Xing Zh., Zhou Sh. Neutrinos in Particle Physics, Astronomy and Cosmology
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296 8 Ultrahigh-energy
C
osmic Neutrinos
p
π
+
μ
+
e
+
ν
μ
ν
¯
ν
μ
ν
ν
e
n
e
−
¯
ν
e
p
p
π
+
μ
+
e
+
n
π
−
μ
−
e
−
p
ν
μ
ν
¯
ν
μ
ν
ν
e
¯
ν
μ
ν
ν
μ
ν
¯
ν
e
Fi
g
.8.3
A
sketch of the neutrino production in an accelerator of UHE cosmic rays.
The relative fluxes depend on the optical thickness of the magnetic confinement
re
g
ion illustrated by the wavy lines. The le
f
t and ri
g
ht panels represent the optically
thin and thick sources, respectively
(
Ahlers et a
l.
, 2006. With
p
ermission
f
ro
m
Elsevier)
E
ν
μ
≈
E
ν
e
≈
0
.
26
E
π
(
Ahlers, 2007
)
. Roughly speaking, about 1
/
4of
the pion’s energy is taken away by each o
f
ν
μ
,
ν
μ
a
n
d
ν
e
.S
o we define a
fl
avor-universal ratio
f
or three relevant neutrinos
,
ν
≡
E
ν
E
n
=
E
ν
E
π
·
E
π
E
n
≈
π
4
,
(
8.2
)
which will later on be used in the calculation o
f
the
U
HE neutrino
fl
ux
.
For a
g
iven optically thin source at the redshift position z,
o
n
e
m
ay co
n
-
s
ider the differential rate of the neutron flux in an energy interval
[
E
1
,
E
2
]
and
that of the neutrino flux in the corresponding energy interval
[
ν
E
1
,
ν
E
2
]:
N
ν
N
N
≡
ν
E
2
ν
E
1
d
E
L
ν
(
z
,E
)
,
N
n
NN
≡
E
2
E
1
d
E
L
n
(
z,
E
)
=
ν
E
2
ν
E
1
d
E
1
ν
L
n
(
z,E
/
ν
)
,
(
8.3
)
where L
ν
(
or
L
n
)
denotes the neutrino
(
or neutron
)
luminosity per comovin
g
volume. Since the rates of the neutron and neutrino fluxes are 1 : 3
(
i.e.,
N
ν
N
N
=
3
N
n
N
N
)
,wehave
(
Ahlers
et al.
,
2006; Ahlers, 2007
)
L
ν
(
z
,E
)=
3
ν
L
n
(
z,E
/
ν
)
.
(
8.4
)
E
xcept for the resonant
(
Z
-
burst
)
interactions in the cosmic neutrino back
-
ground
(
Weiler, 1982, 1999; Fargio
n
et al.
,
1999
)
, the UHE neutrinos ma
y
8
.1 Possible
S
ources o
fU
HE
C
osmic Neutrinos 2
97
only under
g
o the redshi
f
tlossoncetheyareemitted
f
rom the source. Thei
r
propa
g
ation function is simply
g
iven by a step function
:
P
ν
|
ν
(
E
;
E
i
,z
)=
Θ
(
E
i
−
(
1+
z
)
E
)
, whose derivative is just the delta function. Then one ca
n
a
rrive at the total flux of UHE neutrinos
(
Ahlers, 2007
)
:
J
ν
JJ
(
E
)=
1
4
π
∞
0
d
E
i
∞
0
d
z
1
H
(
z
)(
1+
z
)
∂P
ν
|
ν
(
E
;
E
i
,z
)
∂
E
L
ν
(
z
,E
i
)
=
1
4
π
·
3
ν
∞
0
d
z
1
H
(
z
)
L
n
(
z
,
(
1
+
z
)
E
/
ν
)
,
(
8.5
)
where
H
(
z
)
is the Hubble expansion rate at the redshift position
z
.S
uch a
U
HE neutrino
fl
ux, which arises
f
rom a transparent source o
f
cosmic rays, is
often referred to as the Waxman-Bahcall flux
(
Waxman and Bahcall, 1999
).
8.1.3 To
p
-downModelsandUHENeutrino
s
In the “bottom-up” approach discussed above, it is very difficult to identify
a
nastroph
y
sical source as the wanted “zevatron” accelerator o
f
cosmic ra
y
s
.
