IPMU 09-0143
CALT-68-2757

Cascade Events at IceCube+DeepCore as a Definitive Constraint
on the Dark Matter Interpretation of the PAMELA and Fermi
Anomalies

Sourav K. Mandal1,2 , Matthew R. Buckley3 , Katherine Freese4 , Douglas Spolyar5,6 , andHitoshi Murayama1,2,7
1
2
34Department of Physics, University of California, Berkeley, CA 94720, USA

IPMU, University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Japan 277-8568

Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA

Michigan Center for Theoretical Physics, Physics Department, University of Michigan,
Ann Arbor, MI 48109, USA
5

Center for Particle Astrophysics, Fermi National Accelerator Laboratory,
Batavia, IL 60510, USA

6

University of California, Santa Cruz, Physics Department, Santa Cruz, CA 95064, USA
7

Theoretical Physics Group, LBNL, Berkeley, CA 94720, USA

Abstract
Dark matter decaying or annihilating into µ+ µ− or τ + τ − has been proposed as an
explanation for the e± anomalies reported by PAMELA and Fermi. Recent analyses
show that IceCube, supplemented by DeepCore, will be able to significantly constrain
the parameter space of decays to µ+ µ− , and rule out decays to τ + τ − and annihilations to µ+ µ− in less than five years of running. These analyses rely on measuring
track-like events in IceCube+DeepCore from down-going νµ . In this paper we showthat by instead measuring cascade events, which are induced by all neutrino flavors,
IceCube+DeepCore can rule out decays to µ+ µ− in only three years of running, andrule out decays to τ + τ − and annihilation to µ+ µ− in only one year of running. These
constraints are highly robust to the choice of dark matter halo profile and independentof dark matter-nucleon cross section.

1

Introduction

The existence of dark matter has been established by numerous observations. Although it
constitutes most of the matter in the universe [1], the nature of dark matter remains largely
unknown. One widely held possibility is that it is a new fundamental particle produced in theearly universe and present today as a thermal relic. Among the best motivated of these are
the so-called weakly interacting massive particles, or “WIMPs” (for reviews, see Refs. [2, 3])
which are predicted to be undergoing annihilations [4, 5, 6, 7] and possibly decays [8] in thecurrent epoch.
Recently, the instruments PAMELA [9], ATIC [10], PPB-BETS [11], and Fermi [12] haveobserved features in the cosmic-ray e± spectrum and a positron fraction that are inconsistent
with known backgrounds. While these anomalies may be due to unidentified astrophysicalsources [13], one exciting possibility is that they are due to the decay [14, 15, 16, 17, 18, 19, 20]
or annihilation [21, 22, 23, 24, 25, 26] of dark matter particles into standard model states.
Even in the case that anomalies are not caused by new physics in the dark sector, theconstraints are generally applicable to dark matter models.
In order for dark matter to explain the anomalies, the products of decay or annihilationmust be primarily leptonic. In either case, the Fermi observation gives the most precise
preferred region in mass and lifetime/cross-section; for decays, only µ+ µ− and τ + τ − final
states fit the data, while for annihilations a small region of e+ e− is also permitted [29]. For
the allowed parameter space, decays or annihilations into hadrons and weak and Higgs bosons
are severely limited. Decays are constrained by the Fermi observation of the isotropic diffuse
gamma-ray flux [31], and annihilations are constrained by the production of antiprotons [32].
Explaining the anomalies with annihilations has an additional challenge. In order tomatch the observed rates, the cross-section required is 103 –104 times that expected for thermal production of the dark matter in the early universe. This necessitates nonthermal
production mechanisms or low-velocity enhancements to the cross-section, such as the Sommerfeld enhancement [24, 26] or the Breit-Wigner enhancement [33, 34]. Moreover, high crosssection annihilations to leptonic states are tightly constrained by synchrotron radio emissions from the galactic center, although this constraint can be evaded if the true galactic dark
matter halo profile is much less steep at the galactic center than benchmark profiles [27, 29].

