PHYSICAL REVIEW D 82, 072003 (2010)

First search for extremely high energy cosmogenic neutrinos
with the IceCube Neutrino Observatory
R. Abbasi,28 Y. Abdou,22 T. Abu-Zayyad,33 J. Adams,16 J. A. Aguilar,28 M. Ahlers,32 K. Andeen,28 J. Auffenberg,39
X. Bai,31 M. Baker,28 S. W. Barwick,24 R. Bay,7 J. L. Bazo Alba,40 K. Beattie,8 J. J. Beatty,18,19 S. Bechet,13 J. K. Becker,10
K.-H. Becker,39 M. L. Benabderrahmane,40 J. Berdermann,40 P. Berghaus,28 D. Berley,17 E. Bernardini,40 D. Bertrand,13
D. Z. Besson,26 M. Bissok,1 E. Blaufuss,17 D. J. Boersma,1 C. Bohm,34 S. Böser,11 O. Botner,37 L. Bradley,36 J. Braun,28
S. Buitink,8 M. Carson,22 D. Chirkin,28 B. Christy,17 J. Clem,31 F. Clevermann,20 S. Cohen,25 C. Colnard,23
D. F. Cowen,36,35 M. V. D’Agostino,7 M. Danninger,34 J. C. Davis,18 C. De Clercq,14 L. Demirörs,25 O. Depaepe,14
F. Descamps,22 P. Desiati,28 G. de Vries-Uiterweerd,22 T. DeYoung,36 J. C. Dı́az-Vélez,28 J. Dreyer,10 J. P. Dumm,28
M. R. Duvoort,38 R. Ehrlich,17 J. Eisch,28 R. W. Ellsworth,17 O. Engdegård,37 S. Euler,1 P. A. Evenson,31 O. Fadiran,4
A. R. Fazely,6 T. Feusels,22 K. Filimonov,7 C. Finley,34 M. M. Foerster,36 B. D. Fox,36 A. Franckowiak,11 R. Franke,40
T. K. Gaisser,31 J. Gallagher,27 R. Ganugapati,28 M. Geisler,1 L. Gerhardt,8,7 L. Gladstone,28 T. Glüsenkamp,1
A. Goldschmidt,8 J. A. Goodman,17 D. Grant,21 T. Griesel,29 A. Groß,16,23 S. Grullon,28 M. Gurtner,39 C. Ha,36
A. Hallgren,37 F. Halzen,28 K. Han,16 K. Hanson,28 K. Helbing,39 P. Herquet,30 S. Hickford,16 G. C. Hill,28
K. D. Hoffman,17 A. Homeier,11 K. Hoshina,28 D. Hubert,14 W. Huelsnitz,17 J.-P. Hülß,1 P. O. Hulth,34 K. Hultqvist,34
S. Hussain,31 R. L. Imlay,6 A. Ishihara,15,* J. Jacobsen,28 G. S. Japaridze,4 H. Johansson,34 J. M. Joseph,8 K.-H. Kampert,39
A. Kappes,28,† T. Karg,39 A. Karle,28 J. L. Kelley,28 N. Kemming,9 P. Kenny,26 J. Kiryluk,8,7 F. Kislat,40 S. R. Klein,8,7
S. Knops,1 J.-H. Köhne,20 G. Kohnen,30 H. Kolanoski,9 L. Köpke,29 D. J. Koskinen,36 M. Kowalski,11 T. Kowarik,29
M. Krasberg,28 T. Krings,1 G. Kroll,29 K. Kuehn,18 T. Kuwabara,31 M. Labare,13 S. Lafebre,36 K. Laihem,1 H. Landsman,28
R. Lauer,40 R. Lehmann,9 D. Lennarz,1 J. Lünemann,29 J. Madsen,33 P. Majumdar,40 R. Maruyama,28 K. Mase,15,‡
H. S. Matis,8 M. Matusik,39 K. Meagher,17 M. Merck,28 P. Mészáros,35,36 T. Meures,1 E. Middell,40 N. Milke,20 J. Miller,37
T. Montaruli,28,x R. Morse,28 S. M. Movit,35 R. Nahnhauer,40 J. W. Nam,24 U. Naumann,39 P. Nießen,31 D. R. Nygren,8
S. Odrowski,23 A. Olivas,17 M. Olivo,37,10 M. Ono,15 S. Panknin,11 L. Paul,1 C. Pérez de los Heros,37 J. Petrovic,13
A. Piegsa,29 D. Pieloth,20 R. Porrata,7 J. Posselt,39 P. B. Price,7 M. Prikockis,36 G. T. Przybylski,8 K. Rawlins,3 P. Redl,17
E. Resconi,23 W. Rhode,20 M. Ribordy,25 A. Rizzo,14 J. P. Rodrigues,28 P. Roth,17 F. Rothmaier,29 C. Rott,18 C. Roucelle,23
T. Ruhe,20 D. Rutledge,36 B. Ruzybayev,31 D. Ryckbosch,22 H.-G. Sander,29 S. Sarkar,32 K. Schatto,29 S. Schlenstedt,40
T. Schmidt,17 D. Schneider,28 A. Schukraft,1 A. Schultes,39 O. Schulz,23 M. Schunck,1 D. Seckel,31 B. Semburg,39
S. H. Seo,34 Y. Sestayo,23 S. Seunarine,12 A. Silvestri,24 A. Slipak,36 G. M. Spiczak,33 C. Spiering,40 M. Stamatikos,18,kT. Stanev,31 G. Stephens,36 T. Stezelberger,8 R. G. Stokstad,8 S. Stoyanov,31 E. A. Strahler,14 T. Straszheim,17
G. W. Sullivan,17 Q. Swillens,13 I. Taboada,5 A. Tamburro,33 O. Tarasova,40 A. Tepe,5 S. Ter-Antonyan,6 S. Tilav,31
P. A. Toale,36 D. Tosi,40 D. Turčan,17 N. van Eijndhoven,14 J. Vandenbroucke,7 A. Van Overloop,22 J. van Santen,9B. Voigt,40 C. Walck,34 T. Waldenmaier,9 M. Wallraff,1 M. Walter,40 C. Wendt,28 S. Westerhoff,28 N. Whitehorn,28
K. Wiebe,29 C. H. Wiebusch,1 G. Wikström,34 D. R. Williams,2 R. Wischnewski,40 H. Wissing,17 K. Woschnagg,7 C. Xu,31
X. W. Xu,6 G. Yodh,24 S. Yoshida,15,{ and P. Zarzhitsky2(IceCube Collaboration)
1

