CERN–TH/2001-061

Non-Baryonic Dark Matter1

Leszek Roszkowski1,2

1Department of Physics, Lancaster University, Lancaster LA1 4YB, England

2TH Division, CERN, CH-1211 Geneva 23, Switzerland

Abstract

There exist several well-motivated candidates for non-baryonic cold dark matter, including neutralinos,

axions, axinos, gravitinos, Wimpzillas. I review the dark matter properties of the neutralino and the

current status of its detection. I also discuss the axino as a new interesting alternative.

CERN–TH/2001-061

February 20011Invited plenary review talk given at 6th International Workshop on Topics in Astroparticle and Underground Physics(TAUP 99), 6-10 September, 1999, Paris, France.

2

Non-Baryonic Dark Matter †

Leszek Roszkowski

Department of Physics, Lancaster University,Lancaster LA1 4YB, England

There exist several well-motivated candidates for non-baryonic cold dark matter, including neutralinos, axions,axinos, gravitinos, Wimpzillas. I review the dark matter properties of the neutralino and the current status of itsdetection. I also discuss the axino as a new interesting alternative.

1. Introduction

The puzzle of the hypothetical dark matter(DM) in the Universe still remains unresolved [1].While there may well be more than one type ofDM, arguments from large structures suggest thata large, and presumably dominant, fraction ofDM in the Universe is made of massive particleswhich at the time of entering the epoch of mat-ter dominance would be already non-relativistic,or cold. From the particle physics point of view,cold DM (CDM) could most plausibly be madeof so-called weakly interacting massive particles(WIMPs).

There exist several interesting WIMP candi-dates for CDM that are well-motivated by theunderlying particle physics. The neutralino isconsidered by many a “front-runner” by be-ing perhaps the most natural WIMP: it comesas an unavoidable prediction of supersymmetry(SUSY). The axion is another well-motivated can-didate [2]. But by no means should one forgetabout some other contenders. While some oldpicks (sneutrinos and neutrinos with mass in theGeV range) have now been ruled out as cosmolog-ically relevant CDM by LEP, axinos (SUSY part-ners of axions) have recently been revamped [3].Another well-known candidate is the fermionicpartner of the graviton, the gravitino. Most ofthe review will be devoted to the neutralino but I

†Invited plenary review talk given at 6th InternationalWorkshop on Topics in Astroparticle and UndergroundPhysics (TAUP 99), 6-10 September, 1999, Paris, France.

will also comment about recent results regardingaxinos.

Neutrinos, the only WIMPs that are actuallyknown to exist, do not seem particularly attrac-tive as DM candidates. It has long been believedthat their mass is probably very tiny, as suggestedby favored solutions to the solar and atmosphericneutrino problems, which would make them hot,rather than cold DM. This picture has recentlybeen given strong support by first direct evidencefrom Superkamiokande for neutrinos’ mass [4].While the new data only gives the µ − τ neu-trino mass-square difference of 2.2× 10−3 eV2, itit very unlikely that there would exist two mas-sive neutrinos with cosmologically relevant massof 5 to 40 eV and such a tiny mass difference.

The strength with which the WIMP candidateslisted above interact with ordinary matter spansmany orders of magnitude. For the neutrali-nos it is a fraction (∼ 10−2− ∼ 10−5) of theweak strength. Interactions of axions and axi-nos are suppressed by (mW /fa)2 ∼ 10−16, wherefa ∼ 1010 GeV is the scale at which the globalPeccei-Quinn U(1) symmetry is broken. Interac-tions of gravitinos and other relics with only grav-itational interactions are typically suppressed by(mW /MPlanck)2 ∼ 10−33. One may wonder howsuch vastly different strengths can all give therelic abundance of the expected order of the crit-ical density. The answer lies in the different waysthey could be produced in the early Universe: theneutralinos are mainly produced “thermally”: atsome temperature they decouple from the ther-

3

mal bath. But in addition there exist also severalmechanisms of “non-thermal” production. Thisis how CDM axinos, gravitinos can be produced(in addition to “thermal” production), as well asWimpzillas [5].

It is obvious that WIMPs do not necessarilyhave to interact only via weak interactions perse. WIMPs are generally required to be electri-cally neutral because of stringent observationalconstraints on the abundance of stable chargedrelics. On the other hand, they could in princi-ple carry color charges. (For example, a stablegluino above 130− 150 GeV [6], or in an experi-mentally allowed window 25 − 35 GeV [7], couldstill be the lightest SUSY particle (LSP) althoughits relic abundance would be very small [6].) In ahalo they would exist as neutral states by form-ing composites with gluon or quarks. We can seethat generally WIMPs are expected to have sup-pressed effective couplings with ordinary matter.Otherwise, they would dissipate their kinetic en-ergy.