2

For either decays or annihilations, neutrino observations may provide the strongest constraints — or the most promising corroborating signatures — for dark matter to be the sourceof the anomalies. With the exception of the disfavored e+ e− channel, the required leptonic
final states decay into neutrinos. These travel undeflected from their sources, eliminating
any uncertainties in modeling their propagation. Moreover, astrophysical sources that may
explain the anomalies are not expected to produce a large flux of neutrinos. Pulsars, forexample, would generate at most O(1) events/year at a full km-scale detector, and only atenergies greater than 10 TeV [35].
There are, however, challenges to constraining dark matter models with neutrinos. As
they are observed only by collecting Cherenkov light from induced particle showers or fromsecondary muons, angular resolution is poor compared to gamma-ray observatories. Also,
there are significant backgrounds from atmospheric muon and neutrino fluxes. However,if these backgrounds can be controlled, the poor angular resolution need not be a barrier;indeed by integrating the flux over a large area of the sky, the resulting constraint is muchless sensitive to the choice of dark matter profile [39, 40]. Moreover, by observing the galacticand extragalactic diffuse dark matter, rather than any that may have been captured by the
Sun or the Earth, any constraints will be independent of the dark matter-nucleon crosssections, which are related to final states in a model-specific way [41].
Recent analyses show the power of neutrino constraints, using various strategies to reduce the effect of atmospheric backgrounds. The Super-Kamiokande observatory resides
in the northern hemisphere, facing away from the galactic center, minimizing atmosphericbackgrounds. Measurements of upward-going muons place a limit on the flux of galactic νµ ,providing a robust constraint that eliminates annihilations to τ + τ − as a source of the e±anomalies [28, 29]. The IceCube observatory, on the other hand, resides at the South Pole
where down-going atmospheric fluxes are coincident with the neutrinos from the galactic
center. The overwhelming background of atmospheric muons can be suppressed by event
selection to establish an isotropic diffuse flux limit [42, 43, 44], but this limit only starts at
a high energy threshold O(10 TeV), and yields a relatively weak constraint as we will show.
Currently under construction is DeepCore [45], an in-fill of the IceCube detector which
will use the outer instrumented volume as a veto on downward-going muons to a level of
one part in 106 [46]. This will allow the galactic neutrino flux to be measured and compared3

against the atmospheric neutrino flux, providing a constraint on dark matter decays andannihilations. Recent work [47, 48] by some of the authors shows that IceCube+DeepCore
will be able to significantly constrain the parameter space of decays to µ+ µ− , and rule out
decays to τ + τ − and annihilation to µ+ µ− as possible sources of the anomalies in less than
five years of running.
Recently, IceCube+DeepCore has demonstrated in simulations the ability to distinguishbetween track-like events, which are due to the charged-current interactions of νµ , and cascade events, which are induced by νe,τ through charged-current interactions and by all neutrino flavors through neutral-current interactions [49, 50]. This is very useful for constraining
dark matter neutrino fluxes because νµ is the dominant flavor of atmospheric neutrinos above
40 GeV [51, 52]. The neutrino-nucleon cross sections are the same for all flavors, so signal
would be considerably enhanced, while background would be reduced because νµ only createscascade events through the neutral-current interaction, which is lower in cross section thanthe charged-current interaction [37, 38, 39] (see Fig. 1). Moreover, cascade events are easy
to distinguish from the tracks caused by any atmospheric muons that are not vetoed by theouter volume.
In this paper we show that observation of cascade events at IceCube+DeepCore canenhance the neutrino constraints on dark matter, and rule out (or corroborate) dark matterdecays to µ+ µ− or τ + τ − and annihilation to µ+ µ− as sources of the observed e± cosmic-ray
anomalies in a much shorter time compared to searches that rely solely on track-like events.

2

Analysis

For brevity, in the expressions below we write only the terms for neutrinos and not the terms
for antineutrinos. The terms are identical, except replacing “ν” by “ν̄”.

2.1

Galactic flux signal and background

The flux of neutrinos from the galactic dark matter halo is given bydΦνi
1
1 dNνi=(r ρ )
J1 (∆Ω)
dEdΩ
4π
mτ dE

(1)

1
dΦνi
1
dNνi
=
(r ρ2 ) 2 hσvi
J2 (∆Ω)
dEdΩ
8π
m
dE

(2)

for decays and by4νN and ν̄N cross-sections

Cross-section [cm2 ]

10-34
10-35
10-36
10-37
101

102

103

Energy [GeV]

104

105

Figure 1: Cross sections for (anti)neutrino-nucleon interactions, given by Ref. [37]. The
blue lines are for charged-current interactions, and the red lines are for neutral-current
interactions. Solid lines are for neutrinos and dashed lines are for antineutrinos.
for annihilations, where r = 8.5 kpc is the distance from the Sun to the galactic center [53],ρ= 0.3 GeV cm−3 is the dark matter density in the solar neighborhood, m is the dark

matter mass, and τ and hσvi are the dark matter lifetime and thermally averaged crosssection respectively. Jn is the line-of-sight (los) integral through the halo profile:
 n
Z
Z
ds ρ
1
dΩ
Jn (∆Ω) =∆Ω ∆Ωρ
l.o.s. r(3)

where ∆Ω is the region of sky observed. In this analysis we use the Navarro-Frenk-White(NFW) halo profile [55]ρ(r) = ρ r   1 + r /r 2sr