A
variet
y
of “top-down” models have so far been proposed to avoid this dif-
ficulty and attribute the observed UHE cosmic ray primaries to the decay
or annihilation
p
roducts o
f
some su
p
ermassive
p
articles. Two classes o
f
th
e
top-down models, the superheavy dark matter
(
DM
)
and topological defects
(
TDs
)
, have attracted some particular interest because they are well moti
-
vatedeveni
f
the ori
g
in o
f
UHE cosmic rays is irrelevant. For instance, TDs
(
e.g., monopoles, cosmic strings, domain walls, etc.
)
are a generic predictio
n
o
f
some
g
rand uni
fi
ed theories and could be
f
ormed in the symmetry-breakin
g
phase transitions in the earl
y
Universe. The superheav
y
DM is an interest
-
i
ng DM can
d
i
d
ate, an
d
its sta
bl
eormetasta
bl
e partic
l
es wit
h
masses aroun
d
10
13
G
eV could be produced durin
g
the in
fl
ation era o
f
the Universe. I
f
on
e
of the top-down models is responsible for the ori
g
in of UHE cosmic rays, i
t
m
ust
b
ea
bl
etopro
d
uce UHE neutrinos an
d
p
h
otons.
S
uperheavy stable or metastable relic particles can be a
g
ood candidat
e
f
or cold DM. The
y
could be produced in the earl
y
Universe in various wa
y
s,
f
or example, by gravitational interactions from vacuum fluctuations at the
endofinflation
(
Chun
g
et al.
, 1999; Kuzmin and Tkachev, 1999
)
. The lifetim
e
of a superheav
y
DM particle
X
h
as to lie in the range 10
17
s
τ
X
τ
1
0
2
8
s
(
Kachelrieß, 2008
)
, longer or much longer than the age of the Universe. Such
a
lon
g
-lived particle mi
g
ht be protected by an underlyin
gg
lobal symmetry
which is broken in a perturbative way by high-dimensional operators sup-
presse
db
y
1
/M
n
w
i
th
n
7, w
h
ere
M
is c
l
ose to t
h
eP
l
anc
k
mass sca
l
e, o
r
i
n a non-perturbative way by wormhole or instanton effects
(
Berezinsk
y
et
a
l
.
,
1997; Kuzmin and Rubakov, 1998; Hamaguchi et al
.
, 1998
)
.Thesuper-
h
eavy DM has several clear observational signatures
(
Kachelrieß, 2008
)
.
(
1
)
It does not predict a GZK cutoff for UHE cosmic ra
y
s; instead, it
y
ields a
298 8 Ultrahigh-energy
C
osmic Neutrinos
s
pectrum, which is
fl
atter than that
g
iven by an astrophysical source, up to
the kinematical cutoff at
E
∼
m
X
/
2.
(
2
)
The decay or annihilation product
s
of the superheavy DM contain a lot o
f
π
±
a
n
d
π
0
events w
h
ose
d
ecays yie
ld
l
ar
g
e UHE neutrino and photon
fl
uxes, usually lar
g
er than those produce
d
f
rom the shock-accelerated protons at an astrophysical source.
(
3
)
The flu
x
of cosmic rays from the superheavy DM should show a galactic anisotropy,
a
s the Sun is not in the center of the Galaxy.
(
4
)
Thereisnocorrelatio
n
between UHE cosmic ra
y
arrival directions and astroph
y
sical sources, sinc
e
extraga
l
actic cosmic rays are strong
l
y suppresse
d
in a super
h
eavy DM mo
d
e
l.
T
Ds, whose existence was in no con
fl
ict with cosmic in
fl
ation, could b
e
produced in the non-thermal phase transitions during the preheating stage
of the Universe
(
Vilenkin and Shellard, 1994
)
. They can naturally produce
particles with su
ffi
ciently hi
g
hener
g
ies, but have problems to produce su
ffi-
c
iently large fluxes of UHE cosmic ray primaries because of the typically larg
e
d
istance between two TDs
(
Kachelrieß, 2008
)
. So the flux of UHE cosmic rays
i
s either exponentially suppressed or stron
g
ly anisotropic i
f
aTDhappensto
be nearby. Note that the energy spectrum of UHE cosmic rays originating
f
rom cosmic strin
g
smi
g
ht have a less pronounced
G
ZK cuto
ff
,simplybecaus
e
i
t is not so steep as usual and is dominated b
y
photons instead of protons
.
Since cosmic strings do not cluster, no correlation is expected between th
e
U
HE cosmic ra
y
arriva
ld
irections an
d
astrop
hy
sica
l
sources.
I
t is worth mentionin
g
that the weakly interactin
g
massive particles
(
WIMPs
)
, which are regarded as one of the most promising DM candidates
,
c
an also produce ener
g
etic neutrinos when they annihilate.
