First observations of separated atmospheric
and
events in the MINOS detector
P. Adamson,
11,33,29
T. Alexopoulos,
36,a
W. W. M. Allison,
23
G. J. Alner,
25
K. Anderson,
11
C. Andreopoulos,
25,2
M. Andrews,
11
R. Andrews,
11
C. Arroyo,
28
S. Avvakumov,
28
D. S. Ayres,
1
B. Baller,
11
B. Barish,
5
M. A. Barker,
23
P. D. Barnes, Jr.,
20
G. Barr,
23
W. L. Barrett,
34
E. Beall,
1,21
B. R. Becker,
21
A. Belias,
25
T. Bergfeld,
27,b
R. H. Bernstein,
11
D. Bhattacharya,
24
M. Bishai,
4
A. Blake,
6
V. Bocean,
11
B. Bock,
22
G. J. Bock,
11
J. Boehm,
12
D. J. Boehnlein,
11
D. Bogert,
11
P. M. Border,
21
C. Bower,
14
S. Boyd,
24
E. Buckley-Geer,
11
A. Byon-Wagner,
11,c
A. Cabrera,
23,d
J. D. Chapman,
6
T. R. Chase,
21
S. K. Chernichenko,
15
S. Childress,
11
B. C. Choudhary,
11,5
J. H. Cobb,
23
J. D. Cossairt,
11
H. Courant,
21
D. A. Crane,
1
A. J. Culling,
6
J. W. Dawson,
1
D. M. DeMuth,
21,e
A. De Santo,
23,f
M. Dierckxsens,
4
M. V. Diwan,
4
M. Dorman,
33,25
G. Drake,
1
R. Ducar,
11
T. Durkin,
25
A. R. Erwin,
36
C. O. Escobar,
7
J. Evans,
23
O. D. Fackler,
20
E. Falk Harris,
29
G. J. Feldman,
12
N. Felt,
12
T. H. Fields,
1
R. Ford,
11
M. V. Frohne,
3,g
H. R. Gallagher,
32,23,1,21
M. Gebhard,
14
A. Godley,
27
J. Gogos,
21
M. C. Goodman,
1
Yu. Gornushkin,
18
P. Gouffon,
26
E. Grashorn,
22
N. Grossman,
11
J. J. Grudzinski,
1
K. Grzelak,
23
V. Guarino,
1
A. Habig,
22
R. Halsall,
25
J. Hanson,
5
D. Harris,
11
P. G. Harris,
29
J. Hartnell,
25,23
E. P. Hartouni,
20
R. Hatcher,
11
K. Heller,
21
N. Hill,
1
Y. Ho,
10,h
C. Howcroft,
5,6
J. Hylen,
11
M. Ignatenko,
18
D. Indurthy,
31
G. M. Irwin,
28
C. James,
11
L. Jenner,
33
D. Jensen,
11
T. Joffe-Minor,
1
T. Kafka,
32
H. J. Kang,
28
S. M. S. Kasahara,
21
J. Kilmer,
11
H. Kim,
5
G. Koizumi,
11
S. Kopp,
31
M. Kordosky,
33,31
D. J. Koskinen,
33,22
M. Kostin,
31,i
D. A. Krakauer,
1
S. Kumaratunga,
21
A. S. Ladran,
20
K. Lang,
31
C. Laughton,
11
A. Lebedev,
12
R. Lee,
12,j
W. Y. Lee,
10,k
M. A. Libkind,
20
J. Liu,
31
P. J. Litchfield,
21,25
R. P. Litchfield,
23
N. P. Longley,
21
P. Lucas,
11
W. Luebke,
13
S. Madani,
25
E. Maher,
21
V. Makeev,
11,15
W. A. Mann,
32
A. Marchionni,
11
A. D. Marino,
11
M. L. Marshak,
21
J. S. Marshall,
6
J. McDonald,
24
A. McGowan,
1,21
J. R. Meier,
21
G. I. Merzon,
19
M. D. Messier,
14,12
D. G. Michael,
5
R. H. Milburn,
32
J. L. Miller,
17,14,l
W. H. Miller,
21
S. R. Mishra,
27,12
P. S. Miyagawa,
23
C. Moore,
11
J. Morfı
́
n,
11
R. Morse,
29
L. Mualem,
21
S. Mufson,
14
S. Murgia,
28
M. J. Murtagh,
4,l
J. Musser,
14
D. Naples,
24
C. Nelson,
11
J. K. Nelson,
35,11,21
H. B. Newman,
5
F. Nezrick,
11
R. J. Nichol,
33,m
T. C. Nicholls,
25
J. P. Ochoa-Ricoux,
5
J. Oliver,
12
W. P. Oliver,
32
V. A. Onuchin,
15
T. Osiecki,
31
R. Ospanov,
31
J. Paley,
14
V. Paolone,
24
A. Para,
11
T. Patzak,
9,32
Z. Pavlovich,
31
G. F. Pearce,
25
N. Pearson,
21
C. W. Peck,
5
C. Perry,
23
E. A. Peterson,
21
D. A. Petyt,
21,25,23
H. Ping,
36
R. Piteira,
9
A. Pla-Dalmau,
11
R. K. Plunkett,
11
L. E. Price,
1
M. Proga,
31
D. R. Pushka,
11
D. Rahman,
21
R. A. Rameika,
11
T. M. Raufer,
23
A. L. Read,
11
B. Rebel,
11,14
D. E. Reyna,
1
C. Rosenfeld,
27
H. A. Rubin,
13
K. Ruddick,
21
V. A. Ryabov,
19
R. Saakyan,
33
M. C. Sanchez,
12,32
N. Saoulidou,
11,2
J. Schneps,
32
P. V. Schoessow,
1
P. Schreiner,
3
R. Schwienhorst,
21
V. K. Semenov,
15
S.-M. Seun,
12
P. Shanahan,
11
P. D. Shield,
23
W. Smart,
11
V. Smirnitsky,
16
C. Smith,
33,29,5
P. N. Smith,
29
A. Sousa,
32
B. Speakman,
21
