Probing the coupling of heavy dark matter to nucleons by detecting neutrino
signature from the Earth
’s core
Guey-Lin Lin, Yen-Hsun Lin, and Fei-Fan Lee
Institute of Physics, National Chiao Tung University, Hsinchu 30010, Taiwan (Received 23 September 2014; published 5 February 2015)
We argue that the detection of the neutrino signature from the Earth’s core can effectively probe the coupling of heavy dark matter (mχ > 104 GeV) to nucleons. We first note that direct searches for dark
matter (DM) in such a mass range provide much less stringent constraint than the constraint provided by such searches for mχ∼ 100 GeV. Furthermore, the energies of neutrinos arising from DM annihilation
inside the Sun cannot exceed a few TeVs at the Sun’s surface due to the attenuation effect. Therefore, the sensitivity to the heavy DM coupling is lost. Finally, the detection of the neutrino signature from the Galactic halo can only probe DM annihilation cross sections. We present neutrino event rates in IceCube and KM3NeT arising from the neutrino flux produced by annihilation of Earth-captured DM heavier than 104 GeV. The IceCube and KM3NeT sensitivities to spin-independent DM-proton scattering cross section
σχp in this mass range are presented for both isospin-symmetric and isospin-violating cases.
DOI:10.1103/PhysRevD.91.033002 PACS numbers: 14.60.Pq, 14.60.St
I. INTRODUCTION
Evidence for dark matter (DM) is provided by many astrophysical observations, although the nature of DM is yet to be uncovered. The most popular candidates for DM are weak interacting massive particles (WIMP), which we shall assume in this work. DM can be detected either directly or indirectly with the former observing the nucleus recoil as DM interacts with the target nuclei in the detector and the latter detecting final state particles resulting from DM annihilation or decays. The direct detection is possible because the dark matter particles constantly bombard the Earth as the Earth sweeps through the local halos. Sensitivities to the DM-nucleon cross sectionσχpfrom DM direct searches are low for large DM mass mχ. Given a
fixed DM mass densityρ0in the solar system, the number density of DM particles is inversely proportional to mχ.
Furthermore, the nuclear form factor suppression is more severe for DM-nucleus scattering for large mχ. For a review
of direct detection, see [1].
In this work, we propose to probe the coupling of heavy DM to nucleons by indirect approach with neutrinos. We note that the flux of DM-induced neutrinos from the Galactic halo is only sensitive to the thermally averaged DM annihilation cross section hσυi. Furthermore, the energies of neutrinos from the Sun cannot exceed a few TeVs due to severe energy attenuation during the propa-gation inside the Sun. Hence, for mχ > 104GeV, we turn
to the possibility of probing such DM with the search for the neutrino signature from the Earth’s core.
In this paper, we study the neutrino signature from DM annihilation channelsχχ → ν¯ν; τþτ−, and WþW−. We do not considerχχ → μþμ− because muons will suffer severe energy losses in the Earth before they decay to neutrinos.
The soft neutrino spectrum in this case is dominated by the atmospheric background. One also expects that the neutrino telescopes are less sensitive to heavy quark channels such as χχ → b¯b than they are to leptonic channels. This is caused by the relatively softer neutrino spectrum resulting from the b-hadron decays compared to the neutrino spectrum from τ decays [2]. For light quark channels χχ → q¯q, the hadronic cascades produce pions or kaons in large multiplicities. These hadrons decay almost at rest and produce MeV neutrino fluxes. Such fluxes are not considered here since we are interested in the sensitivities of IceCube and KM3NeT, which have much higher thresh-old energies. However, for detectors aiming at lower-energy neutrinos, such neutrino fluxes might be of interest. For DM annihilation in the Sun, the detectability of such neutrino fluxes has been demonstrated in Refs.[3,4].
The status of the IceCube search for neutrinos coming from DM annihilation in the Earth’s core has been reported
[5]. The earlier IceCube data on the search for astrophysical muon neutrinos was used to constrain the cross section of DM annihilationχχ → ν¯ν in the Earth’s core[6]for mχ in
the favored range of the PAMELA and Fermi experiments
[7,8]. The sensitivity of the IceCube-DeepCore detector to various DM annihilation channels in the Earth’s core for low mass DM has also been studied in Ref. [9]. In this work, we shall extend such an analysis to mχ > 104GeV as
mentioned before. We consider both muon track events and cascade events induced by neutrinos in the IceCube observatory. The DM annihilation channels χχ → τþτ−, WþW−, andν¯ν will be analyzed. Besides analyzing these signatures in IceCube, we also study the sensitivity of the KM3NeT observatory to the same signature. The KM3NeT observatory[10]is a multi-cubic-kilometer-scale deep sea neutrino telescope to be built in the Mediterranean Sea. PHYSICAL REVIEW D 91, 033002 (2015)
KM3NeT will act as IceCube’s counterpart in the northern hemisphere. Because of its instrumental volume of several cubic kilometers, KM3NeT will be the largest and most sensitive water Cherenkov neutrino detector. The sensitiv-ities to DM annihilation cross sectionhσυi and DM-proton scattering cross section σχp are expected to be enhanced significantly by KM3NeT.
