of 9
B
A
B
AR
-PUB-17/001
SLAC-PUB-16923
Search for invisible decays of a dark photon produced in
e
+
e
collisions at
B
A
B
AR
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3
G. Eigen,
4
D. N. Brown,
5
M. Derdzinski,
5
A. Giuffrida,
5
Yu. G. Kolomensky,
5
M. Fritsch,
6
H. Koch,
6
T. Schroeder,
6
C. Hearty
ab
,
7
T. S. Mattison
b
,
7
J. A. McKenna
b
,
7
R. Y. So
b
,
7
V. E. Blinov
abc
,
8
A. R. Buzykaev
a
,
8
V. P. Druzhinin
ab
,
8
V. B. Golubev
ab
,
8
E. A. Kravchenko
ab
,
8
A. P. Onuchin
abc
,
8
S. I. Serednyakov
ab
,
8
Yu. I. Skovpen
ab
,
8
E. P. Solodov
ab
,
8
K. Yu. Todyshev
ab
,
8
A. J. Lankford,
9
J. W. Gary,
10
O. Long,
10
A. M. Eisner,
11
W. S. Lockman,
11
W. Panduro
Vazquez,
11
D. S. Chao,
12
C. H. Cheng,
12
B. Echenard,
12
K. T. Flood,
12
D. G. Hitlin,
12
J. Kim,
12
T. S. Miyashita,
12
P. Ongmongkolkul,
12
F. C. Porter,
12
M. R ̈ohrken,
12
Z. Huard,
13
B. T. Meadows,
13
B. G. Pushpawela,
13
M. D. Sokoloff,
13
L. Sun,
13,
J. G. Smith,
14
S. R. Wagner,
14
D. Bernard,
15
M. Verderi,
15
D. Bettoni
a
,
16
C. Bozzi
a
,
16
R. Calabrese
ab
,
16
G. Cibinetto
ab
,
16
E. Fioravanti
ab
,
16
I. Garzia
ab
,
16
E. Luppi
ab
,
16
V. Santoro
a
,
16
A. Calcaterra,
17
R. de Sangro,
17
G. Finocchiaro,
17
S. Martellotti,
17
P. Patteri,
17
I. M. Peruzzi,
17
M. Piccolo,
17
M. Rotondo,
17
A. Zallo,
17
S. Passaggio,
18
C. Patrignani,
18,
H. M. Lacker,
19
B. Bhuyan,
20
U. Mallik,
21
C. Chen,
22
J. Cochran,
22
S. Prell,
22
H. Ahmed,
23
A. V. Gritsan,
24
N. Arnaud,
25
M. Davier,
25
F. Le Diberder,
25
A. M. Lutz,
25
G. Wormser,
25
D. J. Lange,
26
D. M. Wright,
26
J. P. Coleman,
27
E. Gabathuler,
27,
D. E. Hutchcroft,
27
D. J. Payne,
27
C. Touramanis,
27
A. J. Bevan,
28
F. Di Lodovico,
28
R. Sacco,
28
G. Cowan,
29
Sw. Banerjee,
30
D. N. Brown,
30
C. L. Davis,
30
A. G. Denig,
31
W. Gradl,
31
K. Griessinger,
31
A. Hafner,
31
K. R. Schubert,
31
R. J. Barlow,
32,
§
G. D. Lafferty,
32
R. Cenci,
33
A. Jawahery,
33
D. A. Roberts,
33
R. Cowan,
34
S. H. Robertson,
35
B. Dey
a
,
36
N. Neri
a
,
36
F. Palombo
ab
,
36
R. Cheaib,
37
L. Cremaldi,
37
R. Godang,
37,
D. J. Summers,
37
P. Taras,
38
G. De Nardo,
39
C. Sciacca,
39
G. Raven,
40
C. P. Jessop,
41
J. M. LoSecco,
41
K. Honscheid,
42
R. Kass,
42
A. Gaz
a
,
43
M. Margoni
ab
,
43
M. Posocco
a
,
43
G. Simi
ab
,
43
F. Simonetto
ab
,
43
R. Stroili
ab
,
43
S. Akar,
44
E. Ben-Haim,
44
M. Bomben,
44
G. R. Bonneaud,
44
G. Calderini,
44
J. Chauveau,
44
G. Marchiori,
44
J. Ocariz,
44
M. Biasini
ab
,
45
E. Manoni
a
,
45
A. Rossi
a
,
45
G. Batignani
ab
,
46
S. Bettarini
ab
,
46
M. Carpinelli
ab
,
46,
∗∗
G. Casarosa
ab
,
46
M. Chrzaszcz
a
,
46
F. Forti
ab
,
46
M. A. Giorgi
ab
,
46
A. Lusiani
ac
,
46
B. Oberhof
ab
,
46
E. Paoloni
ab
,
46
M. Rama
a
,
46
G. Rizzo
ab
,
46
J. J. Walsh
a
,
46
A. J. S. Smith,
47
F. Anulli
a
,
48
R. Faccini
ab
,
48
F. Ferrarotto
a
,
48
F. Ferroni
ab
,
48
A. Pilloni
ab
,
48
G. Piredda
a
,
48,
C. B ̈unger,
49
S. Dittrich,
49
O. Gr ̈unberg,
49
M. Heß,
49
T. Leddig,
49
C. Voß,
49
R. Waldi,
49
T. Adye,
50
F. F. Wilson,
50
S. Emery,
51
G. Vasseur,
51
D. Aston,
52
C. Cartaro,
52
M. R. Convery,
52
J. Dorfan,
52
W. Dunwoodie,
52
M. Ebert,
52
R. C. Field,
52
B. G. Fulsom,
52
M. T. Graham,
52
C. Hast,
52
W. R. Innes,
52
P. Kim,
52
D. W. G. S. Leith,
52
S. Luitz,
52
D. B. MacFarlane,
52
D. R. Muller,
52
H. Neal,
52
B. N. Ratcliff,
52
A. Roodman,
52
M. K. Sullivan,
52
J. Va’vra,
52
W. J. Wisniewski,
52
M. V. Purohit,
53
J. R. Wilson,
53
A. Randle-Conde,
54
S. J. Sekula,
54
M. Bellis,
55
P. R. Burchat,
55
E. M. T. Puccio,
55
M. S. Alam,
56
J. A. Ernst,
56
R. Gorodeisky,
57
N. Guttman,
57
D. R. Peimer,
57
A. Soffer,
57
S. M. Spanier,
58