1 + r/rs(4)

with rs = 20 kpc.
The neutrino source spectra dNνi /dE for flavors i are given by PYTHIA [56] simulation.
Assuming sin2 2θ12 : sin2 2θ13 : sin2 2θ23 ≈ 1 : 1 : 0, the flavor distribution will be 1 : 1 : 1 as
the neutrinos reach the Earth, having traveled a variety of long distances across the galaxy
and being well mixed through vacuum oscillations.
As discussed in the Introduction, the only background to cascade events is atmospheric5neutrinos after the veto suppresses the background of atmospheric muons to one part in 106
and event selection is used to eliminate the rest. The νµ and νe fluxes are given by Ref. [51],where the νµ flux agrees well with AMANDA observation [54]. At low zenith angles, the fluxof background νµ is ∼ 20 times greater than the flux of νe from 40 GeV to 100 TeV; it is∼ 1000 times greater than the flux of ντ (see Ref. [52]). However, below 40 GeV, especiallyat high zenith angles, the atmospheric fluxes of the three flavors only differ by O(1) due
to flavor mixing. Since modeling the background (and signal) below 40 GeV would require
simulating flavor mixing as the neutrinos propagate through the limb of the Earth, for thisanalysis we simply set an energy cutoff of Ethresh = 40 GeV.
To obtain the event rates due to the galactic and background fluxes, we first set energy
bins for dark matter of mass m to be [max(Ethresh , m/10), m/2] for decays and [max(Ethresh , m/5), m]
for annihilations. Note that the bin width is much greater than the energy resolution,
log10 (Emax /Emin ) ' 0.4 for track-like events and log10 (Emax /Emin ) ' 0.18 for cascade events [46].
We then integrate the flux times the effective area over the energy for each bin.
For track-like events due to νµ , the event rate is
Z EmaxZ
Γtr. =

dΩ
Emin



dΦνµ
dE ρice NA Vtr. [σνN (E)]CC
dEdΩ

(5)

where ρice = 0.9 g cm−3 is the density of ice, NA = 6.022 × 1023 g−1 is Avogadro’s number (toconvert mass to number of nucleons), [σνN (E)]CC is the neutrino-nucleon cross section for the
charged-current interaction, and Vtr. ≈ 0.04 km3 is the effective volume of the detector for
track-like events [46]. Note that we do not add the residual atmospheric muon backgroundto the background of track-like events due to the uncertainty in its value.
For cascade events we use the instrumented volume Vcasc ≈ 0.02 km3 [46, 57], the chargedcurrent interaction for νe,τ , and the neutral-current interaction for all flavors to obtain
Z EmaxZΓcasc. =

dΩ
Emin



dΦνe,τ
dΦνe,µ,τdE ρice NA Vcasc. [σνN (E)]CC+ [σνN (E)]NC
.
dEdΩ
dEdΩ

(6)

Unlike track-like events, cascade events are well contained, so the effective volume for theirdetection will vary little with energy. Also, we assume that in neutral-current interactions
all the energy of the neutrino goes into the cascade. Taking partial energy transfer into
account would yield a modest improvement in significance, since most of the signal is from6

νe,τ charged-current interactions but most of the background is from νµ neutral-current
interactions.1
Finally, because the pointing capability for cascades is approximately 50◦ [46, 49] andthe pointing capability for track-like events has yet to be established, we integrate over the
2π field of view around the galactic center. As mentioned before, this should provide aconstraint which is robust to changes in dark matter halo profile. Specifically, the fractionalchange between the NFW profile used here and the much less steep isothermal profile forJ1 (2π) is O(10−3 ), and for J2 (2π) is O(0.1).

