The Indirect Search for Dark Matter with IceCube
TThe Indirect Search for Dark Matter with IceCube
Francis Halzen a , Dan Hooper b,c a University of Wisconsin, Madison, USA b Fermi National Accelerator Laboratory, USA c University of Chicago, USA
1. The First Kilometer-Scale High Energy Neutrino Detector: IceCube
A series of first-generation experiments [1] have demonstrated that high energy neutrinos with ∼
10 GeV energy and above can be detected by observing the Cherenkov radiation fromsecondary particles produced in neutrino interactions inside large volumes of highly transparentice or water instrumented with a lattice of photomultiplier tubes. The first second-generationdetector, IceCube, is under construction at the geographic South Pole [2]. IceCube will consistof 80 kilometer-length strings, each instrumented with 60 10-inch photomultipliers spaced by17 m. The deepest module is located at a depth of 2.450 km so that the instrument is shieldedfrom the large background of cosmic rays at the surface by approximately 1.5 km of ice. Thestrings are arranged at the apexes of equilateral triangles 125m on a side. The instrumenteddetector volume is a cubic kilometer of dark, highly transparent and totally sterile Antarcticice. The radioactive background is dominated by the instrumentation deployed into the naturalice. A surface air shower detector, IceTop, consisting of 160 Auger-style 2.7m diameter ice-filledCherenkov detectors deployed pairwise at the top of each in-ice string, augments the deep-icecomponent by providing a tool for calibration, background rejection and cosmic ray studies.Each optical sensor consists of a glass sphere containing the photomultiplier and theelectronics board that digitizes the signals locally using an on-board computer. The digitizedsignals are given a global time stamp with residuals accurate to less than 3 ns and aresubsequently transmitted to the surface. Processors at the surface continuously collect thetime-stamped signals from the optical modules that each function independently. The digitalmessages are sent to a string processor and a global event trigger. They are subsequently sortedinto the Cherenkov patterns emitted by secondary muon tracks that reveal the direction of theparent neutrino. In this context we will focus on the neutrino flux from the direction of the Sunand the Earth.IceCube detects neutrinos with energies in excess of 0.1 TeV. An upgrade of the detector,dubbed Deep Core, consists of an infill of 6 strings with 60 DOMs with high quantum efficiency.They are mostly deployed in the highly transparent ice making up the bottom half of theIceCube detector. Deep Core will decrease the threshold to ∼
10 GeV over a significant fractionof IceCube’s fiducial volume and will be complete by February 2010; see Fig 1.The main scientific goals of IceCube fall into broad categories:(i) Detect astrophysical neutrinos produced in cosmic sources with an energy densitycomparable to the energy density in cosmic rays [3]. Supernova remnants satisfy thisrequirement if they are indeed the sources of the galactic cosmic rays as first proposedby Zwicky; his proposal is a matter of debate after more than seventy years. The sources ofthe extragalactic cosmic rays naturally satisfy the prerequisite when particles accelerated a r X i v : . [ a s t r o - ph . H E ] O c t igure 1. The IceCube detector, consisting of IceCube and IceTop and the low-energy sub-detector DeepCore.near black holes, possibly the central engines of active galaxies or gamma ray bursts, collidewith photons in the associated radiation fields. While the secondary protons may remaintrapped in the acceleration region, approximately equal numbers of neutrons, neutral andcharged pions escape. The energy escaping the source is therefore distributed betweencosmic rays, gamma rays and neutrinos produced by the decay of neutrons and neutral andcharged pions, respectively.(ii) As for conventional astronomy, neutrino astronomers observe the neutrino sky through theatmosphere. This is a curse and a blessing; the background of neutrinos produced by cosmicays in interactions with atmospheric nuclei provides a beam essential for calibrating theinstrument. It also presents us with an opportunity to do particle physics [4]. Especiallyunique is the energy range of the background atmospheric neutrinos covering the range0 . − TeV, energies not within reach of accelerators. Cosmic beams of even higher energymay exist, but the atmospheric beam is guaranteed. IceCube is expected to collect a data setof order one million neutrinos over ten years with a scientific potential that is only limitedby our imagination. With the Deep Core upgrade, IceCube will accumulate atmosphericneutrinos with sufficient statistics to determine the flavor hierarchy by observing the mattereffect of the atmospheric neutrino beam near the first oscillation dip just below 10 GeV. Apositive result will require a sufficient understanding of the systematics and, of course, amixing angle θ that is not too small. Neither one is guaranteed at this point but the goodnews is that the relevant data are forthcoming in the next few years.(iii) The passage of a large flux of MeV-energy neutrinos produced by a galactic supernova overa period of seconds will be detected as an excess of the background counting rate in allindividual optical modules [5]. Although only a counting experiment, IceCube will measurethe time profile of a neutrino burst near the center of the Galaxy with the statistics of aboutone million events, equivalent to the sensitivity of a 2 megaton detector.(iv) Finally, the subject of this chapter, IceCube will search for neutrinos from the annihilationof dark matter particles gravitationally trapped at the center of the Sun and the Earth[6].These scientific missions have historically set the scale of the detector. In this contextit is worthy of note that the AMANDA detector, the forerunner and proof of concept forIceCube, received a significant fraction of its initial funding from the Berkeley Center for ParticleAstrophysics to search for dark matter.
