Observation of Muon Neutrino Disappearance with the MINOS Detectors
in the NuMI Neutrino Beam
D. G. Michael,
5,
*
P. Adamson,
11,21,30
T. Alexopoulos,
36
W. W. M. Allison,
24
G. J. Alner,
26
K. Anderson,
11
C. Andreopoulos,
26,2
M. Andrews,
11
R. Andrews,
11
K. E. Arms,
22
R. Armstrong,
14
C. Arroyo,
29
D. J. Auty,
30
S. Avvakumov,
29
D. S. Ayres,
1
B. Baller,
11
B. Barish,
5
M. A. Barker,
24
P. D. Barnes, Jr.,
20
G. Barr,
24
W. L. Barrett,
34
E. Beall,
1,22
B. R. Becker,
22
A. Belias,
26
T. Bergfeld,
28
R. H. Bernstein,
11
D. Bhattacharya,
25
M. Bishai,
4
A. Blake,
6
V. Bocean,
11
B. Bock,
23
G. J. Bock,
11
J. Boehm,
12
D. J. Boehnlein,
11
D. Bogert,
11
P. M. Border,
22
C. Bower,
14
S. Boyd,
25
E. Buckley-Geer,
11
C. Bungau,
30
A. Byon-Wagner,
11
A. Cabrera,
24
J. D. Chapman,
6
T. R. Chase,
22
D. Cherdack,
33
S. K. Chernichenko,
15
S. Childress,
11
B. C. Choudhary,
11,5
J. H. Cobb,
24
J. D. Cossairt,
11
H. Courant,
22
D. A. Crane,
1
A. J. Culling,
6
J. W. Dawson,
1
J. K. de Jong,
13
D. M. DeMuth,
22
A. De Santo,
24
M. Dierckxsens,
4
M. V. Diwan,
4
M. Dorman,
24,26
G. Drake,
1
D. Drakoulakos,
2
R. Ducar,
11
T. Durkin,
26
A. R. Erwin,
36
C. O. Escobar,
7
J. J. Evans,
24
O. D. Fackler,
20
E. Falk Harris,
30
G. J. Feldman,
12
N. Felt,
12
T. H. Fields,
1
R. Ford,
11
M. V. Frohne,
3
H. R. Gallagher,
33,24,1,22
M. Gebhard,
14
G. A. Giurgiu,
1
A. Godley,
28
J. Gogos,
22
M. C. Goodman,
1
Yu. Gornushkin,
18
P. Gouffon,
27
R. Gran,
23
E. Grashorn,
22,23
N. Grossman,
11
J. J. Grudzinski,
1
K. Grzelak,
24
V. Guarino,
1
A. Habig,
23
R. Halsall,
26
J. Hanson,
5
D. Harris,
11
P. G. Harris,
30
J. Hartnell,
26,24
E. P. Hartouni,
20
R. Hatcher,
11
K. Heller,
22
N. Hill,
11
Y. Ho,
10
A. Holin,
21
C. Howcroft,
5,6
J. Hylen,
11
M. Ignatenko,
18
D. Indurthy,
32
G. M. Irwin,
29
M. Ishitsuka,
14
D. E. Jaffe,
12
C. James,
11
L. Jenner,
21
D. Jensen,
11
T. Joffe-Minor,
1
T. Kafka,
33
H. J. Kang,
29
S. M. S. Kasahara,
22
J. Kilmer,
11
H. Kim,
5
M. S. Kim,
25
G. Koizumi,
11
S. Kopp,
32
M. Kordosky,
21,32
D. J. Koskinen,
21,23
M. Kostin,
32
S. K. Kotelnikov,
19
D. A. Krakauer,
1
A. Kreymer,
11
S. Kumaratunga,
22
A. S. Ladran,
20
K. Lang,
32
C. Laughton,
11
A. Lebedev,
12
R. Lee,
12
W. Y. Lee,
10
M. A. Libkind,
20
J. Ling,
28
J. Liu,
32
P. J. Litchfield,
22,26
R. P. Litchfield,
24
N. P. Longley,
22
P. Lucas,
11
W. Luebke,
13
S. Madani,
26
E. Maher,
22
V. Makeev,
11,15
W. A. Mann,
33
A. Marchionni,
11
A. D. Marino,
11
M. L. Marshak,
22
J. S. Marshall,
6
N. Mayer,
23
J. McDonald,
25
A. M. McGowan,
1,22
J. R. Meier,
22
G. I. Merzon,
19
M. D. Messier,
14,12
R. H. Milburn,
33
J. L. Miller,
17,14,
*
W. H. Miller,
22
S. R. Mishra,
28,12
A. Mislivec,
23
P. S. Miyagawa,
24
C. D. Moore,
11
J. Morfı
́
n,
11
R. Morse,
30
L. Mualem,
22
S. Mufson,
14
S. Murgia,
29
M. J. Murtagh,
4,
*
J. Musser,
14
D. Naples,
25
C. Nelson,
11
J. K. Nelson,
35,11,22
H. B. Newman,
5
F. Nezrick,
11
R. J. Nichol,
21
T. C. Nicholls,
26
J. P. Ochoa-Ricoux,
5
J. Oliver,
12
W. P. Oliver,
33
V. A. Onuchin,
15
T. Osiecki,
32
R. Ospanov,
32
J. Paley,
14
V. Paolone,
25
A. Para,
11
T. Patzak,
9,33
Z
ˇ
. Pavlovic
́
,
32
G. F. Pearce,
26
N. Pearson,