2.2

Extragalactic isotropic diffuse flux

For comparison to the DeepCore constraints from down-going fluxes, we calculate the constraint from the isotropic diffuse flux limit for AMANDA-II from track-like events [43] andthe projected limit for IceCube from cascade events [44].
The main contribution from dark matter decay to the isotropic diffuse flux is that fromextragalactic dark matter residing on cosmological scales. The flux from the decay of cosmological dark matter is given by the previously derived [30, 31] formula


dΦνi
dEdΩ

(ex.)c ΩDM ρc 1=
1/2 mτ
4π H0 ΩMZ ∞1y −3/2dy p
1 + ΩΛ /ΩM y −3



dNνi
d(Ey)


(7)

where y ≡ 1 + z, with z being the redshift, H0 = 71.9 km s−1 Mpc−1 is the Hubble constant,ρc = 3H02 /(8πGN ) is the critical density, ΩM = 0.258, ΩDM = 0.214, and ΩΛ = 0.721 are,respectively, the total matter, dark matter, and dark energy densities divided by the criticaldensity [1]. The isotropic diffuse flux from the annihilations of cosmological dark matter is
too small to be relevant, since the density of dark matter on cosmological scales is very low,
and the flux is suppressed by another power of ρc /m.
Because of the loss of signal due to event selection and the presence of background fluxes,
both the AMANDA-II limit and the projected IceCube limit are only valid at energies greaterthan ∼ 20 TeV. Below these thresholds we add the atmospheric background flux to theselimits, and use these total fluxes to calculate the constraints on the dark matter lifetime.

1

Inelasticity curves are given in Ref. [36], but only for energies 10 TeV and higher.

7DM → µ + µ−
yr
sc. 3
a
c
e
Cor
. 5yr
Deep pCore tr
Dee

DA
AN
AM

104

DM Mass [GeV]

1024102

ec

b
Cu

Ice

105

103

.
asc

iff.

FERMI

C

1025

p-µ
r-K u
e
p
Su

103

Deep

C
Deep
1yr
asc.
c
e
r
o

-II
d

-II
d

iff.

1026

Ice
C

1025
1024102

iff.
asc
.d

Core

yr
ub
ec

Deep

.1
casc

PAMELA

DA

FERMI

1026

C

Deep
r
r. 5y
ore t

1027

AN

PAMELA

yr

asc.3
ore c

f.

AM

DM Lifetime [s]1027

DM → τ + τ−

1028

DM Lifetime [s]

1028

dif

er-K
Sup

up-µ

104

DM Mass [GeV]105

Figure 2: Constraints for decay to µ+ µ− (left) and τ + τ − (right); the regions below thecontours are excluded. The black contour (“Super-K up-µ”) is the Super-Kamiokande limit
to 3σ from up-going muons, the orange band is the PAMELA-preferred region, and the red
ellipses are the Fermi-preferred region; these three are given by Ref. [29]. The dashed green
line (“AMANDA-II diff.”) is the constraint to 90% confidence from the AMANDA-II limiton the isotropic diffuse flux of νµ , and the solid green line (“IceCube casc. diff.”) is theconstraint to 90% confidence from the projected IceCube limit on the isotropic diffuse flux
using cascade events. The dashed blue line (“DeepCore tr. 5yr”) is the constraint to 2σfrom IceCube+DeepCore for νµ track-like events after five years of running, and the solid
blue lines are the constraints to 2σ for all-flavor cascade events after one year (“DeepCore
casc. 1yr”) and three years (“DeepCore casc. 3yr”) of running.

3

Results

The results for dark matter decays are shown in Fig. 2; the regions below the contours are
excluded. The black contour (“Super-K up-µ”) is the Super-Kamiokande limit to 3σ fromup-going muons discussed in the Introduction. The orange band is the preferred region to fit
the PAMELA e± anomaly, and the red ellipses are the preferred region to fit the Fermi e±anomaly. These three regions are given by Ref. [29] up to mass 30 TeV and lifetime 1027 s.
The dashed green line (“AMANDA-II diff.”) is the constraint to 90% confidence from the
AMANDA-II limit on the isotropic diffuse flux of νµ , and the solid green line (“IceCube casc.
diff.”) is the constraint to 90% confidence from the projected IceCube limit on the isotropic8