What is the WIMP relic abundance Ωχh2 =ρχ/ρcrit [8]? Current estimates of the lowerbound on the age of the Universe lead toΩTOTALh2 < 0.25. Recent results from rich clus-ters of galaxies and high-redshift supernovae typeIa imply Ωmatter ' 0.3. The Hubble parameter isnow constrained to 0.65 ± 0.1. Big Bang nucle-osynthesis requires Ωbaryonh2 ∼< 0.015. Assumingthat most matter in the Universe is made of CDMWIMPs, one therefore obtains

0.1 ∼< Ωχh2 ∼< 0.15 (1)

or so. At the very least, requiring that a dominantfraction of CDM is located only in galactic halosgives Ωχh2 ∼> 0.025.

2. Neutralinos

The DM candidate that has attracted perhapsthe most wide-spread attention from both thetheoretical and experimental communities is theneutralino. It is a neutral Majorana particle, thelightest of the mass eigenstates of the fermionicpartners of the gauge and Higgs bosons: the bino,wino and the two neutral higgsinos. If it is thelightest SUSY particle, it is massive and stable,

due to assumed R-parity. A perfect candidate fora WIMP!

The neutralino is a well-motivated candidate.It is an inherent element of any phenomenologi-cally relevant SUSY model. Being neutral, it isa natural candidate for the LSP (although oneshould remember that this is often only an as-sumption); it couples to ordinary matter with aweak-interaction strength (reduced by mixing an-gles) which is within the range of sensitivity ofpresent-day high energy, as well as dark matter,detectors. Finally, as a bonus, it naturally givesΩχh2 ∼ 1 for broad ranges of masses of SUSYparticles below a few TeV and for natural rangesof other SUSY parameters.

Much literature has been devoted to the neu-tralino as DM, including a number of comprehen-sive and topical reviews (see, e.g., Refs. [9,10]).Here I will only summarize the main results andcomment on some recent developments and up-dates.

Neutralino properties as DM and ensuing im-plications for SUSY spectra are quite model de-pendent but certain general conclusions can bedrawn. First, its cosmological properties are verydifferent depending on a neutralino type. Therelic abundance of gaugino-like (mostly bino-like)neutralinos is primarily determined by the (light-est) sfermion exchange in the LSP annihilationinto f f : Ωh2 ∝ m4

f/m2

χ. In order to have Ωχ ∼ 1,

the lightest sfermion cannot be too light (below∼ 100 GeV) nor too heavy (heavier than a fewhundred GeV) [11] which is a perfectly naturalrange of values.

On the other hand, higgsino-like χ’s arestrongly disfavored. Firstly, due to GUT relationsamong gaugino masses, higgsinos correspond torather large gluino mass values, above 1 TeV,which may be considered as unnatural [11]. Fur-thermore, higgsino-like neutralinos have beenshown to provide very little relic abundance. Formχ > mZ , mW , mt the χ pair-annihilation intothose respective final states (ZZ, WW , tt) isvery strong. But both below and above thosethresholds, there are additional co-annihilation[12] processes of the LSP with χ±1 and χ0

2, whichare in this case almost mass-degenerate with the

4

LSP. Co-annihilation typically reduces Ωχh2 be-low any interesting level although it has been re-cently argued that the effect of co-annihilation isnot always as strong as previously claimed [13].Higgsino-like LSPs are thus rather unattractive,although still possible DM candidates, especiallyin the large mass (mχ ∼> 500 GeV) regime. Onealso arrives at the same conclusions in the caseof ‘mixed’ neutralinos composed of comparablefractions of gauginos and higgsinos. This is be-cause, even without co-annihilation, in this casethe neutralino pair-annihilation is less suppressedand one invariably finds very small Ωχ there [11].

