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Measurement of the cosmic ray and neutrino-induced muon flux at the Sudbury neutrino observatory


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Results are reported on the measurement of the atmospheric neutrino-induced muon flux at a depth of 2 kilometers below the Earth's surface from 1229 days of operation of the Sudbury Neutrino Observatory (SNO). By measuring the flux of through-going muons as a function of zenith angle, the SNO experiment can distinguish between the oscillated and unoscillated portion of the neutrino flux. A total of 514 muonlike events are measured between -1{
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Measurement of the Cosmic Ray and Neutrino-Induced Muon Flux at the Sudbury
Neutrino Observatory
B. Aharmim,6S.N. Ahmed,14 T.C. Andersen,5A.E. Anthony,17 N. Barros,8E.W. Beier,13 A. Bellerive,4
B. Beltran,1, 14 M. Bergevin,7, 5 S.D. Biller,12 K. Boudjemline,4M.G. Boulay,14, 9 T.H. Burritt,19 B. Cai,14
Y.D. Chan,7M. Chen,14 M.C. Chon,5B.T. Cleveland,12 G.A. Cox-Mobrand,19 C.A. Currat,7, a X. Dai,14, 12, 4
F. Dalnoki-Veress,4, b H. Deng,13 J. Detwiler,19, 7 P.J. Doe,19 R.S. Dosanjh,4G. Doucas,12 P.-L. Drouin,4
F.A. Duncan,16, 14 M. Dunford,13, c S.R. Elliott,9, 19 H.C. Evans,14 G.T. Ewan,14 J. Farine,6H. Fergani,12
F. Fleurot,6R.J. Ford,16, 14 J.A. Formaggio,11, 19 N. Gagnon,19, 9, 7, 12 J.TM. Goon,10 D.R. Grant,4, d E. Guillian,14
S. Habib,1, 14 R.L. Hahn,3A.L. Hallin,1, 14 E.D. Hallman,6C.K. Hargrove,4P.J. Harvey,14 R. Hazama,19, e
K.M. Heeger,19, f W.J. Heintzelman,13 J. Heise,14, 9, 2 R.L. Helmer,18 R.J. Hemingway,4R. Henning,7, g A. Hime,9
C. Howard,1, 14 M.A. Howe,19 M. Huang,17, 6 B. Jamieson,2N.A. Jelley,12 J.R. Klein,17, 13 M. Kos,14 A. Kr¨uger,6
C. Kraus,14 C.B. Krauss,1, 14 T. Kutter,10 C.C.M. Kyba,13 R. Lange,3J. Law,5I.T. Lawson,16,5 K.T. Lesko,7
J.R. Leslie,14 I. Levine,4, h J.C. Loach,12, 7 S. Luoma,6R. MacLellan,14 S. Majerus,12 H.B. Mak,14 J. Maneira,8
A.D. Marino,7, i R. Martin,14 N. McCauley,13, 12 , j A.B. McDonald,14 S. McGee,19 C. Mifflin,4M.L. Miller,11, 19
B. Monreal,11, k J. Monroe,11 A.J. Noble,14 N.S. Oblath,19 C.E. Okada,7, l H.M. O’Keeffe,12 Y. Opachich,7, m
G.D. Orebi Gann,12 S.M. Oser,2R.A. Ott,11 S.J.M. Peeters,12, n A.W.P. Poon,7G. Prior,7, o K. Rielage,9, 19
B.C. Robertson,14 R.G.H. Robertson,19 E. Rollin,4M.H. Schwendener,6J.A. Secrest,13 S.R. Seibert,17, 9
O. Simard,4J.J. Simpson,5D. Sinclair,4, 18 P. Skensved,14 M.W.E. Smith,19,9 T.J. Sonley,11 , p T.D. Steiger,19
L.C. Stonehill,9, 19 N. Tagg,5, 12, q G. Teˇsi´c,4N. Tolich,7, 19 T. Tsui,2R.G. Van de Water,9, 13 B.A. VanDevender,19
C.J. Virtue,6D. Waller,4C.E. Waltham,2H. Wan Chan Tseung,12 D.L. Wark,15, r P. Watson,4J. Wendland,2
N. West,12 J.F. Wilkerson,19 J.R. Wilson,12 J.M. Wouters,9A. Wright,14 M. Yeh,3F. Zhang,4and K. Zuber12, s
(SNO Collaboration)
1Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2R3, Canada
2Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
3Chemistry Department, Brookhaven National Laboratory, Upton, NY 11973-5000
4Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada
5Physics Department, University of Guelph, Guelph, Ontario N1G 2W1, Canada
6Department of Physics and Astronomy, Laurentian University, Sudbury, Ontario P3E 2C6, Canada
7Institute for Nuclear and Particle Astrophysics and Nuclear Science
Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
8Laborat´orio de Instrumenta¸ao e F´ısica Experimental de Part´ıculas, Av. Elias Garcia 14, 1, 1000-149 Lisboa, Portugal
9Los Alamos National Laboratory, Los Alamos, NM 87545
10Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803
11Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139
12Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
13Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396
14Department of Physics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
15Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK
16SNOLAB, Sudbury, ON P3Y 1M3, Canada
17Department of Physics, University of Texas at Austin, Austin, TX 78712-0264
18TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
19Center for Experimental Nuclear Physics and Astrophysics, and
Department of Physics, University of Washington, Seattle, WA 98195
(Dated: February 16, 2009)
Results are reported on the measurement of the atmospheric neutrino-induced muon flux at
a depth of 2 kilometers below the Earth’s surface from 1229 days of operation of the Sudbury
Neutrino Observatory (SNO). By measuring the flux of through-going muons as a function of
zenith angle, the SNO experiment can distinguish between the oscillated and un-oscillated portion
of the neutrino flux. A total of 514 muon-like events are measured between 1cos θzenith0.4 in
a total exposure of 2.30 ×1014 cm2s. The measured flux normalization is 1.22 ±0.09 times the
Bartol three-dimensional flux prediction. This is the first measurement of the neutrino-induced
flux where neutrino oscillations are minimized. The zenith distribution is consistent with previ-
ously measured atmospheric neutrino oscillation parameters. The cosmic ray muon flux at SNO
with zenith angle cos θzenith>0.4 is measured to be (3.31±0.01 (stat.)±0.09 (sys.))×1010 µ/s/cm2.
PACS numbers: 14.60.Lm, 96.50.S-, 14.60.Pq
arXiv:0902.2776v1 [hep-ex] 16 Feb 2009
Atmospheric neutrinos are produced from the decay of
charged mesons created by the interactions of primary
cosmic rays with the Earth’s atmosphere. Atmospheric
neutrinos can be detected either via direct interactions
within the fiducial volume of a given detector or indi-
rectly from the observation of high-energy muons cre-
ated via the charged current interaction νµ+Nµ+X
on materials that surround the detector. Although the
latter process produces muons propagating at all zenith
angles, overhead portions of the sky are typically domi-
nated by cosmic-ray muons created in the Earth’s upper
The flux of atmospheric neutrinos has been a topic of
study since the mid-1960’s. Early experiments [1, 2] in-
ferred the presence of atmospheric neutrinos by measur-
ing the muon flux created by neutrino interactions taking
place in rock surrounding a detector. Subsequent studies
of the atmospheric neutrino flux as a function of zenith
angle [3, 4, 5], the ratio of electron and muon neutri-
nos [6, 7, 8, 9, 10], and combined measurements [11] have
provided a more direct measurement of the atmospheric
neutrino flux and revealed evidence for neutrino oscil-
lations. Results gathered from these experiments have
been further verified by long baseline accelerator mea-
surements [12, 13], thereby providing strong constraints
on the neutrino oscillation parameters.