J. L. Ritchie,
59
R. F. Schwitters,
59
J. M. Izen,
60
X. C. Lou,
60
F. Bianchi
ab
,
61
F. De Mori
ab
,
61
A. Filippi
a
,
61
D. Gamba
ab
,
61
L. Lanceri,
62
L. Vitale,
62
F. Martinez-Vidal,
63
A. Oyanguren,
63
J. Albert
b
,
64
A. Beaulieu
b
,
64
F. U. Bernlochner
b
,
64
G. J. King
b
,
64
R. Kowalewski
b
,
64
T. Lueck
b
,
64
I. M. Nugent
b
,
64
J. M. Roney
b
,
64
R. J. Sobie
ab
,
64
N. Tasneem
b
,
64
T. J. Gershon,
65
P. F. Harrison,
65
T. E. Latham,
65
R. Prepost,
66
and S. L. Wu
66
(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 and Dipartimento di Fisica, Universit`a 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 Universit ̈at Bochum, Institut f ̈ur Experimentalphysik 1, D-44780 Bochum, Germany
7
Institute of Particle Physics
a
; University of British Columbia
b
, Vancouver, British Columbia, Canada V6T 1Z1
8
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 630092
c
, Russia
9
University of California at Irvine, Irvine, California 92697, USA
10
University of California at Riverside, Riverside, California 92521, USA
arXiv:1702.03327v1 [hep-ex] 10 Feb 2017
2
11
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
12
California Institute of Technology, Pasadena, California 91125, USA
13
University of Cincinnati, Cincinnati, Ohio 45221, USA
14
University of Colorado, Boulder, Colorado 80309, USA
15
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
16
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara
b
, I-44122 Ferrara, Italy
17
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
18
INFN Sezione di Genova, I-16146 Genova, Italy
19
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-12489 Berlin, Germany
20
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
21
University of Iowa, Iowa City, Iowa 52242, USA
22
Iowa State University, Ames, Iowa 50011, USA
23
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
24
Johns Hopkins University, Baltimore, Maryland 21218, USA
25
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
26
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
27
University of Liverpool, Liverpool L69 7ZE, United Kingdom
28
Queen Mary, University of London, London, E1 4NS, United Kingdom
29
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
30
University of Louisville, Louisville, Kentucky 40292, USA
31
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Kernphysik, D-55099 Mainz, Germany
32
University of Manchester, Manchester M13 9PL, United Kingdom
33
University of Maryland, College Park, Maryland 20742, USA
34
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
35
Institute of Particle Physics and McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
36
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
37
University of Mississippi, University, Mississippi 38677, USA
38
Universit ́e de Montr ́eal, Physique des Particules, Montr ́eal, Qu ́ebec, Canada H3C 3J7
39
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II, I-80126 Napoli, Italy
40
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
41
University of Notre Dame, Notre Dame, Indiana 46556, USA
42
Ohio State University, Columbus, Ohio 43210, USA
43
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
44
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
45
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
46
INFN Sezione di Pisa
a
; Dipartimento di Fisica,
Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
47
Princeton University, Princeton, New Jersey 08544, USA
48
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
49
Universit ̈at Rostock, D-18051 Rostock, Germany
50
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
51