Remarkably, just such a cosmologically pre-ferred gaugino type of neutralino typicallyemerges in a grand-unified scenario with addi-tional assumptions that the mass parameters ofall spin-zero particles are equal at the unificationscale ∼ 1016 GeV. What one finds there is thatthe lightest bino-like neutralino emerges as essen-tially the only choice for a neutral LSP [14,15]. (Itis still possible to find cases with a higgsino-likeLSPs but they are relatively rare.) Furthermore,in order for Ωχh2 not to exceed one or so, other(most notably sfermion) SUSY partner masseshave to be typically less than 1 TeV [14,15].Thus our phenomenological expectations for low-energy SUSY to be realized roughly below 1 TeVare nicely consistent with a bino-like neutralinoas a dominant component of DM in the Universe.

What about the neutralino mass? In princi-ple, it could be considered as a nearly free pa-rameter. It would be constrained from belowby the requirement Ωχh2 < 1 to lie above some2−3 GeV [16] which is a neutralino version of theLee-Weinberg bound [1]. This is because, in thismass range, the neutralino may be viewed as amassive neutrino with somewhat suppressed cou-plings. Much stronger bounds are in many casesprovided by LEP. Unfortunately, collider boundsare rather model dependent and are no longerprovided for the general SUSY model normallyconsidered in DM studies. Nevertheless, one canreasonably expect that mχ is now ruled out belowroughly 30GeV, except in cases when the sneu-trino is nearly degenerate with the LSP in whichcase the lower bound may disappear altogether.

A rough upper bound of 1 TeV follows from

the theoretical criterion of naturalness: expectingthat no SUSY masses should significantly exceedthat value. Again, GUT relations among gauginomasses cause the above constraint to provide amuch more stringent (although still only indica-tive) bound of about 150−200 GeV. Remarkably,in the scenario with additional GUT unificationof spin-zero mass parameters, just such a typi-cal upper bound derives from the cosmologicalconstraint Ωχh2 < 1. Only in a relatively nar-row range of parameters where the neutralino be-comes nearly mass degenerate with a SUSY part-ner of the tau, τR, the effect of the neutralino’sco-annihilation opens up the allowed range of mχ

up to about 600 GeV [17].Summarizing, we can see that, despite the com-

plexity of the neutralino parameter space and alarge number of neutralino annihilation channels,one can, remarkably, select the gaugino-like neu-tralino in the mass range between roughly 30 and150 GeV as a natural and attractive DM candi-date. Furthermore, one is able to derive relativelystringent conditions on the mass range of somesfermions, which are consistent with our basic ex-pectations for where SUSY might be realized.

3. Neutralino WIMP Detection

3.1. PredictionsThe local halo density of our Milky Way is es-

timated at 0.3 GeV/cm3 with a factor of two orso uncertainty [9]. For neutralino WIMPs as adominant component of the halo this translatesto about 3000 LSPs with mass mχ = 100 GeVper cubic meter. With typical velocities in therange of a few hundred km/s, the resulting fluxof WIMPs is actually quite large

Φ = vρχ/mχ ≈ 109 (100 GeV/mχ)χ′s/m2/s. (2)

A massive experimental WIMP search pro-gramme has been developed during the last fewyears. Although a variety of techniques have beenexplored, most of them follow one of the two ba-sic strategies. One can look for DM neutralinosdirectly, through the halo WIMP elastic scatter-ing off nuclei, χN → χN , in a detector. Indi-rect searches look for traces of decays of WIMPpair-annihilation products. One promising way

5

is to look for multi-GeV energy neutrinos com-ing from the Sun and/or the core of the Earth.One can also look for monochromatic photons,positrons or antiprotons produced in WIMP pair-annihilation in a Galactic halo. I will not discussthese indirect methods here. Perhaps I shouldonly mention about an interesting new way oflooking for WIMPs at the Galactic center [20].If there is a super-massive black hole there (forwhich there is now some evidence), it will ac-crete WIMPs and thus increase their density inthe core. They will then be annihilating muchmore effectively and the resulting flux of neutri-nos, photons and other products from the cen-ter of the Milky Way may be strongly enhanced,even up to a factor of 105 in halo models withcentral spikes in their profiles. Such spiked halomodels have been obtained in recent N-body sim-ulations [18].

In the following I would like to make severalcomments about direct detection and in particu-lar about an intriguing claim made by the DAMACollaboration regarding a possible evidence for aWIMP signal in their data. For a more detailedreview, see Ref. [19]. First, I will briefly summa-rize the theoretical aspects and predictions.

In direct searches one of the most sig-nificant quantities is the event rate R ∼σ(χN) (ρχ/mχv) (1/mN) - the product of theelastic cross section σ(χN) of neutralinos fromnuclei, their flux ρχ/mχv and the density of tar-get nuclei with mass mN .