The Sudbury Neutrino Observatory (SNO) is located
in the Vale-Inco Creighton mine in Ontario, Canada at
a depth of 2.092 km (5890 ±94 meters water equiva-
lent) with a flat overburden[14]. The combination of large
depth and flat overburden attenuates almost all cosmic-
ray muons entering the detector at zenith angles less than
cos θzenith= 0.4. Because of this depth, SNO is sensitive
to neutrino-induced through-going muons over a large
range of zenith angles, including angles above the hori-
This paper presents a measurement of the flux of
muons traversing the SNO detector. Measuring the
through-going muon flux, as a function of zenith angle,
for cos θzenith<0.4 provides sensitivity to both the oscil-
lated and un-oscillated portions of the atmospheric neu-
trino flux. Measuring the muon angular spectrum above
this cutoff provides access to the flux of cosmic-ray muons
created in the upper atmosphere. This paper is divided as
follows: Section II describes the experimental details of
the SNO detector, Section III describes the Monte Carlo
model used to predict the observed muon flux, Section IV
describes the data collection and event reconstruction,
and Section V discusses the signal extraction and error
analysis used for the measurements presented herein.
The Sudbury Neutrino Observatory is located
at 4628030”N latitude (56330magnetic north),
8112004”W longitude near the city of Sudbury, Ontario.
The center of the detector is at a depth of 2092 ±6 me-
ters from the Earth’s surface. The Earth’s surface im-
mediately above the SNO detector is 309 meters above
sea level. Within a 5 km radius on the surface above
the detector, the local topology lies between 300 and 320
meters above sea level, although small localizations with
±50 meters level variations do occur. The norite rock
that dominates the overburden is mostly oxygen (45%),
silicon (26%), aluminum (9%), and iron (4%). A com-
bination of bore samples taken at different depths and
gravity measurements taken at the surface show varia-
tions in the rock density, from 2.8 g/cm3near the surface
and closer to 2.9 g/cm3in the vicinity of the detector.
A fault line located 70 meters southwest of the detector
serves as a boundary to a deposit of granite/gabbro rock
of similar density (2.83 ±0.10 g/cm3) but slightly differ-
ent chemical composition (hZ2/Aiof 5.84 versus 6.01).
An average rock density of 2.83 ±0.05 g/cm3is used in
overburden calculations, independent of depth. The un-
certainty in the density takes into account the variation
as measured in the rock volume surrounding the detector.
The total depth to the center of the SNO detector, tak-
ing into account air and water filled cavities, is 5890 ±94
meters water equivalent.
The SNO detector itself includes a 600.5 cm radius
acrylic vessel filled with 99.92% isotopically pure heavy
water (D2O). The 5.5-cm thick acrylic vessel is sur-
rounded by 7.4 kilotons of ultra-pure H2O encased within
an approximately barrel-shaped cavity measuring 34 m in
height and 22 m (maximum) in diameter. A 17.8-meter
diameter stainless steel geodesic structure surrounds the
acrylic vessel. The geodesic is equipped with 9456 20-
cm photo-multiplier tubes (PMTs) pointed toward the
center of the detector. A non-imaging light concentrator
is mounted on each PMT to increase the total effective
photocathode coverage to 54%.
SNO is primarily designed to measure the solar neu-
trino flux originating from 8B decay in the sun above
a threshold of several MeV by comparing the observed
rates of the following three reactions:
The charged current (CC), neutral current (NC), and
elastic scattering (ES) reactions outlined above are sensi-
tive to different neutrino flavors. Data taking in the SNO
experiment is subdivided into three distinct phases, with
each phase providing a unique tag for the final states of
the neutral current interaction. In the first phase, the
experiment ran with pure D2O only. The neutral current
reaction was observed by detecting the 6.25-MeV γ-ray
following the capture of the neutron by a deuteron. For
the second phase of data taking, approximately 0.2% by
weight of purified NaCl was added to the D2O to enhance
the sensitivity to neutrons via their capture on 35Cl. In
the third and final phase of the experiment, 40 discrete
3He or 4He-filled proportional tubes were inserted within
the fiducial volume of the detector to enhance the capture
cross-section and make an independent measurement of
neutrons by observing their capture on 3He in the pro-
portional counters. Results from the measurements of the
solar neutrino flux for these phases have been reported
elsewhere [15, 16, 17, 18, 19].
Muons entering the detector produce Cherenkov light
at an angle of 42with respect to the direction of the
muon track. Cherenkov light and light from delta rays
produced collinear to the muon track illuminate an aver-
age of 5500 PMTs. The charge and timing distribution
of the PMTs is recorded. The amplitude and timing re-
sponse of the PMTs is calibrated in situ using a light dif-
fusing sphere illuminated by a laser at six distinct wave-
lengths [20]. This “laser ball” calibration is of particular
relevance to the muon analysis since it provides a tim-
ing and charge calibration for the PMTs which accounts
for multiple photon strikes on a single PMT. Other cal-
ibration sources used in SNO are described in the refer-
ences [14, 21].
For a period at the end of the third phase of the exper-
iment, a series of instrumented wire tracking chambers
and scintillator panels were installed immediately above
the SNO water cavity to provide a cross-check on the ac-
curacy of the muon reconstruction algorithm. Details of
the apparatus and results obtained from this calibration
are reported later in this paper.
Candidate neutrino-induced through-going muon
events can arise from a variety of sources. These include:
(a) muons created from neutrino-induced interactions
in the rock surrounding the SNO cavity; (b) muons
created from neutrino-induced interactions in the H2O
volume surrounding the PMT support structure; (c) νµ
interactions that take place inside the fiducial volume
but are misidentified as through-going muons; (d) νe
interactions that take place inside the outlined fiducial
volume but mis-reconstruct as through-going muons; (e)
cosmic-ray muons created in the upper atmosphere that
pass the zenith angle cut; and (f) events created by in-
strumental activity in the detector. The first three event
types are proportional to the νµatmospheric neutrino
flux and can undergo oscillations. The νe-induced flux
is also proportional to the overall atmospheric neutrino
flux, but the currently measured neutrino oscillation
parameters indicate that their probability for undergoing
oscillations is highly suppressed. The last two entries
constitute a genuine source of background to the signal.
In order to understand the measured neutrino-induced
flux, a proper model of the initial neutrino flux and sub-
sequent propagation is necessary. SNO uses the Bartol
group’s three-dimensional calculation of the atmospheric
neutrino flux [22]. Figure 1 shows the predicted flux
for cosmic rays and muons from the interaction of muon
neutrinos and anti-neutrinos as a function of muon en-
ergy. The neutrino energy spectrum is correlated with
the primary H and He cosmic flux, both of which are
strongly constrained by data. The uncertainties that
dominate the neutrino energy distribution relate to the
primary cosmic-ray energy spectrum, the πand Kpro-
duction ratio, and hadronic cross sections. Treatment of
the systematic errors in the neutrino flux is discussed in
greater detail in Ref [23] and [24]. Current estimates of
the neutrino flux uncertainties are approximately ±15%
and depend strongly on neutrino energy. Because the
normalization of the neutrino flux and the energy spec-
tral shape are highly correlated, the fits to the data re-
ported herein assume a fixed neutrino energy spectrum.
We also assume that the flux and energy spectra do not
change significantly with solar activity. Although vari-
ations throughout the solar cycle are expected, the ma-
jority of this variation is confined to neutrinos of energy
below 10 GeV, so the impact on the fluxes predicted at
SNO is expected to be small. A flux uncertainty of ±1%
is included to account for variations due to solar cycle
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Arbitrary Units
FIG. 1: The muon energy spectrum (given in log10(Eµ)) in the
SNO detector from cosmic-ray muons (triangles) as predicted
from MUSIC, and from neutrino-induced muons (boxes) cre-
ated in the surrounding rock as predicted from the Bartol
3D Monte Carlo. The expected spectrum after oscillations is
shown by the solid line. The distributions are not to scale.
Neutrino interactions in the rock surrounding the de-
tector are simulated by the NUANCE v3 Monte Carlo
neutrino event generator [25]. NUANCE includes a com-
prehensive model of neutrino cross sections applicable
across a wide range of neutrino energies. Neutrino quasi-
elastic interactions are modeled according to the formal-
ism of Llewellyn-Smith [26]. A relativistic Fermi gas
model by Smith and Moniz [27] is used to model the low
momentum transfer effects in the nucleus. The quasi-
elastic cross-section depends strongly on the value of the
axial mass used in the axial form factor. Recent mea-
surements from K2K [28] and MiniBooNE [29] show a
higher value of the axial mass than previously reported
(maxial = 1.20 ±0.12 GeV and maxial = 1.23 ±0.20, re-
spectively). Though this analysis uses the previous world
average for the axial mass (maxial = 1.03±0.15 GeV) [30],
the systematic uncertainty encompasses these more re-
cent measurements. For the Fermi gas model, we assume
a Fermi momentum of 225 MeV/c and a binding energy
of 27 MeV for light elements such as oxygen, carbon, and
silicon, and a 2.22 MeV binding energy for deuterium.