This paper is organized as follows. In Sec.II, we discuss DM capture and annihilation rates inside the Earth and the resulting neutrino flux. We note that the neutrino flux in this case depends on both the DM annihilation cross section hσυi and the DM-proton scattering cross section σχp. In
Sec. III, we discuss the track and cascade event rates resulting from DM annihilation in the Earth’s core. The background event rates from the atmospheric neutrino flux are also calculated. In Sec. IV, we compare signature and background event rates and obtain the sensitivities of the neutrino telescopes to the DM-proton scattering cross section. We present those sensitivities in both the iso-spin-symmetric and isospin-violating[11,12]cases, respec-tively. We present the summary and conclusion in Sec.V.
II. DARK MATTER ANNIHILATION IN THE EARTH’S CORE A. DM capture and annihilation rates
in the Earth’s core
For our interested mass range, mχ> 104 GeV, DM
particles are trapped in a small spherical region in the Earth’s core, which can be approximated as a point. In fact, the volume of dark matter occupation in the Earth’s core is given by VχðmχÞ ¼ V0ð20 GeV=mχÞ2=3 with V0¼ 2.3 ×
1025 cm3 [13]. For m
χ¼ 104 GeV, the radius for Vχ is
only about 100 km. Hence, the neutrino differential flux dΦνi=d ¯Eνi from the annihilation channel χχ → f ¯f can be
expressed as
dΦνi
d ¯Eνi ¼
Z
dEνiTνið ¯Eνi; EνiÞ4πRΓA2 ⊕ X f Bf dNνi dEνi f ; ð1Þ where R⊕is the Earth’s radius, Bfis the branching ratio of
the annihilation channelχχ → f ¯f, dNνi=dEνiis the energy
spectrum ofνiproduced per DM annihilation in the Earth’s core, ΓA is the DM annihilation rate in the Earth, and Tνið ¯Eνi; EνiÞ summarizes the neutrino propagation effects
including attenuation, regeneration, and energy losses from the source to the detector. We stress that the above propagation effects are treated as stochastic processes. The variable Eνi denotes the neutrino energy at the
production point, while ¯Eνi is the neutrino energy at
the detector. The integration over Eνi in Eq. (1) reflects
the stochastic nature of neutrino energy loss; i.e., Eνi and
¯Eνiare not in one-to-one correspondence. In the absence of
propagation effects, we have Tνið ¯Eνi; EνiÞ ¼ δð ¯Eνi− EνiÞ.
In general, Tνið ¯Eνi; EνiÞ is a smooth function and
R
d ¯EνiTνið ¯Eνi; EνiÞ < 1 is due to the neutrino flux
attenu-ation. To compute dΦνi=d ¯Eνi, we employed WIMPSIM[14]
so that the neutrino propagation effects summarized by Tνið ¯Eνi; EνiÞ are fully taken care of.
We note that WIMPSIM only provides the neutrino
spectrum dNνi=dEνi for mχ ≤ 104 GeV on its web site.
For mχ > 104GeV, we obtain dNνi=dEνi by assuming
dNνi=dZi (Zi≡ Eνi=mχ) is independent of mχ. We have
verified such an assumption for103≤ mχ=GeV ≤ 104. We further note that the calculation of Tνið ¯Eνi; EνiÞ is not
limited to mχ< 104 GeV in WIMPSIM [15].
Although Tνið ¯Eνi; EνiÞ can be calculated by WIMPSIM, it
is useful to discuss the qualitative features of this function. For Eν≳ 100 TeV, all flavors of neutrinos interact with
nucleons inside the Earth with a total cross sectionσ ∝ E0.5
[16]. Charged current (CC) and neutral current (NC) neutrino-nucleon interactions occur in the ratio 0.71:0.29, and the resulting lepton carries about 75% of the initial neutrino energy in both cases [16]. For CC interaction, initial νe and νμ will disappear, and the resulting e and μ will be brought to rest due to their electromagnetic energy losses. Thus, high-energy νe and νμ are absorbed by the Earth; i.e., CC interaction affects the normalization of Tνeð ¯Eνe; EνeÞ [such as
R
d ¯EνeTνeð ¯Eνe; EνeÞ] and Tνμð ¯Eνμ; EνμÞ. However, the
sit-uation is very different forντ [17,18]because, except for very high energies (≳106 TeV), the tau lepton decay length
is less than its range. Hence, the tau lepton decays in flight without significant energy loss. In every branch of tau decays, ντ is produced. In this regeneration process ντ → τ → ντ, the regenerated ντ carries about 1=3 of the
initialντ energy[19,20]. Thoseντ arriving at the detector site can be identified through cascade events. Therefore, the functional form rather than the normalization of Tντð ¯Eντ; EντÞ is affected by CC interaction. In NC
inter-actions, the initial neutrinos of all flavors are subject to the same energy losses. Hence, the neutrino spectrum of each flavor is shifted to the lower energy range. As a result, only the functional form of Tνið ¯Eνi; EνiÞ is affected by NC
interaction.
