The University of Manchester Research
Search for Invisible Decays of a Dark Photon Produced in
e+e- Collisions at B a B ar
DOI:
10.1103/PhysRevLett.119.131804
Document Version
Final published version
Link to publication record in Manchester Research Explorer
Citation for published version (APA):
Lees, J. P., Poireau, V., Tisserand, V., Grauges, E., Palano, A., Eigen, G., Brown, D. N., Derdzinski, M., Giuffrida,
A., Kolomensky, Y. G., Fritsch, M., Koch, H., Schroeder, T., Hearty, C., Mattison, T. S., McKenna, J. A., So, R. Y.,
Blinov, V. E., Buzykaev, A. R., ... The BaBar Collaboration (2017). Search for Invisible Decays of a Dark Photon
Produced in e+e- Collisions at B a B ar. Physical Review Letters, 119(13), [131804].
https://doi.org/10.1103/PhysRevLett.119.131804
Published in:
Physical Review Letters
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Download date:26. Aug. 2022
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,
7a,7b
T. S. Mattison,
7b
J. A. McKenna,
7b
R. Y. So,
7b
V. E. Blinov,
8a,8b,8c
A. R. Buzykaev,
8a
V. P. Druzhinin,
8a,8b
V. B. Golubev,
8a,8b
E. A. Kravchenko,
8a,8b
A. P. Onuchin,
8a,8b,8c
S. I. Serednyakov,
8a,8b
Yu. I. Skovpen,
8a,8b
E. P. Solodov,
8a,8b
K. Yu. Todyshev,
8a,8b
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. Röhrken,
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,
16a
C. Bozzi,
16a
R. Calabrese,
16a,16b
G. Cibinetto,
16a,16b
E. Fioravanti,
16a,16b
I. Garzia,
16a,16b
E. Luppi,
16a,16b
V. Santoro,
16a
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,
36a
N. Neri,
36a
F. Palombo,
36a,36b
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,
43a
M. Margoni,
43a,43b
M. Posocco,
43a
G. Simi,
43a,43b
F. Simonetto,
43a,43b
R. Stroili,
43a,43b
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,
45a,45b
E. Manoni,
45a
A. Rossi,
45a
G. Batignani,
46a,46b
S. Bettarini,
46a,46b
M. Carpinelli,
46a,46b,**
G. Casarosa,
46a,46b
M. Chrzaszcz,
46a
F. Forti,
46a,46b
M. A. Giorgi,
46a,46b
A. Lusiani,
46a,46c
B. Oberhof,
46a,46b
E. Paoloni,
46a,46b
M. Rama,
46a
G. Rizzo,
46a,46b
J. J. Walsh,
46a
A. J. S. Smith,
47
F. Anulli,
48a
R. Faccini,
48a,48b
F. Ferrarotto,
48a
F. Ferroni,
48a,48b
A. Pilloni,
48a,48b
G. Piredda,
48a,*
C. Bünger,
49
S. Dittrich,
49
O. Grünberg,
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,
61a,61b
F. De Mori,
61a,61b
A. Filippi,
61a
D. Gamba,
61a,61b
L. Lanceri,
62
L. Vitale,
62
F. Martinez-Vidal,
63
A. Oyanguren,
63
J. Albert,
64b
A. Beaulieu,
64b
F. U. Bernlochner,
64b
G. J. King,
64b
R. Kowalewski,
64b
T. Lueck,
64b
I. M. Nugent,
64b
J. M. Roney,
64b
R. J. Sobie,
64a,64b
N. Tasneem,
64b
T. J. Gershon,
65
P. F. Harrison,
65
T. E. Latham,
65
R. Prepost,
66
and S. L. Wu
66
(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
3
INFN Sezione di Bari and Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
7a
Institute of Particle Physics, Vancouver, British Columbia V6T 1Z1, Canada
7b
University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
8a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
8b
Novosibirsk State University, Novosibirsk 630090, Russia
8c
Novosibirsk State Technical University, Novosibirsk 630092, Russia
9
University of California at Irvine, Irvine, California 92697, USA
10
University of California at Riverside, Riverside, California 92521, USA
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
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0031-9007=17=119(13)=131804(7) 131804-1 © 2017 American Physical Society
14
University of Colorado, Boulder, Colorado 80309, USA
15
Laboratoire Le prince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
16a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
16b
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy
17
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
18
INFN Sez ione di Genova, I-16146 Genova, Italy
19
Humboldt-Universität zu Berlin, Institut für 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, Saudi Arabia
24
Johns Hopkins University, Baltimore, Maryland 21218, USA
25
Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université 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 Kin gdom
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-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
32
University of Manchester, Manche ster 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, Montréal, Québec H3A 2T8, Canada
36a
INFN Sezione di Milano, I-20133 Milano, Italy
36b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
37
University of Mississippi, University, Mississippi 38677, USA
38
Université de Montréal, Physique des Particules, Montréal, Québec H3C 3J7, Canada
39
INFN Sez ione di Napoli and Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
40
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, Netherlands
41
University of Notre Dame, Notre Dame, Indiana 46556, USA
42
The Ohio State University, Columbus, Ohio 43210, USA