For neutrino reactions where a single charged or neu-
tral pion is resonantly produced, NUANCE employs a
modified model of Rein and Sehgal [31]. Experimental
constraints on this cross-section are of order ±20%, not as
strong as those placed on the quasi-elastic cross-section.
Many of the other parameters used for the quasi-elastic
cross-section are also used for this process.
The largest contributor to the atmospheric neutrino-
induced muon flux is deep inelastic scattering of neutri-
nos in the surrounding rock where the hadronic invariant
mass is above 2 GeV/c2. The uncertainty on the cross-
section for this process is strongly constrained by ac-
celerator produced high energy neutrino experiments to
±3% [32, 33, 34]. The transition between resonance and
deep inelastic scattering cross-section uses the method-
ology developed by Yang and Bodek [35]. Other minor
processes that can produce muons in the final states, such
as coherent pion production and νµescattering, are
also included.
Transport of muons through the rock from neutrino-
induced interactions is calculated using the PROPMU
muon transport code [36], which is integrated into the
NUANCE Monte Carlo framework. Rock compositions
and densities consistent with measured values are imple-
mented in PROPMU. Simulation of muon transport in
the D2O and H2O and subsequent detector response is
handled by the SNO Monte Carlo and Analysis (SNO-
MAN) code. SNOMAN propagates the primary par-
ticles and any secondary particles (such as Compton
electrons) that are created, models the detection of the
optical photons by the PMTs, and simulates the elec-
tronics response. The SNOMAN code has been bench-
marked against calibration neutron, gamma, and electron
data taken during the lifetime of SNO. With the excep-
tion of a few physics processes (such as optical photon
propagation), widely used packages such as EGS4 [37],
MCNP [38] and FLUKA [39] are used in SNOMAN. Ex-
plicit muon energy loss mechanisms such as ionization,
pair production, bremsstrahlung, muon capture and de-
cay, and photonuclear interactions are all included in the
simulation, allowing modeling of the muon track from
rest energies up to several TeV. Energy losses due to
photonuclear interactions are simulated using the for-
malism of Bezzukov and Bugaev [40, 41]. Production of
secondary particles from muon interactions, which con-
tributes to the total energy deposited in the detector, is
included in the model as described above.
In addition to the through-going signal from atmo-
spheric neutrinos, a number of backgrounds which have
muon signatures are simulated in the analysis. These in-
clude νµinteractions inside the H2O and D2O volumes
of the detector, and νeinteractions that either have a
muon in the final state or are misidentified as a through-
going muon. Cosmic-ray muons incident on the detector
constitute an additional source of high-energy muons and
are treated separately. Their flux is estimated using the
formalism of Gaisser [42],
1 + 1.1Eµcos θµ
115 GeV
1 + 1.1Eµcos θµ
850 GeV
) cm2sr1GeV1(2)
where Eµand θµare the muon energy and zenith an-
gle at the Earth’s surface, γ2.77 ±0.03 is the muon
spectral index, and I0is a normalization constant. Al-
though Eq. 2 is inaccurate at low energies, the minimum
energy required for surface muons to reach the SNO de-
tector is 3 TeV. Transport of such high-energy muons
in the rock is performed by the MUSIC muon transport
code [43]. The average energy of these muons as they en-
ter the SNO detector is 350 GeV. After incorporating
the detector response, simulated events for cosmic-ray
and neutrino-induced muon candidates are used to con-
struct probability distribution functions (PDFs). The
reconstructed zenith angle is used to establish PDFs for
both signal and background.
A. Livetime
The data included in this analysis were collected dur-
ing all three SNO operation phases. During the initial
phase, data were collected from November 2, 1999 until
May 28, 2001. During the second phase of SNO, data
were recorded between July 26, 2001 and August 28,
2003. The third and final phase of SNO operations col-
lected data between November 27, 2004 and November
28, 2006. Data were collected in discrete time intervals,
or runs, that range from 30 minutes to 96 hours in length.
Runs that were flagged with unusual circumstances (pres-
ence of a calibration source in the detector, maintenance,
etc.) were removed from the analysis. The raw live time
of the data set is calculated using a GPS-sychronized 10
MHz clock on a run-by-run basis, checked against an in-
dependent 50 MHz system clock, and corrected for time
removed by certain data selection cuts. The livetime of
the dataset here is 1229.30±0.03 days. The livetime used
in this analysis differs from previously published analy-
ses because requirements that have a strong impact on
solar neutrino analyses, such as radon activity levels, are
relaxed here.
B. Event Reconstruction
The SNO detector has a nearly ideal spherically sym-
metric fiducial volume. The algorithm used to recon-
struct muon candidates makes use of this symmetry in
finding the best fit track. A two-tiered algorithm is used
whereby a preliminary track is reconstructed which later
serves as a seed for a more comprehensive fit to the
muon candidate event. In the preliminary fit, the en-
trance position is determined by looking at the earliest
hit PMTs, and the exit position is determined by the
charge-weighted position of all fired PMTs. In our spher-
ical geometry, the impact parameter is the distance from
the center of the sphere to the midpoint of the line con-
necting the entrance and exit points. The fitter corrects
the track fit for biases in charge collection and geome-
try, and provides a first estimate of the direction of the
incoming muon. The first-order reconstructed track is
then passed to a full likelihood fit to determine the muon
track parameters to greater accuracy. The likelihood fit
uses three distributions: (a) the number of detected pho-
toelectrons, (b) the PMT charge distribution, and (c) the
PMT timing distribution. The charge and timing distri-
butions are conditional on the number of photoelectrons
incident on a given PMT. These distributions are cor-
rected according to biases measured during laser calibra-
tions. Figure 2 shows the timing distribution expected
for different numbers of photoelectrons that are above de-
tection threshold. Both changes in pre and post-pulsing
and biasing can be seen in the timing distributions due
to multiple photon hits on a given PMT event.
The use of conditional distributions helps remove re-
construction biases due to multiple photoelectrons de-
tected on a single PMT. This is important for impact
parameter values close to the PMT support structure
(bµ830 cm). The quality of reconstruction for the bias
of the fitted track and for the mis-reconstruction angle as
a function of impact parameter were examined. Figure 3
FIG. 2: The probability distribution of PMT firing times
based on simulation for events with one (dashed), two (dot-
ted), and three (solid) photons striking the photocathode.
shows the cosine of the mis-reconstruction angle, defined
as the dot-product between the true muon direction vec-
tor and the reconstructed vector. Approximately 87%
(97%) of all simulated muons with an impact parameter
of less than 830 cm reconstruct within 1(2) of the true
track direction; respectively (see Figure 3). Monte Carlo
studies also show that bias effects on the reconstructed
impact parameter to be less than ±4 cm (see Figure 4).
C. Event Selection
After run selection, low-level cuts are applied to mea-
surements of PMT outputs before reconstruction in order
to separate through-going muon candidate events from
instrumental background activity. We require a mini-
mum of 500 valid (or calibrated) PMT hits for an event
to be a muon candidate. Events with more than 250
hit PMTs within a 5 µs window of a previously tagged
event, or when 4 or more such events occur within a 2 s
window, are identified as burst events. Burst events are
often associated with instrumental backgrounds and are
removed from the analysis. Instrumental activity typi-
cally has broad PMT timing distributions and/or low to-
tal charge; events with these characteristics are removed.
Finally, events that possess 4 or more hit PMTs in the
aperture of the D2O vessel (neck) are removed from the
data to eliminate occurrences where light enters the de-
tector from the top of the acrylic vessel.