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
52
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
53
University of South Carolina, Columbia, South Carolina 29208, USA
54
Southern Methodist University, Dallas, Texas 75275, USA
55
Stanford University, Stanford, California 94305, USA
56
State University of New York, Albany, New York 12222, USA
57
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
58
University of Tennessee, Knoxville, Tennessee 37996, USA
59
University of Texas at Austin, Austin, Texas 78712, USA
60
University of Texas at Dallas, Richardson, Texas 75083, USA
61
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
62
INFN Sezione di Trieste and Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy
63
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
64
Institute of Particle Physics
a
; University of Victoria
b
, Victoria, British Columbia, Canada V8W 3P6
65
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
66
University of Wisconsin, Madison, Wisconsin 53706, USA
3
We search for single-photon events in 53 fb
1
of
e
+
e
collision data collected with the
B
A
B
AR
detector at the PEP-II B-factory. We look for events with a single high-energy photon and a large
missing momentum and energy, consistent with production of a spin-1 particle
A
through the
process
e
+
e
γA
;
A
invisible. Such particles, referred to as “dark photons”, are motivated
by theories applying a
U
(1) gauge symmetry to dark matter. We find no evidence for such processes
and set 90% confidence level upper limits on the coupling strength of
A
to
e
+
e
in the mass range
m
A
8 GeV. In particular, our limits exclude the values of the
A
coupling suggested by the
dark-photon interpretation of the muon (
g
2)
μ
anomaly, as well as a broad range of parameters
for the dark-sector models.
PACS numbers: 12.15.Ji, 95.35.+d
The nature of dark matter is one of the greatest mys-
teries of modern physics. It is transparent to electromag-
netic radiation and we have only been able to infer its
existence through gravitational effects. Since terrestrial
searches for dark matter interactions have so far yielded
null results, it is postulated to interact very weakly with
ordinary matter. Recently, models attempting to explain
certain astrophysical observations [1–4] as well as the
muon (
g
2)
μ
anomaly [5] have introduced an appealing
idea of a low-mass spin-1 particle, referred to as
A
or
U
, that would possess a gauge coupling of electroweak
strength to dark matter, but with a much smaller cou-
pling to the Standard Model (SM) hypercharge [6, 7].
Such a boson may be associated with a
U
(1) gauge sym-
metry in the dark sector and kinetically mix with the SM
photon with a mixing strength
ε

1; hence the name
“dark photon”. Values as high as
ε
10
3
and masses in
a GeV range have been predicted in the literature [6, 7].
The decay modes of the dark photon depend on its
mass and couplings, as well as on the particle spectrum
of the dark sector. If the lowest-mass dark matter state
χ
is sufficiently light:
m
χ
< m
A
/
2, then the dominant
decay mode of the
A
is invisible:
A
χ
χ
. The clean-
est collider signature of such particles is the production of
monochromatic single photons in
e
+
e
γA
, accompa-
nied by significant missing energy and momentum. The
photon energy
E
γ
in the
e
+
e
center-of-mass (CM) is re-
lated to the missing mass
M
X
through
M
2
X
=
s
2
E
γ
s
,
where
s
is the square of the CM energy, and the aster-
isk hereafter denotes a CM quantity. We seek a signal
of the dark photon
A
as a narrow peak in the distribu-
tion of
M
2
X
in events with a single high-energy photon.