22
C. W. Peck,
5
C. Perry,
24
E. A. Peterson,
22
D. A. Petyt,
22,26,24
H. Ping,
36
R. Piteira,
9
R. Pittam,
24
A. Pla-Dalmau,
11
R. K. Plunkett,
11
L. E. Price,
1
M. Proga,
32
D. R. Pushka,
11
D. Rahman,
22
R. A. Rameika,
11
T. M. Raufer,
24
A. L. Read,
11
B. Rebel,
11,14
J. Reichenbacher,
1
D. E. Reyna,
1
C. Rosenfeld,
28
H. A. Rubin,
13
K. Ruddick,
22
V. A. Ryabov,
19
R. Saakyan,
21
M. C. Sanchez,
12,33
N. Saoulidou,
11,2
J. Schneps,
33
P. V. Schoessow,
1
P. Schreiner,
3
R. Schwienhorst,
22
V. K. Semenov,
15
S.-M. Seun,
12
P. Shanahan,
11
P. D. Shield,
24
W. Smart,
11
V. Smirnitsky,
16
C. Smith,
21,30,5
P. N. Smith,
30
A. Sousa,
24,33
B. Speakman,
22
P. Stamoulis,
2
A. Stefanik,
11
P. Sullivan,
24
J. M. Swan,
20
P. A. Symes,
30
N. Tagg,
33,24
R. L. Talaga,
1
A. Terekhov,
19
E. Tetteh-Lartey,
31
J. Thomas,
21,24,11
J. Thompson,
25,
*
M. A. Thomson,
6
J. L. Thron,
1
G. Tinti,
24
R. Trendler,
11
J. Trevor,
5
I. Trostin,
16
V. A. Tsarev,
19
G. Tzanakos,
2
J. Urheim,
14,22
P. Vahle,
21,32
M. Vakili,
31
K. Vaziri,
11
C. Velissaris,
36
V. Verebryusov,
16
B. Viren,
4
L. Wai,
29
C. P. Ward,
6
D. R. Ward,
6
M. Watabe,
31
A. Weber,
24,26
R. C. Webb,
31
A. Wehmann,
11
N. West,
24
C. White,
13
R. F. White,
30
S. G. Wojcicki,
29
D. M. Wright,
20
Q. K. Wu,
28
W. G. Yan,
8
T. Yang,
29
F. X. Yumiceva,
35
J. C. Yun,
11
H. Zheng,
5
M. Zois,
2
and R. Zwaska
11,32
(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 Laboratory, California Institute of Technology, Pasadena, California 91125, USA
6
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 a
̃
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
PRL
97,
191801 (2006)
PHYSICAL REVIEW LETTERS
week ending
10 NOVEMBER 2006
0031-9007
=
06
=
97(19)
=
191801(6)
191801-1
©
2006 The American Physical Society
11
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
12
Department of Physics, 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
16
High Energy Experimental Physics Department, Institute of Theoretical and Experimental 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 Institute, Leninsky Prospect 53, 117924 Moscow, Russia
20
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
21
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
22
University of Minnesota, Minneapolis, Minnesota 55455, USA
23
Department of Physics, University of Minnesota –Duluth, Duluth, Minnesota 55812, USA
24
Subdepartment of Particle Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom
25
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
26
Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom
27
Instituto de Fı
́
sica, Universidade de Sa
̃
o Paulo, CP 66318, 05315-970, Sa
̃
o Paulo, SP, Brazil
28
Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA
29
Department of Physics, Stanford University, Stanford, California 94305, USA
30
Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom
31
Physics Department, Texas A&M University, College Station, Texas 77843, USA
32
Department of Physics, University of Texas, 1 University Station, Austin, Texas 78712, USA
33
Physics Department, Tufts University, Medford, Massachusetts 02155, USA
