630092
c
, 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 Universit ̈at Dortmund, Fakult ̈at 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
21
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara
b
, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
23
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
25
Universit ̈at Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
26
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur 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’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et Universit ́e 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-Universit ̈at Mainz, Institut f ̈ur 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, Montr ́eal, Qu ́ebec, Canada H3A 2T8
43
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
44
University of Mississippi, University, Mississippi 38677, USA
45
Universit ́e de Montr ́eal, Physique des Particules, Montr ́eal, Qu ́ebec, Canada H3C 3J7
46
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
47
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
48
University of Notre Dame, Notre Dame, Indiana 46556, USA
49
Ohio State University, Columbus, Ohio 43210, USA
50
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
51
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
52
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
53
INFN Sezione di Pisa
a
; Dipartimento di Fisica,
Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
54
Princeton University, Princeton, New Jersey 08544, USA
2
55
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
56
Universit ̈at 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
68
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
69
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, 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
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
′
), connecting the dark sector to the Standard Model. We present a search for a
dark photon in the reaction
e
+
e
−
→
γA
′
,A
′
→
e
+
e
−
,μ
+
μ
−
using 514 fb
−
1
of data collected with
the
B
A
B
AR
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.
PACS numbers: 12.60.-i, 14.80.-j, 13.66.Hk, 95.35.+d
Dark sectors, which introduce new particles neutral un-
der 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 renormal-
izable interactions provide a portal into dark sectors.
One of the simplest realizations consists of a dark sector
charged under a new gauge group
U
(1)
′
. The correspond-
ing gauge boson, dubbed the dark photon (
A
′
), couples
to the SM hypercharge via kinetic mixing [2] with a mix-
ing strength
. This results in an effective interaction
eA
′
μ
J
μ
EM
between the dark photon and the electromag-
netic 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 reside in a dark sector charged under
a new Abelian interaction [3–5]. Within this framework,
dark photons would mediate the annihilation of WIMP
particles 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
+
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
+
e
−
collisions, and decay back to SM fermions if other dark
sector states are kinematically inaccessible. The dark
photon width, suppressed by a factor
2
, is expected to
be well below the experimental resolution. Dark pho-
tons could therefore be detected as narrow resonances in
radiative
e
+
e
−
→
γl
+
l
−
(
l
=
e,μ
) events. No unambigu-
ous 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.
We report herein a search for dark photons in the re-
action
e
+
e
−
→
γA
′
,A
′
→
l
+
l
−
(
l
=
e,μ
) with data
recorded by the
B
A
B
AR
detector [25, 26]. This search
is based on 514 fb
−
1
of data collected mostly at the
Υ
(4
S
) resonance, but also at the
Υ
(3
S
) and
Υ
(2
S
) peaks,
as well as data in the vicinity of these resonances [27].
We probe dark photon masses in the range 0
.
02 GeV
<
m
A
′
<
10
.
2 GeV [28]. To avoid experimental bias, we
examine the data only after finalizing the analysis strat-
egy. About 5% of the dataset 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 Mad-
Graph [29] for 35 different
A
′
mass hypotheses. The
background processes
e
+
e
−
→
e
+
e
−
(
γ
) and
e
+
e
−
→
3
γγ
(
γ
) are simulated using BHWIDE [30] (see below),
and
e
+
e
−
→
μ
+
μ
−
(
γ
) events are generated with KK [31].
Resonance production processes in initial state radiation,
e
+
e
−
→
γX
(
X
=
J/ψ,ψ
(2
S
)
,Υ
(1
S
)
,Υ
(2
S
)), are simu-
lated using a structure function technique [32, 33]. The
detector acceptance and reconstruction efficiencies are
determined using a Monte Carlo (MC) simulation based
on GEANT4 [34].
We select events containing two oppositely charged
tracks and a single photon having a center-of-mass (CM)
energy greater than 0
.
2 GeV. Additional low-energy pho-
tons are allowed if their energies measured in the labora-
tory 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 CM frame in the
A
′
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 CM frame to be larger than
−
0
.
5, and that of the electron to be less than 0
.
5. The
γl
+
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 in-
teraction point to within its spread. Finally, we require
the
χ
2
of the fit to be less than 30 (for 8 d.o.f). These cri-
teria are chosen to maximize the signal significance over
a broad mass range.
A large contribution from converted photons produced
in
e
+
e
−
→
γγ,γ
→
e
+
e
−
events is still present at low
e
+
e
−
invariant mass. A neural network is trained to fur-
ther reduce this background using the following variables:
the flight length of the
e
+
e
−
pair in the plane transverse
to the beam, and the corresponding flight significance,
the electron helicity angle, the polar angle of the
e
+
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 as-
sociated with this selection criterion, estimated from a
sample of
π
0
→
γe
+
e
−
decays, is at the level of 2% at
m
A
′
∼
20 MeV, and decreases rapidly to negligible levels
above
m
A
′
∼
50 MeV.
The resulting dielectron and reduced dimuon mass dis-
tributions are displayed in Fig. 1, together with the pre-
dictions of various simulated SM processes. The reduced
dimuon mass,
m
R
=
√
m
2
μμ
−
4
m
2
μ
, is easier to model
near threshold than the dimuon mass. The dielectron
(reduced dimuon) mass spectrum is dominated by ra-
diative Bhabha (dimuon) production, with smaller peak-
ing contributions from ISR production of
J/ψ,ψ
(2
S
),
Υ
(1
S
), and
Υ
(2
S
) resonances. The contribution from
φ
→
K
+
K
−
, where both kaons are misidentified as elec-
trons or muons, is found to be negligible. The mass dis-
tributions are generally well described by the simulation,
except in the low
e
+
e
−
mass region, where, as expected,
BHWIDE fails to reproduce events in which the two lep-
tons are separated by a small angle. Since the signal ex-
traction procedure 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. Correc-
tion factors to the efficiency, which vary between 0.5%
to 3%, account for the effects of triggers, charged parti-
cle identification, and track and photon reconstruction.
