neutrino

attempt to fit the Pioneer anomaly with dark matter has been suggested. Remarkably, MOG provides a closely fit
solution to the Pioneer 10/11 anomaly and is consistent with the accurate equivalence principle, all current satellite,
laser ranging observations for the inner planets, and the precession of perihelion for all of the planets.
Afittotheacousticalwavepeaksobservedinthecosmicmicrowave background (CMB) data using MOG has been
achieved without dark matter. Moreover, a possible explanation for the accelerated expansion of the Universe has
been obtained in MOG (Moffat, 2007).
Presently, on both an empirical and theoretical level, MOG is themostsuccessfulalternativetodarkmatter.The
successful application of MOG across scales ranging from clusters of galaxies (Megaparsecs) to HSB, LSB and dwarf
galaxies (kiloparsecs), to the solar system (AU’s) provides acluetothequestionofmissingmass. Theapparent
necessity of the dark matter paradigm may be an artifact of applying the Newtonian 1/r 2 gravitational force law to
scales where it is not valid, where a theory such as MOG takes over. The “excess gravity” that MOG accounts for
may have nothing to do with the hypothesized missing mass of dark matter. But how can we distinguish the two?
In most observable systems, gravity creates a central potential, where the baryon density is naturally the highest.
So in most situations, the matter which is creating the gravity potential occupies the same volume as the visible
Probing Dark Matter with Neutrinos
Ina Sarcevic
matter. Clowe et al. (2006c) describesthisasadegeneracybetweenwhethergravitycomes from dark matter, or
from the observed baryonic mass of the hot ICM and visible galaxies where the excess gravity is due to MOG. This
degeneracy may be split by examining a system that is out of steady state, where there is spatial separation between
the hot ICM and visible galaxies. This is precisely the case in galaxy cluster mergers: the galaxies will experience
University of Arizona
adifferent gravitational potential created by the hot ICM than if they were concentrated at the center of the ICM.
Moffat (2006a) consideredthepossibilitythatMOGmayprovidetheexplanation of the recently reported “extra
gravity” without non-baryonic dark matter which has so far been interpreted as direct evidence of dark matter. The
research presented here addresses the full-sky data product for the Bullet Cluster 1E0657-558, recently released to
the public (Clowe et al., 2006b).
NPAC Seminar
September 29,2011
In collaboration with
Arif Erkoca, Graciela Gelmini
and Mary Hall Reno
FIG. 1:
False colour image of Bullet Cluster 1E0657-558.
The surface density Σ-map reconstructed from
X-ray imaging observations is shown in red
and the convergence κ-map as reconstructed
from strong and weak gravitational lensing observations
is shown in blue. Image provided
courtesy of Chandra X-ray Observatory.

EVIDENCE FOR DARK MATTER
In 1930’s Zwicky observed the
Coma cluster and found that
galaxies were moving too fast
to be contained by the visible
matter.
In 1970’s Vera Rubin and
collaborators discovered that
stars in galaxies were rotating
too fast implying existance of
invisible matter
Observations indicate the existence of
non-luminous matter with density profile at
far distances in the form
ρ ∼ 1 r 2

Bergstrom, Rep. Prog. Phys. 63, 793 (2000)
Non-baryonic dark matter 813
successful application of MOG across scales ranging from clusters of
galaxies (kiloparsecs), to the solar system (AU’s) provides acluet
necessity of the dark matter paradigm may be an artifact of applyin
scales where it is not valid, where a theory such as MOG takes ove
may have nothing to do with the hypothesized missing mass of dar
In most observable systems, gravity creates a central potential, wh
So in most situations, the matter which is creating the gravity po
matter. Clowe et al. (2006c) describesthisasadegeneracybetwee
from the observed baryonic mass of the hot ICM and visible galaxie
Non-baryonic Dark Matter
Many observations indicate presence of dark matter:
Galaxy rotation curves, galaxy clusters, BBN, CMB radiation,
gravitational lensing, etc.
degeneracy may be split by examining a system that is out of steady
the hot ICM and visible galaxies. This is precisely the case in gala
adifferent gravitational potential created by the hot ICM than if th
Moffat (2006a) consideredthepossibilitythatMOGmayprovide
gravity” without non-baryonic dark matter which has so far been int
research presented here addresses the full-sky data product for the
the public (Clowe et al., 2006b).
Bullet Cluster (IE0657-56)
v (km/s)
observed
100
50
expected
from
luminous disk
5 10
R (kpc)
M33 rotation curve
Figure 4. Observed HI rotation curve of the nearby dwarf spiral galaxy M33 (adapted
from [74]), superimposed on an optical image (NED image from STScI Digitized Sky Survey,
http://nedwww.ipac.caltech.edu. The NASA/IPAC Extragalactic Database (NED) is operated by