The elastic cross section σ(χN) of relic WIMPsscattering off nuclei in the detector depends onthe individual cross sections of the WIMP scat-tering off constituent quarks and gluons. Fornon-relativistic Majorana particles, these can bedivided into two separate types. The coherentpart described by an effective scalar coupling be-tween the WIMP and the nucleus is proportionalto the number of nucleons in the nucleus. It re-ceives a tree-level contribution from scattering offquarks, χq → χq, as described by a LagrangianL ∼ (χχ) (qq). The incoherent component of theWIMP-nucleus cross section results from an axialcurrent interaction of a WIMP with constituentquarks, given by L ∼ (χγµγ5χ) (qγµγ5q), andcouples the spin of the WIMP to the total spin of

the nucleus.The differential cross section for a WIMP scat-

tering off a nucleus XAZ with mass mA is therefore

given by

dσ

d|~q|2 =dσscalar

d|~q|2 +dσaxial

d|~q|2 , (3)

where the transferred momentum ~q = mAmχ

mA+mχ~v

depends on the velocity ~v of the incidentWIMP. The effective WIMP-nucleon cross sec-tions σscalar and σaxial are computed by evalu-ating nucleonic matrix elements of correspondingWIMP-quark and WIMP-gluon interaction oper-ators.

In the scalar part contributions from individualnucleons in the nucleus add coherently and the fi-nite size effects are accounted for by including thescalar nuclear form factor F (q). (The effective in-teraction in general also includes tensor compo-nents but the relevant nucleonic matrix elementscan be expanded in the low momentum-transferlimit in terms of the nucleon four-momentumand the quark (gluon) parton distribution func-tion. As a result, the non-relativistic WIMP-nucleon Lagrangian contains only scalar interac-tion terms.) The differential cross section for thescalar part then takes the form [9]

dσscalar

d|~q|2 =1

πv2[Zfp + (A− Z)fn]2F 2(q), (4)

where fp and fn are the effective WIMP couplingsto protons and neutrons, respectively, and typi-cally fn ≈ fp. Explicit expressions for the caseof the supersymmetric neutralino can be found,e.g., in the Appendix of Ref. [21].

The effective axial WIMP coupling to the nu-cleus depends on the spin content of the nucleon∆qp,n and the overall expectation value of the nu-cleon group spin in the nucleus < Sp,n >. Fora nucleus with a total angular momentum J wehave

dσaxial

d|~q|2 =8

πv2Λ2J(J + 1)S(q), (5)

with Λ = 1J [ap〈Sp〉+an〈Sn〉]. The axial couplings

ap =1√2

∑u,d,s

dq∆q(p), an =1√2

∑u,d,s

dq∆q(n)(6)

6

are determined by the experimental values of thespin constants ∆u(p) = ∆d(n) = 0.78, ∆d(p) =∆u(n) = −0.5 and ∆s(p) = ∆s(n) = −0.16. Theeffective couplings dq depend on the WIMP prop-erties and for the neutralino they can be found,e.g., in the Appendix of Ref. [21].

In translating σ(χq) and σ(χg) into the WIMP-nucleon cross section in Eq. (3) several uncertain-ties arise. The nucleonic matrix element coeffi-cients for the scalar interaction are not preciselyknown. Also, the spin content of the nucleon andthe expectation values of the proton (neutron)group spin in a particular nucleus are fraught withsignificant uncertainty and nuclear model depen-dence. These ambiguities have to be considered innumerical calculations. Finally, in order to obtainσ(χN), models of nuclear wave functions must beused. The scalar nuclear form factor reflects themass density distribution in the nucleus [9].

The resulting cross section for scalar (or coher-ent) interactions is

σscalar(χN) ∼ G2F

m2χm2

N

(mN + mχ)2A2 (7)

and is proportional to the mass of the nucleus.For axial (or incoherent) interactions one finds

σaxial(χN) ∼ G2F

m2χm2

N

(mN + mχ)2(8)

which can be shown to be proportional to the spinof the nucleus. (GF is the Fermi constant.)

Unfortunately, in supersymmetric models ac-tual calculations produce a rather broad range ofvalues, R ∼ 10−5 − 10 events/kg/day. The ratesare also very small. The reason why this is so isclear: this is because of smallness of σ(χN). Theelastic cross section is related by crossing sym-metry to the neutralino annihilation cross sectionσann which is of weak interaction strength andsuch as to give Ωχh2 ∼ 1, and therefore verysmall.