A
typical exampl
e
of WIMPs is the lightest supersymmetric particle, such as the neutralino. If
the masses of WIMPs are around the electroweak scale, their annihilation wil
l
produce neutrinos and antineutrinos with ener
g
ies o
f
O
(
1
0
2
)
GeV t
o
O
(
1
)
TeV. The detection of such signatures at a neutrino telescope can serve for a
n
i
ndirect search for DM
(
Bell, 2008; Halzen and Hooper, 2009
)
. In comparison,
the detection o
f
UHE neutrinos wit
h
E
O
(
1
)
PeV will indirectly probe th
e
existence of the superheavy DM or TDs.
8
.2 Detection of
U
HE
C
osmic Neutrinos
A
n important subject of high-energy neutrino astronomy is to search for the
point-
l
i
k
e neutrino sources, w
h
ic
h
wou
ld h
e
l
pso
l
ve a
l
on
g
stan
d
in
g
pro
bl
em
— the origin of UHE cosmic rays. The detection of UHE cosmic neutrinos
requires the construction of huge detectors, the so-called neutrino telescopes
,
w
h
ic
h
are we
ll
motivate
dby
t
h
eir
d
iscover
y
potentia
l
in astronom
y
,astro
-
physics, cosmology and particle physics
(
Halzen, 2006a
)
. Because the fluxe
s
of cosmic rays above the knee are too small to be detected in the satellite o
r
balloon experiments, lar
g
e
g
round-based or under
g
round detectors with lar
g
e
effective detection areas have to be built. The most im
p
ortant ex
p
erimental
8
.2 Detection o
fU
HE
C
osmic Neutrinos 2
99
Fig. 8.4 A sketch of the experimental techniques for ground-based or underground
detection of high-energy cosmic rays, gamma rays and neutrinos
(
Lohse, 2005
)
techniques
f
or
g
round-based or under
g
round observation o
f
hi
g
h-ener
g
y cos-
m
ic rays, gamma rays and neutrinos are sketched in Fig. 8.4
(
Lohse, 2005
).
To detect UHE cosmic neutrinos, a deep underground ice or water Cherenko
v
d
etector is needed. In addition, radio and acoustic detection techniques
f
or
the detection of neutrino interactions have been develo
p
ed.
8.2.1 A km
3
-scale UHE Neutrino Telescope
A
n optical Cherenkov neutrino telescope consists of lar
g
e arrays of photomul
-
tiplier tubes underwater or under ice. It detects the Cherenkov li
g
ht emitted
b
yc
h
arge
dl
eptons w
h
ic
hh
ave
b
een pro
d
uce
d
in neutrino interactions wit
h
the medium
(
water or ice
)
. This technique was established by two pioneer
-
i
ng detectors, NT200 in Lake Baikal
(
Balkano
v
e
tal
.
,
1998
)
and AMAND
A
a
t the South Pole
(
Ahren
s
e
ta
l.
,
2004
;
Ackermann et a
l.
,
2006
)
. At presen
t
three underwater neutrino telescope projects, ANTARES
(
Aslanides
et al.
,
1
999
)
, NESTOR
(
Tzamarias
e
tal
.
,
2003
)
and NEMO
(
Piatell
i
e
tal., 2005
),
a
re
b
eing pursue
d
in t
h
eMe
d
iterranean sea. T
h
e most impressive optica
l
C
herenkov neutrino telescope is Ice
C
ube, a k
m
3
-
sca
l
e successo
r
o
f
A
M
A
ND
A
a
t the South Pole
(
Achterberg et al., 2006
)
.
I
ce
C
ubeisak
m
3
-volu
m
eu
n
de
r-i
ce
n
eut
rin
o detecto
r
u
n
de
r
co
n
st
r
uct
i
on
a
tthe
S
outh Pole.
O
nce its deplo
y
ment is completed in 2011, Ice
C
ube wil
l
c
omprise 4800 digital optical modules
(
DOMs
)
along 80 vertical strings de
-
ployed in the ice at depths
f
rom 1450 m to 2450 m. The distance betwee
n
300 8 Ultrahigh-energy
C
osmic Neutrinos
two nei
g
hborin
g
strin
g
s is 125 m. Each strin
g
consists o
f
60 D
O
Ms at a verti
-
c
al spacin
g
of 16.7 m. Each DOM consists of a 25-cm-diameter Hamamatsu
photomultiplier tube, the electronics for waveform digitization and a spher-
i
cal pressure-resistant
g
lass housin
g
. Hal
f
o
f
the array con
fig
uration with 4
0
s
trings had been finished before
A
pril 2008, and it has began operating since
May 2008. The IceCube facility is complemented with an air shower array
,
IceTop, which covers a sur
f
ace o
f
1km
2
above the Ice
C
ube detector and is
c
omposed of 80 detector stations
(
Bernardini, 2009
)
. Each station is equippe
d
with two ice Cherenkov tanks. The IceTop facility serves as a veto to cosmic
ra
y
s
h
owers an
d
as a ca
l
i
b
ration arra
y
,an
d
it can a
l
so
b
euse
d
to stu
dy
som
e
other scientific topics on cosmic rays.