A series of high-level analysis cuts use reconstructed
track parameters to isolate a pure through-going muon
data set. A cut on the reconstructed impact parameter of
bµ<830 cm is applied to the data to ensure accurate re-
construction of through-going tracks. These cuts define
a total fiducial area of 216.42 m2and a minimal track
length of 367 cm. The minimum (mean) muon energy
needed to traverse this length of track is 0.8 (2.6) GeV.
Muon events characteristically produce ample amounts
of light in the detector. The number of Cherenkov pho-
0 0.5 1 1.5 2 2.5 3
Arbitrary Units
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FIG. 3: Distribution of mis-reconstructed zenith angle (left) and as a function of normalized impact parameter, ρ2=
µ/(850 cm)2, (right) for Monte Carlo cosmic-ray muons. The points and error bars on the right-hand side plot refer to
the mean and RMS of the mis-reconstructed angle, respectively.
tons produced by the muon, scaled by the appropriate
detection efficiency for photons produced at the given
impact parameter, is reconstructed for each candidate
event. Each track is required to possess a minimum of
2000 detected photoelectrons. A cut is also made on the
estimated energy loss (dE/dX ) of the muon. The quan-
tity dE/dX is determined from the amount of detected
light, corrected for geometric and photon attenuation ef-
fects, divided by the reconstructed track length. The
dE/dX variable depends on both the ionization and ra-
diation losses, and has a peak at around 225 MeV/m.
Events with dE/dX 200 MeV/m are retained for fur-
ther analysis. Further, a cut is imposed on the fraction
of photoelectrons within the predicted Cherenkov cone
for the muon track, and on the timing of these in-cone
photons. Finally, a linear combination (Fisher discrim-
inant) formed from the fraction of in-time hits and the
time residuals from the muon fit is used to reduce the
contamination of contained atmospheric neutrino events
in our final data sample. A list of all cuts and their effects
on the data is shown in Table I and in Figure 6.
The reconstructed cosmic-ray tracks, after all selec-
tion criteria are applied, exhibit a flat distribution ver-
sus impact area, as expected (see Figures 4 and 5). The
reconstruction efficiency is also robust to a number of
changes in the optical and energy loss model of the recon-
struction. Monte Carlo simulation shows that changes in
the parameters of the detector model, including Rayleigh
scattering, secondary electron production, PMT photo-
cathode efficiency, and PMT angular response, all have
minimal impact on the reconstruction performance. An
uncertainty on the reconstruction efficiency of ±0.3% is
assigned due to detector model dependence. The effi-
ciency of the event selection depends most sensitively
on the energy loss parameter, dE/dX. We determine
the energy loss model uncertainty on the reconstruc-
tion efficiency by studying the level of data-Monte Carlo
agreement. For through-going cosmic-ray muons it is
±0.2% and for neutrino-induced muons it is ±2.5%. Sim-
ilar uncertainties in reconstruction efficiency arise from
the PMT charge model invoked in reconstructing events
and in the rejection of events from the linear discrimi-
nat cut previously mentioned. This leads to a ±0.05%
(±1.0%) and ±0.37% (±2.1%) uncertainty on the cosmic-
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
True ! Reconstructed Impact (cm)
Number of Events (a.u.)
0 2 4 6
FIG. 4: Left: Comparison of true and reconstructed impact parameter versus normalized impact parameter, ρ2=b2
µ/(850 cm)2
for Monte Carlo cosmic-ray muons. Data points indicate mean and error bars for a given impact parameter. Right: Projection
of difference between reconstructed and generated tracks. Dashed lines indicate uncertainty in impact parameter reconstruction
as adopted for this analysis.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FIG. 5: Distribution of the normalized impact parameter,
µ/(850 cm)2for cosmic-ray muon data (points) and
Monte Carlo (solid line).
ray (neutrino-induced) flux from the charge and linear
discriminant cuts, respectively. The differences seen in
the two muon sources are due to the differences in muon
energy distribution. Monte Carlo studies of cosmic-ray
events that pass through the SNO detector show the to-
tal event selection cut efficiency to be 99.2% for through-
going muons.
D. Quality Checks and Calibration
Neutrino-induced muons have a minimum energy of
about 2 GeV with significant intensity extending into
the hundreds of GeV range. There is no readily available
controlled calibration source that can provide multi-GeV
muons as a benchmark to test the reconstruction algo-
rithms. Instead, a number of checks have been carried
out to test the performance of the Monte Carlo by com-
paring with data.
The majority of checks are performed using muons that
reconstruct in the downward direction (cos (θzenith)>
TABLE I: Summary of low- and high-level cleaning cuts ap-
plied to the data and their effect on the data population. Cuts
are applied in sequence as they appear in this table.
Level Type of Cut No. of Events
Raw number of tubes firing >250 378219
Timing and burst requirements 375374
Low Number of calibrated tubes firing 100396
Raw PMT charge requirement 85703
Raw PMT timing RMS 84414
Number of neck tubes firing 84038
Impact parameter 830 cm 80165
Fit number of photoelectrons 79998
High Energy loss (dE/dX) 79268
Linear discriminant cut 77321
Cherenkov cone in-time fraction 77321
Cherenkov cone fraction of tubes firing 77263
Zenith cos θzenith>0.4 76749
cos θzenith<0.4 514
2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4
Number of Events
25000 All Data
Burst Cuts Applied
Calibrated PMT Tube Cut
Low Level Cuts Applied
High Level Cuts Applied
FIG. 6: The number of muon candidate events as a function
of the log of the number of tubes that fire. Plot shows events
with no cuts applied (solid), after the burst cut (dashed), cal-
ibrated tubes cut (dotted), all low-level cuts (red) and high-
level cuts (filled area) are applied.
0.4). Although the total energy of these cosmic-ray
muons extends much higher than those from neutrino-
induced muons, the amount of energy deposited in the
detector by both is very similar. The slight differences
between the two energy loss distributions arise mainly
from the relative fraction of radiative processes contribut-
ing to the energy loss mechanisms. Figure 7 shows the
distribution of total hit PMTs (NHit) for reconstructed
cosmic-ray muons. In general, there is good agreement
between data and Monte Carlo simulations.
FIG. 7: The distribution of hit tubes (NHit) for muon events
that pass all cuts for data (crosses) and Monte Carlo (line).
The Monte Carlo has been normalized to the total number of
events seen in the data. Only statistical errors are shown in
the figure.
The neutrino oscillation analysis is particularly sen-
sitive to two parameters: (a) the fitter bias in recon-
structing events at the edge of the impact parameter
acceptance and (b) the angular resolution of the muon
zenith angle. The former affects the fiducial area of the
experiment, while the latter affects the neutrino angu-
lar distribution, thereby affecting the oscillation param-
eter extraction. To test the accuracy of the muon track
reconstruction, data and Monte Carlo distributions for
cosmic-ray muons are compared at high impact parame-
ters. A chi-square (∆χ2
ν) test is performed between data
and Monte Carlo simulations for impact parameter dis-
tributions under different models of impact parameter
bias and resolution: (a) a constant shift (b0
(b), a linear bias (b0
µ=bµ·(1 + δx)), and (c) a larger
impact parameter resolution. Results are summarized
in Table II and show that our reconstruction model is
consistent with the data and a small reconstruction bias
(δbµ<4 cm at 68% C.L.).
The muon fitter uses both time and charge to recon-
struct muon tracks. To test the robustness of the algo-
rithm, tracks are fit under two conditions, using “charge
only” and“time-only” information in order to search for
potential biases in reconstruction (Figure 8). Differences
between the two tracking methods are well-modeled by
the Monte Carlo simulations(see also Table II). The ob-
served 1.1 cm shift is interpreted as the lower limit on the
accuracy of the muon impact parameter reconstruction.