The annihilation rate,ΓA, can be obtained by solving the DM evolution equation in the Earth’s core[21,22],
_N ¼ CC− CAN2− CEN; ð2Þ
where N is the DM number density in the Earth’s core, CC
is the capture rate, and CE is the evaporation rate. The
evaporation rate is only relevant when mχ≲ 5 GeV [23–25], while a more refined calculation found, mχ≲
3.3 GeV [26], which is much lower than our interested mass scale. Thus, CE can be ignored in this work.
equation(2)can be found in Refs.[23–27]. Solving Eq.(2), thus, gives the annihilation rate
ΓA¼ CC 2 tanh2 t τ⊕ ; ð3Þ
where τ⊕ is the time scale when the DM capture and annihilation in the Earth’s core reach the equilibrium state. Taking t ≈ 1017 s as the lifetime of the solar system, we have[27] t τ⊕≈ 1.9 × 10 4 CC s−1 1=2 hσυi cm3s−1 1=2 mχ 10 GeV 3=4 ; ð4Þ wherehσυi is the DM annihilation cross section, mχ is the DM mass, and CC is the DM capture rate which can be
expressed as[27] CC∝ ρ0 0.3 GeV cm−3 270 km s−1 ¯υ GeV mχ × σχp pb X i FAiðmχÞ; ð5Þ
where ρ0 is the local DM density, ¯υ is the DM velocity dispersion, σχp is the DM-nucleon cross section, and FAiðmχÞ is the product of various factors for element Ai,
including the mass fraction, chemical element distribution, kinematic suppression, form factor, and reduced mass. We note that σχp is spin independent in the Earth’s case. We also point out that the factors FAibehave as1=mχwhen mχ
is much heavier than the nucleus mass mAi. Thus, the mass
dependence of the capture rate goes as1=m2χ.
B. Isospin violation effects to bounds set by direct and indirect searches
Recent studies[11,12,28,29]suggested that DM-nucleon interactions do not necessarily respect the isospin sym-metry. It has been shown that[12,29,30]isospin violation can dramatically change the bound onσχp from the current direct search. Therefore, the isospin violation effect is also taken into consideration in our analysis.
Given an isotope with atomic number Z, atom number Ai, and the reduced massμAi≡ mχmAi=ðmχþ mAiÞ for the
isotope and the DM particle, the usual DM-nucleus cross section with the approximation mp≈ mn can be
written as [27] σχAi¼ 4μ2 Ai π ½Zfpþ ðAi− ZÞfn2 ¼μ2Ai μ2 p Z þ ðAi− ZÞ fn fp 2 σχp; ð6Þ
where fp and fn are the effective couplings of DM to
protons. It is useful to define the ratio betweenσ0χAiandσχAi where the former is the DM-nucleus cross section assuming isopin symmetry and the latter is the cross section with isospin violation. In this ratio, the DM-proton cross section σχp is held fixed. For a particular species of chemical
element with atomic number Z, we have σ0 χAi σχAi ¼ P iηiμ2AiA2i P iηiμ2Ai½Z þ ðAi− ZÞfn=fp2 ≡ FZ; ð7Þ
whereηiis the percentage of the isotope Ai. We note that
for a target containing multiple species of chemical elements, the factor FZ should be modified into
¯F ≡ PZfZFZ, where fZ is the fraction of proton targets
originating from elements with the atomic number Z. Figure1shows the numerical values of ¯F versus different fn=fp at mχ ¼ 500 TeV. Since mχ is taken to be much
larger than mAi, ¯F is insensitive to mχ.