III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA
3
Department of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, Alaska 99508, USA
4
CTSPS, Clark-Atlanta University, Atlanta, Georgia 30314, USA
5
School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
6
Department of Physics, Southern University, Baton Rouge, Louisiana 70813, USA
7
Department of Physics, University of California, Berkeley, California 94720, USA
8
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
9
Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
10
Fakultät für Physik and Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
11
Physikalisches Institut, Universität Bonn, Nussallee 12, D-53115 Bonn, Germany
12
Department of Physics, University of the West Indies, Cave Hill Campus, Bridgetown BB11000, Barbados
13
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
14
Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium
15Department of Physics, Chiba University, Chiba 263-8522, Japan
16
Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand21550-7998= 2010=82(7)=072003(11)072003-1

Ó 2010 The American Physical Society

R. ABBASI et al.

PHYSICAL REVIEW D 82, 072003 (2010)17

18

Department of Physics, University of Maryland, College Park, Maryland 20742, USA
Department of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, Ohio 43210, USA
19
Department of Astronomy, Ohio State University, Columbus, Ohio 43210, USA
20
Department of Physics, TU Dortmund University, D-44221 Dortmund, Germany
21
Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2G7
22Department of Subatomic and Radiation Physics, University of Gent, B-9000 Gent, Belgium
23
Max-Planck-Institut für Kernphysik, D-69177 Heidelberg, Germany
24
Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
25
Laboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne, Switzerland
26
Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
27
Department of Astronomy, University of Wisconsin, Madison, Wisconsin 53706, USA
28
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
29
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
30
Université de Mons, 7000 Mons, Belgium
31
Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
32
Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
33
Department of Physics, University of Wisconsin, River Falls, Wisconsin 54022, USA
34
Oskar Klein Centre and Department of Physics, Stockholm University, SE-10691 Stockholm, Sweden
35
Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
36
Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA37
Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
38
Department of Physics and Astronomy, Utrecht University/SRON, NL-3584 CC Utrecht, The Netherlands
39
Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
40
DESY, D-15735 Zeuthen, Germany(Received 7 July 2010; published 7 October 2010)
We report on the results of the search for extremely-high energy neutrinos with energies above 107 GeV
obtained with the partially (  30%) constructed IceCube in 2007. From the absence of signal events inthe sample of 242.1 days of effective live time, we derive a 90% C.L. model independent differential upper
limit based on the number of signal events per energy decade at E2 e þ þ ’ 1:4 
106 GeV cm2 sec1 sr1 for neutrinos in the energy range from 3  107 to 3  109 GeV.
DOI: 10.1103/PhysRevD.82.072003

PACS numbers: 98.70.Sa, 95.85.Ry

I. INTRODUCTION
Detection of extremely-high energy (EHE) neutrinos
with energies greater than 107 GeV may shed light on
the long standing puzzle of the origin of EHE cosmic
rays [1,2]. Several observational results have indicatedthat these EHE cosmic rays (EHECRs) are of extragalactic
origin [3]. Further elucidation of their production mechanism by EHECR observation is, however, limited because
the collisions of EHECR with the cosmic microwave background photons—known as the Greisen-Zatsepin-Kuzmin(GZK) mechanism [4]—prevent EHECRs from propagating over cosmological distances without losing a sizable*Corresponding author.
aya@hepburn.s.chiba-u.ac.jp†
Also at Universität Erlangen-Nürnberg, Physikalisches
Institut, D-91058, Erlangen, Germany.
‡
Corresponding author.
mase@hepburn.s.chiba-u.ac.jp
xAlso at Università di Bari and Sezione INFN, Dipartimento di
Fisica, I-70126, Bari, Italy.
k
Also at NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA.
{
Corresponding author.
syoshida@hepburn.s.chiba-u.ac.jp

fraction of their energy. On the other hand, cosmogenic
neutrinos [5] produced by the GZK mechanism via photoproduced  meson decay as  !   ! e e 
carry information on the EHECR source evolution andthe maximum energy of EHECRs at their production
sites [6].
Detection of these EHE neutrinos is an experimental
challenge because the very low EHE neutrino fluxes require a very large detector. The large size of the IceCube
neutrino observatory [7], currently under construction at
the geographic South Pole, will make it more effective thanprevious experiments in the search for these neutrinos[8,9]. Interactions of  , e , and  and their antiparticles
are observed through the Cherenkov radiation emitted
by secondary particles. In the following, we do not distinguish between  and ; the simulations and sensitivity
calculations assume an equal mixture of particles andantiparticles.
In this paper we will describe the first results of a searchfor signatures of cosmogenic neutrinos in the 2007 dataacquired by the partially constructed IceCube neutrino
observatory. This analysis selects events which produce alarge amount of light in the detector. Based on simple
criteria, such as the total number of observed Cherenkov

