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Searching for TeV dark matter by atmospheric

arXiv:hep-ph/9208255v1 27 Aug 1992Searching for TeV dark matter by atmospheric˘Cerenkov techniquesM. Urban∗A.

Bouquet†B.Degrange∗P. Fleury∗J.

Kaplan†A.L. Melchior† and E. Par´e∗AbstractThere is a growing interest in the possibility that dark matter could be formedof weakly interacting particles with a mass in the 100 GeV - 2 TeV range, andsupersymmetric particles are favorite candidates.

If they constitute the darkhalo of our Galaxy, their mutual annihilations produce energetic gamma raysthat could be detected using existing atmospheric ˘Cerenkov techniques.To appear in Physics Letters B July 1992∗Laboratoire de Physique Nucl´eaire et Hautes Energies, Ecole Polytechnique/CNRS-IN2P3, 91128 Palaiseau Cedex ,FRANCE†LPTHE Universit´es PARIS 6 and 7, Unit´e associ´ee au CNRS UA 280, 2 Place Jussieu, 75251 Paris Cedex 05 , FRANCE1

1IntroductionGalaxies seem embedded in massive spheroidal dark halos [1, 2, 3, 4]. Extensions of the standard modelof particle physics often predict the existence of a new stable particle, a natural candidate for halo darkmatter.

The residual abundance of a particle after the Big-Bang depends on its mass and interactions,and to account for the dark matter puzzle a weakly interacting massive particle (W.I.M.P.) is needed, forinstance a neutrino-like particle with a mass around 1 TeV.

Such particles will be very difficult to detect,even by accelerator experiments (LHC-SSC) of next century. Halo particles can be directly detectedwhen they cross a bolometer detector [5, 6] but the flux is low above 50 GeV.

They can also be indirectlydetected through their annihilation products [7, 8, 9, 10, 11, 12] : annihilations after their capture in theEarth or in the Sun producing neutrinos, or annihilations in the halo producing energetic cosmic rays(gamma rays, electrons, protons, antiprotons. .

. ).

Existing models for our galactic halo predict a strongannihilation rate near the center of the Galaxy. We focus here on the annihilations into photons, becausephotons conserve their initial direction.

Each annihilation produces either primary photons (leading toa gamma line signal) or secondary photons from the decay of primary annihilation products. The fluxesare low again for a large WIMP mass, but this can be balanced by the large acceptance of detectorsusing the atmospheric ˘Cerenkov technique like the existing Atmospheric ˘Cerenkov Telescope (ACT) ofthe Whipple Observatory [13].

With similar instruments, it should be possible to detect for instance theleading WIMP candidate, the neutralino predicted by supersymmetry [14].2ACT’s and backgroundsThe ACT detects incoming cosmic rays through the ˘Cerenkov light emitted by the shower of secondaryparticles created when the cosmic ray (photon, electron, proton, heavier nucleus. .

.) collides with anucleus in the upper atmosphere [13].

The image shape analysis affords an efficient gamma versus hadronseparation. The ˘Cerenkov light covers a disk of about 120 m radius on the Earth surface (an area of 45000m2), and the detector must be somewhere in this area to see the cosmic ray shower.

Less energetic cosmicrays produce less ˘Cerenkov light, and the minimal detectable energy (threshold) is linked to the size ofthe mirrors which collect this light. The best observation conditions correspond to a cosmic ray within45 degrees from the zenith.

As we shall see, the photon flux from WIMP annihilations is largest from thegalactic center, which can be seen at zenith only if the observatory is built in the southern hemisphere,at a latitude near -29 degrees. Observation of ˘Cerenkov light is only possible at night when there is nomoon, and so the galactic center can be observed for tobs ≃2 × 106 s per year.

The effective angularacceptance ∆Ωof present ACT’s is about 10−3 sr with an angular resolution of 3 × 10−6 sr, so that theyare well suited to the study of localized sources. The usual procedure consists in the comparison of theflux from an expected source with neighbouring sky regions (on-offexperiment).To be definite, we shall use as a reference ACT the Granite set-up at the Whipple Observatory, whichuses two mirrors of about 10 m diameter, 120 m apart, leading at present to a minimal detectable energyaround 200 GeV.