2. Indirect Search for Dark Matter with Neutrinos: Status
The evidence that yet to be detected weakly interacting massive particles (WIMPs) make up thedark matter is compelling. WIMPs are swept up by the Sun as the Solar System moves about thegalactic halo. Though interacting weakly, they will ocassionally scatter elastically with nucleiin the Sun and lose enough momentum to become gravitationally bound. Over the lifetime ofthe Sun, a sufficient density of WIMPs may accumulate in its center so that an equilibrium isestablished between their capture and annihilation. The annihilation products of these WIMPsrepresent an indirect signature of halo dark matter, their presence revealed by neutrinos whichescape the Sun with minimal absorption. The neutrinos are, for instance, the decay productsof heavy quarks and weak bosons resulting from the annihilation of WIMPs into χχ → b ¯ b or W + W − . These can be efficiently identified by the neutrino detectors discussed above becauseof the relatively large neutrino energy of order of the mass of the WIMP.The beauty of the indirect detection technique using neutrinos is that the astrophysics of theproblem is understood. The source in the sun has built up over solar time sampling the darkmatter throughout the galaxy; therefore, any possible structure in the halo has been averagedout. Given a WIMP mass and properties, one can unambiguously predict the signal in a neutrinotelescope. If not observed, the model is ruled out. This is in contrast to indirect searchesfor photons from WIMP annihilation, whose sensitivity depends critically on the structure ofhalo dark matter; observation requires cuspy structure near the galactic center or clustering onappropriate scales elsewhere. Observation not only necessitates appropriate WIMP properties,but also favorable astrophysical circumstances.Extensions of the Standard Model of quarks and leptons, required to solve the hierarchyproblem, naturally yield dark matter candidates. For instance, the neutralino, the lighteststable particle in supersymmetric models, has been intensively studied as a possible dark mattercandidate. Detecting it has become the benchmark by which experiments are evaluated andutually compared. We will follow this tradition here. Supersymmetric models allow for a largenumber of free parameters and, unfortunately, for a variety of parameter sets that are able togenerate the observed dark matter density in the context of standard big bang cosmology. Howto meaningfully sample this parameter space is not straightforward. In this chapter we will firstdemonstrate the considerable potential of neutrino telescopes for detecting dark matter based ona set of very general models. These models satisfy all experimental and cosmological constraintsbut do not assume a particular form of symmetry breaking. Subsequently, we will revisitIceCube’s sensitivity based on a more constrained set selected for assessing the performanceof the LHC; the experimental input has been updated [7].The neutralino interacts with ordinary matter by spin-independent (e.g. Higgs exchange)and by spin-dependent (e.g. Z-boson exchange) interactions. The first mechanism favors directdetection experiments [8] because the WIMP interacts coherently, resulting in an increase insensitivity proportional to the square of the atomic number of the detector material. Althoughcompetitive now for larger WIMP masses, indirect detection experiments are unlikely to remaincompetitive in the future given the rapid improvement of the sensitivity of direct experiments.We will show that this is not the case for spin-dependent models, however. Within the contextof supersymmetry, direct and indirect experiments are complementary.Although IceCube detects neutrinos of all flavors, sensitivity to neutrinos produced by WIMPsin the sun is achieved by exploiting the degree accuracy with which muon neutrinos can bepointed back to the Sun. Data taken with the first 22 strings of IceCube has resulted in a limit onan excess flux from the Sun shown in Fig. 2. This figure shows the current limits on the neutrinoinduced muon flux from the direction of the Sun, as well as the projected sensitivity of IceCube.Also shown is a sampling of the supersymmetric parameter space. The current limit improves onprevious results of the Super-Kamiokande [9] and AMANDA [10] collaborations by factors of 3 to5 for WIMPs heavier than approximately 250 GeV. The current IceCube limit is transformed intoa limit on the spin-dependent cross section in Fig 3. Forthcoming analyses using the completeAMANDA data set will improve on the result shown and will probe the model space shownin Fig. 2 for masses below 250 GeV. Deep Core is under construction and will enable IceCubeto place the strongest limits to-date for WIMPs as light as 50 GeV. Results from the Antarescollaboration obtained with data from the recently completed detector, are forthcoming[12]. ForWIMPs lighter than approximately 50 GeV, the reach of Super-Kamiokande is unmatched byexisting detectors.In the remainder of this chapter, we describe the processes of capture and annihilation ofWIMPs in the Sun, and predict the resulting flux of high energy neutrinos. In the later sectionsof this chapter, we will discuss the sensitivity of this technique to neutralino dark matter. Wewill also comment at the end on the excellent sensitivity of IceCube to Kaluza-Klein dark mattercandidates.