Dark Matter Density Profiles
[87] wwww
In the Milkyway, the rotation curves of the stars suggest that the dark
matter density in the vicinity of our Solar System is:

Dark Matter –What do we know?
Dark matter is about 23% of the total
density of the Universe, while baryonic matter
is only 4%
Large-scale structure formation in the
Universe imply that dark matter is “cold”
(i.e. non-relativistic at freeze-out time)

DM produced as a thermal relic of the
Big Bang (Zeldovich,Steigman,Turner)
Comoving number density Y
Dark Matter as a Cold Relic
χχ ↔ ¯ff
n ∼ e −m χ/T
n eq
Feng, arXiv:1003.0904
(time )
dn
dt = −3Hn− < σv >(n2 − n 2 eq)
Initially DM is in thermal
equilibrium
χχ ↔ ¯ff
Universe cools
n ∼ e −m χ/T
Freese out time when
n= H
Thermal relic density:
< σv >f.o.
Ω χ =0.23
3 × 10 −26 cm 3 /s
The current dark matter abundance in the Universe depends on
the annihilation cross section at freeze-out.
−1

What is dark matter? The unknowns:
Modification of the standard, Newtonian
1/r 2
law, so that the observed effect is due
to only baryonic matter is ruled out by Bullet
Cluster observations
Particle physics candidate for dark matter:
weakly interacting particle which is non
-relativistic at the time of freeze-out.
No viable candidate for dark matter in the
Standard Model

DARK MATTER DETECTION
annihilation
(Indirect detection)
χ
q
χ
q
production
(Particle colliders)
scattering
(Direct detection)

Dark Matter Detection
Direct Detection Experiments :
Look for energy deposition via nuclear recoils from dark
matter scattering by using different target nuclei and
detection strategies
DAMA, NAIAD, KIMS, CDMS, EDELWEISS, EURECA,
ZEPLIN, XENON, WARP, LUX
Indirect Detection Experiments :
Look for annihilation products of dark matter (Gamma-rays,
positrons, electrons, neutrinos )
HESS, MAGIC, VERITAS, CANGAROO-III, EGRET,
Fermi/LAT, INTEGRAL, PAMELA, ATIC, AMS, HEAT,
ICECUBE, KM3NET

Direct searches:
look for DM interactions with target
nuclei (XENON, CDMS, CoGeNT, DAMA,
CRESST-II)
Dark Matter Searches
CoGeNT Collaboration:
arXiv:1002.4703v2, PRL 106,
131301 (2011)

σ
Recent CRESST-II data (4.7 )
CRESST-II Collaboration:
arXiv:1109.0702

!"##$%$"&'()*+'%,"-#.'/,)&0+')%'
1)(*,2%'3+#"/$*4')..%'
!"##$%$"&'()*+'%,"-#.'/,)&0+')%'
/"&%*(-/*$3+#45.+%*(-/*$3+#4'6$*,'*,+'
1)(*,2%'3+#"/$*4')..%'
Earth’s velocity adds
RICCARDO CERULLI
RICCARDO CERULLI
7-&2%' /"&%*(-/*$3+#45.+%*(-/*$3+#4'6$*,'*,+'
)&&-)#'8".-#)*$"&
constructively/destructively
7-&2%' )&&-)#'8".-#)*$"&
2-6 2-6 keV
2-6 keV
to the Sun’s DAMA/LIBRA DAMA/LIBRA ! ! 250 250 250 kg kg kg (0.87 (0.87 ton"yr)
9(-:$+(;'?@ABC
-> annual modulation
ton"yr)
9(-:$+(;'?@ABC
DE'F)('?? DE'F)('??
NOP'FG77'DHHAC