T
he Ice
C
ube detector is optimized to detect cosmic neutrinos o
f
all
fl
avor
s
i
n the ener
g
yran
g
e
f
rom TeV to EeV. The si
g
nal wave
f
orms recorded b
y
i
ndividual photomultipliers are digitized in each DOM and transmitted to
the surface by twisted-pair cables
(
Bernardini, 2009
)
. Experimental data ca
n
be processed by several hardware and so
f
tware tri
gg
ers, which are responsiv
e
to different event topologies. A series of reconstruction algorithms and even
t
fi
lters are applied in situ to the calibrated data so as to reduce the tri
gg
er rate
to a total data volume
,
which can then be transferred north via a satellite.
Such events will later on be fitted to the templates representing differen
t
n
eutrino interaction modes
(
Bernardini, 2009
)
. The IceCube Collaboratio
n
h
as so far searched for
p
ossible
p
oint-like sources of cosmic neutrinos in th
e
n
orthern sky by using the data recorded from 2007 to 2008 with 22 strings o
f
the detector and 275.7 days of live time
(
Abbas
i
et al
., 2009
)
. The final sampl
e
of 5114 neutrino candidate events agrees well with the expected background
of atmospheric muon neutrinos and a small component of atmospheric muons,
a
nd shows no evidence
f
or a point-like source
.
T
o build a k
m
3
-scale neutrino telesco
p
e in the northern hemis
p
here as
a
c
ounterpart of IceCube is well motivated
(
Avignone
et al
.
,
2008
)
.Ontheon
e
h
and, the candidate sources
f
or hi
g
h-ener
g
y neutrinos are not isotropically
d
istributed in the local Universe. This fact, together with the probably mod-
est number o
f
detectable sources, calls
f
or a complete covera
g
eo
f
the sky.
O
n the other hand, onl
y
a telescope in the northern hemisphere is able to
s
ee the upward-going neutrinos coming from the galactic center — a plac
e
o
f
particular interest. Hence KM3NeT, a km
3
-
sca
l
e UHE neutrino te
l
escope
i
n the Mediterranean sea to com
p
lement the IceCube detector at the Sout
h
P
ole, has been proposed
(
Car
r
et a
l
.
,
2007
)
. The KM3NeT design study i
s
c
urrentl
y
underwa
y
to address man
y
important issues, such as its scienti
fic
s
ensitivit
y
, fast and secure installation, stable operation and maintainabilit
y,
a
n
dl
ong-term
d
eep-sea measurements
.
8.2.2 Identi
fi
cation o
f
UHE Neutrino Flavors
F
or either Ice
C
ube or KM3NeT, the detection o
f
all neutrino
fl
avors is im
-
portant because of the tau neutrino “regeneration” through the Earth and
8
.2 Detection o
fU
HE
C
osmic Neutrinos
301
n
eutrino oscillations
(
Halzen, 2006a
)
. A generic cosmic accelerator is ex-
pected to produce UHE neutrinos from the decays of char
g
ed pions, and
thus the ratio of initial
(
ν
e
+
ν
e
)
,
(
ν
μ
+
ν
μ
)
and
(
ν
τ
+
ν
τ
)
fluxes should be
φ
e
:
φ
μ
:
φ
τ
=1:2:0.T
h
an
k
s to neutrino osci
ll
ations, t
h
is ratio turns out to
be 1 : 1 : 1 at a neutrino telesco
p
e, as one can see in Section 8.3. The a
pp
ear
-
a
n
ce o
f
ν
τ
(
o
r
ν
τ
)
events is a natural consequence of neutrino oscillations
.