III. DM SIGNAL AND ATMOSPHERIC BACKGROUND EVENTS
The neutrino event rate in the detector resulting from DM annihilation in the Earth’s core is
Nν¼ Z Emax Eth dΦν dEνAνðEνÞdEνdΩ; ð8Þ Xe Earth 1.0 0.5 0.0 0.5 1.0 10 4 10 3 10 2 10 1 100 fn fp F m 500 TeV fn fp 0.7
FIG. 1 (color online). Isospin violation effect versus fn=fp
for different targets at mχ¼ 500 TeV. For the Xenon target, ¯F
reduces to FZ. In this case, FZ reaches a minimum at
fn=fp¼ −0.7. With the Earth as the target, ¯F ≡
P
ZfZFZwhere
fZ is the fraction of proton targets originating from chemical
elements with the atomic number Z. In this case, ¯F reaches a minimum for fn=fp≈ −0.9. We have taken the Earth’s
compo-sition from Ref. [27]. The fraction fZ is taken as the average
fraction of a chemical species inside the Earth.
where Eth is the detector threshold energy taken to be
104GeV, E
maxis the energy upper cut, and dΦν=dEνis the
neutrino flux from DM annihilation. As neutrinos arrive at the detector, they interact with the medium enclosed by the detector and produce track events through νμ CC inter-action. Cascade events are produced viaνe;τ CC and allνi NC interactions. The quantity Aν is the detector effective
area with contained vertex andΩ is the solid angle for the event direction. Given the sizes of IceCube and KM3NeT, we take Emax¼ 107GeV.
As seen from the detector, the DM-induced neutrino flux comes from a small angular range surrounding the direction to the center of the Earth. The solid angle ΔΩ subtended by the cross sectional area of the DM-populated region Vχis given byΔΩ ¼ 2πð1 − cos ψχÞ with ψχgiven
by[9] ψχðmχÞ ¼ sin−1 1 R⊕ × 3VχðmχÞ 4π 1=3 : ð9Þ
For mχ¼ 104 GeV, we have ψχ ¼ 0.9°. Hence, ψχ is
always less than 1° in our interested DM mass range. Ideally, one may select neutrino events by setting the observation open angle, ψ ¼ ψχðmχÞ. However, due to the detector angular resolution, we choose the open angle, ψ ¼ 1°, for track events and ψ ¼ 30° for cascade events to reflect the current IceCube performance[31,32].
In this work, we consider neutrino events in neutrino detectors IceCube and KM3NeT. To compute the event rates in IceCube, the effective areas Aν for different
neutrino flavors with CC and NC interactions in Eq. (8)
can be evaluated from the effective volume Veff[31]by the
following relation,
AνðEνÞ ¼ Veff
NA
Mice
ðnpσνpðEνÞ þ nnσνnðEνÞÞ; ð10Þ
where NAis the Avogadro constant, Miceis the molar mass
of ice, np;n is the number density of proton/neutron per
mole of ice, and σνp;n is the neutrino-proton/neutron cross section. One simply swaps the sign ν → ¯ν for the antineutrino.
We note that another neutrino telescope KM3NeT located in the northern hemisphere is also capable of detecting the neutrino signal from DM annihilation in the Earth. At the present stage, KM3NeT has only published the νμ CC effective area [10,32]. Therefore, we consider only track events in KM3NeT.
The atmospheric background event rate is similar to Eq. (8) by replacing dΦν=dEν with the atmospheric
neutrino flux, Natm¼ Z Emax Eth dΦatm ν dEν AνðEνÞdEνdΩ: ð11Þ
To facilitate our calculation, the atmospheric neutrino flux dΦatm
ν =dEνshown in Fig.2is taken from Refs.[33,34]and
extrapolated to Eν≃ 107 GeV.
IV. RESULTS
We present the sensitivity as a2σ detection significance in five years, calculated with the convention
s ffiffiffiffiffiffiffiffiffiffiffi s þ b
p ¼ 2.0; ð12Þ
where s is the DM signal, b is the atmospheric background, and 2.0 refers to the 2σ detection significance. The atmosphericντ flux is extremely small and can be ignored in our analysis. Thus, we take νe and νμ as our major background sources. The detector threshold energy Eth in
Eqs.(8)and(11)is set to be104 GeV in order to suppress the background events. In the following two subsections, we present two isospin scenarios for the constraints onhσυi andσχp. One is fn=fp¼ 1, the isospin-symmetry case, and
the other is fn=fp¼ −0.7, the isospin-violation one. The
isospin-violation scenario is often used to alleviate the inconsistency between the results of different DM direct detection experiments for low mχ. The ratio fn=fp¼ −0.7
is the value for which the σχp sensitivity of a Xenon detector is maximally suppressed by isospin violation. Although our study focuses on heavy DM accumulated inside the Earth and Xenon is very rare among the constituent elements of the Earth, we shall see that fn=fp∼
−0.7 leads to the most optimistic IceCube sensitivities on both hσυi and σχp. In the next subsection, we present various fn=fp values and their impact on the IceCube
sensitivities to various annihilation channels.