As expected for the dark matter coupling
α
D
<
1 [7],
we assume that the decay width of the
A
is negligi-
ble compared to the experimental resolution, and that
the
A
decays predominantly to dark matter (
i.e.
the
invisible branching fraction is
100%). Furthermore,
we assume that a single
A
state exists in the range
0
< m
A
8 GeV; or if two or more states are present,
they do not interfere.
The current best limits on the mixing strength
ε
of the
dark photon are from searches for narrow peaks in the
e
+
e
or
μ
+
μ
invariant mass spectra [8–14] and from
beam-dump and neutrino experiments [15, 16]. These
limits assume that the dominant decays of the
A
are to
the visible SM particles, but are not valid if there are low-
mass invisible degrees of freedom. There are constraints
on invisible decays of the
A
from kaon decays [17–19]
and from the recent search for missing energy events in
electron-nucleus scattering [20].
We search for the process
e
+
e
γA
, followed by in-
visible decays of the
A
in a 53 fb
1
dataset [21] collected
with the
B
A
B
AR
detector at the PEP-II asymmetric-
energy
e
+
e
collider at the SLAC National Accelera-
tor Laboratory. The data were collected with CM ener-
gies near the
Υ
(2
S
),
Υ
(3
S
), and
Υ
(4
S
) resonances with
a special “single photon” trigger described below. The
e
+
e
CM frame was boosted relative to the detector ap-
proximately along the detector’s magnetic field axis by
β
z
0
.
5. Since the production of the
A
is not expected
to be enhanced by the presence of the
Υ
resonances, we
combine the datasets collected in the vicinity of each
Υ
resonance. In order to properly account for acceptance
effects and changes in the cross section as a function of
s
, we measure the signal event yields separately for the
Υ
(2
S
),
Υ
(3
S
), and
Υ
(4
S
) datasets.
Since the
B
A
B
AR
detector is described in detail else-
where [22], only the components of the detector crucial
to this analysis are summarized below. Charged parti-
cle tracking is provided by a five-layer double-sided sili-
con vertex tracker (SVT) and a 40-layer drift chamber
(DCH). Photons and neutral pions are identified and
measured using the electromagnetic calorimeter (EMC),
which comprises 6580 thallium-doped CsI crystals. These
systems are mounted inside a 1.5 T solenoidal supercon-
ducting magnet. The Instrumented Flux Return (IFR)
forms the return yoke of the superconducting coil, instru-
mented in the central barrel region with limited streamer
tubes for the identification of muons and the detection
of clusters produced by neutral hadrons. We use the
Geant4
[23] software to simulate interactions of parti-
cles traversing the
B
A
B
AR
detector, taking into account
the varying detector conditions and beam backgrounds.
Detection of low-multiplicity single photon events re-
quires dedicated trigger lines. Event processing and se-
lection proceeds in three steps. First, the hardware-
based Level-1 (L1) trigger accepts single-photon events
if they contain at least one EMC cluster with energy
above 800 MeV (in the laboratory frame). Second, L1-
accepted events are forwarded to a software-based Level-
4
3 (L3) trigger, which forms DCH tracks and EMC clus-
ters and makes decisions for a variety of physics signa-
tures. Two single-photon L3 trigger lines were active
during the data-taking period. The high-energy pho-
ton line (low
M
X
, “LowM” hereafter) requires an iso-
lated EMC cluster with energy
E
γ
>
2 GeV, and no
tracks originating from the
e
+
e
interaction region (IR).
The “LowM” dataset amounts to 5
.
9 fb
1
collected at
the
Υ
(4
S
) resonance, 28
.
5 fb
1
collected at the
Υ
(3
S
)
resonance, 2
.
7 fb
1
collected 30 MeV below the
Υ
(3
S
),
14
.
4 fb
1
collected at the
Υ
(2
S
) resonance, and 1
.