U
n
l
i
k
e UHE
ν
e
a
n
d
ν
μ
neutrinos, w
h
ic
h
can
b
ea
b
sor
b
e
db
yt
h
eir c
h
ar
g
e
d
-
c
urrent interactions with matter in the Earth
,
UH
E
ν
τ
neutrinos cannot b
e
a
bsorbed in the Earth due to the charged-current regeneration effect
(
Halze
n
a
nd Saltzberg, 1998
)
.Inotherwords
,
ν
τ
n
eutrinos wit
h
ener
g
ies
l
ar
g
er t
h
a
n
1
PeV can pass through the Earth and then emerge with energies of abou
t
1
PeV. T
h
e reason is simp
l
e: an UH
E
ν
τ
n
eutrino interactin
g
in t
h
e Eart
h
c
an
p
roduce anothe
r
ν
τ
neutrino, whose ener
g
y is somewhat lower, either di
-
rectly via the neutral-current interaction o
f
ν
τ
w
ith matter or indirectly via
the decay o
f
a
τ
lepton produced
f
rom the char
g
ed-current interaction o
f
ν
τ
with matter. UH
E
ν
τ
n
eutrinos will there
f
ore cascade down to the PeV level
a
tw
h
ic
h
t
h
e Eart
h
is essentia
ll
y transparent
.
Akm
3
-sca
l
eneutrinote
l
escope is in
g
enera
ld
esi
g
ne
d
to
d
etect cosmic
n
eutrinos of all possible ener
g
ies above
O
(
1
0
2
)
GeV. It actually detects the
s
econdary particle showers initiated by neutrinos of all flavors as well as th
e
l
eading secondary muon tracks initiated only by muon neutrinos
(
Halzen,
2
006b
)
. Let us briefly describe how to identify different neutrino flavors at
the IceCube
(
or KM3NeT
)
detector.
(
1
)
I
denti
fi
cation o
f
electron neutrinos
.
Hi
gh
-ener
g
ye
l
ectron neutrinos
c
an onl
y
deposit
1
% of their energy into an electromagnetic shower ini-
tiated by the leading final-state electrons
(
e.g.,
ν
e
+
n
→
p
+
e
−
)(
Halzen
,
2
006a
)
4
.
The rest o
f
their ener
g
y
g
oes into the
f
ra
g
ments o
f
the tar
g
et
s
which produce a second subdominant shower. The span of the electromag
-
n
etic shower is only a
f
ew meters in ice or water, much smaller than th
e
h
orizontal spacing of the DOMs
(
∼
1
25 m
)
. Hence such a shower approxi-
m
ates to a point-like source of Cherenkov photons radiated by its charged
particles. These
C
herenkov photons tri
gg
er the D
O
Matthesin
g
le photo
-
electron level over a s
p
herical volume whose radius scales u
p
with the showe
r
energy
(
Halzen, 2006a
)
, as illustrated in Fig. 8.5. A measurement of the ra
-
d
ius o
f
this sphere in the lattice o
f
D
O
Ms can then be used to determine th
e
ener
g
y of the incident electron neutrinos. Because the shower itself and its
a
ccompanying Cherenkov lightpool are not completely symmetric but elon
-
g
ated in the direction o
f
the leadin
g
electron, the direction o
f
the incident
n
eutrino can then be reconstructed to a reasonable degree of accuracy
(
wit
h
a
n
e
rr
o
r
bar
10
◦
)(
Halzen, 2006b
).
4
F
or
h
ig
h
-energy e
l
ectron antineutrinos,
ν
e
+
p
→
n
+
e
+
a
n
dothe
r
s
imi
lar
char
g
ed-current interactions take place in the detector.
O
ne may there
f
ore identi
f
y
ν
e
a
nd
ν
e
events by observin
g
e
−
a
nd
e
+
e
vents, respectively.
302 8 Ultrahigh-energy
C
osmic Neutrinos
Fig. 8.5 Cherenkov light patterns produced by muons
(
left
)
and by secondary
showers initiated by electron and tau neutrinos (right) in IceCube (Halzen, 2006b.
With permission from Springer Science+Business Media
)
(
2
)
I
denti
fi
cation o
f
muon neutrinos.