To derive sensitivities to the DM-annihilation cross sectionhσυi, we make use of the σχpfrom the extrapolation of the LUX bound[35]to mχ > 10 TeV. Such an input σχp
represents the best scenario in our analysis. Once a more
e: Aartsen et al. : Abbasi et al. Conventional 1010 109 108 107 106 105 104 103 log10E GeV E 2 GeV cm 2s 1sr 1 Atmospheric neutrino 2 3 4 5 6 7
stringent bound on σχp is obtained in the future, the sensitivities to hσυi presented in this work will be worse. The extrapolation of the LUX bound to our interested mχ
range can be justified as follows. The total rate R measured by the direct search is given by R ∝ σχpρ0=mχmAi for
mχ ≫ mAi[27], withρ0the local DM density, mAithe mass
of the target, and i the index for isotopes. Thus, σχp ∝ mχmAiR=ρ0. Hence, the linear extrapolation of the
LUX bound in the mass range mχ> 10 TeV is reasonable.
A. IceCube sensitivities
In Fig.3we present the IceCube sensitivities tohσυi of χχ → τþτ−, WþW−, and ν¯ν annihilation channels in the
Earth’s core with both track and cascade events. For the χχ → ν¯ν production mode, we assume equal-flavor distri-bution (1=3 for each flavor). In the left panel where fn¼ fp, the IceCube sensitivities to χχ → τþτ− and
χχ → WþW− annihilation channels with track events are
only available in a narrow DM mass range. For most of the DM mass range considered here, the estimated sensitivities are either disfavored by the CMB constraint or reach into the equilibrium region where the2σ sensitivity cannot be achieved. The raising tails for all sensitivities are due to the neutrino attenuation in the high energy such that largerhσυi is required to generate sufficient number of events.
For mχ≳ 106GeV, it is seen that IceCube is more
sensitive toχχ → τþτ−than toχχ → ν¯ν for cascade events. This can be understood by the fact that the neutrino spectrum from χχ → ν¯ν is almost like a spike near mχ. As mχ becomes larger, neutrinos produced by the
annihi-lation are subject to more severe energy attenuation. On the other hand, the neutrino spectrum from χχ → τþτ− is
relatively flat in the whole energy range. The energy attenuation only affects the higher energy neutrinos.
In the isospin violation scenario, the ratio fn=fp¼ −0.7
reduces the scattering cross section between DM and Xenon by 4 orders of magnitude with a fixed σχp. This is easily seen from Fig.1. Hence, the LUX upper bound on σχp is raised by 4 orders of magnitude. With the same
fn=fp ratio, one can also see that the DM capture rate by
the Earth is suppressed by 2 orders of magnitude. If one takes the LUX upper bound onσχpfor fn=fp¼ −0.7 as the
input, the capture rate CC of the Earth is enhanced by 2
orders of magnitude. One can estimate the enhancement on the neutrino flux by Eq.(3). We note that the number of DM particles inside the Earth is still far from the equilib-rium, i.e., tanhðt=τ⊕Þ ≈ t=τ⊕. Hence, we can see thatΓAis proportional to C2Chσvi by using Eq. (4). This is rather different from the equilibrium case where ΓA is propor-tional to CC. Since CCis 2 orders of magnitude larger for
fn=fp¼ −0.7, the bound on hσvi derived from ΓA is
improved by 4 orders of magnitude.
For DM produced as a thermal relic of the big bang, the DM relic density Ωχ is related to the thermally averaged annihilation cross sectionhσvi by [27]
Ωχh2≈3 × 10
−27 cm3s−1
hσvi : ð13Þ
By substitutingΩχh2 forOð0.1Þ in the present epoch, we have hσυi ≃ 3 × 10−26 cm3s−1, which is known as the thermal relic scale. We note that Eq.(13) is a simplified relation ignoring its dependence on the WIMP mass. With the mass dependence treated carefully, one obtainshσυi ≈ ð2–5Þ × 10−26 cm3s−1 for Ω χh2¼ 0.11 [37]. We should 104 105 106 107 10 26 10 25 10 24 10 23 10 22 10 21 10 20 m GeV cm 3s 1 IceCube, fnfp 1
thermal relic scale
CMB Slatyer et al. tanh t 1 unitarity W cascade track 104 105 106 107 10 28 10 27 10 26 10 25 10 24 10 23 m GeV cm 3s 1 IceCube, fnfp 0.7
thermal relic scale tanh t
1
unitarity
FIG. 3 (color online). The IceCube five-year sensitivities at2σ to hσυi for χχ → τþτ−, WþW−, andν¯ν annihilation channels with track and cascade events. We take ψ ¼ 1° for track events and ψ ¼ 30° for cascade events. The isospin-symmetry case, fn=fp¼ 1, is
presented in the left panel, and the isospin- violation case, fn=fp¼ −0.7, is presented in the right panel. The yellow-shaded region is the
parameter space for the equilibrium state, and the blue-shaded region is the constraint from CMB [36].