Increasing the number and/or the size of mirrors may lower this threshold. The twotelescopes effectively survey 63000 m2 if they are used independantly, but their effective detection area Sis only 18000 m2 when the two telescopes are used in coincidence to give the best energy resolution andan increased hadronic rejection.

The energy of a gamma cosmic ray is determined from a stereoscopicview with a precision σ(E)/E ≃0.1 . Adding other telescopes, about 120 m apart, would increase theeffective area and therefore lower the detectable cosmic flux.

The product S∆Ωtobs is a measure of the2

efficiency of the telescope to detect cosmic rays, and S∆Ωtobs = 3.6 × 1011 cm2 sr s for our referenceACT.There is a large background to the WIMP annihilation signal that we are looking for. Cosmic rayhadrons must be rejected, and experience at the Whipple Observatory shows that a rejection factor of103 should be reached for two detectors in coincidence.

The flux of misidentified hadrons then follows apower law [13] :dNhdt dS dΩdE = 6 × 10−9E1 TeV−2.75photon −like hadrons (s cm2 sr TeV)−1(1)When a hadron is misidentified as a photon, its energy is underestimated, and the preceding formulatakes this effect into account. Electrons cannot be distinguished from photons with atmospheric ˘Cerenkovdetectors, as their showers have the same development as photons in the atmosphere.

The electron fluxis measured at energies up to 1 TeV [15, 16]. The spectrum also follows a power law :dNedt dS dΩdE = 6 × 10−9E1 TeV−3.3electrons (s cm2 sr TeV)−1(2)The electron background dominates the background of misidentified hadrons up to 1 TeV.

The fluxes ofelectrons or hadrons are isotropic. Finally, there is the diffuse photon background itself, supposed to bedue to the collisions of cosmic ray protons on interstellar gas.

The spectrum from the galactic center wasmeasured by the COS-B satellite [17, 18, 19] up to 5 GeV :dNγdt dS dΩdE = 0.35 × 10−9E1 TeV−2.75photons (s cm2 sr TeV)−1(3)This power law is the same as for the hadron spectrum, and we may assume that Equation 3 extends tohigher energies. This is not in disagreement with upper bounds on the photon flux above 5 GeV [15, 16].This flux is smaller than the electron background.A signal can be detected even if it is small compared to the background, provided that the backgroundis measured with a good precision.

In our case, an on source-offsource method will be available, allowingfor a reliable estimation of this background. The noise is the uncertainty on the background, that is thesquare root of the number Nbackgr of all photon-like events (including electrons and misidentified hadrons)detected during the experiment time tobs in a given energy bin ∆E, that we shall take as 3σ(E) ≃0.3E.For a detector of acceptance S∆Ω, this number is :Nbackgr = S ∆ΩtobsdNγdt dS dΩdE +dNedt dS dΩdE +dNhdt dS dΩdE∆E(4)We must now compare these numbers to the expected signal flux from halo WIMP annihilations.3WIMP annihilation from the galactic centerWe assume that our Galaxy is embedded in a dark halo made of WIMP’s of mass mχ which annihilatein pairs.

The annihilation rate is < σV >halo n2χ, where < σV >halo is the (thermal average in the haloof the) annihilation cross-section σ times the relative WIMP velocity V , nχ = ρχ/mχ is the dark matternumber density. At large distance r from the center, the halo density decreases as :ρ(r) ≃ρ⊙a2 + r2⊙a2 + r2(5)3

where ρ⊙= 0.3 ± 0.1 GeV/cm3 is the dark matter density in the solar neighbourhood, a = 5 ± 3 kpc isthe core radius and r⊙= 8.5 kpc is the distance of the Sun to the galactic center [20, 21, 22, 23]. Theannihilation rate of this dark matter far away from the galactic center turns out to be too low to bedetected with present size ACT’s.The dark matter density may however be much larger at the center, as there seems to be a massivenucleus at the center of the Galaxy [24, 25].