3. The Capture and Annihilation of WIMPs in the Sun
Beginning with a simple estimate, we expect WIMPs to be captured in the Sun at a rateapproximately given by: C (cid:12) ∼ φ χ ( M (cid:12) /m p ) σ χp , (1)where φ χ is the flux of WIMPs in the Solar System, M (cid:12) is the mass of the Sun, σ χp is the WIMP-proton elastic scattering cross section and m p the proton mass. Reasonable estimates of the localdistribution of WIMPs leads to a capture rate of C (cid:12) ∼ sec − × (100 GeV /m χ ) ( σ χp / − pb),where m χ is the mass of the WIMP. This neglects a number of potentially important factors,including the gravitational focusing of the WIMP flux toward the Sun, and the fact that notevery scattered WIMP will ultimately be captured. Taking these effects into account leads us igure 2. The current status of indirect searches for dark matter using high energy neutrinos.In addition to the various experimental constraints, the projected sensitivity of IceCube is shown,along with the flux of neutrino induced muons predicted over the parameter space of the MinimalSupersymmetric Standard Model [11]. Muons, simulated with energies in excess of 1 GeV, arerequired to trigger the detector.to a solar capture rate of [13]: C (cid:12) ≈ . × sec − (cid:18) ρ local . / cm (cid:19) (cid:18)
270 km / s¯ v local (cid:19) × (cid:32)
100 GeV m χ (cid:33) (cid:88) i (cid:18) A i ( σ χ i , SD + σ χ i , SI ) S ( m χ /m i )10 − pb (cid:19) , (2)where ρ local is the local dark matter density and ¯ v local is the local rms velocity of halo dark matterparticles. σ χ i , SD and σ χ i , SI are the spin-dependent and spin-independent elastic scattering crosssections of the WIMP with nuclei species i , and A i is a factor denoting the relative abundanceand form factor for each species. In the case of the Sun, A H ≈ . A He ≈ .
07, and A O ≈ . S contains dynamical information and is given by: eutralino mass (GeV) ) N e u t r a li no - p r o t on S D c r o ss - sec t i on ( c m -41 -40 -39 -38 -37 -36 -35 -34 -33 CDMS(2008)+XENON10(2007) limSI ! < SI ! < 0.20 h " -41 -40 -39 -38 -37 -36 -35 -34 -33 Figure 3.
Upper limits at 90% confidence level on the spin-dependent neutralino-proton crosssection assuming that the neutrinos are produced by b ¯ b and WW annihilation [11]. The limitshave been obtained with IceCube operated with 22 out of 80 strings. Also shown is the reach ofthe completed detector. Limits from the Super-Kamiokande and direct detection experimentsare shown for comparison. The shaded region represent supersymmetric models not ruled outby direct experiments. S ( x ) = (cid:20) A ( x ) / A ( x ) / (cid:21) / (3)where A ( x ) = 32 x ( x − (cid:18) v esc ¯ v local (cid:19) , (4)and v esc ≈ / s is the escape velocity of the Sun. Notice that for WIMPs much heavierthan the target nuclei S ∝ /m χ , leading the capture rate to be suppressed by two factors ofthe WIMP mass. In this case ( m χ > ∼
30 GeV), the capture rate can be approximated as: C (cid:12) ≈ . × sec − (cid:18) ρ local . / cm (cid:19) (cid:18)
270 km / s¯ v local (cid:19) (cid:32)
100 GeV m χ (cid:33) × (cid:18) σ χ H , SD + σ χ H , SI + 0 . σ χ He , SI + 0 . S ( m χ /m O ) σ χ O , SI − pb (cid:19) . (5)If the capture rate and annihilation cross sections are sufficiently large, equilibrium will bereached between these processes. The time dependence of the number of WIMPs N ( t ) in theSun is given by N ( t ) = C (cid:12) − A (cid:12) N ( t ) − E (cid:12) N, (6)where C (cid:12) is the capture rate described above and A (cid:12) is the annihilation cross section times therelative WIMP velocity per volume. E (cid:12) is the inverse time for a WIMP to escape the Sun byevaporation. Evaporation is highly suppressed for WIMPs heavier than a few GeV [14, 15]. A (cid:12) can be approximated by A (cid:12) = (cid:104) σv (cid:105) V eff , (7)where V eff is the effective volume of the core of the Sun determined by matching the coretemperature with the gravitational potential energy of a single WIMP at the core radius. It isgiven by [14, 15] V eff = 5 . × cm (cid:32)
