of 5
V
OLUME
76, N
UMBER
15
PHYSICAL REVIEW LETTERS
8 A
PRIL
1996
Tau Decays into Three Charged Leptons and Two Neutrinos
M. S. Alam,
1
I. J. Kim,
1
Z. Ling,
1
A. H. Mahmood,
1
J. J. O’Neill,
1
H. Severini,
1
C. R. Sun,
1
S. Timm,
1
F. Wappler,
1
J. E. Duboscq,
2
R. Fulton,
2
D. Fujino,
2
K. K. Gan,
2
K. Honscheid,
2
H. Kagan,
2
R. Kass,
2
J. Lee,
2
M. Sung,
2
C. White,
2
R. Wanke,
2
A. Wolf,
2
M. M. Zoeller,
2
X. Fu,
3
B. Nemati,
3
S. J. Richichi,
3
W. R. Ross,
3
P. Skubic,
3
M. Wood,
3
M. Bishai,
4
J. Fast,
4
E. Gerndt,
4
J. W. Hinson,
4
T. Miao,
4
D. H. Miller,
4
M. Modesitt,
4
E. I. Shibata,
4
I. P. J. Shipsey,
4
P. N. Wang,
4
L. Gibbons,
5
S. D. Johnson,
5
Y. Kwon,
5
S. Roberts,
5
E. H. Thorndike,
5
C. P. Jessop,
6
K. Lingel,
6
H. Marsiske,
6
M. L. Perl,
6
S. F. Schaffner,
6
R. Wang,
6
T. E. Coan,
7
J. Dominick,
7
V. Fadeyev,
7
I. Korolkov,
7
M. Lambrecht,
7
S. Sanghera,
7
V. Shelkov,
7
R. Stroynowski,
7
I. Volobouev,
7
G. Wei,
7
M. Artuso,
8
A. Efimov,
8
M. Gao,
8
M. Goldberg,
8
D. He,
8
N. Horwitz,
8
S. Kopp,
8
G. C. Moneti,
8
R. Mountain,
8
Y. Mukhin,
8
S. Playfer,
8
T. Skwarnicki,
8
S. Stone,
8
X. Xing,
8
J. Bartelt,
9
S. E. Csorna,
9
V. Jain,
9
S. Marka,
9
D. Gibaut,
10
K. Kinoshita,
10
P. Pomianowski,
10
S. Schrenk,
10
B. Barish,
11
M. Chadha,
11
S. Chan,
11
G. Eigen,
11
J. S. Miller,
11
C. O’Grady,
11
M. Schmidtler,
11
J. Urheim,
11
A. J. Weinstein,
11
F. Würthwein,
11
D. M. Asner,
12
M. Athanas,
12
D. W. Bliss,
12
W. S. Brower,
12
G. Masek,
12
H. P. Paar,
12
J. Gronberg,
13
C. M. Korte,
13
R. Kutschke,
13
S. Menary,
13
R. J. Morrison,
13
S. Nakanishi,
13
H. N. Nelson,
13
T. K. Nelson,
13
C. Qiao,
13
J. D. Richman,
13
D. Roberts,
13
A. Ryd,
13
H. Tajima,
13
M. S. Witherell,
13
R. Balest,
14
K. Cho,
14
W. T. Ford,
14
M. Lohner,
14
H. Park,
14
P. Rankin,
14
J. Roy,
14
J. G. Smith,
14
J. P. Alexander,
15
C. Bebek,
15
B. E. Berger,
15
K. Berkelman,
15
K. Bloom,
15
D. G. Cassel,
15
H. A. Cho,
15
D. M. Coffman,
15
D. S. Crowcroft,
15
M. Dickson,
15
P. S. Drell,
15
D. J. Dumas,
15
R. Ehrlich,
15
R. Elia,
15
P. Gaidarev,
15
R. S. Galik,
15
B. Gittelman,
15
S. W. Gray,
15
D. L. Hartill,
15
B. K. Heltsley,
15
C. D. Jones,
15
S. L. Jones,
15
J. Kandaswamy,
15
N. Katayama,
15
P. C. Kim,
15
D. L. Kreinick,
15
T. Lee,
15
Y. Liu,
15
G. S. Ludwig,
15
J. Masui,
15
J. Mevissen,
15
N. B. Mistry,
15
C. R. Ng,
15
E. Nordberg,
15
J. R. Patterson,
15
D. Peterson,
15
D. Riley,
15
A. Soffer,
15
C. Ward,
15
P. Avery,
16
A. Freyberger,
16
C. Prescott,
16
S. Yang,
16
J. Yelton,
16
G. Brandenburg,
17
R. A. Briere,
17
D. Cinabro,
17
T. Liu,
17
M. Saulnier,
17
R. Wilson,
17
H. Yamamoto,
17
T. E. Browder,
18
F. Li,
18
J. L. Rodriguez,
18
T. Bergfeld,
19
B. I. Eisenstein,
19
J. Ernst,
19
G. E. Gladding,
19
G. D. Gollin,