Such small event rates are clearly an enormouschallenge to experimentalists aiming to search fordark matter. One may realistically expect thatcontinuing SUSY searches in high energy accel-erators and improving measurements of ΩCDM

and the Hubble parameter will cause those broadranges of R to gradually shrink.

The not so good news is that the choices ofSUSY parameters for which one finds the favoredrange of the relic abundance, 0.1 ∼< Ωχh2 ∼< 0.15,correspond to rather low values of the event rateR ∼< 10−2 events/kg/day or so, typically aboutan order of magnitude below the reach of today’sdetectors.

3.2. Annual ModulationOne promising way of detecting a WIMP is to

look for yearly time variation in the measured en-ergy spectrum. It has been pointed out [22,23]that a halo WIMP signal should show a peri-odic effect due to the Sun’s motion through theGalactic halo, combined with the Earth’s rotationaround the Sun. The peaks of the effect are onthe 2nd of June and half a year later.

The effect, called “annual modulation”, wouldprovide a convincing halo WIMP signal. Unfortu-nately, in SUSY models the effect is usually small,∆R ∼< 5% [9,21]. With the absolute event ratesbeing already very small, it is going to be a greatchallenge to detect the effect.

Here I would like to make some commentsabout possible evidence for a WIMP signal in an-nual modulation that has been claimed by theDAMA Collaboration. Based on the statistics of14, 962 kg×day of data collected in a NaI detec-tor over a period from November ’96 to July ’97(part of run II), the Collaboration has reported[24] a statistically significant effect which couldbe caused by an annual modulation signal due toa WIMP with mass mχ and WIMP-proton crosssection σp given as

mχ = 59 GeV+22−14 GeV, (9)

ξ0.3σp = 7.0+0.4−1.7 × 10−6 pb (10)

at 99.6% CL, where ξ0.3 = ρχ/ρ0.3 stands for thelocal WIMP mass density ρχ normalized to ρ0.3 =0.3 GeV/cm3. (See also Figure 6 in Ref. [24] fora 2σ signal region in the (mχ, ξ0.3σp) plane.) Ac-cording to DAMA, the new analysis is consis-tent with and confirms the Collaboration’s earlierhint [25] for the presence of the signal based on4, 549 kg×day of data.

The claimed effect comes from a few lowestbins of the scintillation light energy, just abovethe software threshold of 2 keV, and predomi-

7

nantly from the first bin (2 − 3 keV). This isindeed what in principle one should expect fromthe annual modulation effect. DAMA appearsconfident about the presence of the effect in theirdata, and claims to have ruled out other possi-ble explanations, like temperature effects, radoncontamination or nitrogen impurities. Accord-ing to DAMA, the effect is caused by single hitevents (characteristic of WIMPs unlike neutronor gamma background) with proper modulationof about one year, peak around June, and smallenough amplitude of the time dependent part ofthe signal.

Nevertheless, several experimental questionsremain and cast much doubt on the validity ofthe claim. Here I will quote some which I findparticularly important to clarify. First, as statedabove, the claimed effect comes from the low-est one or two energy bins. This is indeed whatone should expect from an annual modulation sig-nal. But is the effect caused by just one or twoenergy bins statistically significant? This is es-pecially important in light of the fact that theshape of the differential energy spectrum dR/dEin the crucial lowest energy bins as measuredby DAMA is very different from the one mea-sured by Gerbier, et al. [26] for the same detec-tor material (NaI). In Ref. [26] the corrected-for-efficiency dR/dE is about 10 events/kg/keV/dayat 3 keV, decreasing monotonically down to about2 events/kg/keV/day at 6 keV. (See Fig. 15in Ref. [26].) In contrast, DAMA’s spectrumshows a dip down to 1 events/kg/keV/dayat 2 keV, above which it increases to nearly2 events/kg/keV/day at 4 keV [24,27]. It is abso-lutely essential for the controversy of the shape ofdR/dE in the lowest energy bins to be resolved.Furthermore, DAMA’s data from the second run(∼ 15000 kg×day) shows that the background inthe crucial lowest bin ([2,3] keV) is only abouthalf or less of that in the next bins [27]. One maywonder why this would be the case. Examiningmore closely the data in the constituent nine NaIcrystals, one finds a rather big spread in the eventrates [27]. In detector 8, in the lowest energy binone finds no contribution from the backgroundwhatsoever!