P. Stamoulis,
2
A. Stefanik,
11
P. Sullivan,
23
J. M. Swan,
20
P. A. Symes,
29
N. Tagg,
23
R. L. Talaga,
1
E. Tetteh-Lartey,
30
J. Thomas,
33,23,11
J. Thompson,
24,l
M. A. Thomson,
6
J. L. Thron,
1,n
R. Trendler,
11
J. Trevor,
5
I. Trostin,
16
V. A. Tsarev,
19
G. Tzanakos,
2
J. Urheim,
14,21
P. Vahle,
33,31
M. Vakili,
30
K. Vaziri,
11
C. Velissaris,
36
V. Verebryusov,
16
B. Viren,
4
L. Wai,
28,o
C. P. Ward,
6
D. R. Ward,
6
M. Watabe,
30
A. Weber,
23,25
R. C. Webb,
30
A. Wehmann,
11
N. West,
23
C. White,
13
R. F. White,
29
S. G. Wojcicki,
28
D. M. Wright,
20
Q. K. Wu,
27
W. G. Yan,
8
T. Yang,
28
F. X. Yumiceva,
35
J. C. Yun,
11
H. Zheng,
5
M. Zois,
2
and R. Zwaska
31,i
(MINOS Collaboration)
1
Argonne National Laboratory, Argonne, Illinois 60439, USA
2
Department of Physics, University of Athens, GR-15771 Athens, Greece
3
Physics Department, Benedictine University, Lisle, Illinois 60532, USA
4
Brookhaven National Laboratory, Upton, New York 11973, USA
5
Lauritsen Lab, California Institute of Technology, Pasadena, California 91125, USA
6
Department of Physics, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom
7
Universidade Estadual de Campinas, IF-UNICAMP, CP 6165, 13083-970, Campinas, SP, Brazil
8
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, China
9
APC –Colle
`
ge de France, 11 Place Marcelin Berthelot, F-75231 Paris Cedex 05, France
10
Physics Department, Columbia University, New York, New York 10027, USA
11
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
12
High Energy Physics Lab, Harvard University, Cambridge, Massachusetts 02138, USA
13
Physics Division, Illinois Institute of Technology, Chicago, Illinois 60616, USA
14
Physics Department, Indiana University, Bloomington, Indiana 47405, USA
15
Institute for High Energy Physics, Protvino, Moscow Region RU-140284, Russia
PHYSICAL REVIEW D
73,
072002 (2006)
1550-7998
=
2006
=
73(7)
=
072002(18)$23.00
072002-1
©
2006 The American Physical Society
16
High Energy Experimental Physics Department, Institute of Theoretical
and Expermental Physics, B. Cheremushkinskaya, 25, 117218 Moscow, Russia
17
Physics Department, James Madison University, Harrisonburg, Virginia 22807, USA
18
Joint Institute for Nuclear Research, Dubna, Moscow Region, RU-141980, Russia
19
Nuclear Physics Department, Lebedev Physical Inst., Leninsky Prospect 53, 117924 Moscow, Russia
20
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
21
University of Minnesota, Minneapolis, Minnesota 55455, USA
22
Department of Physics, University of Minnesota –Duluth, Duluth, Minnesota 55812, USA
23
Sub-deptartment of Particle Physics, University of Oxford, Denys Wilkinson Bldg, Keble Road, Oxford OX1 3RH, United Kingdom
24
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
25
Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom
26
Instituto de Fı
́
sica, Universidade de Sa
̃
o Paulo, CP 66318, 05315-970, Sa
̃
o Paulo, SP, Brazil
27
Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA
28
Department of Physics, Stanford University, Stanford, California 94305, USA
29
Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom
30
Physics Department, Texas A&M University, College Station, Texas 77843, USA
31
Department of Physics, University of Texas, 1 University Station, Austin, Texas 78712, USA
32
Physics Department, Tufts University, Medford, Massachusetts 02155, USA
33
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
34