point out that the DM in our considered mass range could be produced nonthermally. In such a case, there is no canonical value forhσυi. However, hσυi is bounded from the above by the unitarity condition [38–40]. The DM annihilation cross section is assumed to be s-wave dominated in the low-velocity limit. Hence, it can be shown that [38] hσυi ≤ 4π m2χυ≃ 1.5 × 10 −13cm3 s GeV mχ 2 300 km=s υrms : ð14Þ This unitarity bound withυrms≃ 13 km s−1 (escape
veloc-ity from the Earth) is also shown in Fig. 3. The unitarity bound can be evaded for nonpointlike DM particles
[39–41].
Galaxy clusters (GCs) are the largest gravitationally bound objects in the Universe, and their masses can be as large as1015 times that of the Sun’s (1015M⊙)[42,43].
Many galaxies (typically∼50–1000) collect into GCs, but their masses consist of mainly dark matter. Thus, GCs are the largest DM reservoirs in the Universe and can be the ideal sources to look for DM annihilation signatures. With DM particles assumed to annihilate into μþμ− pairs, the predicted full IceCube2σ sensitivity in five years to hσυi for the Virgo cluster in the presence of substructures with track events is derived in Ref. [44]. We present this sensitivity in Fig. 4, and we can see that it is better than our expected IceCube five-year sensitivity at 2σ to hσðχχ → τþτ−Þυi with ν
μtrack events. One of the reasons
is because only 18% of τ decay to νμ. However, if we consider the isospin-violation scenario, our expected IceCube sensitivity with fn=fp¼ −0.7 will be much better
than that for the Virgo cluster. Except for neutrinos, DM annihilation in GCs can also produce a high luminosity in gamma rays. In Ref.[44], the authors also estimate gamma-ray constraints taking into account electromagnetic cascades caused by pair production on the cosmic photon backgrounds from the flux upper limits derived by Fermi-LAT observations of GCs [45,46]. We show in Fig.4 the gamma-ray constraint on theχχ → μþμ−annihilation cross section [44] from observations of the Virgo cluster. We can see that this constraint is weaker than our expected IceCube five-year sensitivity at2σ to hσðχχ → τþτ−Þυi for mχ≳ 105GeV. We note however that the constraint on
hσυi from the Virgo cluster is independent of σχp, while our
expected sensitivity withσχp taken from the LUX bound represents the best scenario. If we reevaluate our expected sensitivity by using smallerσχp, the results could be weaker than the constraint from the Virgo cluster.
The diffuse gamma-ray background (DGB) was mea-sured by the Fermi Large Area Telescope (Fermi-LAT) above 200 MeV in 2010 [47]. Radio-loud active galactic nuclei (AGN), including blazars [48], star-forming and
star-burst galaxies[49,50], and heavy DM are the possible sources. In Ref.[41], the authors derive cascade gamma-ray constraints on the annihilation cross section of heavy DM by requiring that the calculated cascade gamma-ray flux not exceed the measured DGB data at any individual energy bin by more than a given significance[51,52]. We present the cascade gamma-ray constraint onhσðχχ → WþW−Þυi for DGB taken from Ref.[41]in Fig.4. We note that this constraint is weaker than our predicted IceCube five-year sensitivity at2σ to hσðχχ → WþW−Þυi. On the other hand, for demonstrating the power of neutrino observations, we also show in Fig.4the predicted full IceCube sensitivity in three years tohσðχχ → WþW−Þυi for the cosmic neutrino background (CNB) with track events taken from Ref.[41]. It is slightly less sensitive compared to our expected IceCube five-year sensitivity at2σ to hσðχχ → WþW−Þυi at mχ∼ 105GeV, while both sensitivities do not reach the
unitarity bound for mχ≳ 3 × 105 GeV. We reiterate that
our derived sensitivity tohσðχχ → WþW−Þυi is the best-scenario result, while constraints obtained in Ref.[41]are independent ofσχp.
Figure 5 shows the IceCube sensitivities to spin-independent cross section σχp by analyzing track and cascade events fromχχ → τþτ−, WþW−, and ν¯ν annihi-lation channels in the Earth’s core. The threshold energy Eth is the same as before, and we take hσυi ¼
3 × 10−26cm2s−1 as our input. Precisely speaking, the track W track Virgo ray Virgo DGB ray WW CNB WW 104 105 106 107 10 26 10 25 10 24 10 23 10 22 10 21 10 20 m GeV cm 3s 1
Comparing with Murase et al.
thermal relic scale
CMBSlatyer
et al.