T
he secondar
y
muons initiated b
y
the incident muon neutrinos may range over a few kilometers when
E
ν
∼O
(
1
)
Te
V
and tens o
f
kilometers whe
n
E
ν
∼O
(
1
)
EeV, generating showers alon
g
their tracks by bremsstrahlun
g
, pair production and photonuclear interac
-
tions
(
Halzen, 2006a
)
. These are the sources of Cherenkov radiation and ca
n
be detected in the same way as that
f
or hi
g
h-ener
g
y electron neutrinos dis
-
c
ussed above. Since the ener
g
y of the muon de
g
rades alon
g
its track, th
e
energy of the secondary showers decreases and thus the distance from th
e
track over which the associated
C
herenkov li
g
ht can tri
gg
er a D
O
M becomes
s
maller and smaller. The geometric pattern of the Cherenkov lightpool sur
-
rounding the muon track is therefore a kilometer-long cone whose radius
g
radually decreases, as shown in Fi
g
. 8.5. For the
fi
rst kilometer, a hi
g
h
-
energy muon typically loses about one tenth of its initial energy in a couple
o
f
s
h
owe
r
s
.H
e
n
ce t
h
e
ini
t
i
a
l
s
iz
eo
f
t
h
eco
n
e
i
st
h
e
r
ad
i
us o
f
as
h
owe
r
w
i
th
a
bout 10% of the muon energy
(
e.g., about 130 m for an 100 TeV muon
)
(
Halzen, 2006b
)
. Near the end of its range the muon becomes minimum ion
-
i
zin
g
an
d
emits
l
i
gh
tw
h
ic
h
creates sin
gl
ep
h
otoe
l
ectron si
g
na
l
sata
d
istanc
e
o
fj
ust over 10 m
f
rom the track. Because o
f
the stochastic nature o
f
muon en
-
ergy loss, only the logarithm of the muon energy can be measured. Althoug
h
U
HE muons initiated by the incident UHE muon neutrinos have ran
g
es o
f
tens of kilometers, the initial ener
g
ies of their events cannot always be mea
-
s
ured. A muon can be produced at one energy, travel several kilometers an
d
then be detected with another
(
much lower
)
energy
(
Halzen, 2006b
).
(
3
)
Identi
fi
cation o
f
tau neutrinos
.
Relative to electron and muon neu
-
trinos, the production rate of tau neutrinos from a cosmic accelerator is
s
uppressed by about
fi
ve orders o
f
ma
g
nitude. But the detection o
f
UHE tau
n
eutrinos at a neutrino telescope makes sense because nearl
y
half of the UH
E
8
.2 Detection o
fU
HE
C
osmic Neutrinos
303
m
uon neutrinos can actua
lly
convert over cosmic
d
istances into tau neutrinos
a
saconse
q
uence of neutrino oscillations. On the other hand, an UHE ta
u
n
eutrino beam is not absorbed by the Earth due to its “regeneration” effect
.
H
ence it can always reach the detector in spite o
f
some ener
g
y loss. There
a
re several wa
y
stoidentif
y
the flavor of UHE tau neutrinos in a k
m
3
-scal
e
n
eutrino telescope. The most striking signature comes from the characteristi
c
d
ouble-ban
g
events, in which the production and decay o
f
a tau are detected
a
s two separated showers inside the detector
(
Learned and Pakvasa, 1995
;
G
aisse
r
et al.
,
1995
)
. It is also possible to identify the “lollipop” events in
w
h
ic
h
a tau neutrino creates a
l
on
g
minimum-ionizin
g
trac
k
t
h
at penetrates
the detector and ends in a high-energy cascade when the tau decays
(
Halzen
,
2
006b
)
. The parent tau track can then be identified by the reduced catas-
trophic ener
g
y loss compared with a muon track with the similar ener
g
y. T
o
i
dentify a double-bang event in the IceCube or KM3NeT detector, the fol
-
l
owing conditions have to be satisfied
(
Halzen, 2006b
)
:
(
a
)
the incident ta
u
n
eutrino has to interact with ice or water via the char
g
ed-current interactions,
pro
d
ucing a
h
a
d
ronic s
h
ower containe
d
insi
d
eorc
l
ose to t
h
e instrumente
d
volume;
(
b
)
the produced tau must decay inside the detector into a final state
which can
g
enerate an electroma
g
netic or hadronic shower contained insid
e
the device;
(
c
)
the travel distance of the tau
(
before it decays
)
has to b
e
s
ufficiently long such that the two showers can be clearly separated; and
(
d
)
the showers must be sufficiently ener
g
etic to tri
gg
er the DOMs.
8.2.3
O
ther Ways to Detect UHE Neutrinos
Besides the optical detection o
f
UHE cosmic neutrinos in ice and water, som
e
other techni
q
ueshavebeendevelo
p
ed to measure the low-
fl
ux tails o
f
UH
E
c
osmic neutrino spectra
(
see Fig. 8.4 for illustration
).
(
1
)
Radio detection o
f
neutrino-induced air showers.
El
ectroma
g
netic cas-
c
ades produced by the interactions of hi
g
h-ener
g
y electron neutrinos ca
n
emit strong coherent Cherenkov radiation in any dielectric medium, the so
-
c
alled Askaryan effect
(
Askaryan, 1962, 1965
)
which was first observed in 2001
(
Saltzber
g
e
tal.
,
2001
)
. The signal strength rises proportionally to
E
2
ν
,
mak-
i
ng this method particularly interesting for detecting UHE cosmic neutrinos
.
In ice or salt domes, attenuation len
g
ths o
f
several kilometers can be reache
d
with the radio detection technique, depending on the frequency band, ice
temperature or salt quality
(
Avignon
e
et al.