19
M. Palmer,
19
M. Selen,
19
J. J. Thaler,
19
K. W. Edwards,
20
K. W. McLean,
20
M. Ogg,
20
A. Bellerive,
21
D. I. Britton,
21
R. Janicek,
21
D. B. MacFarlane,
21
P. M. Patel,
21
B. Spaan,
21
A. J. Sadoff,
22
R. Ammar,
23
P. Baringer,
23
A. Bean,
23
D. Besson,
23
D. Coppage,
23
N. Copty,
23
R. Davis,
23
N. Hancock,
23
S. Kotov,
23
I. Kravchenko,
23
N. Kwak,
23
Y. Kubota,
24
M. Lattery,
24
J. K. Nelson,
24
S. Patton,
24
R. Poling,
24
T. Riehle,
24
and V. Savinov
24
(CLEO Collaboration)
1
State University of New York at Albany, Albany, New York 12222
2
The Ohio State University, Columbus, Ohio 43210
3
University of Oklahoma, Norman, Oklahoma 73019
4
Purdue University, West Lafayette, Indiana 47907
5
University of Rochester, Rochester, New York 14627
6
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309
7
Southern Methodist University, Dallas, Texas 75275
8
Syracuse University, Syracuse, New York 13244
9
Vanderbilt University, Nashville, Tennessee 37235
10
Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
11
California Institute of Technology, Pasadena, California 91125
12
University of California, San Diego, La Jolla, California 92093
13
University of California, Santa Barbara, California 93106
14
University of Colorado, Boulder, Colorado 80309-0390
15
Cornell University, Ithaca, New York 14853
16
University of Florida, Gainesville, Florida 32611
17
Harvard University, Cambridge, Massachusetts 02138
18
University of Hawaii at Manoa, Honolulu, Hawaii 96822
19
University of Illinois, Champaign-Urbana, Illinois 61801
20
Carleton University, Ottawa, Ontario, Canada K1S 5B6
and the Institute of Particle Physics, Montréal, Québec, Canada
21
McGill University, Montréal, Québec, Canada H3A 2T8
and the Institute of Particle Physics, Montréal, Québec, Canada
22
Ithaca College, Ithaca, New York 14850
23
University of Kansas, Lawrence, Kansas 66045
0031-9007
y
96
y
76(15)
y
2637(5)$10.00
© 1996 The American Physical Society
2637
V
OLUME
76, N
UMBER
15
PHYSICAL REVIEW LETTERS
8 A
PRIL
1996
24
University of Minnesota, Minneapolis, Minnesota 55455
(
Received 22 November 1995; revised manuscript received 8 February 1996
)
We search for the radiative leptonic tau decays
t
!
ee
1
e
2
n
t
n
e
and
t
!
m
e
1
e
2
n
t
n
m
using
3.60
fb
2
1
of data collected by the CLEO-II experiment at the Cornell Electron Storage Ring. We
present a first observation of the
t
!
ee
1
e
2
n
t
n
e
process. For this channel we measure the branching
fraction
B
s
t
!
ee
1
e
2
n
t
n
e
d
s
2.7
1
1.5
1
0.4
1
0.1
2
1.1
2
0.4
2
0.3
d
3
10
2
5
. An upper limit is established for the second
channel:
B
s
t
!
m
e
1
e
2
n
t
n
m
d
,
3.2
3
10
2
5
at 90% C.L. Both results are consistent with the rates
expected from standard model predictions.