These are assessed by fitting the ratios of the measured
and simulated
e
+
e
−
→
e
+
e
−
γ
and
e
+
e
−
→
μ
+
μ
−
γ
dif-
ferential mass distributions, as shown in Fig. 1. For the
dielectron channel, we fit the ratio only in the region
m
e
+
e
−
>
3 GeV, where the simulation is expected to pro-
vide 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 statisti-
cal variations between neighboring mass points and the
uncertainty associated to the extrapolation procedure.
The signal yield as a function of
m
A
′
is extracted by
performing a series of independent fits to the dielectron
and the reduced dimuon mass spectra for each beam en-
ergy. The fits are performed in the range 0
.
02 GeV
<
m
A
′
<
10
.
2 GeV (0
.
212 GeV
< m
A
′
<
10
.
2 GeV) for the
dielectron (dimuon) sample taken near the
Υ
(4
S
) reso-
nance, and up to 9
.
6 GeV and 10
.
0 GeV for the dataset
collected near the
Υ
(2
S
) and
Υ
(3
S
) resonances, respec-
tively [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 in-
terval at least 20 times broader than the signal resolution
at that mass, with the constraint
m
e
+
e
−
>
0
.
015 GeV for
the dielectron channel. For the purposes of determin-
ing the mass steps, the signal resolution is estimated by
Gaussian fits to several simulated
A
′
samples, and inter-
polated to all other masses. It varies between 1
.
5 and
8 MeV. We sample a total of 5704 (5370) mass hypothe-
ses 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
pseudo-experiments and found to be negligible.
The likelihood function, described below, contains con-
tributions from signal, radiative dilepton background,
and peaking background where appropriate. The sig-
nal probability density function (pdf) is modeled directly
from the signal Monte Carlo mass distribution using a
non-parametric kernel pdf, and interpolated between the
known simulated masses using an algorithm based on the
4
0
2
4
6
8
10
Entries / 0.1 GeV
5
10
6
10
0
2
4
6
8
10
Entries / 0.1 GeV
5
10
6
10
Data
-
e
+
e
γ
→
-
e
+
MC e
R
γ
→
-
e
+
MC e
(GeV)
ee
m
0
2
4
6
8
10
Data/MC
0.9
1
1.1
0
2
4
6
8
10
Entries / 0.1 GeV
5
10
6
10
0
2
4
6
8
10
Entries / 0.1 GeV
5
10
6
10
Data
-
μ
+
μ
γ
→
-
e
+
MC e
R
γ
→
-
e
+
MC e
(GeV)
2
μ
- 4m
2
μμ
m
=
R
m
0
2
4
6
8
10
Data/MC
0.9
1
FIG. 1: Distribution of the final dielectron (top) and reduced
dimuon invariant masses (bottom), together with the predic-
tions of various simulated SM processes and ISR production
of
J/ψ,ψ
(2
S
),
Υ
(1
S
), and
Υ
(2
S
) resonances (collectively la-
beled as R). The fit to the ratio between data and simulated
events is described in the text.
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
+
e
−
→
γJ/ψ,J/ψ
→
l
+
l
−
events indi-
cate 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 de-
scribed by a fourth order polynomial, and elsewhere by
a third order polynomial. The radiative dimuon back-
ground is parametrized by a third order polynomial, con-
strained to pass through the origin for fits in the re-
gion below 0
.
05 GeV. Peaking contributions from the
J/ψ
,
ψ
(2
S
),
Υ
(1
S
), and
Υ
(2
S
) resonances for both final
states are included where appropriate. Their shapes are
modeled as Crystal Ball or Gaussian functions with pa-
rameters extracted from fits to the corresponding Monte
Carlo 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 production is observed for the
ω
and
φ
mesons, and is fit with the following empirical function:
f
(
m
) = (
a
+
bm
+
cm
2
+
dm
3
)
∣
∣
∣
∣
∣
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 reso-
nance,
Q
the resonant fraction, and
a,b,c,d
are free pa-
rameters. We fix the masses and widths to their nom-
inal values [37], and let their fractions float. We ex-
clude 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
(2
S
), and
Υ
(1
S,
2
S
) resonances (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 parametriza-
tion has been performed for the
μ
+
μ
−
channel. The re-
sults of both methods are statistically consistent with
each other. The uncertainty on the background mod-
eling 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 hypothesis. 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
(1
S,
2
S
) 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 correc-
tions applied to the signal width, as well as the uncer-
tainties on the
ω
and
φ
masses and widths, as systematic
uncertainties on the fitted signal yields.
The
e
+
e
−
→
γA
′
,A
′
→
e
+
e
−
and
e
+
e
−
→
γA
′
,A
′
→
μ
+
μ
−
cross-sections as a function of the dark photon
mass are obtained by combining the signal yields of each
data sample, divided by the efficiency and luminosity.
The cross-sections as a function of
m
A
′
are shown in
Fig. 2; the distributions of the statistical significances
of the fits are displayed in Fig. 3. The statistical signif-
icance of each fit is taken as
S
=
√
2 log (
L
/
L
0
), where
L
and
L
0
are the likelihood values for fits with a free
signal and the pure background hypothesis, respectively.
We estimate trial factors by generating a large sample of
Monte Carlo experiments. The largest local significance
is 3
.
4
σ
(2
.
9
σ
), observed near
m
A
′
= 7
.
02 GeV (6
.
09 GeV)
for the dielectron (dimuon) final state. Including trial
factors, the corresponding p-value is 0.57 (0.94), consis-
tent with the null hypothesis.
5