Indirect DM searches:
Detection of the products of DM
annihilation (or decay) in the Galactic
Center, Sun, Earth, DM halo, etc.
producing electrons, positrons, gammarays
(PAMELA, ATIC, FERMI/LAT,
HESS, Veritas …) and neutrinos (IceCube,
KM3Net…)

Indirect Dark Matter Detection
PAMELA
AMS
FERMI/LAT
HESS
ATIC

PAMELA Positron Fraction

FERMI Cosmic Ray Electron Spectrum

If the observed anomalies are due to dark matter
annihilation the annihilation cross sections must be
10-1000 times more than the thermal relic value of
< σv >=3× 10 −26 cm 3 /s
The required enhancement in the signal is quantified by
the factor called the “Boost Factor” :
Low-velocity enhancement
(particle physics) Sub-halo structures in the
Galaxy (astrophysics)

Dark Matter Signals in Neutrino Telescopes
Neutrinos are highly stable, neutral particles.
Detection of neutrinos depend on their interactions, i.e
cross section.
IceCube
Annihilation of dark matter particles
could produce neutrinos, directly or via
decay of Standard Model particles
Neutrinos interacting with the matter,i.e
nucleons, produce muons which leave
charged tracks in the neutrino detector

Neutrino flux from DM annihilation in
the core of the Sun/Earth, produced
directly or from particles that decay
into neutrinos (taus, Ws, bs)
Erkoca, Reno and Sarcevic, PRD 80, 043514 (2009)
Model-independent results for neutrino
signal from DM annihilation in the
Galactic Center
Erkoca, Gelimini, Reno and Sarcevic, PRD 81, 096007 (2010)
Signals for dark matter when DM is
gravitino, Kaluza-Klein particle or
leptophilic DM.
Erkoca, Reno and Sarcevic, PRD 82, 113006 (2010)

Neutrinos from DM annihilations in
the core of the Sun/Earth
Neutrino flux depends on annihilation
rate, distance to source (Earths core or
Sun-Earth distance) and energy
distribution of neutrinos, i.e.
In equilibrium, annihila/on rate and capture rate related:

● Dark Matter Capture Rate :
C ∼
ρ
DM M
σ χN
p
ρ DM =0.3 GeV cm −3
v DM ∼ 270 km s −1
v esc = 1156 km/s v esc = 13.2 km/s
for the Sun
for the Earth
M is the mass of the Sun/Earth
Capture rate in the Sun is about 10 9 times
larger than capture rate in the Earth
For the Sun, annihilation rate = C/2

Neutrinos from DM annihilation
=⇒
interact with matter
attenuation of the neutrino Flux in
the Sun is important effect
Neutrinos also interact as they
propagate through the Earth
producing muons below the detector
ν µ + N → µ + X
ν e + N → e + X
ν µ,e,τ + N → ν µ,e,τ + X

Neutrino Detection
Neutrinos interact as they propagate
through the Earth producing muons
below the detector (upward muons) or
in the detector (contained muons) or
producing showers/cascades in the
detector:
ν µ + N → µ + X
ν µ,e,τ + N → ν µ,e,τ + X
ν e + N → e + X

Muon Flux
The probability of the conversion of a neutrino
into a muon over a distance dr via CC interactions:
where the neutrino scattering cross section is:
● Muons can be created in the detector (contained
events) or in the rock below the detector (upward
events).