5 fb
1
collected 30 MeV below the
Υ
(2
S
) resonance. The to-
tal data sample collected with the “LowM” triggers is
53 fb
1
.
A low-energy (high
M
X
, “HighM”) L3 single-photon
trigger, which requires an EMC cluster with energy
E
γ
>
1 GeV and no tracks originating from the
e
+
e
interaction region, was active for a subset of the data:
20 fb
1
collected at the
Υ
(3
S
) resonance as well as all
of the data collected at the
Υ
(2
S
) resonance. The to-
tal data sample collected with the “HighM” triggers is
35
.
9 fb
1
.
Additional offline software filters are applied to the
stored data. We accept single-photon events if they sa-
tisfy one of the two following criteria. The “LowM” se-
lection requires one EMC cluster in the event with
E
γ
>
3 GeV and no DCH tracks with momentum
p
>
1 GeV.
The “HighM” selection requires one EMC cluster with
the transverse profile consistent with an electromagnetic
shower and
E
γ
>
1
.
5 GeV, and no DCH tracks with mo-
mentum
p
>
0
.
1 GeV. The two selection criteria are not
mutually exclusive.
The trigger and reconstruction selections naturally
split the dataset into two broad
M
X
ranges.
The
“LowM” selections are used for the low
M
X
region
4
<
M
2
X
<
36 GeV
2
. The backgrounds in this region are
dominated by the QED process
e
+
e
γγ
, especially
near
M
X
0 (
E
γ
s/
2). Due to the orientation
of the EMC crystals, which point towards the IR, one
of the photons may escape detection even if it is within
the nominal EMC acceptance. The event selection is op-
timized to reduce this peaking background as much as
possible. The “HighM” trigger selection defines the high
M
X
range 24
< M
2
X
<
69 (63
.
5) GeV
2
for the
Υ
(3
S
)
(
Υ
(2
S
)) dataset. This region is dominated by the low-
angle radiative Bhabha events
e
+
e
e
+
e
γ
, in which
both the electron and the positron escape the detector.
We suppress the SM backgrounds, which involve one
or more particles that escape detection, by requiring
that a candidate event be consistent with a single iso-
lated photon shower in the EMC. We accept photons in
the polar angle range
|
cos
θ
γ
|
<
0
.
6, rejecting radiative
Bhabha events that strongly peak in the forward and
backward directions, and we require that the event con-
tain no charged particle tracks.
The signal events are further selected by a multivariate
Boosted Decision Tree (BDT) discriminant [24], based on
the following 12 discriminating variables. First, after a
relatively coarse selection, we include the EMC variables
that describe the shape of the electromagnetic shower:
the difference between the number of crystals in the EMC
cluster and the expectation for a single photon of given
energy, and two transverse shower moments [25]. Sec-
ond, we include both the total excess EMC energy in the
laboratory frame not associated with the highest-energy
photon, and the CM energy and polar angle of the sec-
ond most energetic EMC cluster. We also compute the
azimuthal angle difference ∆
φ
12
between the highest and
second-highest energy EMC clusters; the
e
+
e
γγ
events with partial energy deposit in the EMC tend to
peak at ∆
φ
12
π
. Third, a number of variables improve
containment of the background events. We extrapolate
the missing momentum vector to the EMC face, and com-
pute the distance (in (
θ,φ
) polar lab-frame coordinates)
to the nearest crystal edge. This allows us to suppress
e
+
e
γγ
events where one of the photons penetrates
the EMC between crystals leaving little detectable en-
ergy. Furthermore, we look for energy deposited in the
IFR, and compute the correlation angle ∆
φ
NH
between
the primary photon and the IFR cluster closest to the
missing momentum direction;
e
+
e
γγ
events pro-
duce a peak at cos ∆
φ
NH
∼ −
1. We also apply a fidu-
cial selection to the azimuthal angle
φ
miss
of the missing
momentum by including cos(6
φ
miss
) into the BDT. This
accounts for uninstrumented regions between six IFR sec-
tors [22]. Finally, cos
θ
γ
is included in the BDT to take
advantage of the different angular distributions for signal
and background events.
The BDT discriminants are trained separately in
LowM and HighM regions. Each BDT is trained us-
ing 2
.
5
×
10
4
simulated signal events with uniformly dis-
tributed
A
masses, and 2
.