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 4 August 2006; published 8 November 2006)
This Letter reports results from the MINOS experiment based on its initial exposure to neutrinos from
the Fermilab NuMI beam. The rates and energy spectra of charged current
interactions are compared in
two detectors located along the beam axis at distances of 1 and 735 km. With
1
:
27
10
20
120 GeV
protons incident on the NuMI target, 215 events with energies below 30 GeV are observed at the Far
Detector, compared to an expectation of
336
14
events. The data are consistent with
disappearance
via oscillations with
j
m
2
32
j
2
:
74
0
:
44
0
:
26
10
3
eV
2
and
sin
2
2
23
>
0
:
87
(68% C.L.).
DOI:
10.1103/PhysRevLett.97.191801
PACS numbers: 14.60.Lm, 14.60.Pq, 29.27.
a, 29.30.
h
There is now substantial evidence [
1
–
8
] that the proper
description of neutrinos involves a rotation between mass
and flavor eigenstates governed by the
3
3
Pontecorvo-
Maki-Nakagawa-Sakata matrix [
9
,
10
]. The parameters of
this mixing matrix, three angles and a phase, as well as the
mass differences between the three mass eigenstates, must
be determined experimentally. The Main Injector neutrino
oscillation search (MINOS) experiment has been designed
to study the flavor composition of a beam of muon neu-
trinos as it travels between the Near Detector (ND) at
Fermilab at 1 km from the target and the Far Detector
(FD) in the Soudan iron mine in Minnesota at 735 km from
the target. From the comparison of the reconstructed neu-
trino energy spectra at the near and far locations, the
oscillation parameters
j
m
2
32
j
and
sin
2
2
23
are extracted.
The neutrinos at the Main Injector (NuMI) neutrino
beam is produced using 120 GeV protons from the Main
Injector. The protons are delivered in
10
s
spills with up
to
3
:
0
10
13
protons per spill. The extracted protons are
bent downward by 3.3
to point at the MINOS detectors.
The global positioning system defined the survey beam
direction to within 12 m of the FD [
11
]. Positively charged
particles produced by the proton beam in the 95.4 cm long
target (mainly
and
K
) are focused by two pulsed
parabolic horns spaced 10 m apart and allowed to decay
in a 675 m long, 2 m diameter, evacuated decay pipe [
12
].
The proton beam [
13
] and tertiary muon beam [
14
] are
monitored on a pulse-by-pulse basis. The target position
relative to the first horn and the horn current are variable
[
15
]. For the majority of the running period described here,
the target was inserted 50.4 cm into the first horn to max-
imize neutrino production in the 1– 3 GeV energy range. A
total of
1
:
27
10
20
protons on target (POT) were taken in
this position and used for this analysis. The charged current
(CC) neutrino event yields at the ND are predicted to be
92.9%
, 5.8%
, 1.2%
e
, and 0.1%
e
. The data
described here were recorded between May 2005 and
February 2006. The average live time of the FD was
99.0% during this period. About one-third of the total
ND events provided a sufficiently large data set for this
analysis of
10
6
events which were sampled throughout
the run period.