PACS numbers: 13.35.Dx
Tau decays into three charged leptons and two neutri-
nos are allowed processes in the standard model. They
proceed via emission of a virtual photon with subsequent
internal conversion into a pair of electrons or muons.
Two Feynman diagrams provide the dominant contribu-
tion to the decay rate. They are shown in Fig. 1 for the
t
2
!
m
2
e
1
e
2
n
t
̄
n
m
decay. The contribution of a third
diagram, with a virtual photon emitted from the
W
boson,
is heavily suppressed by the
W
propagator. For tau de-
cays with two identical charged leptons in the final state,
two additional exchange diagrams are involved. Branch-
ing fractions for these processes have been recently calcu-
lated by Dicus and Vega [1] and are listed in Table I. The
branching fractions for tau decays with a virtual photon
conversion into two muons,
t
!
e
m
1
m
2
n
t
n
e
and
t
!
mm
1
m
2
n
t
n
m
, are expected to be at the level of
10
2
7
, too
small to be observed in existing data. On the other hand,
the expected branching fractions for
t
!
ee
1
e
2
n
t
n
e
and
t
!
m
e
1
e
2
n
t
n
m
are at the level of
10
2
5
, which is com-
parable to the sensitivity reached in a recent search for
neutrinoless tau decays into three charged particles [2].
In this Letter, we report on a follow-up study in which we
have searched for these two decays. Radiative tau decays
into a muon, two neutrinos, and a photon without internal
conversion have been previously observed [3].
The data used in this analysis were collected with the
CLEO-II detector at the Cornell Electron Storage Ring
(CESR), in which tau leptons are produced in pairs in
e
1
e
2
collisions. They correspond to an integrated lumi-
nosity of about
3.60
fb
2
1
and the number of produced
tau pairs,
N
tt
,is
s
3.28
6
0.05
d
3
10
6
. About 60% of
the events were obtained at the
Y
s
4
S
d
resonance (
p
s
.
10.59
GeV ) while the rest were obtained at energies ap-
proximately 60 MeV lower. We use information from a
67-layer tracking system which also provides specific ion-
ization measurements (
dE
y
dx
), time-of-flight scintillation
counters, and a 7800-crystal CsI calorimeter. These ele-
ments are inside a 1.5 T superconducting solenoidal mag-
net whose iron yoke also serves as a hadron absorber for a
muon identification system. A detailed description of the
apparatus can be found in Ref. [4].
In order to obtain a Monte Carlo event generator which
we needed to design the event selection procedure and to
estimate the detector acceptance, we performed the cal-
culation of the relevant matrix elements using the sym-
bolic manipulation program
FORM
[5]. No tau polariza-
tion effects or higher order radiative corrections were
taken into account. To check our generator, we calculated
the branching fraction for the known five lepton decay of
the muon,
m
!
eee
n
m
n
e
. The result, listed in Table I, is
consistent with the calculation of Dicus and Vega [1]and
with an earlier estimate
B
s
m
!
eee
n
m
n
e
d
s
3.54
6
0.09
d
3
10
2
5
by Bardin, Istatkov, and Mitsel’makher [6].
It also agrees with the measurement
B
s
m
!
eee
n
m
n
e
d
s
3.4
6
0.4
d
3
10
2
5
by the SINDRUM Collaboration [7].
For tau decays our branching fraction estimates are (6 –
7)% higher than those of Ref. [1]. We generated 100 000
t
!
m
e
1
e
2
n
t
n
m
and 60 000
t
!
ee
1
e
2
n
t
n
e
Monte
Carlo decays to study their kinematical properties and the
response of the detector. The
KORALB
y
TAUOLA
program
package [8] was used to simulate the tau-pair production
and the decay of the other tau in the event. Detector sig-
nals were simulated by the standard CLEO-II simulation
program [9].
To extract from our data tau decays into three charged
leptons and two neutrinos, we search for events where one
tau decays into a single charged particle (1-prong decay)
and the other tau decays into three charged particles (3-
prong decay). The 3-prong decay is a signal candidate
and the 1-prong is an allowed tau decay with one charged
particle, zero or more photons and at least one neutrino in
the final state. For each candidate event we require four
well-reconstructed charged particle tracks with zero total
charge. The most isolated track must be separated by at
least 90
±
from all other tracks. We also reject events with
photons with energies larger than 60 MeV on the 3-prong
side.