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photons and the results of reconstruction algorithms, it
selects candidate neutrino events. Although  , e , and interactions look very different in IceCube, the selection
criteria are sensitive to all three flavors.
II. THE ICECUBE DETECTOR
IceCube is a cubic-kilometer, high-energy cosmic neutrino telescope which is currently under construction. It
uses the 2800 m thick glacial ice as a Cherenkov medium.
Cherenkov photons emitted by relativistic charged particles, notably muons, electrons, and taus produced incharged current interactions and their secondaries, aredetected by an array of photon sensors, known as digital
optical modules (DOMs) [10]. The DOMs deep below theice surface are deployed along electrical cable bundles thatcarry power and communication between the DOMs andsurface electronics. The cable assemblies, often called
strings, are lowered into holes drilled to a depth of
2450 m. The DOMs, spaced at intervals of 17 m, occupy
the bottom 1000 m of each string. The strings are arranged
in a hexagonal lattice pattern with a spacing of approximately 125 m. DOMs are also frozen into tanks located at
the surface near the top of each hole. The tanks constitutean air shower array called IceTop [11].
The DOMs enclose a down-looking 25 cm photomultiplier tube (PMT) [12] with data acquisition and calibrationelectronics, light emitting diodes for calibration, and also
data compression, communications, and control hardware[10] in a 35 cm diameter pressure sphere. Almost all of the
PMTs are run at a gain of 107 ; PMT saturation effects
become important at signal levels of about 5000 photoelectrons in a single DOM in 50 ns. When the DOM detects
a photoelectron, it initiates an acquisition cycle, recording
the PMT output with two waveform digitizer systems. The
first system samples every 3.3 ns for 400 ns, with 14 bits ofdynamic range. The second system samples every 25 ns for
6:4 s, with 10 bits of dynamic range. The data acquisition
system is designed such that the first system is sensitive to abright photon source at close distance and the second
system captures signal induced by photons emitted at large
distance. This analysis uses the total number of photoelectrons detected by the PMTs as a measure of the event
energy. For each DOM, the charge used is the one fromwhichever system recorded a larger number of photoelectrons. Because of the significant DOM-to-DOM differences in saturation behavior, the current analysis does not
attempt to correct for PMT saturation. So, the signals frombrightly illuminated DOMs are naturally truncated.
III. DATA AND SIMULATIONThis analysis uses data collected from May 2007
through April 2008, when IceCube consisted of 22 strings(IC-22; 1320 DOMs) and 52 IceTop tanks. In order togreatly reduce random noise from radioactivity, in IC22

the DOMs only recorded signal waveforms when a local
coincidence condition was satisfied, i.e. when an adjoiningor next-to-nearest neighbor DOM was triggered within1 s. In 2007, the trigger selected time periods when 8
or more DOMs recorded local coincidence signals within
5 s; when this happened, all hits within a 20 s window
were stored as an event. The average trigger rate was about
550 Hz. The high-multiplicity event sample used in thisanalysis imposes an additional condition requiring NDOM
 80, where NDOM is the number of hit DOMs in an
event. The average high-multiplicity event rate was approximately 1.5 Hz with a seasonal variation of 17%. A
total of 3:2  107 events were tagged as high-multiplicity
during the effective live time of 242.1 days (excluding theperiods of unstable operation).
The high-multiplicity cut reduces the data by a factor of3  103 while preserving approximately 70% of the
GZK neutrinos with projected trajectories that pass within
880 m of the center of IceCube. Here, and below, the GZK
signal rates are based on the GZK spectra and flux calculated by Ref. [6] assuming an all-proton composition witha moderately strong source evolution, ðz þ 1Þm with m ¼ 4extending to z ¼ 4:0. Neutrino oscillations modify theneutrino flavor ratio over the cosmological distances they
travel and the fluxes at the Earth were calculated as inRef. [13]. Note that the flavor ratio e : : of cosmogenic neutrinos at the Earth is different from 1:1:1 asprimary energy spectra of e and  produced by the
GZK mechanism are different because of a significant
contribution of e from neutron decay. This enhancement
was included in the GZK neutrino flux calculations
used here.
EHE neutrinos were simulated with the JULIET package[9] to generate and propagate the neutrinos through the
Earth. All three flavors of neutrinos were simulated withenergies between 105 and 1011 GeV. The resulting secondary muons and taus produced in the neutrino interactions
are propagated through the rock and ice near the IceCube
volume, also by JULIET. Hadronic and electromagnetic
showers are also simulated; all of these showers are treatedas point sources, without accounting for the LPM effect.
The background muon bundles from cosmic rays in theenergy range 106 to 1010 GeV were generated using
CORSIKA [14] version 6.720 with the SIBYLL 2.1 hadronicinteraction model or with QGSJET-II, without charm production [15]. The uncertain prompt muon component fromcharm decay may contribute to the background events [16].
The muons were propagated through the Earth using MMC[17]. Departures of observed data distributions from thoseof the CORSIKA based background events prompted us toalso develop a phenomenological background model basedon fits to data. Emission of Cherenkov photons and theirpropagation in the ice was simulated by the Photonics
package [18]. Measurement of the absolute number of
Cherenkov photons is important in the EHE neutrino

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search as it closely relates to the energy of the high-energymuons, taus, or electrons produced by EHE neutrinos.
Therefore, the detection efficiency of the DOMs must be
understood with good precision. The primary element, thePMT, is calibrated in the laboratory using a nitrogen laser
to measure the photon detection efficiency [12]. This bare
PMT data are used in a simulation package which propagates photons inside the glass sphere and the optical gel tothe photocathode surface. The DOM simulation is followed by waveform calibration and the trigger condition
is included in the simulation chain.

µ

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IV. ANALYSIS

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The event signatures from  , e , and  are very different. IceCube mainly detects cosmogenic neutrinos by thesignals from the secondary muons and taus generated in theneutrino interaction in the rock or ice. At high energies,
these particles are seen in the detector as series of energetic
cascades from radiative energy loss processes such as paircreation, bremsstrahlung, and photonuclear interactions,rather than minimum-ionizing tracks. The radiative energy
losses are approximately proportional to the energy of themuon or the tau, and so is the Cherenkov light yield.
Electron neutrinos produce electromagnetic and hadronic
showers, which are relatively compact sources of
Cherenkov light. Muon and tau neutrinos within IceCube
will also produce a hadronic shower from the struck nucleon, in addition to the muon or tau secondary.
Shown in Fig. 1 is the simulated distribution of the total
number of photoelectrons per event (NPE) recorded by thethe IC-22 detector as a function of the simulated true muonenergy. A clear correlation between NPE and the energy ofparticles measured near IceCube is observed. The energies
are sampled at a radius of 880 m from the IceCube center.
This definition of energy is labeled ‘‘in-ice energy’’ andused throughout this paper. The visible departure fromlinearity for large NPE stems from the saturation of thedetector during signal capture. Approximately 30% of
EHE signal events are due to neutrino interactions inside
the IceCube detector volume initiating a hadronic or electromagnetic cascade. The correlation between NPE andincoming neutrino energy also holds for these events.
Electron neutrinos are detectable via this channel.
Because the energy spectrum of background atmospheric muons (both single muons and bundles) falls steeply
with energy, the GZK neutrino flux should dominate overbackground in the high NPE region. Since the throughgoing muons and taus induced by EHE neutrinos enter into
the IceCube volume mainly horizontally [8,9], the signal
search criteria are chosen to favor roughly horizontal highNPE events.
The high-multiplicity NDOM  80 sample is dominatedby atmospheric background muons. The next step of the

