of 7
Search for a muonic dark force 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
Yu. G. Kolomensky,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
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
A. Zallo,
17
S. Passaggio,
18
C. Patrignani,
18
,
B. Bhuyan,
19
U. Mallik,
20
C. Chen,
21
J. Cochran,
21
S. Prell,
21
H. Ahmed,
22
A. V. Gritsan,
23
N. Arnaud,
24
M. Davier,
24
F. Le Diberder,
24
A. M. Lutz,
24
G. Wormser,
24
D. J. Lange,
25
D. M. Wright,
25
J. P. Coleman,
26
E. Gabathuler,
26
D. E. Hutchcroft,
26
D. J. Payne,
26
C. Touramanis,
26
A. J. Bevan,
27
F. Di Lodovico,
27
R. Sacco,
27
G. Cowan,
28
Sw. Banerjee,
29
D. N. Brown,
29
C. L. Davis,
29
A. G. Denig,
30
M. Fritsch,
30
W. Gradl,
30
K. Griessinger,
30
A. Hafner,
30
K. R. Schubert,
30
R. J. Barlow,
31
,
G. D. Lafferty,
31
R. Cenci,
32
A. Jawahery,
32
D. A. Roberts,
32
R. Cowan,
33
R. Cheaib,
34
S. H. Robertson,
34
B. Dey,
35a
N. Neri,
35a
F. Palombo,
35a,35b
L. Cremaldi,
36
R. Godang,
36
D. J. Summers,
36
P. Taras,
37
G. De Nardo,
38
C. Sciacca,
38
G. Raven,
39
C. P. Jessop,
40
J. M. LoSecco,
40
K. Honscheid,
41
R. Kass,
41
A. Gaz,
42a
M. Margoni,
42a,42b
M. Posocco,
42a
M. Rotondo,
42a
G. Simi,
42a,42b
F. Simonetto,
42a,42b
R. Stroili,
42a,42b
S. Akar,
43
E. Ben-Haim,
43
M. Bomben,
43
G. R. Bonneaud,
43
G. Calderini,
43
J. Chauveau,
43
G. Marchiori,
43
J. Ocariz,
43
M. Biasini,
44a,44b
E. Manoni,
44a
A. Rossi,
44a
G. Batignani,
45a,45b
S. Bettarini,
45a,45b
M. Carpinelli,
45a,45b
G. Casarosa,
45a,45b
M. Chrzaszcz,
45a
F. Forti,
45a,45b
M. A. Giorgi,
45a,45b
A. Lusiani,
45a,45c
B. Oberhof,
45a,45b
E. Paoloni,
45a,45b
M. Rama,
45a
G. Rizzo,
45a,45b
J. J. Walsh,
45a
A. J. S. Smith,
46
F. Anulli,
47a
R. Faccini,
47a,47b
F. Ferrarotto,
47a
F. Ferroni,
47a,47b
A. Pilloni,
47a,47b
G. Piredda,
47a
C. Bünger,
48
S. Dittrich,
48
O. Grünberg,
48
M. Heß,
48
T. Leddig,
48
C. Voß,
48
R. Waldi,
48
T. Adye,
49
F. F. Wilson,
49
S. Emery,
50
G. Vasseur,
50
D. Aston,
51
C. Cartaro,
51
M. R. Convery,
51
J. Dorfan,
51
W. Dunwoodie,
51
M. Ebert,
51
R. C. Field,
51
B. G. Fulsom,
51
M. T. Graham,
51
C. Hast,
51
W. R. Innes,
51
P. Kim,
51
D. W. G. S. Leith,
51
S. Luitz,
51
V. Luth,
51
D. B. MacFarlane,
51
D. R. Muller,
51
H. Neal,
51
B. N. Ratcliff,
51
A. Roodman,
51
M. K. Sullivan,
51
J. Va
vra,
51
W. J. Wisniewski,
51
M. V. Purohit,
52
J. R. Wilson,
52
A. Randle-Conde,
53
S. J. Sekula,
53
M. Bellis,
54
P. R. Burchat,
54
E. M. T. Puccio,
54
M. S. Alam,
55
J. A. Ernst,
55
R. Gorodeisky,
56
N. Guttman,
56
D. R. Peimer,
56
A. Soffer,
56
S. M. Spanier,
57
J. L. Ritchie,
58
R. F. Schwitters,
58
J. M. Izen,
59
X. C. Lou,
59
F. Bianchi,
60a,60b
F. De Mori,
60a,60b
A. Filippi,
60a
D. Gamba,
60a,60b
L. Lanceri,
61
L. Vitale,
61
F. Martinez-Vidal,
62
A. Oyanguren,
62
J. Albert,
63
A. Beaulieu,
63
F. U. Bernlochner,
63
G. J. King,
63
R. Kowalewski,
63
T. Lueck,
63
I. M. Nugent,
63
J. M. Roney,
63
B. Shuve,
63
N. Tasneem,
63
T. J. Gershon,
64
P. F. Harrison,
64
T. E. Latham,
64
R. Prepost,
65
and S. L. Wu
65
(
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
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
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
14
University of Colorado, Boulder, Colorado 80309, USA
15
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
16a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
PHYSICAL REVIEW D
94,
011102(R) (2016)
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=
2016
=
94(1)
=
011102(7)
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© 2016 American Physical Society
RAPID COMMUNICATIONS
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 Sezione di Genova, I-16146 Genova, Italy
19
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
20
University of Iowa, Iowa City, Iowa 52242, USA
21
Iowa State University, Ames, Iowa 50011, USA
22
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
23
Johns Hopkins University, Baltimore, Maryland 21218, USA
24
Laboratoire de l
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
Orsay, F-91898 Orsay Cedex, France
25
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
26
University of Liverpool, Liverpool L69 7ZE, United Kingdom
27
Queen Mary, University of London, London E1 4NS, United Kingdom
28
University of London, Royal Holloway and Bedford New College,
Egham, Surrey TW20 0EX, United Kingdom
29