Contained and Upward Muon Flux
● The contained muon flux, for a detector
with size l
● The upward muon flux is given by

where the neutrino flux is
Muon survival probabilty is
where
R E = 6400 km (Earth) or
R SE =150 Mkm (Sun-Earth distance)

Neutrinos from DM annihilations
Neutrinos from DM annihilations
eutrinos produced directly or through
Neutrinos ecays of leptons, produced quarks directly and gauge or through bosons:
decays of leptons, quarks and gauge bosons:

Neutrino Energy Distribution
● channel :
● channels :

than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
0 0.2 0.4 0.6 0.8 1
x
0.001
0.01
0.1
1
10
100
1000
(1/B f ) dN / dx
!! -> ZZ, m ! = 100 GeV
!! -> " + " #
! -> Z$ , m ! = 400 GeV
! -> l + l - $
FIG. 1: Muon neutrino (ν µ ) spectra in terms of x =
E ν /E ν,max from the three-body decay of gravitino (dot-dash-
10
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 11
10 12
10 13
d% / dE $µ (GeV -1 km -2 yr -1 )
FIG. 2: Muon neutri
Kaluza-Klein (dotte
x = E ν /E ν,max

units of GeV −1 km −2 yr −1 sr −1 .
Upward and Contained Muon Flux from
DM Annihilation in the Core of the Earth
1
m "
= 500 GeV
""->## (upward)
d! / dE µ
(GeV -1 km -2 yr -1 )
0.1
0.01
""->## (contained)
""->$ + $ % (upward)
""->$ + $ % (contained)
ATM (contained)
ATM (upward)
F
χ
b
f
w
fl
0.001
200 400 600 800
E µ
(GeV)
fl
E

!
Attenuation Attenuation of of the the neutrino neutrino Flux Flux in in the the Sun Sun
!
The The muon muon flux flux decreases decreases by by a a factor factor of of
3, 3, 10, 10, 100 100 for for m= m= 250 250 GeV, GeV, 500 500 GeV, GeV, 11 TeV. TeV.

itaoes
Upward and contained muon flux from
DM annihilation in the core of the Sun
1
0.1
m "
= 500 GeV
aparas
un.
30
the
3 ).
ven
We
ich
d! / dE µ
(GeV -1 km -2 yr -1 )
0.01
0.001
0.0001
1e-05
1e-06
""->## (upward)
""->## (contained)
""->$ + $ % (upward)
""->$ + $ % (contained)
""->$ + $ % (Ref. [22])
ATM (contained)
ATM (upward)
200 400 600 800 1000
E µ
(GeV)

low energies, but it does not change the large discrepancies
between our upward muon rates compared with Eq.
(27) at energies closer to E µ ∼ m χ .
10
∫
dN / dE µ
(GeV -1 yr -1 )
2
1.5
1
0.5
0
m !
= 500 GeV
(Earth, upward)
(Sun, upward)
(Earth, contained)
(Sun, contained)
!! -> ""
100 200 300 400 500
E µ
(GeV)
whe
give
TeV
In
from
2π s
dom
shap
the
trin
mos
from
muo
T
mos
the

Neutrino Flux from DM Annihilation in
the Galactic Center
Erkoca, Gelmini, Reno and Sarcevic,
Phys. Rev. D81, 096007 (2010)
Model independent DM signals: neutrinoinduced
upward and contained muons and
cascades (showers)
For dark matter density, we use
different DM density profiles (Navarro-
Frenk-White, isothermal, etc)
Predictions for IceCube and Km3Net

Neutrino Flux from Dark Matter
Neutrino flux from DM annihilation/decay:
here R for DM annihilation is:
and for DM decay:

Define
as:
distance from us in the direction of the
cone-half angle from the GC
is density distribution of dark mater halos
is distance of the solar system from the GC
is local dark matter density near the solar
system

Dark Matter Density Profiles
[87] wwww
In the Milkyway, the rotation curves of the stars suggest that the dark
matter density in the vicinity of our Solar System is:

Neutrino Flux (
) at the Production
Neutrinos can be produced directly or
through decays of leptons, quarks and
gauge bosons:

Detection: neutrinos interacting
below detector or in the detector
producing muons
Signals: upward and contained muons
and cascade/showers
Upward muons lose energy before
reaching the detector

Energy loss of the muons over a distance dz :
α : ionization energy loss α = 10 -3 GeVcm 2 /g.
β : bremsstrahlung, pair production and
photonuclear interactions β=10 -6 cm 2 /g.
Relation between the initial and the final muon
!
energy:
Muon range:

Contained and Upward Muon Flux
Contained muon flux is given by
dφ µ
dE µ
=
Emax
E µ
dE ν
dN
dE ν
N A ρ dσ ν(E ν )
dE µ
Upward muon flux is given by
dφ µ
dE µ
=
Rµ (E i µ ,E µ)
0
e βρz dz
Emax
E i µ
dE ν
dN
dE ν
N A ρ
×P surv (E i µ,E µ ) dσ ν(E ν )
dE µ

dφ sh
dE sh
=
Emax
E sh
dE ν
dφν
dE ν
N A ρ dσ ν(E ν ,E ν − E sh )
dE sh

Muon Flux

Muon Flux for Different DM
Annihilation Modes

Muon Rates

Shower Rates

Hadronic Shower Spectra without
track-like events

Hadronic and EM Showers

Probing the Nature of Dark Matter
with Neutrinos
Erkoca, Reno and Sarcevic, Phys. Rev. D82,
113006 (2010)
DM candidates: gravitino, Kaluza-Klein
particle, a particle in leptophilic models.
Dark matter signals: upward and
contained muon flux and cascades
(showers) from neutrino interactions
We include neutrino oscillations
Experimental signatures that would
distinguish between different DM
candidates

Probing Dark Matter Models with Neutrinos
PAMELA
FERMI
HESS
Gravitino decay
Ψ → l + l − ν
B. Bajc et al.
JHEP 1005 (2010) 048
KK Dark matter annihilation
B (1) B (1) → l + l − ,W + W − ,ZZ,q¯q,
L. Bergstrom et al.
Phys.Rev.Let.94:131301,2005
Leptophilic Dark Matter
Annihilation/Decay
V. Barger et al.
hys. Lett. B678:283, 2009

E I: Branching fractions for the two-body gravi
into different R-parity violating channels for diffe
s [15].
Particle/mode mass B τ or
ψ 3/2 → l + l − ν 400 GeV B τ =2
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2
χ → µ + µ − 2TeV B τ =2
B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =2
χχ → µ + µ − 1TeV B =4
E II: Model parameters characterizing fits to exp
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
of
n
ge
or
i
].
e
a-
i-
ly,
2)
rs
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
τ = B τ × 10 26 s