According to the isothermal model of Ipser and Sikivie [26],this nucleus induces an enhancement of the dark matter density within a 150 pc radius around the center,with a density at center of :ρ ≃0.34 α TeV/cm3(6)The α parameter (0.1 < α < 3) reflects the uncertainties on the rotation velocity of the galaxy, and onthe contribution of luminous matter to this velocity. Annihilation photons in the TeV energy range areunlikely to be absorbed by baryonic matter in the galactic center since, in the worst case of a completelygaseous core, a γ-ray crosses less than one radiation length.

As seen from Earth, the central region covers∆Ω= 10−3 sr, nicely corresponding to the acceptance of present ACT’s. We can perform an on-offexperiment, aiming at the galactic center and comparing with the result offcenter.

The 10−6 sr ACTangular resolution is small enough to distinguish point sources inside these 10−3 sr from the more diffuseWIMP annihilation cloud.Photons appear in the decay chain of the primary annihilation products (quarks, leptons, Higgs scalars,W± or Z0’s, etc. ), and their energy is then continuously distributed.

Their distribution dnγ(E)/dE canbe computed through a Lund Monte-Carlo [27] (Figure 1), and depends only weakly on the WIMP model.The integral R dnγ(E) is the photon multiplicity per annihilation. The number of photons due to WIMPannihilations within 150 pc from the center, and received on our reference telescope is :Nγ(E) dE = S tobsdnγ(E) < σV >halo4πr2⊙Z 150 pc0ρ(r)mχ24πr2dr(7)WIMP annihilations outside the 150 pc sphere, but inside the 10−3 sr cone, do not contribute to a signaldefined by an on-source minus off-source subtraction.

The cross-sections σ and the corresponding energyspectra dnγ(E)/dE , reduced to a delta function in the case of monochromatic photons, are summedover all relevant annihilation channels.Two different signals can be looked for at the same time. We can look for a gamma line due to thedirect annihilation of WIMP’s into photons, or we can look for the total excess of soft photons due tothe decays of all annihilation products.Soft photonsThe Lund Monte-Carlo codes [27] typically indicate that 50 photons or so are produced in the decaychains, but that most of them are at a very low energy compared to the WIMP mass mχ (see Figure 1).The signal is the number of photons received above the ACT energy threshold Ethresh.

Table 1 showsthe integralRdnγ(E) from Ethresh to mχ as a function of mχ for a quark-antiquark channel (the resultbeing very similar for other channels).mχ (TeV)0.40.81.02.04.0Ethresh = 0.1 TeV0.020.170.321.454.40Ethresh = 0.2, TeV0.00040.020.050.351.554

Table 1 : Number of soft decay photons above threshold. The first line gives the mass mχ of theparticles which annihilate into a quark-antiquark pair, the second line gives the number of decayphotons with an energy above 0.1 TeV, and the third line the number of photons above 0.2 TeV.Note the great sensitivity to the threshold : the number of photons above the treshold increasesroughly as m2χ, and, as a result, the signal can only be detected if the WIMP mass is far above threshold.From Equation 7, and for our reference telescope, this signal is :Soft photon signal =Z mχEthreshNγ(E) dE = 8300 photons/yearα2Zdnγ(E) < σV >halo10−26 cm3/s1 TeVmχ2(8)The corresponding noise is the square root of the total number of background photons received aboveEthresh.

From Equations 1, 2 and 3, it is approximately :Soft photon noise =Z mχEthreshNbackgr(E) dE1/2≃220 photons/√year 0.2 TeVEthresh(9)Note that we are conservative in integrating up to mχ because the integralRdnγ(E) is saturated wellbefore mχ, and therefore we are adding noise for no signal.The signal to noise ratio will be very low below mχ ≃1 TeV unless annihilation cross-sections arelarge. But they cannot be very far from < σV >halo≃10−26 cm3/s , if WIMP’s constitute the darkmatter of the universe.