100 GeV m χ (cid:33) / . (8)Neglecting evaporation, the present WIMP annihilation rate is given byΓ = 12 A (cid:12) N ( t (cid:12) ) = 12 C (cid:12) tanh (cid:16) √ C (cid:12) A (cid:12) t (cid:12) (cid:17) , (9)where t (cid:12) ≈ . √ C (cid:12) A (cid:12) t (cid:12) (cid:29) . (10)If this condition is met, the final annihilation rate (and corresponding neutrino flux and eventrate) is determined entirely by the capture rate and has no further dependence on the darkmatter particle’s annihilation cross section.The muon neutrino spectrum at the Earth resulting from WIMP annihilations in the Sun isgiven by: dN ν µ dE ν µ = C (cid:12) F Eq πD (cid:18) dN ν µ dE ν µ (cid:19) Inj , (11)where C (cid:12) is the WIMP capture rate in the Sun, F Eq is the non-equilibrium suppression factor( ≈ D ES is the Earth-Sun distance and ( dN νµ dE νµ ) Inj is themuon neutrino spectrum from the Sun per WIMP annihilating. This result is modified bypropagation effects, i.e. by neutrino oscillations and by the absorption of neutrinos on their wayout of the core of the Sun.
4. The Neutrino Spectrum
The annihilation of WIMPs generates neutrinos through a variety of channels. The annihilationproducts are heavy quarks, tau leptons, gauge bosons and/or Higgs bosons that decay intoenergetic neutrinos [16]. In some models, WIMPs can also annihilate directly to neutrino-antineutrino pairs. Annihilations to light quarks or muons, however, do not contribute to thehigh energy neutrino spectrum because they are absorbed by the Sun before decaying.Neglecting oscillations and the absorption of neutrinos in the Sun, the spectrum of neutrinosfrom WIMP annihilations to a final state, X ¯ X , is given by: dN ν dE ν = 12 (cid:90) E ν /γ (1 − β ) E ν /γ (1+ β ) γβ dE (cid:48) E (cid:48) (cid:18) dN ν dE ν (cid:19) rest XX , (12)here γ = m χ /m X , β = (cid:112) − γ − , and ( dN ν /dE ν ) rest XX is the spectrum of neutrinos producedin the decay of an X at rest.As an example, consider the simple case of WIMPs annihilating to a pair of Z bosons, χχ → ZZ . In this case, the most energetic neutrinos are produced by the direct decay of a Z into a neutrino-antineutrino pair. In this case (cid:18) dN ν dE ν (cid:19) rest ZZ = 2Γ Z → ν ¯ ν δ ( E ν − m Z / , (13)which leads to (cid:18) dN ν dE ν (cid:19) ZZ = 2 Γ Z → ν ¯ ν m Z γ β , for m χ (1 − β ) / < E ν < m χ (1 + β ) / , (14)where Γ Z → ν ¯ ν ≈ .
067 is the branching fraction to neutrino pairs (per flavor). In addition, Z -bosons also produce neutrinos through their decays to τ + τ − , b ¯ b and c ¯ c . An expression similarto Eq. 14 can be written down for the case of WIMP annihilations to W + W − , followed by W ± → l ± ν .Tau leptons produce neutrinos through a variety of channels, including through the leptonicdecays τ → µνν , eνν , and the semi-leptonic decays τ → πν , Kν , ππν , and πππν . Top quarksdecay to a W ± and a bottom quark nearly 100% of the time, each can generate neutrinos intheir subsequent decay. For bottom and charm quarks, only the semi-leptonic decays contributeto the neutrino spectrum (with the exception of the neutrinos resulting from taus and c -quarksproduced in decays of b -quarks). Hadronization of b and c quark reduces the fraction of energythat is transferred to the resulting neutrinos and other decay products. To fully and accuratelyaccount for all such effects, programs such as PYTHIA are often used.Once produced in the Sun’s core, neutrinos propagate through the solar medium beforedetection at Earth and may be absorbed and/or change flavor. In particular, absorption is theresult of charged current interactions of electron and muon neutrinos in the Sun. The probabilityof absorption is given by 1 − exp( − E ν /E abs ), where E abs is approximately 130 GeV for electronor muon neutrinos and 200 GeV for electron or muon antineutrinos. Absorption mostly affectthe neutrinos in the case of relatively heavy WIMPs. For charged current intereactions of tauneutrinos, the tau leptons produced decay and thus regenerate a neutrino, albeit with a reducedenergy. Neutral current interactions of all three neutrino flavors similarly reduce the neutrino’senergy without depleting their number.Good sensitivity to neutrinos produced by WIMPS in the sun is achieved exploiting IceCube’sdegree accuracy with which secondary muon tracks, approximately aligned with the parentneutrino, can be pointed back to the Sun. The neutrinos oscillate before reaching the detector.Vacuum oscillations fully mix muon and tau neutrinos resulting into a muon neutrino spectrumthat is the average of the muon and tau flavors prior to mixing. Electron neutrinos oscillate intomuon flavor through matter effects in the Sun (the MSW effect). Electron antineutrinos cangenerally be neglected, as their oscillations to muon or tau flavors are highly suppressed [17].Program such as DarkSUSY [18], which include effects such as hadronization, absorption,regeneration, and oscillations, are very useful in making detailed predictions for the neutrinospectrum resulting from WIMP annihilations in the Sun.