Physics Department, Western Washington University, Bellingham, Washington 98225, USA
35
Department of Physics, College of William & Mary, Williamsburg, Virginia 23187, USA
36
Physics Department, University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 15 December 2005; published 6 April 2006)
The complete 5.4 kton MINOS far detector has been taking data since the beginning of August 2003 at a
depth of 2070 meters water-equivalent in the Soudan mine, Minnesota. This paper presents the first
MINOS observations of
and
charged-current atmospheric neutrino interactions based on an
exposure of 418 days. The ratio of upward- to downward-going events in the data is compared to the
Monte Carlo expectation in the absence of neutrino oscillations, giving
R
data
up
=
down
=R
MC
up
=
down
0
:
62
0
:
19
0
:
14
stat
:
0
:
02
sys
:
. An extended maximum likelihood analysis of the observed
L=E
distributions
excludes the null hypothesis of no neutrino oscillations at the 98% confidence level. Using the curvature of
the observed muons in the 1.3 T MINOS magnetic field
and
interactions are separated. The ratio of
to
events in the data is compared to the Monte Carlo expectation assuming neutrinos and
antineutrinos oscillate in the same manner, giving
R
data
=
=R
MC
=
0
:
96
0
:
38
0
:
27
stat
:
0
:
15
sys
:
, where
the errors are the statistical and systematic uncertainties. Although the statistics are limited, this is the first
direct observation of atmospheric neutrino interactions separately for
and
.
DOI:
10.1103/PhysRevD.73.072002
PACS numbers: 14.60.Pq
I. INTRODUCTION
Over the course of the past ten years the deficit of muon
neutrinos from cosmic-ray showers in the atmosphere has
been firmly established by the Super-Kamiokande experi-
ment [1–6] and confirmed by the MACRO [7] and Soudan
2 [8] experiments. The favored interpretation of the data
is
$
neutrino oscillations. Recent results from
the Super-Kamiokande experiment [9] provide direct
a
Now at Department of Physics, National Technical University of Athens, GR-15780 Athens, Greece.
g
Now at Holy Cross College, Notre Dame, IN 46556, USA.
e
Now at Math, Science and Technology Department, University of Minnesota– Crookston, Crookston, MN 56716, USA.
o
Now at Stanford Linear Accelerator Center, Stanford, CA 94309, USA.
d
Now at APC–Colle
`
ge de France, 11 Place Marcelin Berthelot, F-75231 Paris Cedex 05, France.
c
Now at Division of High Energy Physics, U.S. Department of Energy, Germantown, MD 20874, USA.
f
Now at Physics Department, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kindom.
b
Now at GE Healthcare, Florence SC 29501, USA.
n
Now at Nuclear Nonproliferation Division, Threat Reduction Directorate, Los Alamos National Laboratory, Los Alamos, NM
87545, USA.
m
Now at Department of Physics, Pennsylvania State University, University Park, PA 16802, USA.
l
Deceased.
k
Now at Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
j
Now at Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA 02420, USA.
i
Now at Fermi National Accelerator Laboratory, Batavia, IL 60510, USA.
h
Now at Department of Radiation Oncology, Beth Israel Medical Center, NY, NY 10003, USA.
P. ADAMSON
et al.
PHYSICAL REVIEW D
73,
072002 (2006)
072002-2
evidence for atmospheric neutrino oscillations and yield
best fit oscillation parameters of
m
2
23
;
sin
2
2
23
0
:
0024 eV
2
;
1
:
0
, where
m
2
23
j
m
2
3
m
2
2
j
. Results
from the K2K experiment [10] provide further confirma-
tion of the
$
oscillation hypothesis.