A more comprehensive test of the muon tracking al-
gorithm is to compare tracks reconstructed in the SNO
Monte Carlo
Time - Charge Impact Paremeter (cm)
Number of Events
10 2
10 3
10 4
-300 -200 -100 0 100 200 300
FIG. 8: Difference in reconstructed impact parameter (bµ)
using “time-only” and “charge-only” information in the like-
lihood minimization scheme for muons that pass all analysis
cuts (points). The mean difference between the two meth-
ods shows a 1.1 cm offset in the reconstruction of the impact
parameter in comparison to simulations (solid line).
detector with an external charged particle tracking sys-
tem. A muon tracker was installed immediately above
the SNO detector. The apparatus took data for a period
at the end of the third phase of the SNO experiment. A
total of four wire planes, each spanning an area of ap-
proximately 2.5×2.4 m2and containing 32 instrumented
wire cells, was arranged in alternating orthogonal coor-
dinates to provide two dimensional track reconstruction.
The overall structure was tilted at a 54-degree angle due
to pre-existing space constraints. Three large scintillator
panels spanned the area covered by the wire chambers,
and provided the trigger for the wire chamber readout.
A common trigger was also sent to the main SNO data
acquisition system to synchronize events. A total of 94.6
days of live time was recorded by the muon calibration
unit. Track reconstruction of muon candidates from this
instrument were compared with the SNO tracking algo-
rithm. Further details on this calibration system will be
described in a future article.
High-energy muons passing through this external
muon tracking system and the SNO detector were recon-
structed by both systems, providing a calibration check
for the main SNO tracking algorithm. A total of 30
tracks were used for comparisons of track reconstruc-
tion between both systems. This test confirms the ac-
curacy of the muon track reconstruction to better than
0.62±0.12. A small shift in the reconstructed impact
parameter is observed in the data, consistent with the
limits from the previously mentioned tests. We take the
uncertainty on the impact parameter reconstruction as
±4 cm.
TABLE II: List of consistency checks for the through-going
muon analysis, including ∆χ2
νtests on the radial distribution
of cosmic-ray muons, charge and time reconstruction differ-
ences, and the external muon tracking data. See text for more
Method Bias
Impact Parameter Bias +1.0%
Impact Parameter Shift +3.8
Impact Parameter Resolution +8.5 cm
Charge-Time Reconstruction
Impact Parameter Shift ±1.1 cm
External Muon Chambers
Angular Resolution <0.6
Impact Parameter Bias 4.2±3.7 cm
A final check is performed on the time interval dis-
tribution between muon events. A fit to an exponential
function yields an average time constant of 21 minutes
and a χ2/dof of 107.7/98, consistent with the hypoth-
esis of a random arrival time of cosmic-ray muons, as
E. Expected Neutrino Signal and Background
Neutrino-induced muons from the H2O and rock sur-
rounding the SNO detector were simulated in the manner
outlined in the previous sections. A zenith angle cut of
cos θzenith0.4 was imposed to reject cosmic-ray muons
from our neutrino-induced signal. Under the assump-
tions of the Bartol [22] atmospheric neutrino flux and no
oscillations, SNO expects a total of 138.4±7.3 neutrino-
induced events per year passing all cuts. A full break-
down of the expected signal contribution is shown in Ta-
ble III.
The efficiency for reconstructing these signal events is
not as high as that for primary cosmic-ray muons be-
cause some of neutrino-induced events stop within the
detector volume. The total efficiency is defined as the
ratio between the number of through-going cosmic rays
that reconstruct with an impact parameter less than 830
cm that pass all cuts versus the number of through-going
muon events with a generated impact parameter less than
830 cm. If the muon is genuinely through-going (exits the
fiducial area of the detector), the total efficiency is 98.0%,
based on Monte Carlo studies.
SNO also has a small acceptance for neutrino-induced
muons whose interaction vertex resides inside a fidu-
cial volume defined by the 830-cm radius. Most of
TABLE III: Summary of Monte Carlo expected signal and background rates contributing to the neutrino-induced muon analysis,
after all cuts, for the full zenith angle range of 1<cos θzenith<0.4 and the unoscillated region of 0 <cos θzenith<0.4. Errors
include full systematic uncertainties assuming no correlations (see Table VII for more details). Neutrino induced interaction
rates assume no oscillations. The last entry in the table shows the measured muon rate passing all cuts.
Source Rate (yr1)
Zenith Range 1<cos θzenith<0.4 0 <cos θzenith<0.4
Through-going νµrock interactions 124.4±6.5 43.2±2.3
Through-going νµwater interactions 9.0±0.5 2.8±0.2
Internal νµinteractions 3.1±0.8 1.0±0.3
Internal νeinteractions 1.9±0.3 0.7±0.1
Total Signal 138.4±7.3 47.8±2.5
Cosmic ray µ1.1±1.2 1.1±1.2
Instrumental contamination 0.3±0.2 0.1±0.2
Total Background 1.4±1.2 1.2±1.2
Total Expected Rate 139.8±7.4 49.0±2.8
Detected Rate 152.7 59.7
these events are removed by the energy loss cut. From
Monte Carlo studies, contamination of 3.1±0.8 con-
tained νµ-events per year is expected in the data. As
these events also depend on the flux and neutrino oscil-
lation parameters, they are included as part of the final
signal extraction. A small number of internal neutrino
events also come from νeinteractions which reconstruct
as through-going muons. The rate of these events is
1.9±0.3 events/year. The cosmic-ray muon background
passing all cuts is estimated to be 1.1±1.2 events per
year. Finally, a negligible amount of instrumental back-
grounds are expected to contaminate the muon signal.
The majority of such instrumentals are due to burst ac-
tivity present in the detector. A bifurcated analysis com-
paring the high-level cuts against the low-level cuts is per-
formed so as to determine the amount of contamination
of these instrumental events in our data [44, 45]. In addi-
tion, events that are explicitly tagged as burst events are
used to test the cut effectiveness in removing instrumen-
tal contamination. Both tests predict an instrumental
background contamination rate of 0.3±0.2 events per
A. Cosmic-Ray Muon Flux
In order to minimize the possibility of introducing bi-
ases, a two-tier blind analysis procedure is employed.
First, only a fraction ('40%) of the data was open for
analysis. Second, a fraction of muon events was removed
from the data set using a zenith angle-dependent weight-
ing function unknown to the analyzers. Only after all
fitter and error analyses were completed were both blind-
ness veils lifted.
A total of 76749 muon candidates passing all se-
lection cuts are reconstructed with a zenith angle of
0.4<cos θzenith<1 for the 1229.30-day dataset. The
data collected corresponds to an exposure of 2.30 ×1014
cm2s. The total measured cosmic-ray muon flux at SNO,
after correcting for acceptance, is (3.31 ±0.01 (stat.)±
0.09 (sys.)) ×1010 µ/s/cm2, or 62.9±0.2 muons/day
passing through a 830-cm radius circular fiducial area.
One can define the vertical muon intensity per solid
angle Iv
µby the expression:
µcos (θz,i) = 1
cos θz,j (3)
where Niis the number of events in a given solid angle
bin Ωiand zenith angle θz,i,Lis the livetime of the mea-
surement, is the detection efficiency for through-going
muons, and Ais the fiducial area. Given the flat over-
burden, it is possible to express Equation 3 in terms of
the slant depth, xSNO. To compare to other vertical flux
measurements, SNO rock can be corrected to standard
rock, CaCO3, using the relation:
xstd = 1.015xSNO +x2
where xSNO is the slant depth expressed in meters water
equivalent. There exists an additional ±1% model uncer-
tainty in converting from SNO to standard rock which is
estimated from differences that arise between the MU-
SIC and PROPMU energy loss models. Flux values for
slant depths ranging from 6 to 15 km water equivalent
are presented in Table IV.
The attenuation of the vertical muon intensity as a
function of depth can be parameterized by:
TABLE IV: Intensity for standard (CaCO3) rock as a function of slant depth (in meters water equivalent) for muons passing
all cuts and which reconstruct with cos θzenith >0.4. Only statistical errors are shown.