5. Neutrino Telescopes
Muon neutrinos produce muons through charged current interactions with nuclei inside or nearIceCube. The rate of neutrino-induced muons observed in a high-energy neutrino telescope isgiven by: events (cid:39) (cid:90) (cid:90) dN ν µ dE ν µ dσ ν dy ( E ν µ , y ) [ R µ ( E µ ) + L ] A eff dE ν µ dy + (cid:90) (cid:90) dN ¯ ν µ dE ¯ ν µ dσ ¯ ν dy ( E ¯ ν µ , y ) [ R µ ( E µ ) + L ] A eff dE ¯ ν µ dy, (15)where σ ν ( σ ¯ ν ) is the neutrino-nucleon (antineutrino-nucleon) charged current interaction crosssection, (1 − y ) is the fraction of neutrino/antineutrino energy transferred to the muon, A eff isthe effective detection area of the detector, R µ ( E µ ) is the distance a muon of energy (1 − y ) E ν travels before falling below the threshold E thr µ of the experiment and L is the depth of thedetector volume linear size of a detector of volume L . The muon range in water/ice is wellapproximated by: R µ ( E µ ) ≈ . × ln (cid:20) . . E µ (GeV)2 . . E thr µ (GeV) (cid:21) . (16)When completed, IceCube’s instrumented volume will reach a L of one kilometer and an effectivearea of well over a full square kilometer for a threshold of approximately 100 GeV. The DeepCore extension of Icecube will lower the threshold to 10 GeV.The flux and spectrum of the neutrinos from WIMP annihilation depend on the modelparameters which determine the dominant annihilation channels. In Fig. 4, we show the eventrate in a kilometer-scale neutrino telescope such as IceCube as a function of the WIMP’selastic scattering cross section for four possible annihilation modes b ¯ b , t ¯ t , τ + τ − and W + W − .The effective elastic scattering cross section used here is defined as σ eff = σ χ H , SD + σ χ H , SI +0 . σ χ He , SI + 0 . S ( m χ /m ) σ χ , SI (see Eq. 5).The elastic scattering cross section of a WIMP is already constrained by the absence of apositive signal in direct detection experiments. Currently the strongest limits on the WIMP-nucleon spin-independent elastic scattering cross section have been obtained by the CDMS [19]and XENON [20] experiments. These results exclude spin-independent cross sections larger thanapproximately 5 × − pb for a 25-100 GeV WIMP and 2 × − pb ( m χ /500 GeV) for a heavierWIMP.With these results in mind, consider as an example a 300 GeV WIMP with an elasticscattering cross section with nucleons which is largely spin-independent. With a cross sectionnear the CDMS bound, say 1 × − pb, we obtain the corresponding signal in a neutrinotelescope from Fig. 4. Sadly, we find that this cross section yields less than 1 event per yearfor annihilations to b ¯ b , about 2 events per year for annihilations to W + W − or t ¯ t and about 8per year for annihilations to τ + τ − , none of which are sufficient to dominate the background ofatmospheric neutrinos (see Fig. 2). Clearly, WIMPs that scatter with nucleons mostly throughspin-independent interactions are not likely to be detected with IceCube or other plannedneutrino telescopes.The state of affairs is diffferent for the case of spin-dependent scattering. The strongestbounds on the WIMP-proton spin-dependent cross section have been placed by the COUPP [21]and KIMS [22] collaborations. These constraints are approximately 7 orders of magnitude lessstringent than those for spin-independent cross sections. As a result, a WIMP with a largelyspin-dependent scattering cross section with protons is capable of generating large event ratesin high energy neutrino telescopes. For a 300 GeV neutralino with a cross section near theexperimental limits indirect rates as high as ∼ per year are expected; see Fig. 4. igure 4. The event rate in a kilometer-scale neutrino telescope such as IceCube as a functionof the WIMP’s effective elastic scattering cross section in the Sun for a variety of annihilationmodes. The effective elastic scattering cross section is defined as σ eff = σ χ H , SD + σ χ H , SI +0 . σ χ He , SI + 0 . S ( m χ /m ) σ χ , SI (see Eq. ). The dashed, solid and dotted lines correspondto WIMPs of mass 100, 300 and 1000 GeV, respectively. A 50 GeV muon energy threshold andan annihilation cross section of 3 × − cm s − have been adopted.