The 5.4 kiloton (kt) mass of the recently constructed
MINOS (Main Injector Neutrino Oscillation Search) far
detector [11] is much less than the
25 kt
fiducial mass of
the Super-Kamiokande detector. However, it does possess
one unique advantage, namely, it is the first large deep
underground detector to have a magnetic field. This allows
studies of neutrino flavor oscillations for neutrinos and
antineutrinos separately by identifying the charge of
muons produced in charged-current
and
interac-
tions. A separate measurement of
and
oscillations
could provide constraints on
CPT
violating models [12,13]
which have been invoked to accommodate simultaneously
the solar, atmospheric and LSND [14] neutrino oscillation
data. It should be noted that a number of recent studies
have indicated difficulties with the
CPT
violating models
(see for example [15]). Nevertheless, a direct measurement
of
and
oscillations is of interest. In addition, MINOS
is unique in its ability to provide an accurate measurement
of the neutrino energy and direction for all contained-
vertex
charged-current (CC) interactions.
This paper presents first results on atmospheric neutri-
nos from the MINOS experiment. Here, only results from
=
CC events with neutrino interaction vertices con-
tained inside the detector volume are considered; results
from events where the neutrino interacts in the surrounding
rock will be the subject of a separate publication. The data
used were recorded between August 2003 and February
2005 and correspond to a live time of 418 days giving an
exposure of 6.18 kiloton years (4.54 kiloton years fiducial).
The data are compared to the expectation in the absence of
neutrino oscillations and the favored hypothesis of
$
oscillations with
m
2
23
0
:
0024 eV
2
and
sin
2
2
23
1
:
0
. The first direct results showing charge-separated
and
atmospheric neutrino interactions are presented.
II. THE MINOS DETECTOR
The MINOS far detector is located at a depth of 2070 -
meters-water-equivalent (mwe) in the Soudan mine,
Northern Minnesota. The far detector is a steel-scintillator
sampling calorimeter consisting of two supermodules
(SM) separated by a gap of 1.1 m. The detector consists
of octagonal planes of 2.54 cm thick steel followed by
planes of 1 cm thick extruded polystyrene scintillators
and a 2 cm wide air gap. The first and second SMs are
comprised of 248 and 236 scintillator planes, respectively.
Each SM is magnetized to an average value of 1.3 T by a
15 kA current loop which runs through the coil hole along
the detector central axis and returns below the detector.
Each scintillator plane is made up of 192 strips of width
4.1 cm and of length between 3.4 m and 8.0 m depending
on position in the plane. The strips in alternating planes are
oriented at
45
to the vertical thereby providing two
orthogonal coordinates.
1
The scintillation light is collected
using wavelength shifting (WLS) fibers embedded within
the scintillator strips. The WLS fibers are coupled to clear
optical fibers at both ends of a strip and are read out using
16-pixel multi-anode photomultiplier tubes (PMTs). The
signals from eight strips, separated by approximately 1 m
within the same plane, are optically summed (multiplexed)
and read out by a single PMT pixel. The multiplexing
pattern is different for the two sides of the detector, which,
for a single hit, enables the resulting eightfold ambiguity to
be resolved. For all types of events, the ambiguities are
efficiently resolved in software using additional informa-
tion from timing and event topology.
The detector is optimized for detecting beam neutrinos
coming from the direction of Fermilab. For the study of
atmospheric neutrinos the planar structure presents a par-
ticular problem: cosmic-ray muons traveling almost paral-
lel to the scintillator planes can penetrate deep into the
detector by traveling in the steel or air between the planes.
To reject this source of background a scintillator veto
shield surrounds the upper part of the main detector. The
veto shield is constructed from the same scintillator mod-
ules as used in the main detector but with the orientation of
strips aligned along the
z
axis. The veto shield comprises a
‘‘ceiling’’ section above the detector, consisting of two
scintillator layers, and ‘‘wall’’ sections along each of the
two sides of the detector formed from a single scintillator
layer.
A. Data acquisition and trigger
The output signals from each PMT pixel are digitized
and time-stamped (with a 1.5625 ns precision) by the
VME-based front-end electronics. The signals from the
pixels are digitized by 14-bit analogue-to-digital convert-
ers (ADC) when the dynode signal from the PMTexceeds a
programmable threshold, corresponding to approximately
one third of a photo-electron (PE). To reduce the data flow,
the pedestal corrected signals are only written to the data
acquisition output buffers if two out of 36 channels on the
same readout board are above threshold. These 36 channels
correspond to the readout on one side of the detector from a
contiguous group of either 20 or 24 planes. The raw data
rate is approximately
8MBs
1
. The raw data are trans-
ferred to a personal-computer-based trigger farm where the
data are divided into blocks bounded by regions of 100
clock ticks (156 ns) or more where no detector activity has
1
The MINOS right-handed coordinate system has the
z
axis
defined along the detector axis pointing away from Fermilab and
the
y
axis vertical. The alternating scintillator planes provide
measurements of the
U
and
V
coordinates which are related to
x
and
y
by
U
1
2
p
x
y
and
V
1
2
p
y
x
.