WIMP’s were produced in large numbers during the hot dense phase of the Big-Bang, and to constitute the dark matter, some fraction must have survived annihilation up to now. Thisannihilation becomes negligible when the temperature gets lower than a critical decoupling temperature,and the present relic density Ωχ (in unit of the critical density) is [28] :Ωχh2 = 2.5 × 10−27 cm3/s< σV >BB(10)up to logarithmic corrections (h is the Hubble constant divided by 100 km/s/Mpc, and we shall takeh = 0.5).

Note that the thermal average < σV >BB of the annihilation cross-section at the Big-Bangcan differ from the thermal average < σV >halo in the halo, since the temperature at decoupling differsfrom the halo equivalent temperature.To account for dark matter in galactic halos, a mean density Ωhalo ≃0.1 is required [1, 2, 3, 4], whilea mean density Ω≃1 seems required on larger scales. When the WIMP annihilation rate is strong,Ωχ << 1, and the density of WIMP’s in the halo cannot be much larger than ρχ ≃ρhaloΩχ/Ωhalo .

Theremaining component could be due to brown dwarfs [29] or to another WIMP. To interpolate the haloWIMP density between this strong annihilation rate and the weak annihilation rate (where ρχ ≃ρhalo),Griest, Kamionkowski and Turner (GKT) [30] suggested the formula ρχ ≃ρhalo/[1 + Ωhalo/Ωχ] , butany smooth interpolation could be chosen.

This GKT correction decreases the expected flux for a largeannihilation cross-section, and Equation 8 becomes :Soft photon signal ≃8300 photons/yearα2Zdnγ(E) < σV >halo10−26 cm3/s1 TeVmχ21[1 + Ωhalo/Ωχ]2(11)”Line” signalTwo WIMP’s can directly annihilate into two photons (Rdnγ(E) = 2), and the energy of the photonsis then equal to the mass mχ of the (non-relativistic) WIMP, leading to a gamma line. A narrow line in5

the range 102±1 GeV would provide a clear signature for dark matter annihilation [7, 8, 9, 10, 11, 12], butthe cross-section σ2γ for annihilation into 2 photons strongly depends on the WIMP model, and moreoverit is expected to be much smaller than the annihilation cross-sections into a pair of quarks, leptons, Higgsor gauge bosons. For our reference telescope, the expected number of annihilation photons in the line atE = mχ is :Line signal = 166 photons/yearα2 < σ2γV >halo10−28 cm3/s1 TeVmχ21[1 + Ωhalo/Ωχ]2(12)From Equation 4, the background noise for such a γ line, with an energy bin ∆E = 3 σ = 0.3 E, is wellapproximated by :Line noise =pNbackgr = 35 photons/√year 1 TeVmχ(13)Annihilations into a photon and another particle of mass M also gives a monochromatic photon, at anenergy E ≃mχ −M 2/4mχ .

Some kind of spectroscopy is thus in principle possible, depending on theenergy resolution.4NeutralinosWe now focus on supersymmetry [14], the favorite extension of the standard model, because the lightestsupersymmetric particle (LSP) χ is stable due to a conserved quantum number, R-parity, and because itsrelic density is naturally Ωχ ≃1, making it a good dark matter candidate. There are two neutral gaugefermions ˜B and ˜W3 and two neutral Higgs fermions ˜H1 and ˜H2 which mix when gauge symmetry is broken,and the four resulting mass eigenstates are called neutralinos.

The lightest one, the neutralino, usually isthe LSP. Its mass and couplings depend on 4 parameters : the masses M1 and M2 of the gauge fermions˜B and ˜W3 before gauge symmetry breaking (usually related by the GUT relation M1 = 53M2 tan2 θW ),the Higgs fermion mass µ and the ratio tan β of the vacuum expectation values of the two Higgs scalars[14, 30, 31, 32, 33, 34].

In addition, the neutralino cross-sections depend on the masses of the quarks andleptons, and of their scalar partners, and on the Higgs bosons masses. There are weak direct experimentallower bounds from LEP on the neutralino mass [35] but, assuming a GUT relation between the gluinomass M3 and the masses M1 and M2, more stringent indirect bounds can be obtained from UA2 [36] andCDF [37] experiments.