PRL
97,
191801 (2006)
PHYSICAL REVIEW LETTERS
week ending
10 NOVEMBER 2006
191801-2
Both MINOS detectors [
16
] are steel-scintillator track-
ing calorimeters [
17
] with toroidal magnetic fields averag-
ing 1.3 T [
18
]. The steel plates are 2.54 cm thick. The
scintillator planes are comprised of 4.1 cm wide and 1 cm
thick plastic strips. Each plane is oriented at 45
from
vertical and at 90
with respect to its neighbors. The light
from the scintillator is transported to the multianode pho-
tomultiplier tubes (PMTs) by embedded 1.2 mm diameter
wavelength shifting (WLS) fibers. In order to cancel the
majority of the uncertainties in the modeling of neutrino
interactions and detector response, the two MINOS detec-
tors are as similar as possible. For example, both detectors
yield 6 –7 photoelectrons (PEs) per plane for normally
incident minimum ionizing particles. However, the data
rate in the ND is
10
5
times larger than in the FD, which
has dictated certain design differences.
The 5.4 kton FD, 705 m underground, has 484 octagonal,
8 m wide instrumented planes read out at both ends via
Hamamatsu M16 PMTs [
19
]. Eight WLS fibers from strips
in the same plane, separated from each other by about 1 m,
are coupled to each pixel. The coupling pattern is different
at the two ends to allow resolution of ambiguities.
The 0.98 kton ND, 103 m underground, has 282 irregular
4
6m
2
octagonal planes. Its geometry optimizes the
containment of hadronic showers and provides sufficient
flux return to achieve a magnetic field similar to the FD.
Each strip is coupled via a WLS fiber to one pixel of a
Hamamatsu M64 PMT [
20
]. The ND readout continuously
integrates the PMT charges with a sampling rate of
53.1 MHz to allow discrimination between successive
Main Injector rf buckets.
The data acquisition [
21
–
23
] accepts data above a
threshold of 0.25 PEs. In the FD, the online trigger con-
ditions require a hit within
100
s
centered on the time of
the expected beam spill, at least 20 PEs inside a four plane
window, or 4 hits in 5 consecutive planes. In the ND, all the
data taken during the beam spill are retained. The trigger
efficiency for both detectors, estimated from Monte Carlo
(MC) simulations, exceeds 99.5% for neutrino events with
a visible energy above 0.5 GeV.
The detectors are calibrated using an
in situ
light injec-
tion system [
24
] and cosmic ray muons. Light-emitting
diode light is distributed to all the WLS fibers to track gain
changes in the PMTs and electronics. The energy deposited
by throughgoing muons is used to equalize the response of
all of the scintillator strips. After calibration, remaining
time- and position-dependent variations in the responses of
the detectors result in an uncertainty in the relative energy
scale between the two detectors of 2%. The energy scale
for single hadrons and electrons was determined from the
results of a test-beam experiment using a small, unmagne-
tized copy of the MINOS calorimeters (CalDet) [
25
].
Stopping muons are then used to relate the results from
CalDet to the response of the ND and FD. From these
studies, the uncertainty on the absolute hadronic energy
scale is estimated to be 6%.
The simulation of the production and detection of neu-
trinos commences with a model of hadron production in
the target using
FLUKA05
[
26
], which has uncertainties at
the 20% – 30% level stemming from a lack of relevant thick
target hadron production data. The shower products are
transported through the horn focusing system and decayed
in a
GEANT3
[
27
] simulation that includes the horns, beam
line material, and the decay pipe. The neutrino event
generator
NEUGEN3
[
28
] is tuned to existing CC cross-
section data where present uncertainties below 10 GeV
are at the 20% level. The products of the neutrino interac-
tion are propagated out of the iron nucleus using the
INTRANUKE
[
29
] code. Some of the energy of absorbed
pions is transferred to clusters of nucleons as motivated by
Ref. [
30
]. The response of the detector is simulated using
GEANT3
with the
GCALOR
[
31
] simulation of hadronic
interactions. The final step in the simulation chain involves
photon generation, propagation and transmission through
the WLS fiber, and conversion to photoelectrons in the
PMTs.