FIG. 1 (color online). Event distribution from Monte Carlosimulations of single muons with the IC-22 detector configurations in a plane of NPE and simulated true energy. The muonenergy is given when the muon is 880 meters from the IceCube
center (in-ice energy). The 80 DOM multiplicity cut (level-1 cut)is applied. The charged lepton energy distribution is assumed tofollow E1 in this plot for illustrative purposes. Only particles
with trajectories intersecting within 880 m from the center of
IceCube array are considered in the plots. More distant events do
not contribute to the data sample.

analysis selects events with NPE > 104 . This reduces the
background by 3 orders of magnitude, leaving 6528 events,
still dominated by background, while the GZK signal
reduction is 24%.
Table I summarizes the number of events remaining at
each level of the initial filtering. In order to estimate thebackground in the very high-energy region, the simulated
data are compared to the experimental data in the region
104 < NPE < 105 . The present analysis follows the blind
analysis technique. In keeping with the IceCube blindness
policy, events with NPE  105 were not used for determining the background or setting cuts. This NPE threshold waschosen so that the possible contribution from signal eventsin the studied sample was negligible.
B. High-energy muon background
Bundles of muons generated in cosmic-ray air showers
are the major background for the EHE neutrino signal
search, because multiple muon tracks with a small geometrical separation resemble a single high-energy muon in
the IceCube detector. The multiplicity, energy distribution,and separation distances for these muon bundles are notfully understood. Two independent Monte Carlo simulations are carried out to estimate the muon-bundle background in this EHE neutrino signal search.
The first is the full cosmic-ray air shower simulation
with light and heavy ion primaries using the CORSIKA(SIBYLL) package [14]. Two extreme cases of composition
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TABLE I. Number of events at different filter levels for 242.1 days in 2007. The simulation predictions for the atmospheric muon
background using the CORSIKA-SIBYLL package, the empirical model, and that for the GZK cosmogenic neutrino model are also listed
for comparison. Errors shown here are statistical only. Refer to Sec. IVA for the definitions.
Filter levels

Observational data

Level 1 (NDOM  80)
Level 2 (NPE > 104 )3:195  107
6528

CORSIKA (iron)

CORSIKA (proton)ð1:84  0:08Þ  107

ð7:71  0:45Þ  106

Empirical modelð886  8:9Þ  103
3
4
3
ð6:82  0:42Þ  10 ð1:09  0:09Þ  10 ð1:63  0:17Þ  10 ð670  7:5Þ  103

uncertainty in the primary cosmic-ray mass population.
While the full air shower simulation includes a calculationof the production spectra of the multiple muons frommeson decay, the simulation still introduces a large uncertainty because both the primary composition at relevant
cosmic-ray energies (> 107 GeV) and the hadronic interaction model are highly uncertain.
The second simulation uses a model relying on a phenomenological fit to part of the experimental high-energy
data. This empirical model approximates multiple muontracks in an event by a single high-energy muon which isadequate at very high energies for the variables used in thisanalysis. The single muon approximation predicts larger
fluctuations in NPE due to radiative energy losses ofenergetic muons, giving a rather conservative estimateof the background passing rate. The two independent setsof simulations with top-down and bottom-up approaches
to describe the observational data complement each otherimproving the reliability of the background estimation.
1. Background estimation with CORSIKA
Figure 2 shows distributions for data and simulations at
level-2 for NPE, the reconstructed zenith angle (), and thecenter-of-gravity depth of the events (zCOG ). The CORSIKA
NPE distribution is extrapolated to the higher NPE region.
Extrapolation was necessary mainly because of a lack ofsimulated CORSIKA events at primary cosmic-ray energies
above 1010 GeV. The extrapolation accounts for the observed GZK cutoff at an energy around 5  1019 eV. The
NPE-weighted LineFit algorithm was used to reconstructzenith angle in this initial study. The NPE-weighted
LineFit is a simple minimization of 2 ¼ i NPEi ðr~i ~ 2 , where ti and NPEi represent, respectively,
r~COG  ti vÞ
the time of the first photoelectron and the number ofphotoelectrons recorded by the ith DOM at the positioni xi i NPEi yi i NPEi zi; i NPEi ; i NPEi Þ is the NPEr~i and r~COG  ði NPE
i NPEiweighted position of the center of gravity of the hits. The
fit ignores the geometry of the Cherenkov cone and theoptical properties of the medium and assumes light traveling with a velocity v~ along a one-dimensional path throughthe detector, passing through the center of gravity.
The measured event rates are close to the simulated rates
based on CORSIKA-SIBYLL with iron primaries and above
those based on CORSIKA-SIBYLL proton data in most regions. A significant discrepancy can be found in the rate ofevents with cos  0:3, i.e. events reconstructed as horizontal or up-going, which is largely underestimated.
Replacing SIBYLL with other hadronization models (e.g.
QGSJET-II) does not change this behavior. The discrepancy
may be due to a combination of uncertainties in the hadronic interaction models, cosmic-ray flux, and Cherenkov
photon propagation in the glacial ice. Since the horizon is
the key region for the EHE neutrino search, the backgroundestimations were supplemented by an empirical model fit
to a subsample of the data.
2. Construction of an empirical model
The empirical model is optimized to match the level-2
experimental data (104 < NPE < 105 ). The possible signal

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zCOG [m]FIG. 2 (color online). Event distributions for NPE, cosine of reconstructed zenith angle, and the NPE-weighted mean depth ofevent (zCOG ) for observational and the background Monte Carlo simulation data. The black dots represent observational data after the
NPE > 104 cut, red for CORSIKA proton (SIBYLL), magenta for CORSIKA iron (SIBYLL). Green shaded regions represent distributions
obtained with the empirical model with the size of shade expressing the uncertainty of the model. See text for the details.