tanh t 1
unitarity
FIG. 4 (color online). The IceCube five-year sensitivities at 2σ to hσvi for χχ → WþW−andτþτ−annihilation channels with
track events. We takeψ ¼ 1°. The dot-dashed line is the gamma-ray constraint on theχχ → μþμ−annihilation cross section in the Virgo cluster[44]. The dashed line is the projected full IceCube 2σ sensitivity in five years to hσðχχ → μþμ−Þvi in the Virgo
cluster in the presence of substructures with track events[44]. The dot-dot-dashed line is the cascade gamma-ray constraint on hσðχχ → WþW−Þvi from diffuse gamma-ray background (DGB) [41]. The thick solid line is the full IceCube sensitivity in three years tohσðχχ → WþW−Þvi from cosmic neutrino background (CNB) with track events[41].
sensitivity to theχχ → ν¯ν channel is the highest when mχ≲ 106GeV andχχ → τþτ−after. However, the sensitivities to
different channels can be taken as comparable since the differences between them are not significant.
When the isospin is a good symmetry, the IceCube sensitivity is not as good as the constraint from the LUX extrapolation. However, with fn=fp¼ −0.7, the capture
rate is reduced to 1% of the isospin symmetric value. Therefore, one requires 100 times largerσχp to reach the same detection significance. However, the ratio fn=fp¼
−0.7 makes a more dramatic impact to the DM direct search using Xenon as the target. The DM scattering cross
section with Xenon is reduced by 4 orders of magnitude. Hence, the indirect search by IceCube could provide better sensitivities on σχp than the direct search in such a case.
B. KM3NeT sensitivities
Besides IceCube, the neutrino telescope KM3NeT located in the northern hemisphere can also reach a promising sensitivity in the near future [53]. Therefore, it is worthwhile to comment on the performance of KM3NeT. Since KM3NeT has only published the νμ CC
W cascade track 104 105 106 107 10 6 10 5 10 4 10 3 10 2 10 1 m GeV p pb IceCube, fnfp 1 LUX 2013 extrapl. tanh t 1 104 105 106 107 10 5 10 4 10 3 10 2 10 1 100 m GeV p pb IceCube, fn fp 0.7 LUX 2013 extrapl., fnfp 0.7 LUX, fnfp 1 tanh t 1 tanh t 1, f nfp 1
FIG. 5 (color online). The IceCube2σ sensitivities in five years to σχpforχχ → τþτ−, WþW−, andν¯ν annihilation channels with both track (ψ ¼ 1°) and cascade events (ψ ¼ 30°). The isospin symmetry case, fn=fp¼ 1, is presented on the left, and the isospin violation
case, fn=fp¼ −0.7, is presented on the right. The blue-shaded region is the parameter space for the equilibrium state and the
light-blue-shaded region in the right panel refers to the equilibrium-state parameter space for the isospin symmetry case as a comparison. An extrapolation of current LUX limit has been shown on the figures.
104 105 106 107 10 26 10 25 10 24 10 23 10 22 10 21 10 20 m GeV cm 3s 1 KM3NeT, fnfp 1
thermal relic scale
CMBSlatyer et al. tanh t 1 unitarity track track W track 104 105 106 107 10 29 10 28 10 27 10 26 10 25 10 24 10 23 m GeV cm 3s 1 KM3NeT, fnfp 0.7
thermal relic scale
tanh t 1
unitarity
FIG. 6 (color online). The KM3NeT2σ sensitivities in five years to hσυi for χχ → τþτ−, WþW−, andν¯ν annihilation channels for track events withψ ¼ 1°. The isospin symmetry case, fn=fp¼ 1, is presented in the left panel, and the isospin violation case, fn=fp¼ −0.7,
is presented in the right panel. The yellow-shaded region is the parameter space for the equilibrium state and the blue-shaded region is the constraint from CMB[36].
effective area [10] at the present stage, we shall only analyze track events.
The results are shown in Figs.6and7with parameters chosen to be the same as those for computing the IceCube sensitivities. The sensitivities of KM3NeT are almost an order of magnitude better than those of IceCube, since itsνμ CC effective area is about 1 order of magnitude larger than that of IceCube.
C. Sensitivities with different fn tofp ratios In the previous subsections, we have presented IceCube and KM3NeT sensitivities tohσυi and σχp for fn=fp¼ 1
and−0.7. To be thorough, it is worth discussing the effect
on the DM search with various fn=fp values. For
sim-plicity, we shall focus on the χχ → τþτ− cascade events in IceCube.
In the left panel of Fig.8, we present IceCube sensitiv-ities tohσυi with fn=fp∈ ½−0.8; 1. We take the rederived
σχp from LUX using Eq.(7), which quantifies the isospin
violation effect. Isospin violation not only leads to the suppression of the DM capture rate by the Earth but also weakens the σχp bound from LUX. The overall effect favors the DM indirect search for a certain range of fn=fp.