43a
INFN Sezione di Padova, I-35131 Padova, Italy
43b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
44
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie Curie-Paris 6,
Université Denis Diderot-Paris 7, F-75252 Paris, France
45a
INFN Sezione di Perugia, I-06123 Perugia, Italy
45b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
46a
INFN Sezione di Pisa, I-56127 Pisa, Italy
46b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
46c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
47
Princeton University, Princeton, New Jersey 08544, USA
48a
INFN Sezione di Roma, I-00185 Roma, Italy
48b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
49
Universität Rostock, D-18051 Rostock, Germany
50
Rutherford App leton 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
School of Physics and Astronomy, Tel Aviv University, 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
61a
INFN Sezione di Torino, I-10125 Torino, Italy
61b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
62
INFN Sezione di Trieste and Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
63
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
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64a
Institute of Particle Physics, Victoria, British Columbia, V8W 3P6, Canada
64b
University of Victoria, Victoria, British Columbia, V8W 3P6, Canada
65
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
66
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 14 February 2017; revised manuscript received 19 August 2017; published 28 September 2017)
We search for single-photon events in 53 fb
−1
of e
þ
e
−
collision data collected with the BABAR 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
0
through the process e
þ
e
−
→ γA
0
;
A
0
→ invisible. Such particles, referred to as “dark photons,” are motivated by theories applying a Uð1Þ
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
0
to e
þ
e
−
in the mass range m
A
0
≤ 8 GeV. In particular, our limits
exclude the values of the A
0
coupling suggested by the dark-photon interpreta tion of the muon ðg − 2Þ
μ
anomaly, as well as a broad range of parameters for the dark-sector models.
DOI: 10.1103/PhysRevLett.119.131804
The nature of dark matter is one of the greatest
mysteries of modern physics. It is transparent to electro-
magnetic radiation and we have only been able to infer
its existence through gravitational effects. Since terres-
trial searches for dark-matter interactions have so far
yielded null results, it is postulated to interact very
weakly with ordinar y matter. Recently, models attempt-
ing to explain certain a strophysical observations [1–4] as
well as the muon ðg − 2Þ
μ
anomaly [5] have introduced
an appealing idea o f a low-mass spin-1 particle, referred
to as A
0
or U, that would possess a gauge coupling of
electroweak strength to dark matter, but with a much
smaller coupling to t he standard model (SM) hyper-
charge [6,7]. Such a boson may be associated with a
Uð1Þ gauge symmetry 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
0
=2, then the dominant decay
mode of the A
0
is invisible, A
0
→ χ
¯
χ. The cleanest collider
signature of such particles is the production of monochro-
matic single photons in e
þ
e
−
→ γA
0
, accompanied by
significant missing energy and momentum. The photon
energy E
γ
in the e
þ
e
−
center-of-mass (c.m.) is related to the
missing mass M
X
through M
2
X
¼ s − 2E
γ
ffiffiffi
s
p
, where s is the
square of the c.m. energy, and the asterisk hereafter denotes
a c.m. quantity. We seek a signal of the dark photon A
0
as a
narrow peak in the distribution 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
0
is negligible compared to the experimental resolution,
and that the A
0
decays predominantly to dark matter (i.e.,
the invisible branching fraction is ≈100%). Furthermore,
we assume that a single A
0
state exists in the range
0 <m
A
0
≤ 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
þ
e
−
or μ
þ
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
0
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
0
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
þ
e
−
→ γA
0
, followed by
invisible decays of the A
0
in a 53 fb
−1
data set [21] collected
with the BABAR detector at the PEP-II asymmetric-energy
e
þ
e
−
collider at the SLAC National Accelerator
Laboratory. The data were collected in 2007–2008 with
c.m. energies near the ϒð2SÞ, ϒð3SÞ, and ϒð4SÞ reso-
nances with a special “single-photon” trigger described
below. The e
þ
e
−
c.m. frame was boosted relative to the
detector approximately along the detector’s magnetic field
axis by β
z
≈ 0.5. Since the production of the A
0
is not
expected to be enhanced by the presence of the ϒ
resonances, we combine the data sets 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
ffiffiffi
s
p
, we measure the signal event yields
separately for the ϒð2SÞ, ϒð3SÞ, and ϒð4SÞ data sets.