6. Neutralino Dark Matter
The elastic scattering and annihilation cross sections of the lightest neutralino depend on itscouplings and on the mass spectrum of the Higgs bosons and superpartners. The couplings,in turn, depend on the neutralino’s composition. In the Minimal Supersymmetric StandardModel (MSSM), the lightest neutralino is a mixture of the bino, neutral wino, and two neutralhiggsinos: χ = f B ˜ B + f W ˜ W + f H ˜ H + f H ˜ H .Spin-dependent, axial-vector, scattering of neutralinos with quarks and gluons is mediated bythe t-channel exchange of a Z -boson, or the s-channel exchange of a squark. Spin-independentscattering occurs at the tree level through s-channel squark exchange and t-channel Higgsexchange, and at the one-loop level through diagrams involving loops of quarks and/or squarks. Figure 5.
The lightest neutralino’s spin-independent (left) and spin-dependent (right)scattering cross sections for a range of MSSM parameters. Also shown are the current limitsfrom direct detection experiments.The cross sections for these processes can vary dramatically with the parameters of theMSSM. A phenomenological description of the MSSM can be reduced to four mass parametersthat determine the masses and couplings of the yet to be discovered supersymmetric particlesand two more parameters that determine the properties of the higgs sector. These are m A the mass of the CP-odd higgs boson and tanβ the ratio of the vacuum expectation values ofthe other higgs bosons. By scanning the parameter space we create a set of models that willbe used to evaluate the sensitivity of a kilometer-scale neutrino telescope. The scan varies allmass parameters up to 10 TeV, m A up to 1 TeV and the value of tanβ between 1 and 60.For generality, we do not assume any particular SUSY breaking scenario or unification scheme.Each model selected is consistent with all constraints for relevant collider experiments and witha thermal relic density not in excess of the value Ω χ h =0.129. We do not impose a lower limiton this quantity, keeping in mind the possibility of non-thermal processes which may contributeto the density of neutralino dark matter. We have performed the scan using the DarkSUSYprogram [18]. In Fig. 5, we show the values of the spin-dependent and independent scatteringcross sections as a function of the WIMP mass for all models generated by the scan.The cross sections for these processes vary dramatically from model to model. It is clear fromFig. 5, however, that for this class of models the spin-dependent cross section can be considerablylarger than the spin-independent cross section, favoring indirect detection[23]. In particular, verylarge spin-dependent cross sections ( σ SD > ∼ − pb) are possible even in models with very smallspin-independent scattering rates. Such a model would go easily undetected in all planned directdetection experiments, while still generating on the order of ∼ Z and, therefore, a large higgsino component. The spin-dependent scattering cross sectionthrough the exchange of a Z is proportional to the square of the quantity | f H | − | f H | . Evenneutralinos with a higgsino fraction of a only a few percent are likely to be within the reach Figure 6.
The rate of events at a kilometer-scale neutrino telescope such as IceCube fromneutralino dark matter annihilations in the Sun, as a function of the neutralino’s spin-dependentelastic scattering cross section. Each point shown is beyond the reach of present and near futuredirect detection experiments.
Figure 7.