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200 400zCOG [m]FIG. 3 (color online). Event distributions from the level-3 samples as functions of NPE (left) and zCOG (right). The black dots
represent observational data, green boxes represent the empirical model including uncertainty. Red and magenta lines are CORSIKA
samples with SIBYLL interaction model and proton and iron primaries, respectively. The left panel also includes the expected NPE
distribution of events induced by the cosmogenic neutrinos [6] shown by the blue line for reference.

region (NPE  105 ) is not used to avoid bias. The model
provides a relation between the NPE of an event and thecosmic-ray primary energy. Its convolution with thecosmic-ray flux then gives the event rate with a given
NPE. The cosmic-ray flux used in the present analysis istaken from the compilation in Ref. [2].
The model is based on the so-called Elbert formula [19]which parametrizes the mean multiplicity of muons withenergies above a certain threshold E :

 

AE
E A2 AE N ¼ T;1
E0 cos0 E0
E0(1)
ET ¼ 14:5 GeV;
where A, E0 , and 0 are the mass number, the energy, andthe zenith angle of the primary cosmic ray [20]. The energy
weighted integration of the formula relates the total energy
carried by a muon-bundle EB to the primary cosmic-ray
energy E0 , þ1
Z E0 =A dN
A
AE dE ’ ET
;
EB 
0
cos   1 E0
dE
(2)
1. Here, is empirically determinedassuming AE =E0
by fit to the observed data. Assuming its corresponding
energy at the IceCube depth, in-ice , is independent ofzenith angle, (and thereby EB ) can be calculated as afunction of zenith angle by taking into account the energy
loss during propagation through the Earth. The optimization of the two parameters  and in-ice is performed bycomparing the observed data to simulation of a single highenergy muon with energy of EB in the NPE and zenith
angle space, independently. A ¼ 1 is assumed in the optimization. The event distributions derived from the empirical model with optimized parameters ( ¼ 1:97 andin-ice¼ 1500 GeV) are given in Fig. 2. The green shaded
region in the plot is obtained by allowing the model parameters to vary within 1 from their optimized values.

The discrepancies of zCOG at large depths for the empiricalmodel and at small depths for CORSIKA/iron seem to be due
to vertical, down-going events because a restriction of thezenith angle, cos < 0:8, improves the agreement in bothcases. Since the majority of the EHE neutrino induced
events is close to the horizon we can discard all eventswith cos < 0:8 without significant loss of signal efficiency (level-3 cut). The resulting distributions are shownin Fig. 3.
C. Search for EHE cosmogenic neutrino signal
The level-4 cut to eliminate the muon background is
carried out in the NPE- cos (NZ) plane. In accordancewith the requirements of blindness, the cuts are finalized on
simulated events alone without referring to real data.
Because the optical properties of the glacial ice vary significantly with depth [21], and because the changing absorption and scattering lengths affect what IceCube
observes, the final cuts are chosen to be depth dependent.
The cuts are chosen based on the depth of the weighted
center of gravity of the event, zCOG . The distribution of
events in the NZ plane depends on zCOG . We divide theevents into two groups according to their zCOG as follows:
region A:  250 < zCOG < 50 m

andzCOG > 50 m;

region B: zCOG < 250 m

and 50 < zCOG < 50 m:
As seen in Fig. 4, region B contains a large number ofhorizontal and up-going mis-reconstructed background
events, whereas the fraction of such events in region A is

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FIRST SEARCH FOR EXTREMELY HIGH ENERGY . . .
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6

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104
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104

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Region B: Experimental data (2007)

4.5

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5

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10

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6

6.5

Region B: GZK signal MCcos(zenith angle)

5cos(zenith angle)

4.5

Region A: GZK signal MCcos(zenith angle)

104

cos(zenith angle)

1

Region A: Background MC (CORSIKA)
104
1

log (NPE)cos(zenith angle)

PHYSICAL REVIEW D 82, 072003 (2010)

Region A: Background MC (empirical)cos(zenith angle)

cos(zenith angle)

Region A: Experimental data (2007)

4

4.5

5.5

6

6.5

10-6

log (NPE)

log (NPE)

10

5
10

10

FIG. 4 (color online). Event number distributions passing the level-2 selection cut (NPE > 104 ) of the experimental data (left), thebackground from the empirical model (middle left), the background from CORSIKA-SIBYLL with iron primaries (middle right), and thesignal (right) on the NZ plane at the IceCube depth. The upper (lower) panels show the distributions in the region A (B). The GZK
neutrino flux [6] determines the event intensity in the signal Monte Carlo plot, adding all three flavors of neutrinos. The series of thicklines in each panel indicates the level-3 ( cosðÞ < 0:8) and the final level-4 cuts.

very small. Figure 4 also shows the distributions of theexperimental data and the simulated GZK neutrino induced
signal events. The latter clearly accumulate near the horizontal direction regardless of the zCOG position and have on
average larger NPE than the background sample. The
selection criteria to separate signal from background aredetermined for region A and region B separately: For eachbin of cos (width 0.1), a threshold NPE is set such that the
number of background events above the threshold is lessthan 104 . Tighter cuts to further reduce the backgroundwould also reduce the signal to an undesirable degree. The
NPE thresholds in all the zenith angle bins are then connected to each other to form a series of lines on the NZ
plane, defining the final level-4 cut, as drawn in Fig. 4. The
cuts were optimized using the empirical model for background simulations, so we used extrapolated CORSIKA/irondata as a check of the final background level. Figure 4 also
shows the distribution of background events in the NZ
plane from the extrapolation. Table II summarizes thenumber of events remaining in the analysis after each of
the cut levels.
The effective area as a function of energy at Earth’s
surface for each neutrino flavor is shown in the left panelof Fig. 5, averaged over all solid angles. The area increases with the energy owing to the increasing neutrino
interaction cross sections and the increased probability ofobserving the interactions, which is different for eachflavor.
At low energies, most of the  signal comes from events
where the  interacts in the detector, or the  decays in it.
At higher energies,  energy loss becomes large enoughthat through-going taus also pass the cuts. Contributions
from  and  dominate over e in the energy range
above 108 GeV, as the secondary produced muons andtaus can travel long distances to reach the detection volume. This trend is reversed at lower energy where tau andmuon energy losses are smaller, and e ’s can deposit all of
their energy into the detector volume. The effective area