FIG. 1. Feynman diagrams for the
t
2
!
m
2
e
1
e
2
n
t
̄
n
m
process.
2638
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PHYSICAL REVIEW LETTERS
8 A
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1996
TABLE I. Calculated
t
and
m
branching fractions. Errors given here are due to inaccuracies
in numerical integration only.
Channel
Dicus and Vega
Our calculation
t
!
eee
n
t
n
e
s
4.15
6
0.06
d
3
10
2
5
s
4.457
6
0.006
d
3
10
2
5
t
!
m
ee
n
t
n
m
s
1.97
6
0.02
d
3
10
2
5
s
2.089
6
0.003
d
3
10
2
5
t
!
e
mmn
t
n
e
s
1.257
6
0.003
d
3
10
2
7
s
1.347
6
0.002
d
3
10
2
7
t
!
mmmn
t
n
m
s
1.190
6
0.002
d
3
10
2
7
s
1.276
6
0.004
d
3
10
2
7
t
!
eee
n
m
n
e
s
3.60
6
0.02
d
3
10
2
5
s
3.605
6
0.005
d
3
10
2
5
Substantial background suppression comes from lep-
ton identification on the 3-prong side.
In the
t
!
m
e
1
e
2
n
t
n
m
channel we require a muon candidate with
momentum less than
2.2
GeV
y
c
to pass through at least
three hadronic absorption lengths of iron and through at
least five absorption lengths if its momentum is greater
than
2.2
GeV
y
c
. For such muon candidates, the energy
deposited in the CsI calorimeter,
E
c
, must be compati-
ble with that expected for a minimum ionizing particle:
0.1
,
E
c
,
0.5
GeV. We also require that the charge
of the muon candidate is opposite to that of the 1-prong
track. For electron identification, we rely mostly on the
dE
y
dx
measurement in the drift chamber. It must dif-
fer from the expected value by less than 3 standard de-
viations,
s
. If there is a time-of-flight measurement, we
require that it is compatible with the electron hypothesis
within
3
s
, and if the electron candidate is fast enough so
that its energy losses in the inner layers of the detector
material can be neglected then we require that its
E
c
is
about the same as expected from its momentum value,
p
e
,
measured in the drift chamber:
0.8
,
E
c
y
p
e
,
1.1
. This
last requirement must be satisfied for at least one elec-
tron candidate in the
t
!
ee
1
e
2
n
t
n
e
channel. In or-
der to suppress a strong
e
1
e
2
!
e
1
e
2
e
1
e
2
background
we also require that in this channel the 1-prong parti-
cle is not consistent with being an electron. It must ei-
ther pass through three absorption lengths of the muon
filter or have a
E
c
y
p
ratio incompatible with an elec-
tron hypothesis. The radiative muon pair background
e
1
e
2
!
m
1
m
2
e
1
e
2
in the
t
!
m
e
1
e
2
n
t
n
m
channel
is reduced by the requirement that the 1-prong particle is
not identified as a muon.
The main sources of background left after lep-
ton identification are as follows: low multiplicity
e
1
e
2
!
q
̄
q
events, 2-photon processes, especially the
e
1
e
2
!
t
1
t
2
e
1
e
2
reaction which can result in a
similar final state, radiative Bhabha,
m
pairs, and radia-
tive leptonic decays
t
!
l
n
t
n
l
g
(
l
stands for
e
or
m
)
with subsequent
g
!
e
1
e
2
conversion in the detector
material, tau decays into three hadrons and a neutrino
where all hadrons are misidentified as leptons, and fi-
nally tau decays into
rn
t
with subsequent
r
!
pp
0
,
p
0
!
e
1
e
2
g
decays, where the
g
escapes detection and
the
p
is misidentified as a lepton.
In order to suppress the non-tau background, we
require undetected neutrinos to be present by selecting
events with large missing energy,
E
miss
.
1.5
GeV, and
with a large value of total transverse momentum of the
charged particles with respect to the beam direction,
p
t
.
150
MeV
y
c
. The
t
!