than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
3
0 0.2 0.4 0.6 0.8 1
x
0.001
0.01
0.1
1
10
100
1000
(1/B f ) dN / dx
!! -> ZZ, m ! = 100 GeV
!! -> " + " #
! -> Z$ , m ! = 400 GeV
! -> l + l - $
FIG. 1: Muon neutrino (ν µ ) spectra in terms of x =
E ν /E ν,max from the three-body decay of gravitino (dot-dashdashed
line), from the decay of τ (dashed line), Z boson (solid
line) and from one of the two-body decay channels of gravitino
(ψ → Zν) forwhichBreit-Wignerdistributionisused. The
distributions should be multiplied by the branching fractions,
100 1000
E $µ (GeV)
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 11
10 12
10 13
d% / dE $µ (GeV -1 km -2 yr -1 )
& 3/2 -> l + l - $, m &3/2 = 400 GeV, " = 2.3 x 10 26 sec
& 3/2 -> (Wl,Z$), m &3/2 = 400 GeV, " = 2.3 x 10 26 sec
! #> µ + µ # , m ! = 2 TeV, " = 2.9 x 10 26 sec
B (1) B (1) ->(qq,l + l - ,W + W - ,ZZ) , m B (1) = 800 GeV , B = 200
!! #> µ + µ # , m ! = 1 TeV, B = 400
ATM
FIG. 2: Muon neutrino (ν µ )fluxesfromtheannihilationofthe
Kaluza-Klein (dotted line), leptophilic (dashed line), and the
decay of leptophilic (dash-dot-dashed line), three-body decay
(dot-dashed line) and two-body decay (dot-dot-dashed line)of
gravitino DM particles. Neutrino oscillations have been taken
into account. The angle-averaged atmospheric muon neutrino
3
0 0.2 0.4 0.6 0.8 1
x
0.001
0.01
0.1
1
10
100
1000
(1/B f ) dN / dx
!! -> ZZ, m ! = 100 GeV
!! -> " + " #
! -> Z$ , m ! = 400 GeV
! -> l + l - $
G. 1: Muon neutrino (ν µ ) spectra in terms of x =
/E ν,max from the three-body decay of gravitino (dot-dashshed
line), from the decay of τ (dashed line), Z boson (solid
e) and from one of the two-body decay channels of gravitino
→ Zν) forwhichBreit-Wignerdistributionisused. The
tributions should be multiplied by the branching fractions,
100 1000
E $µ (GeV)
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 11
10 12
10 13
d% / dE $µ (GeV -1 km -2 yr -1 )
& 3/2 -> l + l - $, m &3/2 = 400 GeV, " = 2.3 x 10 26 sec
& 3/2 -> (Wl,Z$), m &3/2 = 400 GeV, " = 2.3 x 10 26 sec
! #> µ + µ # , m ! = 2 TeV, " = 2.9 x 10 26 sec
B (1) B (1) ->(qq,l + l - ,W + W - ,ZZ) , m B (1) = 800 GeV , B = 200
!! #> µ + µ # , m ! = 1 TeV, B = 400
ATM
FIG. 2: Muon neutrino (ν µ )fluxesfromtheannihilationofthe
Kaluza-Klein (dotted line), leptophilic (dashed line), and the
decay of leptophilic (dash-dot-dashed line), three-body decay
(dot-dashed line) and two-body decay (dot-dot-dashed line)of
gravitino DM particles. Neutrino oscillations have been taken
into account. The angle-averaged atmospheric muon neutrino
x = E ν /E ν,max