FIRST OBSERVATIONS OF SEPARATED ATMOSPHERIC
...
PHYSICAL REVIEW D
73,
072002 (2006)
072002-3
been recorded. The primary trigger algorithm, applied to
these blocks of data, requires there to be activity in at least
four planes out of any contiguous group of five planes. The
veto shield is read out in the same manner as the main
detector except that the two out of 36 requirement is not
applied and the dynode threshold is set to a level corre-
sponding to approximately one and a half photo-electrons.
The MINOS far detector front-end electronics and data
acquisition system are described in detail in [16,17].
B. Detector calibration
A minimum ionizing particle crossing at normal inci-
dence to a plane gives a combined signal of approximately
ten photo-electrons registered by the PMTs at the two ends
of the strip. The detector is calibrated using both a dedi-
cated light-emitting diode (LED) system [18] and cosmic-
ray muons. The ADC to PE calibration is performed using
the LED system and the cosmic-ray muon sample is then
used to give a uniform response across the detector. From
studies of cosmic-ray muons in the MINOS detector [19],
the current uncertainty in the PE calibration is 5%.
Cosmic-ray muons are also used to calibrate the recorded
times. After calibration, a single hit timing resolution of
approximately 2.3 ns is achieved. The timing calibration
tracks all hardware changes.
III. DATA AND MONTE CARLO SAMPLES
The data described in this paper were recorded in the
18 month period from August 2003 to February 2005. Only
data taken when the MINOS far detector, including the
veto shield, was fully operational are used. The final data
sample corresponds to a live time of 418 days giving an
exposure of 6.18 kiloton-years (4.54 kiloton-years
fiducial).
The selection of contained-vertex neutrino interactions
was optimized using a
GEANT 3
[20] simulation of the
MINOS detector. For the simulation of atmospheric neu-
trino events the 3D flux calculation of Barr
et al.
[21] was
used (Bartol 3D). The
NEUGEN3
program [22] was used to
simulate the neutrino interactions (cross sections and had-
ronic final states). The earlier 1D flux calculation from the
Bartol group [23] (Bartol 1D) and the 3D calculation of
Battistoni
et al.
[24] were used to assign systematic un-
certainties. The response of the MINOS detector to elec-
trons, muons, and hadrons has been studied in a test beam
at the CERN PS using the 12.5 ton MINOS calibration
detector [25]. The test beam detector was constructed and
read out in the same manner as the MINOS far detector.
The interactions of hadronic particles are modeled with the
GCALOR
package [26], which is found to give a reasonable
description of low energy hadronic interactions in the
MINOS calibration detector [27], rather than the default
version of
GHEISHA
(see [20] and references therein). The
‘‘SLAC version’’ [28] of
GHEISHA
, which also provides a
reasonable description of the test beam data, is used as an
alternative model for hadronic interactions. A Monte Carlo
(MC) sample of atmospheric neutrino interactions corre-
sponding to over 1000 live years was generated and used to
optimize both the reconstruction algorithms and the event
selection criteria. Two large cosmic-ray muon background
samples were generated: a sample of
19
10
6
events full
spectrum (corresponding to approximately 280 days live
time) and a further
2
10
6
events with
E
<
2 GeV
(cor-
responding to a live time of 4.1 years) as lower energy
events are an important component of the cosmic-ray muon
background to the contained-vertex atmospheric neutrino
selection. A 10% uncertainty on the normalization of the
cosmic-ray background is assigned. The error reflects the
different normalization obtained when normalizing to the
entire cosmic-ray sample or normalizing to just those
cosmic-ray muons which stop in the detector (these form
the main background to the event selection described
below). It should be noted that for the results presented
in this paper the cosmic-ray background in the selected
event sample is estimated from data. The 10% uncertainty
in the cosmic-ray normalization is only used when com-
paring data and Monte Carlo samples at various stages in
the event selection.