diffuse flux using cascade events. Since the flux from cosmological dark matter is weak to
begin with, contributing only 1% of the total flux over the 2π facing the galactic center, we
see that it is quickly overwhelmed by the atmospheric flux below ∼ 40 TeV. Nonetheless,due to the lower background of atmospheric νe compared to νµ at these high energies, using
cascade events improves the constraint by a factor of ∼ 5.
The dashed blue line (“DeepCore tr. 5yr”) is the constraint to 2σ from IceCube+DeepCore
for track-like events after five years of running, and the solid blue lines are the constraints
to 2σ for cascade events after one year (“DeepCore casc. 1yr”) and three years (“DeepCore
casc. 3yr”) of running. We see that for the µ+ µ− final state, while track-like events can only
reduce the available Fermi-preferred parameter space in five years, cascade events can rule
it out altogether in only three years. Similarly for the τ + τ − final state, track-like events canrule out the parameter space in less than five years, but with cascade events it will only takeone year. Note the weakening of the constraints below m = 250 GeV, where the energy per
final-state particle is less than 125 GeV. This is caused by the energy cutoff at 40 GeV.
The results for annihilation are shown in Fig. 3; the regions above the contours are
excluded. The plots show the same constraints as for decay, except that no isotropic limits
are shown because they are weaker than the Super-Kamiokande limit by a factor ∼ 105 dueto the low density of dark matter on cosmological scales. As with decays, cascade events
greatly accelerate the development of a useful constraint. For the µ+ µ− final state the region
by the Fermi data can be eliminated in only one year.
The exclusion plot for annihilations to τ + τ − is shown only for completeness, as the
Fermi-preferred region has already been eliminated by the Super-Kamiokande observation of
upward-going muons. However, it may provide a useful generic constraint on all dark mattermodels irrespective of the e± anomalies.

4

Conclusion

We have shown that, by using cascade events, IceCube+DeepCore can more quickly establish
constraints on dark matter models that would explain the reported e± anomalies, and overtime establish stronger constraints than from track-like events. Specifically, track-like events
will be able to significantly constrain the parameter space of decays to µ+ µ− , and rule out

9DM DM → µ + µ−

104

PAMELA

yr

FERMI

10-23

yr

.3
casc
e
r
o
C
Deep

103

102

10-24
102

103

104

DM Mass [GeV]

101
105

1yr
asc.
c
e
r
Co
Deep
5yr
e tr.
r
o
C
Deep

PAMELA

10-23
yr

10-24
102

Dee

3
asc.
c
e
r
pCo

103

p-µ
-K u

104

103

Boost

sc. 1
e ca
r
o
C
Deep 5yr
tr.
Core
p
e
e
D

er
Sup

10-22

Boost

<σv > [cm3 s−1 ]

10-22

FERMI

<σv > [cm3 s−1 ]

p-µ
-K u
r
e
Sup

DM DM → τ + τ−

102

104

DM Mass [GeV]

101
105

Figure 3: Constraints for annihilation to µ+ µ− (left) and τ + τ − (right); the regions above
the contours are excluded. The black contour (“Super-K up-µ”) is the Super-Kamiokande
limit to 3σ from up-going muons, the orange band is the PAMELA-preferred region, and thered ellipses are the Fermi-preferred region; these three are given by Ref. [29]. The dashedblue line (“DeepCore tr. 5yr”) is the constraint to 2σ from IceCube+DeepCore for νµ tracklike events after five years of running, and the solid blue lines are the constraints to 2σ for
all-flavor cascade events after one year (“DeepCore casc. 1yr”) and three years (“DeepCore
casc. 3yr”) of running.
decays to τ + τ − and annihilations to µ+ µ− in less than five years of running. In comparison,cascade events can rule out decays to µ+ µ− in only three years, and rule out decays toτ + τ − and annihilation to µ+ µ− after only one year. Moreover, these constraints are highlyrobust to the choice of dark matter halo profile and independent of dark matter-nucleon
cross section.
In closing, we note two interesting possibilities for future work. First, if the pointing
accuracy for track-like events at IceCube+DeepCore is established to be less than 10◦ , thesignal-to-noise for annihilations may be significantly enhanced by observing a smaller region
around the galactic center, possibly out-performing cascade searches (albeit with greater
dependence on the choice of dark matter halo profile). This would strengthen the discovery
potential for dark matter because the galactic center could be identified as a localized source10

of excess neutrinos. Second, because the ντ atmospheric background is so low at energies
above 40 GeV and at low zenith angles, if IceCube+DeepCore can demonstrate efficient ντdiscrimination [50], signal to noise could be increased by a factor ∼ 100. This would put
leptophilic dark matter to a severe test.

5

Acknowledgments

The authors would like to thank D. Grant, D. J. Koskinen, and I. Taboada for answering
questions about DeepCore.
SKM is supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and would also like to thank G. Lambard for useful discussions. MRB
is supported by the U.S. Department of Energy, under Grant No. DE-FG03-92-ER40701. KF
is supported by the U.S. Department of Energy and MCTP via the University of Michigan.
DS is supported by NSF Grant No. AST-0507117 and GAANN (D.S.). HM is supported
in part by World Premier International Research Center Initiative (WPI Initiative), MEXT,
Japan, in part by the U.S. DOE under Contract No. DE-AC03-76SF00098, and in part by
the NSF under Grant No. PHY-04-57315.

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