In CalDet,
GEANT3
with
GCALOR
is found to reproduce
the hadronic and electromagnetic (EM) responses of the
detector to single particles to 4% and 2%, respectively.
Below 10 GeV, the hadronic energy resolution was mea-
sured to be
56%
=
E
GeV
p
2%
[
32
] and the EM resolu-
tion to be
21
:
4%
=
E
GeV
p
4
:
1%
=E
GeV
[
33
]. The
muon energy resolution
E
=E
varies smoothly from
6% for
E
above 1 GeV, where most tracks are contained
and measured by range, to 13% at high energies, where the
curvature measurement is primarily used.
The initial step in the reconstruction of the FD data is the
removal of the eightfold hit-to-strip ambiguity using infor-
mation from both strip ends. In the ND, timing and spatial
information is first used to separate individual neutrino
interactions from the same spill. Subsequently, tracks are
found and fitted, and showers are reconstructed, in the
same way in both detectors. For
CC events, the total
reconstructed event energy (
E
reco
) is obtained by summing
the muon energy and the visible energy of the hadronic
system.
The FD data set was left blind until the selection proce-
dure had been defined and the prediction of the unoscil-
lated spectrum was understood. The blinding procedure hid
a substantial fraction of the FD events with the precise
fraction and energy spectrum of the hidden sample un-
known. Events are preselected in both detectors, by requir-
ing
E
reco
below 30 GeV and a negatively charged track to
suppress events that originate from
or
K
. The track
vertex must be within a fiducial volume such that cosmic
rays are rejected and the hadronic energy of the event is
contained within the volume of the detector. The event time
must fall within a
50
s
window around the spill time. The
cosmic ray background is suppressed further in the FD by
requiring the track to point within 53
of the neutrino beam
direction. This is the only significant nonbeam back-
PRL
97,
191801 (2006)
PHYSICAL REVIEW LETTERS
week ending
10 NOVEMBER 2006
191801-3
ground. The preselected
event sample is predominantly
CC with a 8.6% neutral current (NC) background estimated
from MC simulations. The fiducial mass of the FD (ND) is
72.9% (4.5%) of the total detector mass.
A particle identification parameter (PID) incorporating
probability density functions for the event length, the
fraction of energy contained in the track, and the average
track pulse height per plane provides separation of
CC
and NC events. The PID is shown in Fig.
1
for ND and FD
data overlaid with simulations of NC and CC events after
the beam reweighting procedure described below. Events
with PID above
0
:
2
(FD) and
0
:
1
(ND) are selected as
being predominantly CC in origin. These values were
optimized for both detectors such that the resulting purity
of each sample is about 98%. The efficiencies for selecting
CC events in the fiducial volume with energy below
30 GeV are 74% (FD) and 67% (ND). From the absence of
any events less than
20
s
before and less than
30
s
after
the spill time, the remaining nonbeam related background
in the FD is estimated to be less than 0.5 events (68% C.L.).
Background from
interactions in the rock surrounding
the FD is estimated from MC simulations to be below 0.4
(68% C.L.) events. The corresponding backgrounds in the
ND are negligible.
To constrain hadron production, a series of six runs of
similar exposure was taken where the position of the target
and the magnitude of the horn magnetic field were varied.
Comparisons of the ND
E
reco
spectra with MC simulations,
shown in Fig.
2
, showed an energy-dependent discrepancy
that changed with the beam settings. This implied beam
modeling, rather than detector or cross-section effects, was
the primary cause. To bring the MC simulations into better
agreement with the data, a tuning of the beam MC was
performed in which pion production off the target was
smoothly varied in transverse and longitudinal momentum
with respect to the
FLUKA05
input, as was the overall kaon
yield. In addition, the potential systematic effects of the
beam focusing, NC background,
energy scale, and off-
set were allowed to vary. All of these parameters were
found to lie within 2 standard deviations of their nominal
values. Figure
2
shows the effect of the full beam parame-
ter tuning for the
E
reco
spectra corresponding to three
different target positions. The resulting agreement is im-
proved in all beams across the 1– 30 GeV
E
reco
region.