5
×
10
4
background events from
the
Υ
(3
S
) on-peak sample that corresponds to approx-
imately 3 fb
1
. We test the BDT, define the final se-
lection, and measure the signal efficiency using sets of
2
.
5
×
10
4
signal and background events statistically in-
dependent from the BDT training samples. The BDT
score is designed so that the signal peaks near 1 while
the background events are generally distributed between
1
<
BDT
<
0.
The event selection is optimized to minimize the ex-
pected upper limit on the
e
+
e
γA
cross section
σ
A
. Since the number of peaking
e
+
e
γγ
events
cannot be reliably estimated and has to be determined
from the fit to the data, this background limits the sen-
sitivity to
e
+
e
γA
at the low
A
masses where the
photon energies for the two types of events are indistin-
guishable. In this regime, we define a “tight” selection
region
R
T
which maximizes the ratio
ε
S
/N
B
for large
N
B
, and
ε
S
/
2
.
3 in the limit
N
B
0, where
ε
S
is the
selection efficiency for the signal and
N
B
is the number
of background events expected in the full data sample.
5
We also require
0
.
4
<
cos
θ
γ
<
0
.
6 in order to suppress
e
+
e
γγ
events in which one of the photons would
have missed the central region of the EMC.
A “loose” selection region
R
L
maximizes
ε
S
/
N
B
.
This selection is appropriate at higher
M
X
where the
background is well described by a featureless continuum
distribution, and maximal
ε
S
/
N
B
corresponds to the
lowest upper limit on the
e
+
e
γA
cross section.
Finally, a background region
R
B
is defined by
0
.
5
<
BDT
<
0 and is used to determine the
M
2
X
distribution
of the background events.
We measure the cross section
σ
A
as a function of
the assumed mass
m
A
by performing a series of un-
binned extended maximum likelihood fits to the distri-
bution of
M
2
X
. For each value of
m
A
, varied from 0
to 8
.
0 GeV in 166 steps roughly equal to half of the
mass resolution, we perform a set of simultaneous fits
to
Υ
(2
S
),
Υ
(3
S
), and for the low-
M
X
region,
Υ
(4
S
)
datasets. Moreover, we subdivide the data into broad
event selection bins:
R
B
used to define the background
probability density functions (PDFs), and signal regions
R
L
(used for 5
.
5
< m
A
8
.
0 GeV),
R
T
, and
R
L
(used
for
m
A
5
.
5 GeV). The region
R
L
is defined to be
the part of
R
L
not overlapping with
R
T
. Thus, the
simultaneous fits are performed to 9 independent sam-
ples for
m
A
5
.
5 GeV, and 4 independent samples
for 5
.
5
< m
A
8
.
0 GeV (missing mass spectra for all
datasets are shown in Fig. 6-7 in [26]).
For the fits to the
R
B
regions, we fix the number of
signal events to zero, and determine the parameters of
the background PDFs. In the fits to the
R
T
and
R
L
regions, we fix the background PDF shape, and vary the
number of background events
N
B
, the number of peaking
background events
e
+
e
γγ
(for
m
A
5
.
5 GeV), and
the
A
mixing strength
ε
2
. The numbers of signal and
background events are constrained:
ε
2
0 and
N
B
>
0.
The signal PDF is described by a Crystal Ball [27] func-
tion centered around the expected value of
M
2
X
=
m
2
A
.
We determine the PDF as a function of
m
A
using high-
statistics simulated samples of signal events, and we cor-
rect it for the difference between the photon energy res-
olution function in data and simulation using a high-
statistics
e
+
e
γγ
sample in which one of the pho-
tons converts to an
e
+
e
pair in the detector mate-
rial [28]. The resolution for signal events decreases mono-
tonically from
σ
(
M
2
X
) = 1
.
5 GeV
2
for
m
A
0 to
σ
(
M
2
X
) = 0
.
7 GeV
2
for
m
A
= 8 GeV. The background
PDF has two components: a peaking background from
e
+
e
γγ
events, described by a Crystal Ball function,
and a smooth function of
M
2
X
dominated by the
e
+
e
γe
+
e
(second order polynomial for
m
A
5
.
5 and a sum
of exponentiated polynomials for 5
.