In the left frame, the spin-dependent elastic scattering cross section of the lightestneutralino with protons is shown as a function of the quantity | f H | − | f H | . In the right frame,the rate in a kilometer-scale neutrino telescope is shown, using a muon energy threshold of 50GeV. Each point shown evades the current constraint of CDMS. See text for more details.of IceCube [24, 25]. This makes the focus point region of supersymmetric parameter spaceespecially promising. In this region, the lightest neutralino is typically a strong mixture of binoand higgsino components, leading to the prediction of hundreds to thousands of events per yearat IceCube. In Fig. 7 we show that neutralinos with a higgsino component | f H | − | f H | ofapproximately one percent or greater are likely to be detectable by IceCube.So far we have matched the prospects for the indirect detection of dark matter using neutrinosagainst a very general and relatively unconstrained set of supersymmetric models. Alternatively,several groups have made more restrictive scans of the MSSM parameter space. For instance,Allanach et al. [7] have identified islands in the m χ , σ χp space of models consistent with allempirical particle physics constraints. They are also constrained to yield the observed darkmatter density of the Universe. Fig. 8 shows the posterior probability for the spin-dependentcross section as a function of the neutralino mass for such a parameter scan. The definition of the igure 8. Posterior probability distribution for the spin-dependent neutralino-proton elasticscattering cross section as a function of the neutralino mass using the higgs parameters (left)and tan β (right) to sample the model space. Contours delineate confidence regions of 68% and95%.posterior probability is not simple, we refer the reader to reference [7]. It represents the productof the likelihood and the prior, integrating over all parameters except for the ones that we areinterested in. Regarding the normalization, the probability is defined relative to the maximumprobability of any point in the parameter space. We conclude that the result is fairly robustbecause it turns out that the range of values for the spin-independent cross section is relativelyinsensitive to how the a priori likelihoods of points in the parameter space are defined. Theside-by-side figures contrast scans using, alternatively, the parameters of the Higgs potential ortan β to define the parameter space.It is well known that the MSSM generically generates values of the dark matter density whichare in excess of the measured value. This is not surprising, as the “WIMP miracle” relating theweak force to Ω ∼ − pb.For the models in the focus region, more than 60% of the posterior probability distributionin the MSSM, we have converted the cross sections σ χp in Fig. 7 into a flux of neutrinos fromneutralino annihilation in the sun assuming a detector with a threshold of 50 GeV. Because ofthe relatively large cross sections, the models typically yield more than a hundred high energyneutrino events per year from the direction of the Sun in a generic kilometer-size detector; seeFig. 9. In fact, the present IceCube limit already excludes such models for the highest neutralinomasses; see Fig. 3. A second island of models clustered at very low masses corresponds to theso-called higgs pole region where efficient annihilation proceeds through the lightest CP-evenhiggs resonance into b and τ pairs. Exploring the set of models with low WIMP masses andcross sections below 10 − pb will be challenging and almost certainly require future megatondetectors.This alternative look at the prospects for the indirect detection of dark matter using neutrinosconfirms the excellent discovery potential derived from our previous less restrictive sample of igure 9. Posterior probability distribution for the rate of neutrino events from neutralinoannihilation in the Sun in a generic square kilometer detector with a threshold of 50 GeV forthe models shown in Fig. 3.minimal models.
7. Alternative Dark Matter Models
A great variety of extensions of the Standard Model have been introduced which include newphysics at or around the TeV-scale. A common feature of many of these scenarios is the inclusionof a symmetry which can stabilize the lightest new state, in much the same way that R-parityconservation stabilizes the lightest neutralino in supersymmetric models. Models with additionaluniversal dimensions are of special interest in this context [26, 27]. In such models the fieldsof the Standard Model may propagate through the extended extra dimensional space, which iscompactified on a small scale R ∼ TeV − . Each Standard Model particle is accompanied byKaluza-Klein (KK) states which appear as heavy versions of their Standard Model counterpartswith masses of ∼ /R . The Lightest KK Particle (LKP) can be naturally stable and is likely tobe the first KK excitation of the hypercharge gauge boson, B (1) . This state can be producedwith an abundance matching the observed dark matter density over a range of masses between500 GeV and a few TeV [29, 30].The spin-independent LKP-nucleon cross section turns out to be small and typically fallswithin the range of 10 − to 10 − pb [28], well beyond the sensitivity of current or upcomingdirect detection experiments. On the other hand, the spin-dependent scattering cross sectionfor the LKP with a proton is considerably larger [28]: σ H,SD = g m p πm B (1) r q (4∆ pu + ∆ pd + ∆ ps ) ≈ . × − pb (cid:18)
800 GeVm B (1) (cid:19) (cid:18) . q (cid:19) , (17)where r q ≡ ( m q (1) − m B (1) ) /m B (1) is fractional shift of the KK quark masses over the LKP mass,which is expected to be on the order of 10%. The ∆’s parameterize the fraction of spin carriedby each variety of quark within the proton. In addition approximately 60% of LKP annihilations igure 10. The event rate in a kilometer-scale neutrino telescope as a function of the LKPmass [31]. The three lines correspond to fractional mass splittings of the KK quarks relative tothe LKP of 20%, 5% and 1%. The solid sections of these lines reflect the approximate range inwhich it is possible to generate the observed thermal relic abundance. A 50 GeV muon energythreshold has been used.generate a pair of charged leptons, 20% to each flavor and about 4% generate neutrino pairs.The neutrino and tau lepton final states each contribute substantially to the event rate in aneutrino telescope.The event rates in a kilometer scale neutrino telescope for KK dark matter annihilating in theSun [31] are shown in Fig. 10. There are competing effects which contribute to these favorableresults. In particular, a small mass splitting between the LKP and KK quarks yields a largespin-dependent elastic scattering cross section; see Eq. 17. On the other hand, KK quarks whichare not much heavier than the LKP contribute to the freeze-out process and increase the rangeof LKP masses in which the thermal abundance matches the observed dark matter density. Forthis range shown as the solid line segments in Fig. 10, between 0.5 and 50 events per year areexpected in a kilometer scale neutrino telescope such as IceCube. Alternatively, if non-thermalmechanisms, such as decays of KK gravitons, contribute to generating the LKP relic abundance,much larger rates are possible.