The measurement of the
E
reco
spectrum at the ND is used
to predict the unoscillated spectrum at the FD. The oscil-
lation hypotheses are then tested relative to this prediction.
The prediction must take into account the ND and FD
spectral differences that are present, even in the absence
of oscillations, due to pion decay kinematics and beam line
geometry. These introduce a ND-FD shape difference of up
to
20%
known to an accuracy of better than 2% between
1 and 5 GeV, where the statistical power of the experiment
lies.
There are two distinct approaches to the beam spectrum
extrapolation. The ND fit method focuses on minimizing
the remaining ND data and MC differences by modifying
MC parameters associated with neutrino interactions and
detector response. The FD MC simulation is then re-
5
10
×
Events
0.0
0.5
1.0
1.5
2.0
MINOS ND
Data
Tuned MC
NC MC
PID Parameter
-1.0
-0.5
0.0
0.5
1.0
Events
0
10
20
30
40
MINOS FD
FIG. 1. Data and tuned MC predictions for the PID variable in
the ND (top) and FD (bottom). The arrows depict the positions of
the ND and FD selection cuts. The FD MC distribution for CC
events uses the best-fit parameters discussed in the text.
(GeV)
Reconstructed E
POT
16
Events / GeV / 10
Ratio
0
5
10
15
1
1.5
10
20
30
40
a
Data
Fluka05 MC
Full MC Tuning
0
5
10
15
1
1.5
20
40
60
80
b
0
5
10
15
1
1.5
20
40
60
80
c
FIG. 2.
E
reco
in the MINOS ND for
three of the six beam configurations be-
fore and after the 15 parameter beam
tuning procedure. The target location
was modified to produce the different
spectra: (a) nominal, (b) target at
90 cm from nominal, and (c) target at
240 cm from nominal. The lower inset
shows the ratio of data to MC simulation
before and after tuning.
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10 NOVEMBER 2006
191801-4
weighted with the best-fit values of these parameters. For
the results presented in this Letter, the beam matrix method
[
34
] is used, in which agreement between MC simulations
and data is much less important because the ND data are
used to measure all of the effects common to both detec-
tors, such as beam modeling, neutrino interactions, and
detector response. It utilizes the beam simulation to derive
a transfer matrix that relates
s
in the two detectors via
their parent hadrons. The matrix element
M
ij
gives the
relative probability that the distribution of secondary had-
rons which produce
s
of energy
E
i
in the ND will give
s
of energy
E
j
in the FD. The ND
E
reco
spectrum is
translated into a flux by first correcting for the simulated
ND acceptance and then dividing by the calculated cross
sections for each energy bin. This flux is multiplied by the
matrix to yield the predicted, unoscillated FD flux. After
the inverse correction for cross section and FD acceptance,
the predicted FD
E
reco
spectrum is obtained.
In total, 215 events are observed in the FD with
E
reco
below 30 GeV compared to the unoscillated expectation of
336
14
. The error is due to the systematic uncertainties
described below. In the region below 10 GeV, 122 events
are observed compared to the expectation of
238
11
. The
observed FD
E
reco
spectrum is shown along with the pre-
dicted spectra for both extrapolation methods in Fig.
3
.
Under the assumption that the observed deficit is due to
!
oscillations [
35
–
37
], a fit is performed to the
parameters
j
m
2
32
j
and
sin
2
2
23
using the expression for
the
survival probability:
P
!
1
sin
2
2
23
sin
2
1
:
27
m
2
32
L
E
;
(1)
where
L
km
is the distance from the target,
E
GeV
is
the neutrino energy, and
j
m
2
32
j
[
38
] is measured in
eV
2
=c
4
. The FD data are binned in reconstructed event
energy, and the observed number of events in each bin is
compared to the expected number of events for this oscil-
lation hypothesis. The best-fit parameters are those which
minimize
2
2ln
, where
is the likelihood ratio:
2
X
nbins
2
e
i
o
i
2
o
i
ln
o
i
=e
i
X
nsys
s
2
j
2
s
j
;
(2)
where
o
i
and
e
i
are the observed and expected numbers of
events in bin
i
, and
s
2
j
=
2
s
j
are the penalty terms for
nuisance parameters associated with the systematic uncer-
tainties. The expected number of events depends on
j
m
2
32
j
,
sin
2
2
23
, and
s
j
. The choice of these systematic
effects and their estimated uncertainties are described be-
low. The
e
i
include the small contribution from selected
events produced in the oscillation process.