than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
than the value required for a thermal relic abundance
[34]: 〈σv〉 0 =3× 10 −26 cm 3 s −1 . Following the current
convention, we write
〈σv〉 = B 〈σv〉 0 , (1)
with a boost factor B. There are theoretical evaluations
of the boost factor [35], however, we treat the boost factor
as a phenomenological parameter in this paper. To
explain the lepton excesses, some models have constraints
on the boost factor as a function of DM mass [16].
In leptophilic DM
models [7, 16] explaining the
PAMELA positron excess, the DM annihilation or decay
must proceed dominantly to leptons in order to avoid
the overproduction of antiprotons. Moreover, according
to the FERMI data, the direct production of electrons
must be suppressed with respect to the production of
electrons (and positrons) as secondaries. It was shown
[16] that the leptophilic DM with mass (m χ ) in the range
between 150 GeV and a few TeV, which annihilates or
decays into τ’s or µ’s can fit the PAMELA [4] and Fermi
[5] data as well as the HESS high energy photon data [6].
The best fit parameters for the boost factor (B) andthe
decay time (τ) which determine the overall normalizations,
for the specific case involving muons from annihilation
(χχ → µ + µ − )ordecay(χ → µ + µ − ), respectively,
are given by [16]
B = 431m χ − 38.9
τ =
(
2.29 + 1.182
m χ )
× 10 26 sec
= B τ × 10 26 sec (2)
for m χ in TeV. The annihilation channel into tau pairs
is less favored by the data [16].
Some Kaluza-Klein models can provide a DM candidate
which gives the correct relic density [30].
To account
for the HESS results [6], the lightest Kaluza-Klein
particle (LKP) would have a mass of the order of a TeV
[14]. The LKP is also assumed to be neutral and nonbaryonic.
In this model, the particle couplings are fixed
such that LKP pairs annihilate into quark pairs (35%),
charged lepton pairs (59%), neutrinos (4%), gauge bosons
(1.5%) and higgs bosons (0.5%) [14, 30].
The first DM candidate proposed in the context of supersymmetry
is the gravitino (ψ 3/2 ) which would be the
lightest supersymmetric particle (LSP). The gravitino is
the superpartner of the graviton. With the existence of
small R-parity breaking to allow the LSP to decay, the
gravitino decays into standard model particles. The decay
rate of the gravitino in this scenario is so small that
it can have a sufficiently long lifetime for the correct DM
relic density today.
GeV and few TeV [17]. To explain the data, the threebody
gravitino decay mode (ψ 3/2 → l + l − ν) was considered
[17]. We use the parameters of this model to explore
neutrino signals from gravitino decay. For illustration, in
addition to three-body decay, we also consider the twobody
gravitino decay modes (ψ 3/2
→ (W ∓ l ± ,Zν, γν))
assuming the same lifetime and mass as for the threebody
decay, and with the branching fractions given in
Table I.
m ψ3/2 (GeV) B F (ψ 3/2 → γν) B F (ψ 3/2 → Wl) B F (ψ 3/2 → Zν)
10 1 0 0
85 0.66 0.34 0
100 0.16 0.76 0.08
150 0.05 0.71 0.24
200 0.03 0.69 0.28
400 0.03 0.68 0.29
TABLE I: Branching fractions for the two-body gravitino
decay into different R-parity violating channels for different
masses [15].
Particle/mode mass B τ or B
ψ 3/2 → l + l − ν 400 GeV B τ =2.3
ψ 3/2 → (Wl,Zν, γν) 400 GeV B τ =2.3
χ → µ + µ − 2TeV B τ =2.9
B (1) B (1) → (q¯q, l + l − ,W + W − ,ZZ,ν¯ν) 800GeVB =200
χχ → µ + µ − 1TeV B =400
TABLE II: Model parameters characterizing fits to explain
FERMI and PAMELA anomalies used as examples in this
paper.
Selected DM model parameters are shown in Table II.
For each of the DM models considered, the decay distribution
of the produced particles to neutrinos in case
of DM annihilation, or the gravitino decay distribution
to neutrinos, enters into the calculation of the neutrino
fluxes that arrive at Earth. For annihilation directly to
neutrinos, the energy distribution of each neutrino is a
delta function in energy, with the energy equal to the DM
mass. This case has been well studied in the literature
[21, 31, 32, 36]. Here, we look at the secondary neutrinos.
Fig. 1 shows neutrino spectra, plotted in terms
of x ≡ E ν /E ν,max where E ν,max = m χ for annihilating
DM and E ν,max = m χ /2 for decaying DM models. The
curves in the figure are normalized to count the number
of neutrinos, and in the case of the Zν final state, the
fraction of Z decays to neutrinos. The muon neutrino
spectra in the figure should be multiplied by the branching
fraction for a specific decay channel in a given model.
using the angle-averaged atmospheric flux gives a small
overestimate of the atmospheric background.
10 2 10 3 10 4 10 5 10 6
E ! (GeV)
10 -10
10 -9
10 -8
10 -7
10 -6
10 -5
10 -4
10 -3
10 -2
10 -1
10 0
E ! 2 d"! / dE ! (GeV cm -2 s -1 sr -1 )
AMANDA-II
ATM # = 60 o
ATM angle-averaged
FIG. 3: Angle-averaged atmospheric muon neutrino (ν µ +ν µ )
◦
as w
the
som
T
Gal
rent
flux
whe
the
and
tion
cros
with
W
curr

Contained Muon Flux
d! / dE µ
(GeV -1 km -3 yr -1 )
10 5
10 4
10 3
10 2
10 1
10 0
10 -1
10 -2
" 3/2
-> l + l - #, m "3/2
= 400 GeV, $ = 2.3 x 10 26 sec
" 3/2
-> (Wl,Z#,%#), m "3/2
= 400 GeV, $ = 2.3 x 10 26 sec
& '> µ + µ ' , m &
= 2 TeV, $ = 2.9 x 10 26 sec
B (1) B (1) ->(qq,l + l - ,W + W - ,ZZ,##) , m (1)
B
= 800 GeV , B = 200
&& -> µ + µ ' , m &
= 1 TeV, B = 400
ATM
10 -3
10 -4
100 1000
E µ
(GeV)