5
< m
A
8
.
0 GeV).
The signal selection efficiency varies slowly as a func-
tion of
m
A
between 2.4-3.1% (
R
T
selection for
m
A
5
.
5 GeV), 3.4-3.8% (
R
L
for
m
A
5
.
5 GeV), and
2
.
0
0
.
2% (
R
L
selection for 5
.
5
< m
A
8
.
0 GeV).
(GeV)
A'
m
0
1
2
3
4
5
6
7
8
2
ε
0
0.5
1
1.5
2
2.5
6
10
×
FIG. 1: Measured maximum-likelihood values of the
A
mix-
ing strength squared
ε
2
as a function of the mass
m
A
.
The largest systematic uncertainties in the signal yield
are from the shape of the signal and background PDFs,
and the uncertainties in the efficiency of signal and trig-
ger selections. We determine the uncertainty in the signal
PDF by comparing the data and simulated distributions
of
e
+
e
γγ
events. We correct for the small observed
differences, and use half of the correction as an estimate
of the systematic uncertainty. We measure the trigger
selection efficiency using single-photon
e
+
e
γγ
and
e
+
e
e
+
e
γ
events that are selected from a sample
of unbiased randomly accepted triggers. We find good
agreement with the simulation estimates of the trigger
efficiency, within the systematic uncertainty of 0
.
4%. We
compare the input BDT observables in simulation and
in a sample of the single-photon data events, counting
the difference as a systematic uncertainty of the signal
selection efficiency. The total multiplicative error on the
signal cross section is 5%, and is small compared to the
statistical uncertainty.
Figure 1 shows the maximum-likelihood estimators of
the
A
mixing strength
ε
2
for the 166
m
A
hypothe-
ses. The values of “local” significance of observation
S ≡
2 ln(
L
max
/L
0
), where
L
max
is the maximum
value of the likelihood, and
L
0
is the value of the like-
lihood with the signal yield fixed to zero, are shown in
Fig. 2. The most significant deviation of

2
from zero
occurs at
m
A
= 6
.
21 GeV and corresponds to
S
= 3
.
1.
Parametrized simulations determine that the probability
to find such a deviation in any of the 166
m
A
points
in the absence of any signal is
1%, corresponding to
a “global” significance of 2
.
6
σ
. A representative fit for
m
A
= 6
.
21 GeV is shown in Fig. 3.
The 90% confidence level (CL) upper limits on
ε
2
as a
function of
m
A
are shown in Fig. 4. We compute both
the Bayesian limits with a uniform prior for
ε
2
>
0 and
6
(GeV)
A'
m
0
1
2
3
4
5
6
7
8
)
σ
Significance (
0
0.5
1
1.5
2
2.5
3
FIG. 2: Signal significance
S
as a function of the mass
m
A
.
)
2
(GeV
2
X
M
25
30
35
40
45
50
55
60
)
2
Events / ( 0.5 GeV
1
10
1
10
/df = 69.0/77
2
χ
25
30
35
40
45
50
55
60
Pull
2
0
2
FIG. 3: Bottom: signal fit for
m
A
= 6
.
21 GeV to a com-
bination of
Υ
(2
S
) and
Υ
(3
S
) datasets, shown for illustration
purposes. The signal peak (red) corresponds to the local sig-
nificance
S
= 3
.
1 (global significance of 2
.
6
σ
). Blue solid
line shows the full PDF, while the magenta dashed line cor-
responds to the background contribution. Top: distribution
of the normalized fit residuals (pulls).
the frequentist profile-likelihood limits [29]. Figure 5
compares our results to other limits on
ε
in channels
where
A
is allowed to decay invisibly, as well as to the
region of parameter space consistent with the (
g
2)
μ
anomaly [5]. At each value of
m
A
we compute a limit
on
ε
as a square root of the Bayesian limit on
ε
2
from
Fig. 4. Our data rules out the dark-photon coupling as
the explanation for the (
g
2)
μ
anomaly. Our limits place
stringent constraints on dark-sector models over a broad
range of parameter space, and represent a significant im-
provement over previously available results.