It is then likely that the mass of the neutralino is larger than about 50 GeV.We are interested in the possibility that the neutralino be heavier than 100 to 200 GeV, the ACTthreshold, because it allows a neutralino relic density near the critical density. We focus in this paperon the two extreme cases of a pure bino or a pure higgsino.

A mixed state is not a priori excluded, butis quite unlikely in this high mass region : when |µ| ≫M2, the lightest neutralino is an almost pure ˜Bstate, and an almost pure ˜H when |µ| ≪M2. The equations for annihilation cross-sections are extremelycomplex [30, 31, 32, 33, 34], and we only give here a sketch of the results.Most of the time, a bino pair annihilates into a quark or a lepton pair, through the exchange ofthe corresponding s-quark or s-lepton of mass m˜f (m˜f > mχ since, by assumption, χ is the LSP).

Thethermally averaged cross-section for binos at temperature T is approximately :< σV >=πα2216 cos4 θWm2χ(m2˜f + m2χ)2(289m2topm2χ+ 9160 Tmχm4˜f + m4χ(m2˜f + m2χ)2)(14)In this equation, α is the fine structure constant. As illustrated by Equation 14, thermally averagedcross-sections for neutralino annihilation can be written as < σV >= a+bT/mχ .

Temperatures are very6

low in the galactic halo and the a term dominates, whereas the b term dominates during the Big-Bang,down to the decoupling temperature Tdec ≃mχ/25. Equations 10 and 14 then yield a relation betweenthe bino mass and its relic density Ωχ :mχ = 0.56 TeV hpΩχ(15)This value was obtained assuming that m˜f = mχ, and it becomes much smaller if m˜f ≫mχ .

Thereforecosmology leads to an upper bound on the bino mass [30, 31, 32, 33, 34]. It is very interesting that asimilar upper bound is also indicated by naturalness arguments in the context of low energy supergravitymodels [38].

A negligibly small relic density is excluded for a bino by the experimental lower bounds onthe neutralino mass and binos should be around us in large numbers, even if they do not solve the darkmatter problem. Assuming again the lightest possible s-top mass, namely m˜f = mχ , the cross-sectionfor annihilation in the halo into a top-antitop pair (for mχ > mtop) is :< σV >halo ≃2.8 × 10−29 cm3/smtop150 GeV2 1 TeVmχ4(16)if the bino is heavier than the top quark.

The top quarks decay into a large number of soft photons,and protons, antiprotons, electrons, positrons, neutrinos and antineutrinos. The photon energy spectrumdnγ/dE is computed by Lund Monte-Carlo [27].

Figure 2 shows the expected excess in the number ofphotons in the direction of the center of the galaxy, seen by our reference telescope, as a function of theneutralino mass mχ . The excess number of photons is compared to the background noise measured indirections away from the center of the Galaxy.

The bino annihilation into soft photons will be difficultto detect, unless the dark matter density enhancement at the galactic center is larger than we assumed(i.e. if α ≫1).Let us now turn to a ˜H-like neutralino.

The dominant higgsino annihilation channels are into WWor ZZ pairs, through the exchange of a chargino or a neutralino. The expression for its annihilationcross-sections is very complicated [30, 31, 32, 33], but, in the mass range we are interested in, it scalesroughly as :< σV >BB ≃2.2 × 10−26 cm3/s1 TeVmχ2(17)leading to :mχ ≃3 TeV hpΩχ(18)The bound is larger than for the bino, because higgsinos are more strongly coupled than binos.

Moreover,at low temperature, the higgsino cross-section scales as 1/m2χ (fermion exchange) while the bino cross-section scales as m2top/m4χ (scalar exchange). In the halo, the cross-section for higgsino pair annihilationinto W’s and Z’s is :< σV >halo ≃πα2162 cos4 θW + 1sin4 θW cos4 θW1m2χ(19)Higgsino annihilation is larger than bino annihilation, both in the Big-Bang (hence a smaller relic densityfor a given mass) and in the halo (hence a larger photon flux).

Figure 2 indeed shows that higgsinoannihilation into soft photons would be easier to detect than bino annihilation. However the signal isstill marginal for our reference telescope.A gamma line would be a clearer signal .