University of Louisville, Louisville, Kentucky 40292, USA
30
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
31
University of Manchester, Manchester M13 9PL, United Kingdom
32
University of Maryland, College Park, Maryland 20742, USA
33
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
34
McGill University, Montréal, Québec, Canada H3A 2T8
35a
INFN Sezione di Milano, I-20133 Milano, Italy
35b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
36
University of Mississippi, University, Mississippi 38677, USA
37
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
38
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche, Università di Napoli Federico II,
I-80126 Napoli, Italy
39
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
40
University of Notre Dame, Notre Dame, Indiana 46556, USA
41
Ohio State University, Columbus, Ohio 43210, USA
42a
INFN Sezione di Padova, I-35131 Padova, Italy
42b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
43
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie
Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France
44a
INFN Sezione di Perugia, I-06123 Perugia, Italy
44b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
45a
INFN Sezione di Pisa, I-56127 Pisa, Italy
45b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
45c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
46
Princeton University, Princeton, New Jersey 08544, USA
47a
INFN Sezione di Roma, I-00185 Roma, Italy
47b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
48
Universität Rostock, D-18051 Rostock, Germany
49
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
50
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
51
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
52
University of South Carolina, Columbia, South Carolina 29208, USA
53
Southern Methodist University, Dallas, Texas 75275, USA
54
Stanford University, Stanford, California 94305, USA
55
State University of New York, Albany, New York 12222, USA
56
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
57
University of Tennessee, Knoxville, Tennessee 37996, USA
58
University of Texas at Austin, Austin, Texas 78712, USA
59
University of Texas at Dallas, Richardson, Texas 75083, USA
60a
INFN Sezione di Torino, I-10125 Torino, Italy
60b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
61
INFN Sezione di Trieste and Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
62
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
J. P. LEES
et al.
PHYSICAL REVIEW D
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011102(R) (2016)
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63
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
64
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
65
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 14 June 2016; published 19 July 2016)
Many models of physics beyond the standard model predict the existence of new Abelian forces with
new gauge bosons mediating interactions between
dark sectors
and the standard model. We report a
search for a dark boson
Z
0
coupling only to the second and third generations of leptons in the reaction
e
þ
e
μ
þ
μ
Z
0
;Z
0
μ
þ
μ
using
514
fb
1
of data collected by the
BABAR
experiment. No significant
signal is observed for
Z
0
masses in the range 0.212
10 GeV. Limits on the coupling parameter
g
0
as low as
7
×
10
4
are derived, leading to improvements in the bounds compared to those previously derived from
neutrino experiments.
DOI:
10.1103/PhysRevD.94.011102
In spite of the many successes of the standard model
(SM), the known particles and interactions are insufficient
to explain cosmological and astrophysical observations of
dark matter. This motivates the possibility of new hidden
sectors that are only feebly coupled to the SM; by analogy
with the SM, such sectors may contain their own inter-
actions with new gauge bosons (
Z
0
). In the simplest case
of a hidden U(1) interaction, SM fields may directly couple
to the
Z
0
, or alternatively the
Z
0
boson may mix with the
SM hypercharge boson, which typically results from an
off-diagonal kinetic term
[1]
. In the latter case, the
Z
0
inherits couplings proportional to the SM gauge couplings;
due to large couplings to electrons and light-flavor
quarks, such scenarios are strongly constrained by existing
searches
[2
8]
.