Slant depth Events Intensity (standard rock)
(meters w.e.) (cm2s1sr1)
6225 4203 (3.71 ±0.53) ×1010
6275 3905 (3.47 ±0.50) ×1010
6325 3576 (3.20 ±0.46) ×1010
6375 3371 (3.05 ±0.44) ×1010
6425 3238 (2.95 ±0.43) ×1010
6475 3000 (2.75 ±0.40) ×1010
6525 2737 (2.53 ±0.37) ×1010
6575 2598 (2.42 ±0.36) ×1010
6625 2369 (2.23 ±0.33) ×1010
6675 2182 (2.07 ±0.31) ×1010
6725 2038 (1.94 ±0.29) ×1010
6775 1911 (1.84 ±0.28) ×1010
6825 1831 (1.77 ±0.27) ×1010
6875 1668 (1.63 ±0.25) ×1010
6925 1552 (1.52 ±0.24) ×1010
6975 1377 (1.36 ±0.21) ×1010
7025 1359 (1.35 ±0.21) ×1010
7075 1247 (1.25 ±0.20) ×1010
7125 1163 (1.18 ±0.19) ×1010
7175 1111 (1.13 ±0.18) ×1010
7225 1043 (1.07 ±0.17) ×1010
7275 910 (9.40 ±1.50) ×1011
7325 897 (9.33 ±1.50) ×1011
7375 830 (8.69 ±1.40) ×1011
7425 790 (8.33 ±1.40) ×1011
7475 758 (8.05 ±1.30) ×1011
7525 683 (7.30 ±1.20) ×1011
7575 713 (7.67 ±1.30) ×1011
7700 2241 (6.13 ±1.00) ×1011
7900 1791 (5.03 ±0.86) ×1011
8100 1378 (3.97 ±0.69) ×1011
8300 1097 (3.24 ±0.58) ×1011
8500 859 (2.60 ±0.47) ×1011
8700 670 (2.08 ±0.39) ×1011
8900 504 (1.60 ±0.31) ×1011
9100 444 (1.44 ±0.28) ×1011
9300 328 (1.09 ±0.22) ×1011
9500 257 (8.7±1.8) ×1012
9700 205 (7.1±1.5) ×1012
9900 183 (6.5±1.4) ×1012
10250 291 (4.3±0.9) ×1012
10750 166 (2.6±0.6) ×1012
11250 100 (1.6±0.4) ×1012
11750 61 (1.0±0.3) ×1012
12250 34 (6.0±1.8) ×1013
12750 31 (5.7±1.7) ×1013
13250 14 (2.7±1.0) ×1013
13750 10 (2.0±0.8) ×1013
14250 11 (2.3±0.9) ×1013
14750 7 (1.5±0.7) ×1013
15250 13 (2.9±1.1) ×1013
µ(xstd) = I0(x0
where I0is an overall normalization constant, and x0
represents an effective attenuation length for high-energy
muons. The remaining free parameter, α, is strongly cor-
related with the spectral index γin Equation 2. Results
from fits of the vertical muon intensity as a function of
depth for various values of these parameters are shown
in Table V. We perform fits whereby the parameter α
is either fixed to what one would expect from the sur-
face (α=γ1=1.77) or allowed to float freely. The
cosmic-ray data tends to prefer larger values of αthan
the expected value of 1.77. A comparison of SNO’s muon
flux to that measured in the LVD [46] and MACRO [47]
is shown in Figure 9. In general, there exists tension be-
tween the different data sets. Fits have been performed
both with and without allowing the slant depth uncer-
tainty to float within its uncertainty. The fits in both
cases are nearly identical, with minimal change (<1σ)
to the slant depth. The fits presented in Table V are with
the slant depth constrained.
To avoid some of the strong correlations between the
three parameters listed in Equation 5, we also perform
the fit using the following parametrization:
µ(x) = e(a0+a1·x+a2·x2)(6)
where ea0represents the muon flux at the surface, a1is
inversely proportional to the muon attenuation length,
and a2represents the deviation from the simple expo-
nential model. Results from fitting to Eq. 6 are shown in
Table VI.
The systematic uncertainties of this measurement are
summarized in Table VII. Certain systematic errors for
the cosmic-ray muon flux are in common with those
for the neutrino-induced muon flux results, including
livetime, impact parameter bias, and angular resolu-
tion. Others are unique to the cosmic-ray muon flux.
These include uncertainties in the rock density, the sur-
face variation, the rock conversion model, muon strag-
gling, instrumental backgrounds, and backgrounds from
neutrino-induced events and multiple muons. This last
background is estimated from events measured from the
MACRO experiment [48]. As the reconstruction for mul-
tiple muon events in the detector is not well known, we as-
sign a ±100% uncertainty on this potential background.
These systematic uncertainties are included as part of the
total error presented in Table V.
B. Atmospheric Neutrino Results
We assume a model for the atmospheric neutrino flux,
and fit for a total flux scaling factor as well as the atmo-
spheric neutrino oscillation parameters. In these fits we
use a two-neutrino mixing model:
Φ(L/Eν, θ, m2)µ= Φ0·[1 sin22θ·sin2(1.27∆m2L
)] (7)
where θis the neutrino mixing angle, ∆m2is the square
mass difference in eV2,Lis the distance traveled by the
neutrino in km, Eνis the neutrino energy in GeV, and
Φ0is the overall normalization of the neutrino-induced
Although the signal uncertainty is dominated by statis-
tics, systematic errors do have an impact on both the
acceptance and zenith angle distribution of events. To
account for distortions in the zenith angle spectrum, we
generalize the χ2-pull technique (see [49] and references
therein) to the case of a maximum likelihood analysis.
This allows us to account for the smallness of statistics
while still incorporating any correlations that may ex-
ist between different systematic error contributions. An
extended likelihood function is constructed using the fol-
lowing equation:
Ltotal = 2(
ln ( Ndata
i)); (8)
where Ndata(MC) represents the number of data (Monte
Carlo) events found in a given zenith bin i. To account for
the effect of systematic errors on our likelihood contours,
we perform a linear expansion of NMC with respect to
a nuisance parameter ~α for each systematic uncertainty
such that:
0,i +
(∂N MC
0,i (1+~
βi·~α) (9)
Note that we have used vector notation to denote a
summation over all nuisance parameters. By expanding
TABLE V: Results from the SNO fit to the vertical muon intensity for cos θzenith >0.4 using Equation 5. The fits were performed
either using only SNO data with the αparameter allowed to float, with the αparameter fixed to the value predicted from the
surface flux of Eq. 2 (α=γ1=1.77), or combined with LVD [46] and MACRO [47] cosmic ray data. Symbols in the table
are as defined in the text. The errors reported are a combination of statistical and systematic uncertainties on the flux and
slant depth.
Dataset I0x0α χ2/dof
(106cm2s1sr1) (km w.e.)
SNO only 1.20 ±0.69 2.32 ±0.27 5.47 ±0.38 34.2 / 44
SNO only 2.31 ±0.32 1.09 ±0.01 1.77 111.0 / 45
SNO + LVD + MACRO 2.16 ±0.03 1.14 ±0.02 1.87 ±0.06 230.2/134
TABLE VI: Results from the SNO fit to the vertical muon intensity for cos θzenith >0.4 using Equation 6. Fits shown using
only SNO data, or combined with LVD [46] and MACRO [47] cosmic ray data. Symbols in table are as defined in the text.
The errors reported are a combination of statistical and systematic uncertainties on the flux and slant depth.
Dataset ea0a1a2χ2/dof
(cm2s1sr1) (m.w.e.)1(m.w.e.)2
SNO only (4.55+0.90
0.75)×106(1.75 ±0.06) ×103(3.9±0.3) ×10841.6 / 44
SNO + LVD + MACRO (1.97 ±0.06) ×106(1.55 ±0.01) ×103(2.78 ±0.08) ×108230.8 / 134
Slant Depth (km w.e.)
4000 6000 8000 10000 12000 14000
cmµVertical Muon Intensity (
FIG. 9: The flux of cosmic-ray muons that pass all cuts as
a function standard rock depth. SNO data (filled circles)
shown with best global fit intensity distribution (dashed line)
and data from LVD [46] (empty circles) and MACRO [47]
(triangles) detectors using Eq. 5. Global fit range extends to
13.5 kilometers water equivalent, beyond which atmospheric
neutrino-induced muons start to become a significant fraction
of the signal.
the logarithmic term to second order and minimizing the
likelihood function with respect to each nuisance param-
eter, one finds an analytical expression [50]:
Ltotal = 2(
ln ( Ndata
0,i Ndata
i)) ~αT
minS2~αmin (10)
where ∆~αT
min represents the minimized nuisance param-
~αmin = (
0,i )~
and the matrix S2is defined as:
Here, σ2is the diagonal error matrix whose entries
represent the size of the systematic error constraints.