A neutralino pair cannot annihilate into two photons at thetree level, one loop graphs are required and probably lead to a tiny cross-section. There are many relevantgraphs, in particular if annihilations into one photon and another particle (Z0, Higgs scalar) are included.7

We are computing these graphs, but this long and tedious work is not yet completed. Nevertheless, anorder of magnitude estimate may be derived from the graphs already computed [39].

For the annihilationof a bino into two photons through quark/s-quark or lepton/s-lepton loops, this leads to :< σ2γV >halo ≃4.2 × 10−29 cm3/s1 TeVmχ2 mχm˜f4(20)Of course, cancellations may happen between graphs, and the cross-section of Equation 20 may be grosslyoverestimated. If it is not the case, Figure 3 shows that a bino could be detected at the 5 standarddeviation level within one year of observation, down to the present 0.2 TeV threshold, again assumingm˜f = mχ.

The cross-section for the annihilation of a higgsino into two photons is not yet known, andwe boldly assumed the same cross-section as for a bino. Figure 3 shows that the GKT correction factorsuppresses the higgsino line signal, due to the smaller higgsino relic density for a given mass.

Thus ahiggsino would be more difficult to detect in this way. The two searches, for a soft photon excess andfor a line signal, are therefore complementary, as they are sensitive to different types of neutralinos, andthey can be done simultaneously within the same experiment.5ConclusionsDark matter made of particles in the 100 GeV - 1 TeV mass region could be detected through itsannihilation products by an atmospheric ˘Cerenkov telescope searching for energetic gamma rays.

Weapply this idea to the neutralino WIMP candidate from supersymmetry, and show that it may work,provided that :i) the neutralino is heavier than about 200 GeV, which is one of the windows allowing a relic densityΩχ larger than 10−2.ii) the density enhancement in the center of the Galaxy is as large as expected by the isothermalIpser-Sikivie model.iii) a large enough atmospheric ˘Cerenkov detector is built in the southern hemisphere, and aimedtowards the galactic center.Improvements of the ACT technique to lower the energy threshold are of paramount importance toclose the gap between the 0.05 TeV or so of present accelerator experiments, and the 0.2 TeV expectedfor our reference telescope. A complementary study could be based on the detection of the charged decayproducts, the electrons, protons and antiprotons.

There is no directionality any more, and so no on-offexperiment is possible, but consequently there is no prefered location for the apparatus. Integrating allover the galactic halo, preliminary calculations suggest that antiprotons (and protons) must display astrong enhancement below the neutralino mass, while other nuclei should not.References[1] S.M.

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D40 (1989) 2549FIGURE CAPTIONSFigure 1 : Photon energy spectrum from the pair annihilation of neutralinos, showing the continuumdue to quarks, leptons, Higgs and gauge boson decays, computed through a Lund Monte-Carlo, and thelines (convolved with experimental energy resolution) due to direct annihilations into two photons, anda heavy particle and a photon. The relative size of the lines and of the continuum is arbitrary.Figure 2 : Soft photon signal.

Expected excess number of events per year above a 100 GeV thresholdfor a bino or a higgsino-like neutralino, as a function of the neutralino mass mχ, compared to the noise(one-sigma fluctuations of the background). The bino and higgsino curves correspond to an Ipser-Sikiviemodel of the halo core with α = 1, using the GKT correction to reduce the flux when the neutralino relicdensity Ωχ is smaller than the halo mean density Ωhalo = 0.1 , and assuming a s-fermion mass m˜f = mχ.The two vertical lines correspond to Ωχh2 = 1 for a bino and for a higgsino.Figure 3 : Line signal.

Expected number of events per year in the line for a bino or higgsino-likeneutralino, as a function of the neutralino mass mχ, compared to the noise (one-sigma fluctuations of thebackground). The bino and higgsino curves correspond to an Ipser-Sikivie model of the halo core withα = 1, using the GKT correction, and assuming a s-fermion mass m˜f = mχ, and an energy resolution∆E = 0.3 E. The two vertical lines correspond to Ωχh2 = 1 for a bino and for a higgsino.10

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