3
h
n
t
decays contribute to the
background in our analysis due to a rather large branching
fraction, about 8.4% [10], and a few percent probability
for pions to fake leptons. To suppress this background,
we estimate the probability that all electron candidates
in the event are pions using
dE
y
dx
measurements. We
define the quantities
k
2
P
e
1
P
e
2
P
e
1
P
e
2
1
P
p
1
P
p
2
,
k
3
P
e
P
e
1
P
e
2
P
e
P
e
1
P
e
2
1
P
p
P
p
1
P
p
2
for the
t
!
m
e
1
e
2
n
t
n
m
and
t
!
ee
1
e
2
n
t
n
e
chan-
nels, respectively, where
P
e
s
2
p
d
2
1
y
2
exp
s
2s
2
e
y
2
d
and
P
p
s
2
p
d
2
1
y
2
exp
s
2s
2
p
y
2
d
. Here,
s
e
and
s
p
are the
numbers of standard deviations of the measured specific
ionization from that expected for an electron and a pion.
k
2
and
k
3
characterize the purity of the sample from a
contamination with events with pions faking electrons.
We require
k
2
and
k
3
to be greater than 0.97.
We check for photon conversions in our data sample
by reconstructing a possible conversion point. At such
a point, the
e
1
and
e
2
tracks should be parallel in the
transverse plane perpendicular to the beam axis. We
require that the distance from this point to the beam
axis must be less than 2 cm. This suppresses photon
conversions because the closest region where photons
can convert in the detector material is the beam pipe
at a radius of 3.5 cm from the beam axis. In the
t
!
ee
1
e
2
n
t
n
e
channel this requirement must be satisfied for
both
e
1
e
2
combinations.
In the
t
!
m
e
1
e
2
n
t
n
m
and
t
!
ee
1
e
2
n
t
n
e
pro-
cesses the invariant mass of the three charged leptons
tends to be small and thus at the interaction point their
tracks are nearly parallel. This feature provides the pos-
sibility of differentiating these decays from the
t
!
rn
t
,
r
!
pp
0
,
p
0
!
e
1
e
2
g
process where the
g
es-
capes detection and the
p
is misidentified as a lepton.
The distribution of the sum of the cosines of the angles
2639
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PHYSICAL REVIEW LETTERS
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1996
FIG. 2. Sum of cosines of the angles
q
ij
between the 3-prong
side tracks for the data (black circles), signal Monte Carlo (solid
line), and generic tau Monte Carlo sample (dashed line) for
the two channels studied. The signal Monte Carlo histograms
are normalized to standard model theoretical predictions. The
generic tau Monte Carlo histograms are normalized to the data
luminosity. In this analysis we require
P
i
,
j
cos
q
ij
.
2.93
for
both channels.
q
ij
between the 3-prong tracks is shown in Fig. 2 for the
data, signal Monte Carlo events, and a sample of generic
tau Monte Carlo events. We compare the distributions for
the signal and generic tau Monte Carlo events and require
P
i
,
j
cos
q
ij
.
2.93
for both channels.
The signal efficiency,
e
, after application of all the
selection requirements and accounting for tau pair tag-
ging, is estimated from the Monte Carlo simulation to
be
s
2.7
6
0.1
d
%
for the
t
!
ee
1
e
2
n
t
n
e
channel and
s
1.9
6
0.1
d
%
for the
t
!
m
e
1
e
2
n
t
n
m
channel (statis-
tical errors only). The main reason for such low effi-
ciencies is a very soft momentum spectrum of the ra-
diative electrons. With these estimates, our calculations
predict that on average 7.8
t
!
ee
1
e
2
n
t
n
e
and 2.6
t
!
m
e
1
e
2
n
t
n
m
events will remain. In the data, five
events satisfy all selection criteria in the
t
!
ee
1
e
2
n
t
n
e
channel and one event in the
t
!
m
e
1
e
2
n
t
n
m
channel.
Distributions of several kinematic variables for both the
signal Monte Carlo and the selected data events are shown
in Fig. 3 for the
t
!
ee
1
e
2
n
t
n
e
channel. They indicate
that the five remaining events in this channel are kinemat-
ically consistent with tau decays into three electrons and
two neutrinos.