As long as the contribution from the systematic errors
is small, the above formalism provides a very efficient
method for evaluating the effect of systematic errors
while also incorporating constraints from the data. A
total of six systematic uncertainties are fit using this
method; five of which (axial mass, quasi-elastic cross-
section, resonance cross-section, deep inelastic scatter-
ing, and energy loss modeling) have explicit zenith angle
dependencies, while the last is flat with respect to the
zenith distribution. This uncertainty is a combination of
all of the remaining systematic errors and is fit as an over-
all normalization error. A summary of all the systematic
errors is shown in Table VII.
Figure 10 shows the zenith angle distribution for
neutrino-induced muons. A total of 514 events are
recorded with 1<cos θzenith<0.4 in the 1229.30 days
of livetime in this analysis. For neutrino-induced
events near the horizon (cosθzenith between 0 and 0.4),
201 events are observed. Given the current measurements
of the atmospheric oscillation parameters, the neutrino-
induced flux is unaffected by oscillations in this latter
region and therefore is a direct measurement of the atmo-
spheric neutrino flux, particularly at high energies. The
corresponding neutrino-induced through-going muon flux
below the horizon (cos θzenith<0) and above the horizon
(0 <cos θzenith<0.4) are 2.10 ±0.12(stat.)±0.08(sys.)×
1013cm2s1sr1and 3.31 ±0.23(stat.)±0.13(sys.)×
1013cm2s1sr1, respectively.
From the measured zenith angle distribution, we can
extract the flux normalization Φ0and the neutrino mix-
ing parameters θand ∆m2in Equation 7. A max-
imum likelihood fit is performed to find the best fit
points, as outlined above. If all parameters are al-
lowed to float, one finds a flux normalization value of
Φ0=1.22 ±0.10 and best fit neutrino oscillation parame-
ters of ∆m2of 2.6×103eV2and maximal mixing. These
!1!0.8 !0.6 !0.4 !0.2 0 0.2 0.4
Number of Events
FIG. 10: The distribution of through-going neutrino-induced
muons that pass all cuts as a function of zenith angle.
Data (crosses) are shown with the best-fit MC spectra of
0,sin22θ, m2) = (1.22 ±0.10, 1.00, 2.6×103eV2) (solid
box) and prediction with no neutrino oscillation and a best
fit normalization of Φ0= 1.09±0.08 (hashed box). The back-
ground due to cosmic-ray muons is shown in the dashed line.
The zenith angle cut is indicated in the figure.
results are with respect to the Bartol three-dimensional
atmospheric flux model and the cross-section model im-
plemented in NUANCE described in Section III [22]. The
zenith angle spectrum is consistent with previously mea-
sured neutrino oscillation parameters. One can also look
at SNO’s sensitivity on the atmospheric flux Φ0by in-
cluding existing constraints on the atmospheric neutrino
oscillation parameters from the Super-Kamiokande [11]
(∆m2,sin22θSK) = (2.1+0.6
0.4×103eV2,1.000 ±0.032)
and MINOS [13, 51] (∆m2
MINOS = (2.43 ±0.13) ×
103eV2) neutrino experiments. The likelihood function
in Eq. 10 is altered to the following:
Lconstrained =Ltotal + (m2m2
)2+ (m2m2
)2+ (sin22θsin22θSK
TABLE VII: Summary of systematic errors for the neutrino-induced and cosmic-ray muon flux measurements. A dagger ()
indicates that the systematic error only affects the cosmic-ray muon intensity fit to Eq. 5 and is not included in the total
systematic error summation below. The total error in the table is determined from the fit including correlations and does not
equal to the quadrature sum of the individual components.
Systematic Error Variation νµ-induced muon flux error Cosmic-ray muon flux error
Detector Propagation Model Various ±0.3% ±0.3%
Angular Resolution ±0.6±0.1% ±0.1%
Energy Loss Model ±5% ±2.5% ±0.2%
Impact Bias/Shift ±4.0 cm ±1.2% ±1.0%
Impact Resolution ±8.5 cm ±0.07% ±0.07%
Livetime Clock ±2600 s ±0.002% ±0.002%
PMT Charge Model ±10% ±1.0% ±0.05%
Fisher Discriminant Cut ±5% ±2.1% ±0.37%
Total Detector Model ±3.7% ±1.1%
Neutrino Cross-Section Model
Axial Mass ±0.15 GeV ±1.1% N/A
Quasi-Elastic ±10% ±0.8% N/A
Resonance ±20% ±1.9% N/A
Deep Inelastic ±3% ±2.1% N/A
Total Cross-Section Model ±3.1% N/A
Muon Propagation Model
Rock Density()±0.05 g/cm3±0.3% ()
Conversion Model()±1% N/A ()
Surface Variation()±50 m N/A ()
Transport Model ±2% N/A
Time/Seasonal Variation ±1% ±2.2%
Total Propagation Model ±2.2% ±2.2%
Instrumental 0.3±0.2 events yr1±0.2% <0.1%
Cosmic ray µ0.6±1.1 events yr1±0.8% N/A
νµ-Induced 45.8±2.3 events yr1N/A ±0.2%
Multiple Muons ±100% 1% ±1%
Total Background Error ±0.8% ±1%
Total Systematic Error ±4.8% ±2.7%
Statistical Error +8.5% ±0.4%
The constraint reduces the uncertainty on the overall
atmospheric neutrino flux normalization to 1.22 ±0.09.
The 68%, 95% and 99.73% confidence level regions for
the parameters as determined by the fits are shown in
Figure 11. The scenario of no neutrino oscillations by
using SNO-only data is excluded at the 99.8% confidence
The Sudbury Neutrino Observatory experiment has
measured the through-going muon flux at a depth of
5890 meters water equivalent. We find the total muon
cosmic-ray flux at this depth to be (3.31 ±0.01 (stat.)±
0.09 (sys.)) ×1010 µ/s/cm2. We measure the through-
going muon flux induced by atmospheric neutrinos. The
zenith angle distribution of events rules out the case of
no neutrino oscillations at the 3σlevel. We measure the
overall flux normalization to be 1.22±0.09, which is larger
than predicted from the Bartol atmospheric neutrino flux
model but consistent within the uncertainties expected
from neutrino flux models. This is the first measure-
ment of the neutrino-induced flux above the horizon in
the angular regime where neutrino oscillations are not an
important effect. The data reported in this paper can be
0.005 0.01 0.015 0.02 0.025 0.03
Flux Normalization
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Flux Normalization
0.8 0.85 0.9 0.95 1
Flux Normalization
FIG. 11: The 68% (blue), 95% (red), and 99.73% (black) confidence level contours for the νµatmospheric neutrino oscillation
parameters based on the muon zenith angle distribution for cos θzenith <0.4. The plots show the SNO-only contours for flux
normalization versus mass splitting (top left), SNO-only mass splitting versus mixing angle (top right), SNO-only contours for
flux normalization versus mixing angle (bottom left) and the flux normalization versus mixing angle including constraints from
the Super-K and MINOS neutrino oscillation experiments (bottom right) [11, 13].
used to help constrain such models in the future.