When SM fields are directly charged under the dark
force, however, the
Z
0
may interact preferentially with
heavy-flavor leptons, greatly reducing the sensitivity of
current searches. Such interactions could account for the
experimentally measured value of the muon anomalous
magnetic dipole moment
[9]
, as well as the discrepancy
in the proton radius extra
cted from measurements
of the Lamb shift in muonic hydrogen compared to
observations in nonmuonic atoms
[10,11]
. Direct
Z
0
couplings to left-handed leptons also lead to new
interactions involving SM neutrinos that increase the
cosmological abundance of sterile neutrinos mixing with
SM neutrinos, consistent with the observed dark matter
abundance
[12]
.
We report herein a search for dark bosons
Z
0
with vector
couplings only to the second and third generations of
leptons
[13,14]
in the reaction
e
þ
e
μ
þ
μ
Z
0
,
Z
0
μ
þ
μ
.
While such a scenario can be additionally constrained by
neutrino-nucleus scattering at neutrino beam experiments,
the measurement presented here is also sensitive to models
where couplings to neutrinos are absent, such as a gauge
boson coupled exclusively to right-handed muons
[15]
.
This search is based on
514
fb
1
of data collected by the
BABAR
detector at the PEP-II
e
þ
e
storage ring, mostly
taken 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 in the vicinity of these resonances
[16]
. The
BABAR
detector is described in detail elsewhere
[17,18]
. Dark boson masses between the dimuon threshold
and 10 GeV are probed
[19]
. To avoid experimental bias,
the data are only examined after finalizing the analysis
strategy. A sample of about 5% of the data set is used to
optimize and validate the analysis strategy, and is then
discarded.
Signal events are simulated by
M
ad
G
raph 5
[20]
and
hadronized in
P
ythia 6
[21]
for
Z
0
mass hypotheses ranging
from the dimuon mass threshold to 10.3 GeV. The back-
ground arises mainly from QED processes. The
e
þ
e
μ
þ
μ
μ
þ
μ
reaction is generated with Diag36
[22]
, which
includes the full set of lowest order diagrams, while the
e
þ
e
μ
þ
μ
ð
γ
Þ
and
e
þ
e
τ
þ
τ
ð
γ
Þ
processes are simu-
lated with KK
[23]
. Other sources of background include
e
þ
e
q
̄
q
(
q
¼
u
,
d
,
s
,
c
) continuum production, simu-
lated with JETSET
[24]
, and
e
þ
e
π
þ
π
J=
ψ
events,
generated using EvtGen
[25]
with a phase-space model.
The detector acceptance and reconstruction efficiencies are
determined using a Monte Carlo (MC) simulation based on
GEANT
4
[26]
.
We select events containing two pairs of oppositely-
charged tracks, where both positively-charged or both
negatively-charged tracks are identified as muons by
particle identification algorithms (PID). Identifying only
two muons maintains high signal efficiency while rejecting
almost all background sources but
e
þ
e
μ
þ
μ
μ
þ
μ
events. In addition, the sum of energies of electromagnetic
clusters above 30 MeV not associated to any track must be
less than 200 MeV to remove background containing
neutral particles. To suppress background from the decay
chain
Υ
ð
3
S;
2
S
Þ
π
þ
π
Υ
ð
1
S
Þ
,
Υ
ð
1
S
Þ
μ
þ
μ
, we reject
events taken on the
Υ
ð
2
S
Þ
or
Υ
ð
3
S
Þ
peaks containing any
*
Present address: Wuhan University, Wuhan 43072, China.
Present address: Università di Bologna and INFN Sezione di
Bologna, I-47921 Rimini, Italy.
Present address: University of Huddersfield, Huddersfield
HD1 3DH, UK.
§
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
Also at: Università di Sassari, I-07100 Sassari, Italy.
SEARCH FOR A MUONIC DARK FORCE AT
B
A
B
AR
PHYSICAL REVIEW D
94,
011102(R) (2016)
011102-3
RAPID COMMUNICATIONS
pair of oppositely charged tracks with any dimuon invariant
mass within 100 MeV of the nominal
Υ
ð
1
S
Þ
mass.
The distribution of the four-muon invariant mass after
these cuts is shown in Fig.
1
for the data taken at the
Υ
ð
4
S
Þ
center-of-mass (CM) energy. The background at low
masses is fairly well reproduced by the simulation, while
the
e
þ
e
μ
þ
μ
μ
þ
μ
Monte Carlo overestimates the full-
energy peak by
30%
and fails to reproduce the radiative
tail. This is expected, since Diag36 does not simulate initial
state radiation (ISR). We further select
e
þ
e
μ
þ
μ
μ
þ
μ
events by requiring a four-muon invariant mass within
500 MeV of the nominal CM energy, allowing for the
possibility of ISR emission. The four-muon system is
finally fitted, constraining its CM energy to be within
the beam energy spread and the tracks to originate from the
interaction point to within its uncertainty. This kinematic fit
is solely used to improve the
Z
0
mass resolution of the bulk
of events near the full-energy peak; no further requirement
is imposed on the fit quality. We do not attempt to select a
single
Z
0
μ
þ
μ
candidate per event, but simply consider
all combinations.