A. Flux normalization and systematic uncertainties
The theoretical prediction for the atmospheric neutrino
event rate has large uncertainties from the primary cosmic-
ray flux, hadron production models, and neutrino interac-
tion cross sections. The analysis of the Soudan 2
e
=
e
data [8] indicates that the combined prediction of the
Bartol 3D model [21] and the
NEUGEN3
[22] neutrino cross
section model should be scaled by
0
:
88
0
:
07
[29], where
the error is statistical and it is implicitly assumed that
atmospheric electron neutrinos are not oscillating. This
normalization result is compatible with the results from a
fit to the Soudan 2 data including oscillations. The MINOS
and Soudan 2 detectors are located in the same mine (i.e. at
the same geomagnetic latitude) and both are constructed
from steel. Consequently, for the analysis presented here
the Soudan 2 scale factor
0
:
88
0
:
07
is used to correct the
combined event rate predictions from the Bartol 3D flux
model and the
NEUGEN3
neutrino interaction model. An
additional 5% uncertainty is added in quadrature to that
estimated by the Soudan 2 Collaboration to account for
differences arising from the different energy thresholds
(300 MeV in the case of Soudan 2 compared to
500 MeV
for MINOS). Finally an additional 2.5% un-
certainty is assigned to account for the different phases in
the solar cycle for the Soudan 2 and MINOS data sets [30];
because of the relatively high neutrino energy threshold the
selected atmospheric neutrino rate in MINOS depends only
weakly on the phase in the solar cycle. The resulting total
P. ADAMSON
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systematic uncertainty on the expected event rate is esti-
mated to be 10%.
IV. EVENT RECONSTRUCTION
The MINOS detector is optimized for beam neutrinos
originating from Fermilab. Because of the curvature of the
Earth, beam neutrinos enter the detector from below the
horizontal at an angle of
3
:
3
with respect to the
z
axis. The
standard MINOS reconstruction software has been devel-
oped for these events. The analysis presented here uses
reconstruction software optimized for atmospheric neutri-
nos [31].
The first stage of the event reconstruction removes the
eightfold ambiguity in the association of raw hits to strips.
This is performed utilizing information from both strip
ends. For cosmic-ray muons, an average of 99% of the
recorded pulse height is associated with the correct strip.
At this stage the data are in the form of two 2D event views
U
z
and
V
z
. An example event display of a cosmic-
ray muon is shown in Fig. 1. Tracks and showers are
reconstructed independently in each view; the two views
are then matched to obtain a three-dimensional event. For
cosmic-ray events that leave hits in both the veto shield and
main MINOS far detector, the root-mean-square (rms)
difference in times recorded in veto shield and the detector
is 4 ns, allowing association of veto shield hits (indicated in
Fig. 1) to activity in the main detector.
A charged-current muon neutrino event is, in general,
reconstructed as a muon track and a hadronic shower. A
typical 1 GeV muon will traverse approximately 25 planes
at normal incidence. Reconstructed tracks are required to
consist of at least 8 planes (corresponding to a minimum
energy of 0.4 GeV). For muons which start and stop within
the detector volume the muon momentum is determined
from a range with a resolution of approximately
p
=p
2
0
:
06
2
0
:
045
=p
2
for muons traveling at nor-
mal incidence to the detector planes (where
p
is measured
in
GeV
=c
). The first term is dominated by fluctuations in
energy loss and the second is dominated by sampling. For
events where the muon exits the detector, the muon mo-
mentum is obtained from the curvature of the track in the
magnetic field. For the selected CC atmospheric
=
interactions, where the momentum is determined from
curvature, the average momentum resolution is approxi-
mately
2
1
=p
0
:
1
2
0
:
3
=p
2
GeV
2
(where
p
is mea-
sured in
GeV
=c
). However, the resolution obtained from
individual events depends strongly on how much of the
trajectory of the muon is observed before it exits the
detector and on the orientation of the trajectory relative
to the local magnetic field. The hadronic energy is obtained
by summing the pulse height in a shower which is spatially
associated with the start of the track. The energy scale is
obtained from Monte Carlo samples using the
GCALOR
[26]
model of hadronic showers, which from the test beam
results is found to provide a good description of the detec-
tor response to single
and protons [27]. The hadronic
energy resolution is approximately
E
=E
0
:
55
=
E
p
,
where
E
is measured in GeV.
For the study of atmospheric neutrinos it is necessary to
determine whether the reconstructed track is upward or
downward going. A relativistic normal incidence particle
traverses ten planes in approximately 2 ns which, when
compared to the single hit resolution of 2.3 ns, is sufficient
to identify the direction of most selected events with little
ambiguity. The sense of the direction of muon tracks is
determined by comparing the hit times along the recon-
structed track with the hypotheses that it is either upward
or downward going (assuming that the particle is traveling
at the speed of light). The rms deviations of hit times about
each of the two hypotheses are calculated,
RMS
UP
and
RMS
DOWN
. The hypothesis with the smallest rms is
chosen. In addition, the magnitude of
RMS
UP
–
RMS
DOWN
provides a measure of the quality of the direction determi-
nation. To test the performance of the algorithm a sample
of stopping cosmic-ray muons is used (all of which are
z / m
0
5
10
15
20
25
30
U / m
0
1
2
3
4
5
6
7
8
z / m
0
5
10
15
20
25
30
V / m
0
1
2
3
4
5
6
7
8
x / m
-6
-4
-2
0
2
4
6
y / m
-5
-4
-3
-2
-1
0
1
2
3
4
5
FIG. 1. An example of a cosmic-ray muon event in the MINOS
far detector. The detector readout corresponds to the two or-
thogonal
U
z
and
V
z
views. The size of the points gives an
indication of the pulse height for each scintillator strip hit. The
large dark points shown in the
x
y
view indicate in-time
activity in the veto shield.