The remaining background from other tau decays is
estimated by applying the same selection criteria to a
sample of generic
e
1
e
2
!
t
1
t
2
Monte Carlo events
without the signal channels which is about 2.8 times larger
than the data. No generic tau Monte Carlo events are
accepted in either of the two channels. Thus, we estimate
the background contribution from other tau decays to be
less than 0.4 event at 68% confidence level (C.L.). We
estimate the background from the
e
1
e
2
!
t
1
t
2
e
1
e
2
process using a sample of
6.6
3
10
5
Monte Carlo events
(ten times larger than the data) generated with the
DIAG36
FIG. 3. Comparison of the kinematical distributions of the
t
!
ee
1
e
2
n
t
n
e
Monte Carlo (solid line) and the data (shaded
histogram) for events passing all selection requirements: (a) the
e
1
e
2
invariant mass averaged over two possible combinations,
M
e
1
e
2
, (b) the 3-prong invariant mass,
M
3
-
prong
, and (c) the
momentum of the electron on the 3-prong side with the charge
opposite to that of the parent tau,
p
opp
. The normalization of
the plots is arbitrary.
program [11]. From this source we expect on average
0.5 event in the
t
!
m
e
1
e
2
n
t
n
m
channel and 0.3 event
in the
t
!
ee
1
e
2
n
t
n
e
channel.
No events satisfied
our selection criteria in either of the two channels from
samples of
e
1
e
2
!
B
̄
B
and continuum (
e
1
e
2
!
q
̄
q
,
q
u
,
d
,
s
,
and
c
) Monte Carlo events which are larger
than the data by factors of 2.6 and 1.2, respectively.
Kinematic properties of the
B
̄
B
and continuum events are
very dissimilar to those of the signal, and we conclude
that backgrounds from these sources are negligible. We
expect no
e
1
e
2
!
e
1
e
2
e
1
e
2
background in the
t
!
ee
1
e
2
n
t
n
e
channel after requiring that the 1-prong track
must not be an electron. We checked this conclusion by
looking at the
dE
y
dx
measurements of the 1-prong tracks.
These measurements favor the pion hypothesis over the
electron one in all five remaining events. In addition, three
of those events have a pair of photons on the 1-prong side
with an invariant mass compatible with that of a
p
0
.
The main systematic errors in this study arise from un-
certainties in our knowledge of the lepton identification
efficiency and the reconstruction efficiency of slow tracks.
2640
V
OLUME
76, N
UMBER
15
PHYSICAL REVIEW LETTERS
8 A
PRIL
1996
Combined together, they are estimated to give an overall
systematic error of 15%. Thus, subtracting the expected
background from
e
1
e
2
!
t
1
t
2
e
1
e
2
events, our esti-
mate of the
t
!
ee
1
e
2
n
t
n
e
branching fraction is
B
s
t
!
ee
1
e
2
n
t
n
e
d
s
2.7
1
1.5
1
0.4
1
0.1
2
1.1
2
0.4
2
0.3
d
3
10
2
5
,
where the first errors account for statistical fluctuations
and show a minimal 68% C.L. interval calculated accord-
ing to Bayesian statistics with an assumption of a flat prior
distribution [12], the second errors are due to systematic
effects and the third set of errors reflects the uncertainty in
our knowledge of background. Neglecting the second and
third errors, our calculated value of
4.46
3
10
2
5
is com-
patible with this result at 24% C.L. (we quote Bayesian
confidence level here).
In the
t
!
m
e
1
e
2
n
t
n
m
channel we calculate an upper
limit on the branching fraction according to a procedure
described in Ref. [10] assuming an expected background
of 0.5 event. As previously, we assign a systematic error
of 15% to this result and increase the branching fraction
limit by this amount. The resulting upper limit is
B
s
t
!
m
e
1
e
2
n
t
n
m
d
,
3.2
3
10
2
5
at
90%
C.L.
We gratefully acknowledge the effort of the CESR staff
in providing us with excellent luminosity and running
conditions. This work was supported by the National
Science Foundation, the U.S. Department of Energy, the
Heisenberg Foundation, the Alexander von Humboldt
Stiftung, the Natural Sciences and Engineering Research
Council of Canada, and the A. P. Sloan Foundation.
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2641