Contained Muon Flux for Leptophilic DM

Upward Muon Flux
1
d! / dE µ
(GeV -1 km -2 yr -1 )
10 4
10 3
10 2
10 1
10 0
10 -1
10 -2
" 3/2
-> l + l - #, m "3/2
= 400 GeV, $ = 2.3 x 10 26 sec
" 3/2
-> (Wl,Z#,%#), m "3/2
= 400 GeV, $ = 2.3 x 10 26 sec
& '> µ + µ ' , µ &
= 2 TeV, $ = 2.9 x 10 26 sec
B (1) B (1) ->(qq,l + l - ,W + W - ,ZZ,##) , m (1)
B
= 800 GeV , B = 200
&& -> µ + µ ' , m &
= 1 TeV, B = 400
ATM
a
f
T
t
s
F
c
a
f
10 -3
10 -4
100 1000
E µ
(GeV)

Decaying DM

Shower Events in IceCube+DeepCore
Annihilating DM

2σ
Decaying DM

Contained Muon Events

N µ
up
(yr
-1
)
Upward Muon Events with
10 5
10 4
10 3
10 2
10 1
10 0
10 -1
10 -2
" 3/2
-> l + l - #
" 3/2
-> (Wl,Z#,$#)
! -> µ + µ %
E th
µ = 50GeV
B (1) B (1) -> (qq,l + l - ,W + W - ,ZZ,##)
!! -> µ + µ %
ATM
1000 10000
m !
(GeV)
can
need
for
for
DM
in o
DM
tion
TeV
ther
para
nific
muo
con
serv
spac
S
uate
In F

value ρ(R o )=0.3 GeV/cm 3 [44]. Using these definitions,
we can write r = √ Ro 2 + l 2 − 2R o l cos θ and the upper
limit for Event the l integral Rates √
in Dependence Eq. (A3) can on be θ max
obtained as
l max = R o cos θ + Rs 2 − Ro 2 sin 2 θ for a given θ.
For the NFW profile, some values for 〈J 2 〉 Ω ∆Ω and
〈J 1 〉 Ω ∆Ω are summarized in Table VII.
0.1 ◦ 1 ◦ 5 ◦ 25 ◦ 50 ◦ 70 ◦ 90 ◦
〈J 2 〉 Ω ∆Ω 0.14 1.35 5.94 19.68 27.75 31.73 33.42
〈J 1 〉 Ω ∆Ω 0.00027 0.018 0.30 3.69 8.79 12.24 14.90
TABLE VII: The values of J factors for NFW profile for
θ max =0.1 ◦ , 1 ◦ , 5 ◦ , 25 ◦ , 50 ◦ , 70 ◦ , 90 ◦ .
In Fig. 20 we show 〈J n 〉 Ω ∆Ω factors as a function of
θ max for DM annihilation (n =2)andDMdecay(n =1)
evaluated for a cone wedge between θ max − 1 ◦ and θ max

Shower Events

Probing the Parameter Space
muon events
Annihilating DM
5 years

Probing the Parameter Space
muon events
Decaying DM
5 years

Contained muon flux

DM Detection with NeutrinoTelescopes
IceCUBE : 1 km 3 neutrino detector at South Pole
● detects Cherenkov radiation from the charged
particles produced in neutrino interactions
● contained and upward muon events and showers
● contained muons from GC
● showers from GC with IceCUBE+DeepCore
KM3Net : a future deep-sea neutrino telescope
● contained and upward muon events and
showers
● upward muons from GC

profiles. We consider only smooth halo profiles. The limits
for ττ and µµ overlay, due to their very similar high energy
neutrino spectra.
10 28 Halo Uncertainty
$ ' && Einasto
10 3 10 4 10 5
Lifetime % [s]
10 26
10 24
m $ [GeV]

Summary
Neutrinos could be used to detect dark
matter and to probe its physical origin
Contained and upward muon flux is sensitive
to the DM annihilation mode and to the
mass of dark matter particle
Combined measurements of cascade events
and muons with IceCube+DeepCore and
KM3Net look promising
Neutrinos can probe DM candidates, such as
gravitino, Kaluza-Klein DM, and a particle in
leptophilic models