FIRST OBSERVATIONS OF SEPARATED ATMOSPHERIC
...
PHYSICAL REVIEW D
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traveling downward). Figure 2 shows a comparison of the
data and Monte Carlo efficiencies for correctly identifying
a stopping muon as downward going as a function of the
number of planes the track crosses. The average efficiency
is above 94% for even the shortest tracks and rapidly
increases to better than 99% for events with hits in 12
planes. The efficiency in data agrees with that from
Monte Carlo samples to better than 1%.
The curvature of
=
tracks in the magnetic field
allows the charge sign to be determined. Figure 3 shows the
distribution of the reconstructed charge divided by mo-
mentum,
Q=p
, divided by its error, for cosmic-ray muons
that stop in the detector. Two peaks, corresponding to
and
events, are clearly seen. The widths of the two
peaks in data and MC agree to better than 2.5%. For the
event samples considered here, the
=
charge is
cleanly identified over the approximate momentum range
1–10 GeV. The efficiency decreases for low momentum
tracks due to the limited number of planes crossed. For
high momentum tracks, which typically leave the detector,
the charge identification efficiency decreases as only the
limited curvature at the start of the track is measured.
V. EVENT SELECTION
At a depth of 2070 mwe the cosmic-ray muon rate is
approximately 50 000 events per day in the MINOS detec-
tor. This rate should be compared to the expected signal
rate of
0
:
54
0
:
05
atmospheric CC
=
interactions
per day,
2
where the uncertainty is from the 10% uncertainty
in the expected event rate (discussed in Sec. III A). In order
to achieve a signal-to-background ratio of ten-to-one it is
necessary to identify the signal events efficiently while
reducing the background by a factor of
10
6
. The event
selection is designed to identify both fully contained
(FC) and partially contained (PC)
=
events. In FC
events the entire event is contained within the fiducial
volume. In PC events the neutrino vertex is within the
fiducial volume but the produced muon exits the detector.
A. Preselection
Candidate CC
neutrino interactions are required to
have a reconstructed track passing some basic quality
requirements. The majority of the background is rejected
by event containment requirements which are applied at
both the hit and reconstructed track level. The sense of the
track direction (up/down) is determined from timing as
described previously. The start of the track, which is con-
sidered to be the neutrino interaction vertex, is required to
lie within the detector fiducial volume. The fiducial volume
is defined as the octagonal region which is at least 50 cm
from the detector edges in the
xy
plane and at least five
planes from the start and end of either SM. In addition, the
region within 40 cm of the axis of the coil hole, which has a
diameter of 25 cm, is excluded from the fiducial volume.
This cut is enlarged to 1 m in the first and last ten planes of
the detector. The event sample is subdivided into FC and
PC events depending on whether the end of the track also
lies within the fiducial region.
Event containment cuts are also made at the hit level to
reduce the sensitivity to possible reconstruction errors
where not all hits are correctly associated with the recon-
structed track. For this purpose, the fiducial volume re-
quirement of 50 cm from the detector edges is relaxed to
30 cm. In order to apply the containment cuts at the hit
level it is necessary to convert the two-dimensional coor-
dinates of a single hit into a point in space. This conversion
is achieved by using the mean value of the orthogonal
(
U=V
) coordinate in the surrounding two planes. Hits out-
(Q/p)
σ
(Q/p)/
-20
-15
-10
-5
0
5
10
15
20
Events
0
5000
10000
15000
20000
25000
30000
Data
+
μ
MC
-
μ
MC
+
μ
+
-
μ
MC
MINOS
FIG. 3. The reconstructed distribution of
Q=p
=
Q=p
for
stopping muon events in data and Monte Carlo samples.
Track Length/Planes
6
8
10
12
14
16
18
20
22
Direction Efficiency
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
MINOS
Data
Cosmic-ray MC
FIG. 2 (color online). The efficiency for correctly reconstruct-
ing stopping muon events as downward going as a function of
the number of planes in the reconstructed track.
2
The signal rate of
0
:
54
0
:
05
(no oscillations) corresponds
to
=
CC interactions where the muon deposits energy in at
least eight planes (before fiducial cuts).