,
2008
)
. This allows large spac
-
i
n
gb
etween t
h
ein
d
ivi
d
ua
ld
etectors an
d
acomparative
l
yc
h
eap extensio
n
to large volumes. Hence radio detection in ice or salt may be competitiv
e
with or superior to optical detection
f
o
r
E
ν
O
(
10
)
PeV. The ANITA Long
D
uration Balloon experiment was desi
g
ned speci
fi
cally to search
f
or cosmi
c
n
eutrinos above
E
ν
∼
10
1
7
eV in an Antarctic circumpolar flight
(
Barwick
et al
.
,
2006
)
. At a typical altitude of about 35 km above the ice surface,
the
A
NIT
A
detector is able to record radio im
p
ulses in the thick ice shee
t
a
nd monitor a huge volume
(
∼
1
.
6
×
10
6
km
3
)
. ANITA’s antennas are 32
304 8 Ultrahigh-energy
C
osmic Neutrinos
q
uad-rid
g
ed dual-linear-polarization horns, each with a
fi
eld o
f
view which
a
vera
g
es about 5
0
◦
a
ngular diameter over their
(
0
.
2
···
1
.
2)
×
1
0
9
Hz workin
g
bandwidth. The combined view of all antennas covers the entire lower hemi
-
s
phere down to an
g
les o
f
about 5
5
◦
,
compr
i
s
i
n
g
9
9
.
4
%
of the area within the
h
orizon
(
Gorha
m
e
tal
.
,
2009
)
. Some initial results from ANITA’s first 35-da
y
flight have recently been reported, but no evidence for a diffuse flux of cosmi
c
neut
rin
os above
E
ν
≈
3
×
10
18
eV is found
(
Gorham
et al.
,
2009
).
(
2
)
A
coustic detection o
f
neutrino-induced showers in water, ice or salt.
This promising technique, based on Gurgen Askaryan’s observation that an
i
nteractin
g
neutrino can emit a t
h
in t
h
ermoacoustic panca
k
enorma
l
to t
h
e
s
hower axis
(
Askaryan, 1962, 1965
)
, remains in its R&D phase. It relies o
n
the ionization loss in hi
g
h-ener
g
y particle cascades trans
f
ormin
g
into heat,
a
nd the subse
q
uent
f
ast ex
p
ansion o
f
the medium leads to a short acousti
c
pulse
(
Avignone
e
tal.
,
2008
)
. The signal power spectrum peaks at 20 kHz,
where the attenuation len
g
th o
f
sea water or ice is expected to be a
f
ew kilo
-
m
eters.
S
uch a lar
g
e theoretical attenuation len
g
th has not been experimen
-
tally demonstrated, but it makes this method attractive for the detectio
n
of extremely energetic cosmic neutrinos
(
in the EeV region
)
because larg
e
d
etector spacin
g
is mandatory in order to achieve a hu
g
e detection volum
e
n
ecessary for a low neutrino flux. Open key issues include the signal strengt
h
a
nd natural background levels
(
Podgorski and Ribordy, 2010
)
. Acoustic de-
tectors might be deployed to surround the optical detectors of KM3NeT i
n
t
h
eMe
d
iterranean sea an
d
en
h
ance its sensitivity to muc
hh
ig
h
er energies
,
but radio does not work in salt water. For Ice
C
ube, a h
y
brid scheme con
-
s
isting of optical, radio and acoustic detection facilities has been propose
d
(
Vandenbroucke
et al.
,
2006; Avignon
e
et al.
,
2008
)
and its total volume will
be of
O
(
1
0
2
)
k
m
3
.
(
3
)
O
ptical detection of neutrino-induced air showers. This techni
q
ue ca
n
b
euse
d
to measure
h
orizonta
l
air s
h
owers initiate
db
y neutrino interaction
s
d
eep in the atmosphere. A large air shower detector
(
e.g., Auger
)
is able t
o
probe cosmic neutrinos in the energy range 0.1 Ee
V
E
ν
1Ee
V
.Ifthe
effective detector mass is sufficiently large
(
e.g., more than 20 gigatons
)
,it
i
s possible to detect UHE tau neutrinos scratchin
g
the Earth and interactin
g
c
lose to the detector array
(
Avignone
e
ta
l.
, 2008
)
. They are known as the
E
arth-skimming neutrinos
(
Fen
g
et al.