TABLE II. Number of events at analysis filter levels for 242.1 days in 2007. The simulation predictions for the atmospheric muon
background using the CORSIKA-SIBYLL package, the empirical model, and that for the GZK cosmogenic neutrino model are also listed
for comparison. Errors shown here are statistical only. See Secs. IV B and IV C for details.
Analysis filter levels
Level 3 ( cosðÞ < 0:8)
Level 4 (EHE  search)

Observational data

Empirical model

CORSIKA (iron)

CORSIKA (proton)

Signal (GZK1 [6])20140

ð2:65  0:21Þ  103

ð2:68  0:19Þ  103

ð4:16  0:40Þ  102

ð620  7:3Þ  103
ð155  1:4Þ  103

ð6:32  1:37Þ  104

ð4:18  1:29Þ  104072003-7

ð1:44  0:58Þ  104

R. ABBASI et al.

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PHYSICAL REVIEW D 82, 072003 (2010)

νe
νµ
ντ

1

Effective area [km2]

Effective area [m2]

104

2

10

10−1
10−2
10−3

µ
τ
νe
νµ
ντ

10−4
10−5

1
6 6.5 7 7.5 8 8.5 9 9.5 1010.5

log 10 (Energy/GeV)

10−6

6 6.5 7 7.5 8 8.5 9 9.5 1010.5

log10(in−ice energy/GeV)

FIG. 5 (color online). The effective area of IC-22 for EHE
neutrino search. The left panel shows the 4 solid angle averaged area as a function of neutrino energy at the Earth surface.
The right panel shows the corresponding effective area forparticles at 880 m from the IceCube center entering into theIC-22 fiducial volume. Muons and taus in this plot are secondary
particles produced by neutrinos before reaching the neighborhood of the detector array. The energy here are defined as in-ice
energy.

for  is larger than that for  at low energies, because of
the events where taus decay inside the detector. At thehighest energies, because of the larger mass of taus andincrease of the tau decay time with energy, the tau range islonger than that of muons, leading to a larger effective area.
The right panel in Fig. 5 shows the effective area as afunction of the in-ice energy (’’in-ice area’’). It represents
the probability of detection of incoming particles with thepresent analysis. The area for incident muons and taus
gradually increases with energy but is limited essentiallyby the physical cross section of the IC-22 array, 0:5 km2 .
Because the Cherenkov yield of taus is smaller than muons
with the same energy due to the smaller radiative energy
loss, the detection probability of incident taus is lower,
leading to the smaller in-ice area. Incoming neutrinos must
interact to yield Cherenkov light to be detected. Therefore,
the neutrino effective area becomes much smaller than thatfor muons or taus.
TABLE III. Expected event numbers passing the final level-4
selection criteria in the 2007 IC-22 observation. Models include
the GZK models [6,22,23] and the Z-burst model [24]. The
predictions are normalized to a live time of 242.1 days. Signal
event numbers represent the sum over all three neutrino flavors.
The first uncertainty is the statistical uncertainty determined bysignal simulation statistics, and the second is the total systematic
uncertainty from sources discussed in Sec. V.
ModelsGZK1 [6]GZK2 [22]GZK3 [23]Z-burst [24]Number of Events per 242.1 days
3
ð155  1:4þ24
40 Þ  10
þ39
ð248  2:3þ65 Þ  103
3
ð83  0:8þþ13
21 Þ  10
þ63
3
ð398  3:495 Þ  10

The expected number of signal events for various neutrino production models after the level-4 cut are summarized in TABLE III. GZK1 [6] represents the case of amoderately strong source evolution, ðz þ 1Þm with m ¼ 4extending to z ¼ 4:0, while GZK2 [22] assumes m ¼ 5 up
to z ¼ 2:0, and GZK3 [23] uses m ¼ 3 with a slightly
different parametrization and a cutoff structure.
V. THE SYSTEMATICSThis search is based on the eventwise NPE and reconstructed zenith angle. The main systematic uncertainties
derive from (1) the necessity to extrapolate the empirical
fit to data by approximately an order of magnitude in NPE
to estimate the background rate at the highest energies andfrom (2) the uncertainty of the absolute NPE scale. Table IVlists the sources of statistical and systematics errors.
A. Uncertainties in the background rate estimation
The largest uncertainty in the background rate estimate
arises from the fact that the parameters of the empiricalmodel were optimized for the observed events with 104 <NPE < 105 after level 2 selection. The limited statistics ofthis sample results in uncertainties on the parameters. The
model was then extrapolated to a higher NPE region for thedetermination of the level-4 cut.
Allowing the parameters to vary within 1 changes
the background rate by between 59% (for the softest
possible NPE spectrum after the level-4 cuts) and þ99%(for the hardest possible NPE spectrum). Uncertainties inthe detector sensitivity are incorporated by the parametrization. The difference in the background level estimatedwith the extrapolated CORSIKA/iron and the empiricalmodel can be taken to indicate the level of systematic
uncertainty due to model dependence. This uncertainty isapproximately 15% and can be assumed to include thepossible contribution from charm decay. An uncertainty
associated with the high-energy hadronic interaction
model is evaluated using simulated muon-bundle intensityfrom SIBYLL and QGSJET-II with iron primaries and found tobe 4%, which is negligible. An additional uncertainty of17% arises from the seasonal variation of the atmospheric muon rate as the signal selection criteria are based
upon the season-averaged data.
B. Uncertainties of the signal rate estimate
The uncertainty in the relationship between measured
NPE and the energies of charged particles is the largest
systematic error affecting the signal event rate. It is theconsequence of our limited understanding of the detector
sensitivity, the photon propagation in ice, and the detector
response to bright signals. It is evaluated using absolutely
calibrated in situ light sources and amounts to a possible
overestimation of NPE in simulation by 18.5%, whichleads to decrease of the GZK signal rate by 21%.