The distribution of the reduced dimuon mass,
m
R
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
2
μ
þ
μ
4
m
2
μ
q
, is shown in Fig.
2
, together with the
predictions of various Monte Carlo simulations. The
reduced mass has a smoother behavior near threshold
and is easier to model than the dimuon mass. The spectrum
is dominated by
e
þ
e
μ
þ
μ
μ
þ
μ
production, with
additional contributions from
e
þ
e
π
þ
π
ρ
,
ρ
π
þ
π
,
e
þ
e
μ
þ
μ
ρ
,
ρ
π
þ
π
, and
e
þ
e
π
þ
π
J=
ψ
,
J=
ψ
μ
þ
μ
events, where one or several pions are
misidentified as muons. A peak corresponding to the
ρ
meson is visible at low mass; the second
Z
0
candidate
reconstructed in these events generates the enhancement
near 9.5 GeV. Other than the
J=
ψ
, no significant signal of
other narrow resonances is observed.
The signal efficiency rises from
35%
at low masses to
50%
around
m
R
¼
6
7
GeV, before dropping again at
higher masses. The signal efficiencies include a correction
factor of 0.82, which primarily accounts for the impact of
ISR not included in the simulation, as well as differences
between data and simulation in trigger efficiency, charged
particle identification, and track and photon reconstruction
efficiencies. This correction factor is derived from the ratio
of the
m
R
distribution in simulated
e
þ
e
μ
þ
μ
μ
þ
μ
events to the observed distribution in the mass region
1
9 GeV, excluding the
J=
ψ
region (light blue line in
Fig.
2
). An uncertainty of 5% is propagated as a systematic
uncertainty, covering the small variations between data-
taking periods and the uncertainties on the
e
þ
e
μ
þ
μ
μ
þ
μ
cross-section.
We extract the signal yield as a function of
m
Z
0
by
performing a series of unbinned maximum likelihood fits
to the reduced dimuon mass spectrum, covering the mass
range
m
R
<
10
GeV for the data taken near the
Υ
ð
4
S
Þ
resonance, and up to 9 GeV for the data sets collected near
the
Υ
ð
2
S
Þ
and
Υ
ð
3
S
Þ
resonances. The search is conducted
in varying mass steps that correspond to the dark boson
mass resolution. Each fit is performed over an interval
50 times broader than the signal resolution at that mass
for
m
R
>
0
.
2
GeV, or over a fixed interval 0
0.3 GeV for
m
R
<
0
.
2
GeV. We estimate the signal resolution by
Gaussian fits to several simulated
Z
0
samples for the
purpose of determining the scan steps, and interpolate
the results to all other masses. The resolution varies
between 1
9 MeV, dominated by experimental effects.
We probe a total of 2219 mass hypotheses. The bias in the
6
7
8
9
10
11
10
2
10
3
10
4
10
5
10
Data
-
μ
+
μ
-
μ
+
μ
-
e
+
e
-
τ
+
τ
-
e
+
e
q=u,d,s,c
q
q
-
e
+
e
)
-
μ
+
μ
(
ψ
J/
-
π
+
π
-
e
+
e
Entries / 0.06 (GeV)
) (GeV)
μ
m(4
FIG. 1. The distribution of the four-muon invariant mass,
m
ð
4
μ
Þ
, for data taken at the
Υ
ð
4
S
Þ
peak together with
Monte Carlo predictions of various processes normalized to data
luminosity. The
e
þ
e
μ
þ
μ
μ
þ
μ
Monte Carlo does not
include ISR corrections.
Entries / 0.1 (GeV)
0
1000
2000
3000
4000
5000
Data
-
μ
+
μ
-
μ
+
μ
-
e
+
e
-
τ
+
τ
-
e
+
e
q=u,d,s,c
q
q
-
e
+
e
)
-
μ
+
μ
(
ψ
J/
-
π
+
π
-
e
+
e
(GeV)
m
R
012345678910
Data/MC
0.8
1
1.2
FIG. 2. The distribution of the reduced dimuon mass,
m
R
,
together with Monte Carlo predictions of various processes
normalized to data luminosity. Four combinations per event
are included. The fit of the ratio between reconstructed and
simulated events is shown as a light blue dashed line. The
e
þ
e
μ
þ
μ
μ
þ
μ
Monte Carlo does not include ISR or other
efficiency corrections (see text).
J. P. LEES
et al.
PHYSICAL REVIEW D
94,
011102(R) (2016)
011102-4
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