P. ADAMSON
et al.
PHYSICAL REVIEW D
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072002 (2006)
072002-6
side the fiducial volume are then assigned to the nearest
octagonal edge/SM end. Edges/ends with summed pulse
height equivalent to more than six PEs outside the fiducial
region are tagged as being uncontained. Candidate FC (PC)
events are required to have no (one) such region. The
containment cuts reject approximately 99.9% of the
cosmic-ray background while retaining 77% of CC
=
interactions in the detector volume. The ineffi-
ciency for signal events is primarily a fiducial effect; the
containment cuts retain 99% of CC
=
interactions in
the fiducial region which produce a muon which spans at
least six planes.
Candidate FC events are required to have a recon-
structed track consisting of hits in at least eight planes.
The PC event selection criteria are optimized separately for
upward- and downward-going events as the backgrounds
for the two categories are very different. To ensure the
track direction is well determined, candidate PC events are
required to have a track of at least 1 m in length and which
consists of hits in at least ten planes.
B. Fully contained and downward partially contained
event selection
The dominant backgrounds in the FC and downward PC
samples arise from steep cosmic-ray muons which enter
the detector at small angles to the detector planes. By
traveling in the steel or air between the scintillator planes,
such events can penetrate a significant distance into the
fiducial volume before leaving a detectable signal. The
selection of FC and downward-traveling PC CC
=
interactions aims to greatly reduce this background and
proceeds in four stages:
(i)
Cosmic-ray rejection (trace cut). —
The recon-
structed track is extrapolated back to the outside
of the detector and the distance traversed in the
direction perpendicular to the detector planes is
calculated,
Z
. Events with small values of
Z
correspond to steep tracks which when extrapolated
to the detector edge traverse only a few scintillator
planes. Figure 4 shows the
Z
distribution for MC
cosmic-ray muons and CC
=
interactions.
Events are rejected if
Z
<
0
:
5m
. Figure 4 also
shows the
Z
distribution for data which is in
reasonable agreement with the MC expectation.
(ii)
Event topology. —
About half of the remaining
background consists of cosmic-ray muon tracks
that bend in the magnetic field and turn over in
the
z
direction. Such events will leave hits in two
separate positions in a particular plane. In addition,
these events typically have large pulse height in the
plane where the muon turns around in
z
. This
category of background event is rejected using the
pulse-height weighted deviations of the hits in the
U
z
and
V
z
views from the fitted track. The
pulse-height weighted mean,
h
UV
i
, and the pulse-
height weighted rms deviation of hits from the
track,
h
2
UV
i
1
=
2
, are calculated. Events are rejected
if there is large scatter about the track,
h
2
UV
i
1
=
2
>
0
:
5m
, or if the pulse-height weighted mean devia-
tion from the track lies significantly above the
reconstructed track,
h
UV
i
>
0
:
25 m
. These em-
pirically determined cuts are applied separately to
the hits in both the
U
z
and
V
z
views. In
addition, the event vertex is defined as the first hit
on the track taking the highest end (largest
y
) as the
start of the track. The maximum displacement from
the event vertex of the hit strips which lie within
4
planes of the event vertex is found,
max
R
.
Events are rejected if
max
R
>
1
:
25 m
.
(iii)
Vertex pulse height/direction. —
After the topology
cut, the signal-to-background ratio is approxi-
mately
1:5
. The remaining background consists of
steep cosmic-ray muons which travel nearly paral-
lel to the scintillator planes and therefore tend to
give a large pulse-height signal in a single plane
near the beginning of the track. These events are
often poorly reconstructed due to the difficulties of
reconstructing tracks for events at small angles to
the detector planes. Figure 5 shows, for signal and
background, the total pulse height in the event
vertex region,
Q
vtx
, plotted against the cosine of
reconstructed zenith angle at the highest end of the
track
3
and the modulus of reconstructed track di-
rection cosine with respect to the
z
axis,
j
cos
z
j
.
/ m
Z
∆
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Events
-1
10
1
10
2
10
3
10
4
10
5
10
data
μ
MC cosmic
ν
MC atmos
MINOS
FIG. 4. The reconstructed
Z
distribution for events passing
the containment cuts. The solid histogram indicates the MC
expectation for cosmic-ray background. The points with error
bars show the observed data. The dashed histogram indicates the
expected distribution for atmospheric neutrino events (without
oscillations).
3
The zenith angle,
zen
, is defined as
minus the angle
between the reconstructed track direction and the local vertical
(the
y
-axis). Negative values of the cosine of the zenith angle
correspond to tracks which are reconstructed as upward going.
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