The effects of different systematic uncertainties were
evaluated by modifying the MC simulation and performing
a fit on this in place of the data. The largest effects were
found to be (a) The uncertainty in the fiducial mass in both
detectors, uncertainty in the event selection efficiency, and
the POT counting accuracy give a 4% uncertainty on the
predicted FD event rate. (b) The absolute hadronic energy
scale is known to 6% as discussed above. This is added in
quadrature to the uncertainty in the effect of intranuclear
rescattering estimated at approximately
10%
of the had-
ronic energy. The total hadronic energy scale uncertainty is
therefore
11%
. (c) The NC component was varied in a fit
to the PID data distribution in six energy bins in the ND. A
50% uncertainty was estimated to encompass the differ-
ences between the fit and ND MC simulations. At the
current level of statistics, uncertainties from CC cross
FIG. 3.
Comparison of the FD
E
reco
spectrum with predictions
for no oscillations for both analysis methods and for oscillations
with the best-fit parameters from the beam matrix extrapolation
method. The estimated NC background is also shown. The last
energy bin contains events between 18– 30 GeV.
)
23
θ
(2
2
sin
0.2
0.4
0.6
0.8
1.0
)
4
/c
2
| (eV
32
2
m
∆
|
1.5
2.0
2.5
3.0
3.5
4.0
-3
10
×
MINOS Best Fit
MINOS 90% C.L.
MINOS 68% C.L.
K2K 90% C.L.
SK 90% C.L.
SK (L/E) 90% C.L.
)
23
θ
(2
2
sin
0.2
0.4
0.6
0.8
1.0
)
4
/c
2
| (eV
32
2
m
∆
|
1.5
2.0
2.5
3.0
3.5
4.0
-3
10
×
FIG. 4.
Confidence intervals for the fit using the beam matrix
method including systematic errors calculated with 2 dof. Also
shown are the contours from the previous highest precision
experiments [
1
,
2
,
5
].
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97,
191801 (2006)
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191801-5
sections, muon momentum, relative ND-FD energy cali-
bration, remaining beam uncertainties, and reconstruction
were found to be negligible. As an example, in the absence
of any beam tuning, the best-fit value shifts only by
0
:
2
10
5
eV
2
=c
4
. The total systematic error is
0
:
13
10
3
eV
2
=c
4
.
In fitting the data to Eq. (
1
),
sin
2
2
23
was constrained
to lie in the physical region and the three main systematic
uncertainties were included as nuisance parameters. The
resulting 68% and 90% confidence intervals are shown in
Fig.
4
as determined from
2
2
:
3
and 4.6, respec-
tively. The best-fit value for
j
m
2
32
j
calculated with 1 de-
gree of freedom is
j
m
2
32
j
2
:
74
0
:
44
0
:
26
10
3
eV
2
=c
4
and
sin
2
2
23
>
0
:
87
at 68% C.L. with a fit probabil-
ity of 8.9%. At 90% C.L.,
2
:
31
<
j
m
2
32
j
<
3
:
43
10
3
eV
2
=c
4
and
sin
2
2
23
>
0
:
78
. The data and best-fit
MC simulation are shown in Fig.
3
. At the best-fit value,
the MC simulation predicts 0.76
events in the final
sample. If the fit is not constrained to be within the physical
region,
j
m
2
32
j
2
:
72
10
3
eV
2
=c
4
and
sin
2
2
23
1
:
01
, with a 0.2 decrease in
2
.
This work was supported by the U.S. DOE; the United
Kingdom PPARC; the U.S. NSF; the State and University
of Minnesota; the University of Athens, Greece; and
Brazil’s FAPESP and CNPq. We are grateful to the
Minnesota Department of Natural Resources, the crew of
the Soudan Underground Laboratory, and the staff of
Fermilab for their contribution to this effort.
*
Deceased.
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