Since the BABAR detector is described in detail elsewhere
[22], only the components of the detector crucial to this
analysis are summarized below. Charged particle tracking is
provided by a five-layer double-sided silicon vertex tracker
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 superconducting magnet. The Instrumented
Flux Return (IFR) forms the return yoke of the
PRL 119, 131804 (2017)
PHYSICAL REVIEW LETTERS
week ending
29 SEPTEMBER 2017
131804-3
superconducting coil, instrumented 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 G
EANT
4 [23] software to simulate
interactions of particles traversing the BABAR detector, taking
into account the varying detector conditions and beam
backgrounds.
Detection of low-multiplicity single-photon events
requires dedicated trigger lines. Event processing and
selection 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-3 (L3)
trigger, which forms DCH tracks and EMC clusters and
makes decisions for a variety of physics signatures. Two
single-photon L3 trigger lines were active during the data-
taking period. The high-energy photon line (low M
X
,
hereafter “LowM”) requires an isolated EMC cluster
with energy E
γ
> 2 GeV, and no tracks originating from
the e
þ
e
−
interaction region (IR). The LowM data set
amounts to 5.9 fb
−1
collected at the ϒð4SÞ resonance
(
ffiffiffi
s
p
¼ 10.58 GeV), 28.5 fb
−1
collected at the ϒð3 SÞ res-
onance (
ffiffiffi
s
p
¼ 10.36 GeV), 2.7 fb
−1
collected 30 MeV
below the ϒð3SÞ resonance, 14.4 fb
−1
collected at the
ϒð2SÞ resonance (
ffiffiffi
s
p
¼ 10.02 GeV), and 1.5 fb
−1
col-
lected 30 MeV below the ϒð2SÞ resonance. The total 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
þ
e
−
interaction
region, was active for a subset of the data: 20 fb
−1
collected
at the ϒð3SÞ resonance as well as all of the data collected
below the ϒð3SÞ and at the ϒð2SÞ resonances. The total
data sample collected with the HighM triggers is 35.9 fb
−1
.
Additional off-line software filters are applied to the
stored data. We accept single-photon events if they satisfy
one of the two following criteria. The LowM selection
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 trans-
verse profile consistent with an electromagnetic shower
and E
γ
> 1. 5 GeV, and no DCH tracks with momentum
p
> 0.1 GeV. The two selection criteria are not mutually
exclusive.
The trigger and reconstruction selections naturally split
the data set 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
þ
e
−
→ γγ, especially near M
X
≈ 0
(E
γ
≈
ffiffiffi
s
p
=2). Because of 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 optimized to reduce this
peaking background as much as possible. The HighM
trigger selection defines the high-M
X
range 24 <M
2
X
<
69ð63.5Þ GeV
2
for the ϒð3SÞ [ϒð2SÞ] data set. This
region is dominated by the low-angle radiative Bhabha
events e
þ
e
−
→ e
þ
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 isolated photon
shower in the EMC. We accept photons in the polar angle
range jcos θ
γ
j < 0.6, rejecting radiative Bhabha events that
strongly peak in the forward and backward directions, and
we require that the event contain 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]. Second,
we include both the total excess EMC energy in the
laboratory frame not associated with the highest-energy
photon, and the c.m. energy and polar angle of the second-
most-energetic EMC cluster. We also compute the azimu-
thal angle difference Δϕ
12
between the highest- and
second-highest-energy EMC clusters; the e
þ
e
−
→ γγ
events with partial energy deposit in the EMC tend to
peak at Δϕ
12
∼ π. Third, a number of variables improve
containment of the background events. We extrapolate the
missing momentum vector to the EMC face, and compute
the distance [in ðθ; ϕÞ polar lab-frame coordinates] to the
nearest crystal edge. This allows us to suppress e
þ
e
−
→ γγ
ev ents where one of the photons penetrates the EMC
between crystals leaving little detectable energy.
Furthermore, we look for energy deposited in the IFR,
and compute the correlation angle Δϕ
NH
between the
primary photon and the IFR cluster closest to the missing
momentum direction; e
þ
e
−
→ γγ eventsproduceapeakat
cos Δϕ
NH
∼−1. We also apply a fiducial selection to the
azimuthal angle ϕ
miss
of the missing momentum by includ-
ing cosð6ϕ
miss
Þ into the BDT. This accounts for uninstru-
mented regions between six IFR sectors [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 using 2.5 × 10
4
simulated signal events with uniformly distributed A
0
masses, and 2.5 × 10
4
background events from the
ϒð3SÞ on-peak sample that corresponds to approximately
3 fb
−1
. We test the BDT, define the final selection, and
measure the signal efficiency using sets of 2.5 × 10
4
signal
and background events statistically independent 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.
PRL 119, 131804 (2017)
PHYSICAL REVIEW LETTERS
week ending
29 SEPTEMBER 2017
131804-4