We are grateful for the excellent luminosity and ma-
chine conditions provided by our PEP-II colleagues, and
(GeV)
A'
m
0
1
2
3
4
5
6
7
8
Upper Limit at 90% CL
2
ε
0
0.5
1
1.5
2
2.5
3
6
10
×
Bayesian limit
Profile-likelihood limit
FIG. 4: Upper limits at 90% CL on
A
mixing strength
squared
ε
2
as a function of
m
A
. Shown are the Bayesian
limit computed with a uniform prior for
ε
2
>
0 (solid red
line) and the profile-likelihood limit (blue dashed line).
(GeV)
A'
m
3
10
2
10
1
10
1
10
ε
4
10
3
10
2
10
e
(g-2)
NA64
ν
ν
π
K
σ
5
±
μ
(g-2)
favored
B
A
B
AR
2017
FIG. 5: Regions of the
A
parameter space (
ε
vs
m
A
) ex-
cluded by this work (green area) compared to the previous
constraints [7, 18–20] as well as the region preferred by the
(
g
2)
μ
anomaly [5].
for the substantial dedicated effort from the comput-
ing organizations that support
B
A
B
AR
. The collaborat-
ing institutions wish to thank SLAC for its support and
kind hospitality. This work is supported by DOE and
NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3
(France), BMBF and DFG (Germany), INFN (Italy),
FOM (The Netherlands), NFR (Norway), MES (Russia),
MINECO (Spain), STFC (United Kingdom), BSF (USA-
Israel). Individuals have received support from the Marie
Curie EIF (European Union) and the A. P. Sloan Foun-
dation (USA).
We wish to acknowledge Adrian Down, Zachary Jud-
kins, and Jesse Reiss for initiating the study of the
7
physics opportunities with the single photon triggers in
B
A
B
AR
, and Rouven Essig for stimulating discussions and
for providing data for Fig. 5.
Now at: Wuhan University, Wuhan 43072, China
Now at: Universit`a di Bologna and INFN Sezione di
Bologna, I-47921 Rimini, Italy
Deceased
§
Now at: University of Huddersfield, Huddersfield HD1
3DH, UK
Now at: University of South Alabama, Mobile, Alabama
36688, USA
∗∗
Also at: Universit`a di Sassari, I-07100 Sassari, Italy
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8
EPAPS MATERIAL
The following includes supplementary material for the Electronic Physics Auxiliary Publication Service.
)
2
(GeV
2
X
M
0
5
10
15
20
25
30
)
2
Events / ( 1 GeV
0
1
2
3
4
5
6
7
8
/df = 16.8/35
2
χ
0
5
10
15
20
25
30
Pull
2
0
2
(a)
)
2
(GeV
2
X
M
0
5
10
15
20
25
30
)
2
Events / ( 1 GeV
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
/df = 6.6/35
2
χ
0
5
10
15
20
25
30
Pull
2
0
2
(b)
)
2
(GeV
2
X
M
0
5
10
15
20
25
30
35
)
2
Events / ( 1 GeV
0
2
4
6
8
10
12
14
16
/df = 29.7/38
2
χ
0
5
10
15
20
25
30
35
Pull
2
0
2
(c)
)
2
(GeV
2
X
M
0
5
10
15
20
25
30
35
)
2
Events / ( 1 GeV
0
1
2
3
4
5
6
/df = 14.1/38
2
χ
0
5
10
15
20
25
30
35
Pull
2
0
2
(d)
)
2
(GeV
2
X
M
0
5
10
15
20
25
30
35
)
2
Events / ( 1 GeV
0
1
2
3
4
5
6
/df = 11.5/38
2
χ
0
5
10
15
20
25
30
35
Pull
2
0
2
(e)
)
2
(GeV
2
X
M
0
5
10
15
20
25
30
35
)
2
Events / ( 1 GeV
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
/df = 9.7/38
2
χ
0
5
10
15
20
25
30
35
Pull
2
0
2
(f)
FIG. 6: Distributions of the missing mass squared
M
2
X
in the “lowM” data samples collected near (a,b)
Υ
(2
S
), (c,d)
Υ
(3
S
),
and (e,f)
Υ
(4
S
) resonances. Data are selected with (a,c,e)
R
L
and (b,d,f)
R
T
selections. The solid blue line represents the
background-only fit with
ε
2
0. Normalized fit residuals are shown above each plot.