References [1] C. Spiering, arXiv:0811.4747 [astro-ph].[2] F. Halzen, Eur. Phys. J. C , 669 (2006) [arXiv:astro-ph/0602132].[3] T. K. Gaisser, F. Halzen and T. Stanev, Phys. Rept. , 173 (1995) [Erratum-ibid. , 355 (1996)][arXiv:hep-ph/9410384].[4] M. C. Gonzalez-Garcia, F. Halzen and M. Maltoni, Phys. Rev. D , 093010 (2005) [arXiv:hep-ph/0502223].[5] F. Halzen, J. E. Jacobsen and E. Zas, Phys. Rev. D , 7359 (1996) [arXiv:astro-ph/9512080].[6] Silk J, Olive K and Srednicki M, Phys. Rev. Lett. , 257 (1985); J.S. Hagelin, K.W. Ng and K.A. Olive,Phys. Lett. B , 375 (1986); K. Freese, Phys. Lett. B167 , 295 (1986); L.M. Krauss, M. Srednicki andF. Wilczek F, Phys. Rev. D , 2079 (1986); T.K. Gaisser, G. Steigman and S. Tilav, Phys. Rev. D ,2206 (1986).[7] B.C. Allanach and D. Hooper, [arXiv:hep-ph/08061923] (2008).[8] B. Sadoulet, Science , 61 (2007).9] S. Desai and others, [Super-Kamiokande collaboration] Phys. Rev. D , 083523 (2004) [arXiv:hep-ex/0404025].[10] M. Ackerman and others, [AMANDA collaboration] Astropart. Phys. , 459 (2006) [arXiv:astro-ph/0508518].[11] R. Abassi and others, submitted for publication; A. Rizzo, Seventh International Heidelberg Conference onDark Matter in Astro- and Particle Physics, Christchurch, New Zealand (2009); C. DeClercq, PANIC 2008,Eilat, Israel (2008).[12] D. J. L. Bailey; The ANTARES Collaboration, Proceedings of the 27th International Cosmic Ray Conference.07-15 August, 2001. Hamburg, Germany. Under the auspices of the International Union of Pure and AppliedPhysics (IUPAP)., p.1556 (2001).[13] A. Gould, “Cosmological density of WIMPs from solar and terrestrial annihilations” (1991)[14] A. Gould, Astrophys. J. , 571 (1987)[15] K. Griest and D. Seckel, Nucl. Phys. B , 681 (1987)[16] G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept. , 195 (1996) [arXiv:hep-ph/9506380].[17] R. Lehnert and T.J. Weiler, Phys. Rev. D , 125004 (2008) [arXiv:hep-ph/07081035].[18] P. Gondolo and others, New Astron. Rev. , 149 (2005)[19] Z. Ahmed and others, [CDMS collaboration] [arXiv:astro-ph/08023530] (2008).[20] J. Angle and others, [XENON collaboration] Phys. Rev. Lett. , 021303 (2008) [arXiv:astro-ph/07060039].[21] E. Behnke and others, [COUPP collaboration] Science , 933 (2008) [arXiv:astro-ph/08042886].[22] H.S.. Lee and others, Phys. Rev. Lett. , 091301 (2007) [arXiv:astro-ph/07040423].[23] P. Ullio, M. Kamionkowski and P. Vogel, JHEP , 044 (2001) [arXiv:hep-ph/0010036].[24] L. Bergstrom, J. Edsjo and P. Gondolo, Phys. Rev. D , 103519 (1998) [arXiv:hep-ph/9806293].[25] F. Halzen and D. Hooper, Phys. Rev. D , 123507 (2006) [arXiv:hep-ph/0510048].[26] G. Servant and T.M.P. Tait, Nucl. Phys. B , 391 (2003) [arXiv:hep-ph/0206071].[27] H.-C. Cheng, J.L. Feng and K.T. Matchev, Phys. Rev. Lett. , 211301 (2002) [arXiv:hep-ph/0207125].[28] G. Servant and T.M.P. Tait, New J. Phys. , 99 (2002) [arXiv:hep-ph/0209262].[29] F. Burnell and G.D. Kribs, Phys. Rev. D , 015001 (2006) [arXiv:hep-ph/0509118].[30] K. Kong and K.T. Matchev, JHEP , 038 (2006) [arXiv:hep-ph/0509119].[31] D. Hooper and G.D. Kribs, Phys. Rev. D67