As shown in Fig. 8, the IceCube sensitivity to hσυi improves as fn=fp→ −0.7 from the above. However,
when fn=fp is smaller than −0.7, the sensitivity to hσυi track track W track 104 105 106 107 10 6 10 5 10 4 10 3 10 2 10 1 m GeV p pb KM3NeT, fn fp 1 LUX2013 extrapl. tanh t 1 104 105 106 107 10 5 10 4 10 3 10 2 10 1 100 m GeV p pb KM3NeT, fnfp 0.7 LUX2013 extrapl., fnfp 0.7 LUX, fnfp 1 tanh t 1 tanh t 1, fnfp 1
FIG. 7 (color online). The KM3NeT2σ sensitivities in five years to σχpforχχ → τþτ−, WþW−, andν¯ν annihilation channels for track events withψ ¼ 1°. The isospin symmetry case, fn=fp¼ 1, is presented in the left panel, and the isospin violation case, fn=fp¼ −0.7,
is presented in the right panel. The blue-shaded region is the parameter space for the equilibrium state, and the light-blue-shaded region in the right panel refers to the equilibrium-state parameter space in the isospin-symmetry case.
104 105 106 107 10 28 10 27 10 26 10 25 10 24 10 23 10 22 m GeV cm 3s 1 IceCube, cascade
thermal relic scale unitarity fnfp 0.8 fn fp 1 fnfp 0.5 fnfp 0.6 fn fp 0.7 0.8 0.7 0.5 IceCube LUX 104 105 106 107 10 5 10 4 10 3 10 2 10 1 m GeV p pb IceCube, cascade LUX, fnfp 1 IceCube, fnfp 1
FIG. 8 (color online). The IceCube five-year sensitivity at2σ to hσvi in the left panel and σχp in the right panel forχχ → τþτ− annihilation channels with cascade events for different degrees of isospin violation. We take the rederivedσχpfrom LUX with isospin violation taken into consideration.
becomes even worse than that in the isospin-sym-metry case.
In the right panel of Fig. 8, we present IceCube sensitivities toσχpwith fn=fp∈ ½−0.8; 1 by taking hσυi ¼
3 × 10−26 cm3s−1 as our input. With isospin symmetry
violated, the DM capture rate is suppressed by the factor ¯F defined right below Eq. (7). Thus, to reach the same detection significance by indirect search, one requires a larger σχp to produce enough events. However, isospin violation also weakens the LUX limit at a certain range of fn=fp. It turns out the sensitivity to σχp by IceCube is
better than the existing limit by LUX only for fn=fp
slightly larger or equal to −0.7. For fn=fp< −0.7, the
LUX limit is more stringent.
V. SUMMARY AND CONCLUSION
In this work we have presented the IceCube and KM3NeT sensitivities to thermally averaged annihilation cross sectionhσυi and DM spin-independent cross section σχp for heavy DM (mχ > 104GeV) by detecting the
DM-induced neutrino signature from the Earth’s core. To probe the former, we take σχp from the LUX bound [35] as the input. To probe the latter, we take hσυi ¼ 3 × 10−26 cm3s−1 as the input. The IceCube sensitivity to
hσðχχ → WþW−Þvi in the present case is slightly better
than its sensitivity to hσðχχ → WþW−Þvi in the case of detecting the cosmic neutrino background [41]. On the other hand, the IceCube sensitivity to hσðχχ → τþτ−Þvi
in the present case is not as good as its sensitivity to hσðχχ → μþμ−Þvi in the case of detecting neutrinos from
the Virgo cluster[44]. We like to emphasize again that our derived sensitivity tohσðχχ → WþW−Þvi uses the current LUX bound onσχpas the input. One expects this sensitivity to become worse as the constraint on σχp improves. Concerning IceCube and KM3NeT sensitivities to σχp, we have shown that they are roughly 1 order of magnitude worse than the LUX bound.
We stress that the above comparison is based upon the assumption of isospin symmetry in DM-nucleon couplings. We have shown that, like the direct search, the indirect search is also affected by the isospin violation. The implications of isospin violation for IceCube and KM3NeT observations are presented in Sec. IV. Taking the isospin-violation effect into account, the sensitivities of the above neutrino telescopes to bothhσvi and σχpthrough detecting the signature of DM annihilation in the Earth’s core can be significantly improved. As fn=fp→ −0.7, the
sensitivities to hσvi can be better than the thermal relic scale, while the sensitivities to σχp can be better than the LUX bound.
ACKNOWLEDGMENTS
We thank Y.-L. Sming Tsai for helpful advice in computations. This work is supported by the National Science Council of Taiwan under Grant No. 102-2112-M-009-017.
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