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PHYSICAL REVIEW D 82, 072003 (2010)

TABLE IV. List of the statistical and systematic errors. The signal rate is estimated byassuming the high evolution flux ðm; Zmax Þ ¼ ð4; 4Þ in Ref [6].

Statistical error
Detector sensitivity
Yearly variation
Empirical model
Background model dep.
NPE yield
Neutrino cross section
Photonuclear interaction
LPM effect
Total

Background rate

Signal (GZK) rate

22%

17%
þ99=  59%
15%




22% (stat.)þ102=  63% (sys.)

0:9%
8%



þ0=  21%
9%
þ10%
1%
0:9% (stat.)þ16=  26% (sys.)

Uncertainties of the relevant particle interactions in the
EHE regime also add systematics in the signal rate estimation. The expected event rate scales nearly linearly with
the neutrino-nucleon inelastic cross section in the EHE
range. This scaling has been confirmed by numerical studies, artificially increasing the cross section. The crosssection uncertainty has been recently reduced to be around9% with the inclusion of the most recent data from
HERA and modern parton distribution functions [25].
Another systematic error arises from the photonuclear
cross section of EHE muons and taus. The present calculation used the model by Bugaev and Shlepin [26], rewritten in Ref. [27], that includes a relatively reliable soft
nonperturbative component and a less certain hard perturbative part. Ignoring the hard component in the simulation
gives the most conservative estimate of the uncertainty andleads to a 10% event rate increase. The suppression ofbremsstrahlung and pair production due to the LPM effect[28], for the relevant electron energies of 10910 GeV,
increases the effective radiation length of the electromagnetic cascade to Oð30–100Þ m from 36 cm [29]. Because
the value is still comparable to the IceCube DOM separation, and the contribution from e constitutes  20% of thetotal event rate in this energy range, the LPM effect has anegligible impact on the event rate. This has been confirmed by a special simulation study on e including theLPM cascade elongation.

width of a decade of energy with condition that energy
dependence of neutrino flux multiplied by the effective
area behaves as 1=E [31]. This limit is presented inFig. 6 including the systematic errors. The plot indicatesthat the EHE neutrino search by the IceCube observatory ismost sensitive to the neutrinos with energies on Earth’s
surface ranging between about 108 and 109 GeV. The
absence of signal events in the sample of 242.1 days ofeffective live time results in a 90% C.L. differential upper
limit on the neutrino flux of E2 e þ þ ’ 1:4 
106 GeV cm2 sec1 sr1 on average for neutrinos with
−4
10−4

10−5

E2 φ(E) [GeV cm−2 sec−1 sr−1]

Error source

−6
10−6

differential upper limits

10−7

−8
10−8

IceCube−22
RICE
Auger
ANITA
AMANDA−II

neutrino models

GZK1
GZK2
GZK3
Z−burst

−9

10

−10
−10
10

7

8

9

10

11

log (Energy/GeV)

VI. RESULTS

10

No events are observed in the final data sample taken in2007 with a live time of 242.1 days when applying the final
level-4 selection criteria, which is consistent with the expected number of background events of 6:3  104 . We
choose to present the resulting all flavor EHE neutrino
upper limit in the quasi-differential form independent of
the neutrino production model. Assuming full mixing due
to oscillations, the experimental 90% confidence level
upper limit is obtained by setting 2.44 events [30] for an
upper bound of the number of events observed with bin

FIG. 6. The all flavor neutrino flux differential limit from theIC-22 EHE analysis (filled circles). The systematic errors areincluded. Also the various model predictions are shown forcomparison: GZK model 1 [6] (short dashed line), GZK model
2 [22] (dotted line), GZK model 3 [23] (long dashed line),
Z-burst model [24] (dashed dot line). The model independent
differential upper limits by other experiments are also shown forAuger [32] (open triangles), RICE [31] (crosses), ANITA [34](open squares), AMANDA [35] (rhombi). Limits from otherexperiments are converted to the all flavor limit assuming fullmixing neutrino oscillations and 90% C.L when necessary.

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PHYSICAL REVIEW D 82, 072003 (2010)7

9

an energy of 3  10  E  3  10 GeV. Heree þ þ denotes the differential flux of the sum over
all three neutrino flavors, i.e. number of neutrinos per unit
energy, area, time and solid angle.
The quasi-differential limit in Fig. 6 takes into accountthe systematic uncertainties. The background rate stays
negligible Oð103 Þ even including the systematic uncertainty and the resultant upper limit is unchanged. The
signal rate uncertainty is strongly dominated by the uncertainty of the NPE yield which influences the number of
expected signal events as a function of the neutrino energy.
The upper limit is calculated by reducing NPE by 18.5% in
the signal simulation to account for this factor. All theother sources of systematic error only slightly change thesignal passing rate; they are independent of energy. They
are included in the analysis by uniformly scaling theeffective area in the limit calculation.
The present limit is approximately a factor of 20–30
higher than the intensity range expected in the GZK cosmogenic neutrino production models [6,22,23], as one cansee in Fig. 6. The current limit for 242.1 days of observation is comparable to the Auger [32] and HiRes [33]bounds by their multiple year operation.

factor of 20 higher than the predicted GZK neutrino flux
from relatively strongly evolved sources. In the future, datataken by IceCube with 40 to 86 strings operating should
lead to a detection of cosmogenic neutrinos or a greatly
improved limit.
ACKNOWLEDGMENTS

The present work has demonstrated that the IceCube
neutrino observatory is capable of searching for signaturesof EHE cosmogenic neutrinos with relatively straightforward event selection methods. The model independent
differential upper limit obtained with 242.1 days ofobservation in 2007, with approximately one quarterof the completed detector is E2 e þ þ ’ 1:4 
106 GeV cm2 sec1 sr1 for neutrinos with an energyof 3  107  E  3  109 GeV. This is approximately a