,
2002; Fargion, 2002
)
. An extremely
ener
g
etic tau produced in such interactions may escape the rock, and th
e
partic
l
e casca
d
epro
d
uce
db
yits
d
ecay in t
h
e atmosp
h
ere a
b
ove t
h
e
d
etecto
r
a
rra
y
can t
h
en
b
e recor
d
e
d
.W
h
en
E
ν
a
pproac
h
es its maximum, one is
l
e
d
to the space-based detectors monitorin
g
lar
g
er volumes than visible fro
m
a
ny point on the Earth’s surface. The EUSO project has been proposed to
l
aunch lar
g
e mirrors with optical detectors to the hei
g
ht o
f
500 km on th
e
International Space Station and search for fluorescence and Cherenkov light
s
ignals arising from UHE neutrino interactions in the atmosphere
(
Agnetta,
2
006
)
. On the other hand, one may simply consider to apply the technique
s
8
.
3
Flavor Distribution o
fU
HE
C
osmic Neutrinos
305
o
f
air shower
fl
uorescence and
C
herenkov li
g
ht detectors with the help o
f
a
mountain or the Earth’s crust. The CRTNT pro
j
ect has therefore bee
n
proposed to detect the Earth-skimming UHE tau neutrinos
(
Cao
e
ta
l
.
,
2005
).
Both pro
j
ects are at present suspended, un
f
ortunatel
y
.
I
t is finally worth mentioning a Chinese version of the CRTNT
(
cosmi
c
ray tau neutrino telescope
)
project
(
Li
u
et al.
, 2009
)
. Such a telescope is as-
s
umed to be located at the
f
oothill o
f
Mt Balikun in Xinjian
g
,
C
hina. The
s
ite is sufficiently dry throughout the year and the mountain is reasonably
thick and sufficiently steep, suitable for detecting the Earth-skimming UH
E
tau neutrinos by means o
f
air shower
fl
uorescence and
C
herenkov li
g
ht detec
-
tors. Because of their charged-current interactions with the rock, the inciden
t
U
HE cosmic neutrinos may convert into c
h
ar
g
e
dl
eptons insi
d
et
h
e mountain
.
The electrons can quickl
y
shower in the rock, while the muons ma
y
travel a
very long distance before decaying. Hence both of them are difficult to be de
-
tecte
d
usin
g
t
h
is met
h
o
d
.T
h
etauspro
d
uce
d
insi
d
et
h
e mountain may
h
ave
a
su
ffi
ciently lon
g
li
f
etime to escape
f
rom the mountain, and then decay an
d
i
n
d
uce air s
h
owers in t
h
e air near t
h
e mountain. For t
h
etime
b
eing it remain
s
u
nclear whether the
C
RTNT project in
C
hina has a bri
g
ht prospect or not.
8
.3 Flavor Distribution of UHE Cosmic Neutrino
s
On the way from a distant astrophysical source to a telescope on the Earth
,
the flavors of UHE cosmic neutrinos must oscillate man
y
times.
A
measure-
m
ent of the flavor distribution of UHE cosmic neutrinos at a telesco
p
eca
n
there
f
ore probe their initial
fl
avor composition, which is closely associate
d
with the source properties, or examine the e
ff
ects o
f
neutrino mixin
g
and
CP
violation in such ultralong-baseline neutrino oscillations. In principle, it is also
possible to use the
fl
avor oscillations o
f
UHE neutrinos to test some
f
unda
-
m
ental symmetries
(
e.g., CPT invariance
)
or explore some “exotic” propertie
s
of neutrinos
(
e.g., neutrino decays
)
.
8
.
3
.1 Flavor Issues of
U
HE Neutrino
s
G
iven the initial
U
HE cosmic neutrino fluxes
Φ
=
{
φ
e
,
φ
μ
,
φ
τ
}
at a d
i
sta
n
t
a
stroph
y
sical source, its
fl
avor components are de
fi
ned a
s
φ
α
=
φ
ν
α
+
φ
ν
α
(
for
α
=
e, μ, τ
)
,where
φ
ν
α
a
n
d
φ
ν
α
d
enote t
he
ν
α
an
d
ν
α
fluxes, respectively. At
a
neutrino telescope one ma
y
similarl
y
de
fi
ne the
fl
uxe
s
Φ
T
=
{
φ
T
e
,φ
T
μ
,φ
T
τ
}
wit
h
φ
T
α
=
φ
T
ν
α
+
φ
T
ν
α
(
for
α
=
e
,μ,τ
)
. The relation between
φ
ν
α
(
o
r
φ
ν
α
)
an
d
φ
T
ν
α
(
or
φ
T
ν
α
)
is given by
φ
T
ν
β
=
α
φ
ν
α
P
(
ν
α
→
ν
β
ν
)
,
φ
T
ν
β
=
α
φ
ν
α
P
(
ν
α
→
ν
β
)
,
(
8.6
)