This research was supported by: Canada: Natural
Sciences and Engineering Research Council, Industry
Canada, National Research Council, Northern Ontario
Heritage Fund, Atomic Energy of Canada, Ltd., On-
tario Power Generation, High Performance Computing
Virtual Laboratory, Canada Foundation for Innovation;
US: Dept. of Energy, National Energy Research Scien-
tific Computing Center; UK: Science and Technology Fa-
cilities Council; Portugal: Funda¸ao para a Ciˆencia e a
Tecnologia. We thank the SNO technical staff for their
strong contributions. We thank Vale Inco for hosting this
aPresent Address: Business Direct, Wells Fargo, San Fran-
cisco, CA
bPresent Address: Department of Physics, Princeton Uni-
versity, Princeton, NJ 08544
cPresent address: Department of Physics, University of
Chicago, Chicago, IL
dPresent address: Department of Physics, Case Western
Reserve University, Cleveland, OH
ePresent address: School of Engineering, Hiroshima Uni-
versity, Hiroshima, Japan
fPresent address: Department of Physics, University of
Wisconsin, Madison, WI
gPresent address: Department of Physics, University of
North Carolina, Chapel Hill, NC
hPresent Address: Department of Physics and Astronomy,
Indiana University, South Bend, IN
iPresent address: Physics Department, University of Col-
orado at Boulder, Boulder, CO
jPresent address: Department of Physics, University of
Liverpool, Liverpool, UK
kPresent address: Department of Physics, University of
California Santa Barbara, Santa Barbara, CA
lPresent address: Remote Sensing Lab, PO Box 98521,
Las Vegas, NV 89193
mPresent address: Department of Chemical Engineering
and Materials Science, University of California, Davis,
nPresent address: Department of Physics and Astronomy,
University of Sussex, Brighton BN1 9QH, UK
oPresent address: CERN (European Laboratory for Par-
ticle Physics), Geneva, Switzerland
pPresent address: University of Utah Department of
Physics, Salt Lake City, Utah
qPresent address: Department of Physics and Astronomy,
Tufts University, Medford, MA
rAdditional Address: Imperial College, London SW7 2AZ,
sPresent address: Institut f¨ur Kern- und Teilchenphysik,
Technische Universit¨at Dresden, 01069 Dresden, Ger-
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... To estimate the flux at different laboratories we have used the spectral shape for LNGS multiplied by the absolute normalization for different labs. While there is an expected hardening of the muon flux for deeper labs, our comparison of the SNOLab flux predicted by simply renormalizing LNGS flux with the measured flux from [47] shows that the effect is negligible within the precision of the present study. To study the expected impact of the muon-material interactions, a high statistics simulation of muons uniformly distributed between 1 GeV and 3 TeV was performed. ...
Full-text available
\Xe{136} is used as the target medium for many experiments searching for \bbnonu. Despite underground operation, cosmic muons that reach the laboratory can produce spallation neutrons causing activation of detector materials. A potential background that is difficult to veto using muon tagging comes in the form of \Xe{137} created by the capture of neutrons on \Xe{136}. This isotope decays via beta decay with a half-life of 3.8 minutes and a \Qb\ of $\sim$4.16 MeV. This work proposes and explores the concept of adding a small percentage of \He{3} to xenon as a means to capture thermal neutrons and reduce the number of activations in the detector volume. When using this technique we find the contamination from \Xe{137} activation can be reduced to negligible levels in tonne and multi-tonne scale high pressure gas xenon neutrinoless double beta decay experiments running at any depth in an underground laboratory.
... Acrylic is a common material used in the scintillator vessels of large-mass neutrino detectors. As the mechanical strength requirement of a kiloton-scale detector requires that the thickness of the vessel should be about 5.5 centimeters as in the SNO experiment [28], the optical transmission of acrylic cannot not be ignored. In this section, we present a qualitative understanding of this transmission. ...
Full-text available
A liquid scintillator Cherenkov detector is proposed for a few future neutrino experiments. The combination of a slow liquid scintillator, with long emission time, and photomultiplier tubes may present a possible detection scheme for liquid scintillator Cherenkov detectors, and the complete setup can be used to distinguish between scintillation and Cherenkov lights. Neutrino detectors of this type could feature directionality and particle identification for charged particles so that better sensitivity may be expected for low-energy (MeV-scale) neutrino physics, such as solar physics, geo-science and supernova relic neutrino search. A slow liquid scintillator cocktail combines linear alkylbenzene (LAB),2,5-diphenyloxazole(PPO),and1,4-bis(2-methylstyryl)-benzene(bis-MSB). We studied the relevant physical aspects of different combinations of LAB, PPO, and bis-MSB, including light yield, time profile, emission spectrum, attenuation length of scintillation emission and visible light yield of Cherenkov emission. We also measured the optical transmission of acrylic, a material commonly used in liquid scintillator containers. Samples of LAB with about 0.07 g/L PPO + 13 mg/L bis-MSB allowed good separation between Cherenkov and scintillation lights and demonstrated a reasonable high light yield.
Full-text available
As a free, intensive, rarely interactive and well directional messenger, solar neutrinos have been driving both solar physics and neutrino physics developments for more than half a century. Since more extensive and advanced neutrino experiments are under construction, being planned or proposed, we are striving toward an era of precise and comprehensive measurement of solar neutrinos in the next decades. In this article, we review recent theoretical and experimental progress achieved in solar neutrino physics. We present not only an introduction to neutrinos from the standard solar model and the standard flavor evolution, but also a compilation of a variety of new physics that could affect and hence be probed by solar neutrinos. After reviewing the latest techniques and issues involved in the measurement of solar neutrino spectra and background reduction, we provide our anticipation on the physics gains from the new generation of neutrino experiments.
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Precise measurements of the muon flux are important for different practical applications, both in environmental studies and for the estimation of the water equivalent depths of underground sites. A mobile detector for cosmic muon flux measurements has been set up at IFIN-HH, Romania. The device is used to measure the muon flux on different locations at the surface and underground. Its first configuration, not used in the present, has been composed of two 1 m2 scintillator plates, each viewed by wave length shifters and read out by two Photomultiplier Tubes (PMTs). A more recent configuration, consists of two 1 m2 detection layers, each one including four 1 · 0,25 m2 large scintillator plates. The light output in each plate is collected by twelve optical fibers and then read out by one PMT. Comparative results were obtained with both configurations.
We report the activity measured in rainwater samples collected in the Greater Sudbury area of eastern Canada on 3, 16, 20, and 26 April 2011. The samples were gamma-ray counted in a germanium detector and the isotopes 131I and 137Cs, produced by the fission of 235U, and 134Cs, produced by neutron capture on 133Cs, were observed at elevated levels compared to a reference sample of ice-water. These elevated activities are ascribed to the accident at the Fukushima Dai-ichi nuclear reactor complex in Japan that followed the 11 March earthquake and tsunami. The activity levels observed at no time presented health concerns.
The EGS (Electron Gamma Shower) system of computer codes is a general purpose package for the Monte Carlo simulation of the coupled transport of electrons and photons in an arbitrary geometry for particles with energies above a few keV up to several TeV. This report introduces a new, enhanced version called EGS4. In addition to explaining and documenting the various enhancements and charges to the previous version (EGS3), this document includes several introductory and advanced tutorials on the use of EGS4 and also contains the EGS4 User Manual, the PEGS4 User Manual and an EGS4 User Guide to Mortran 3. 81 refs., 40 figs., 9 tabs. (WRF)
We present a new three-dimensional Monte-Carlo code MUSIC (MUon SImulation Code) for muon propagation through the rock. All processes of muon interaction with matter with high energy loss (including the knock-on electron production) are treated as stochastic processes. The angular deviation and lateral displacement of muons due to multiple scattering, as well as bremsstrahlung, pair production and inelastic scattering are taken into account. The code has been applied to obtain the energy distribution and angular and lateral deviations of single muons at different depths underground. The muon multiplicity distributions obtained with MUSIC and CORSIKA (Extensive Air Shower simulation code) are also presented. We discuss the systematic uncertainties of the results due to different muon bremsstrahlung cross-sections.
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P. Lipari and T. Stanev, Phys. Rev. D 44, 3543 (1991).
Particle Transport Code System, Radiation Shielding Information Center
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MCNP4A, A Monte Carlo N-Particle Transport Code System, Radiation Shielding Information Center, Los Alamos National Laboratory, Los Alamos, Nov. 1993 (unpublished).
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R. Becker-Szendy et al., Phys. Rev. D46, 3720 (1992).
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R. Gran et al., Phys. Rev. D 74, 0502002 (2006).
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H. Gallagher, J. Phys. Conf. Ser. 136, 022014 (2008).
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D. MacFarlane et al., Z. Phys. C26, 1 (1984).
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L. B. Bezrukov et al., Sov. J. Nucl. Phys. 17:51 (1973)