We acknowledge the support from the following agencies: U.S. National Science Foundation - Office of Polar
Programs, U.S. National Science Foundation - Physics
Division, University of Wisconsin Alumni Research
Foundation, U.S. Department of Energy, and National
Energy Research Scientific Computing Center, theLouisiana Optical Network Initiative (LONI) grid computing resources; Swedish Research Council, Swedish Polar
Research Secretariat, Swedish National Infrastructure for
Computing (SNIC), and Knut and Alice Wallenberg
Foundation, Sweden; German Ministry for Education andResearch (BMBF), Deutsche Forschungsgemeinschaft(DFG), Research Department of Plasmas with Complex
Interactions (Bochum), Germany; Fund for Scientific
Research (FNRS-FWO), FWO Odysseus programme,
Flanders Institute to encourage scientific and technologicalresearch in industry (IWT), Belgian Federal Science Policy
Office (Belspo); University of Oxford, United Kingdom;
Marsden Fund, New Zealand; Japan Society for Promotionof Science (JSPS); the Swiss National Science Foundation(SNSF), Switzerland. A. Kappes and A. Groß acknowledge
support by the EU Marie Curie OIF Program.
J. P. Rodrigues acknowledges support by the Capes
Foundation, Ministry of Education of Brazil. This analysis
work has been particularly supported by the Japan-US
Bilateral Joint Projects in the Japan Society for the
Promotion of Science.

[1] For a review, see, e.g. J. W. Cronin, Rev. Mod. Phys. 71,
S165 (1999); S. Yoshida and H. Dai, J. Phys. G 24, 905(1998).
[2] M. Nagano and A. A. Watson, Rev. Mod. Phys. 72, 689(2000).
[3] N. Hayashida et al., Phys. Rev. Lett. 77, 1000 (1996); J.
Abraham et al. (Pierre Auger Collaboration), Science 318,
938 (2007).
[4] K. Greisen, Phys. Rev. Lett. 16, 748 (1966); G. T. Zatsepin
and V. A. Kuzmin, Pis’ma Zh. Eksp. Teor. Fiz. 4, 114(1966) [JETP Lett. 4, 78 (1966)].
[5] V. S. Berezinsky and G. T. Zatsepin, Phys. Lett. 28B, 423(1969).
[6] S. Yoshida and M. Teshima, Prog. Theor. Phys. 89, 833(1993).
[7] A. Achterberg et al. (IceCube Collaboration), Astropart.
Phys. 26, 155 (2006).

[8] F. Halzen and D. Hooper, Phys. Rev. Lett. 97, 071101(2006).
[9] S. Yoshida et al., Phys. Rev. D 69, 103004 (2004).
[10] R. Abbasi et al. (IceCube Collaboration), Nucl. Instrum.
Methods Phys. Res., Sect. A 601, 294 (2009).
[11] R. Abbasi et al. (IceCube Collaboration), Astrophys. J.
Lett. 689, L65 (2008).
[12] R. Abbasi et al. (IceCube Collaboration), Nucl. Instrum.
Methods Phys. Res., Sect. A 618, 139 (2010).
[13] J. Jones, I. Mocioiu, M. H. Reno, and I. Sarcevic, Phys.
Rev. D 69, 033004 (2004).
[14] D. Heck et al., Forschungszentrum Karlsruhe Report
No. FZKA 6019 (1998).
[15] T. S. Sinegovskaya and S. I. Sinegovsky, Phys. Rev. D 63,
096004 (2001).
[16] R. Enberg, M. H. Reno, and I. Sarcevic, Phys. Rev. D 78,
043005 (2008).

VII. CONCLUSIONS

072003-10

FIRST SEARCH FOR EXTREMELY HIGH ENERGY . . .

PHYSICAL REVIEW D 82, 072003 (2010)[17] D. Chirkin and W. Rhode, arXiv:hep-ph/0407075v2.
[18] J. Lundberg et al., Nucl. Instrum. Methods Phys. Res.,
Sect. A 581, 619 (2007).
[19] T. K. Gaisser, Cosmic Rays and Particle Physics(Cambridge University Press, Cambridge, England,1990), p. 206.
[20] J. W. Elbert, in Proceedings of the DUMAND Summer
Workshop, La Jolla, California, 1978, edited by A.
Roberts (Scripps Institution of Oceanography, La Jolla,
CA, 1979) Vol. 2, p. 101.
[21] M. Ackermann et al., J. Geophys. Res. 111, D13203(2006).
[22] O. E. Kalashev, V. A. Kuzmin, D. V. Semikoz, and G. Sigl,
Phys. Rev. D 66, 063004 (2002).
[23] R. Engel, D. Seckel, and T. Stanev, Phys. Rev. D 64,
093010 (2001).
[24] S. Yoshida, G. Sigl, and S. Lee, Phys. Rev. Lett. 81, 5505
(1998).
[25] A. Cooper-Sarkar and S. Sarkar, J. High Energy Phys. 01(2008) 075.

[26] E. V. Bugaev and Yu. V. Shlepin, Phys. Rev. D 67, 034027(2003).
[27] E. Bugaev, T. Montaruli, Y. Shlepin, and I. Sokalski,
Astropart. Phys. 21, 491 (2004).
[28] L. Landau and I. Pomeranchuk, Dokl. Akad. NaukSSSR 92, 535 (1953); A. Migdal, JETP 5, 527(1953).
[29] S. Klein, Rev. Mod. Phys. 71, 1501 (1999).
[30] G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873
(1998).
[31] I. Kravchenko et al. (Rice Collaboration), Phys. Rev. D
73, 082002 (2006).
[32] J. Abraham et al. (Pierre Auger Collaboration), Phys. Rev.
D 79, 102001 (2009).
[33] R. U. Abbasi et al. (HiRes Collaboration), Astrophys. J.
684, 790 (2008).
[34] P. W. Gorham et al. (ANITA Collaboration), Phys. Rev. D
82, 022004 (2010).
[35] M. Ackermann et al. (IceCube Collaboration), Astrophys.
J. 675, 1014 (2008).

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