Two other groups which have also used NaI

have reported [26,28] robust evidence of events ofunexpected characteristics and unknown origin.The data of both teams has been analyzed usinga pulse shape analysis (PSA). A small but statis-tically significant component was found with thedecay time even shorter than the one expectedfrom WIMPs or neutrons. While the popula-tion of those events appears to be too small toexplain DAMA’s effect, a question remains notonly about their origin (contamination?, externaleffect?) but also how they contribute to the en-ergy spectrum in the crucial lowest bins. DAMAclaims not to have seen such events.

DAMA has not yet published the data overa full annual cycle.3 In particular, no evidencehas been published of the signal going down withtime. So far, the claimed signal has been based ontwo periods of data taking. Ref. [25] was basedon two relatively short runs, one in winter andone in summer. The second analysis [24] usedthe data collected between November and July.Much more data has been collected and will soonbe published. One should hope that a full andclear analysis of statistical and systematic errorswill also be performed.

In Ref. [29] annual modulation was reanalyzedfor germanium and NaI. It was concluded that theeffect would be too small to be seen with currentsensitivity. Particularly illuminating is Fig. 6.awhere DAMA’s data from Ref. [25] (run one) wasre-plotted along with an expected signal for themodulated part of the spectrum for the centralvalues of the ranges of the WIMP mass and crosssection (σp) selected by DAMA. One can hardlysee any correlation between the data and the ex-pected signal.

A controversy over DAMA’s alleged signal isof experimental nature. One may therefore hopethat it will be definitively resolved. It would beof particular importance for another experimentusing different detector material to put DAMA’sclaim to test. The CDMS cryogenic detection ex-periment using germanium and silicon crystals atStanford has now reached an adequate sensitivityand has already ruled out about a half of the re-

3See Note Added.

8

101

102

103

10-44

10-43

10-42

10-41

10-40

10-39

WIMP Mass [GeV]

Cro

ss-s

ecti

on [

cm2 ]

(nor

mal

ised

to n

ucle

on)

Figure 1. The current and some recent limits onthe WIMP-proton spin-independent (scalar) cross-section. The legend is as follows: dot: Heidelberg-Moscow Ge [30], solid: DAMA NaI [31], dash: CDMS1999 4 kg×day Ge with neutron background sub-traction [27]. Marked also are the 2 − σ DAMA re-gions: solid closed curve: 15, 000 kg×day, filled re-gion: 20, 000 kg×day [24].

gion selected by DAMA [27].4 Let us hope thatDAMA’s claim will be falsified soon.

Figure 1 shows the current status of WIMPsearches in the plane of the WIMP-proton scalarcross-section σp versus the WIMP mass.5 Aclaimed DAMA region is also indicated.

It is worth pointing out that the claimed sig-nal region selected by DAMA [24] was too re-strictive as it did not include astrophysical un-certainties. The effect is rather sensitive to as-sumptions about a model of the Galactic halo.In the DAMA analysis the peak of the WIMP

4See Note Added.5The figure has been produced with the help ofa particularly useful plotting facility of Gaitskell& Mandic which is now available on the Web:http://cdms.berkeley.edu/limitplots/.

(Maxwellian) velocity distribution was fixed atv0 = 220 km/s. Since the Galactic halo has notbeen directly observed and there still is a consid-erable disagreement about a correct halo model,quoted error bars for v0 and the local halo densityshould, in my opinion, be treated with much cau-tion. Varying v0 within a reasonable range leadsto a significant enlargement of the region selectedby DAMA, [24] as first shown in Ref. [32]. Thisis so because of the significant dependence on v0

of the differential event rate spectrum, as can beseen in Fig. 1 in Ref. [32].

As a result, the upper limit of mχ correspond-ing to the claimed signal region increases consid-erably, from about 100 GeV for the initially as-sumed value v0 = 220 km/s up to over 180 GeVat v0 = 170 km/s [33] (at 2σ CL). On the otherhand the range of ξ0.3σp is not much affected.

Assuming that the effect claimed by DAMAwere indeed caused by DM WIMPs, it is interest-ing to ask what ranges of SUSY parameters andLSP relic abundance it would correspond to. Thisissue was addressed by three groups, each usingtheir own code for computing the direct detec-tion rate and the relic abundance [34–36]. Whilethere is some difference in approach (somewhatdifferent ranges of input parameters, techniquesand assumptions, etc.) the overall outcome isthat it is indeed possible to find such SUSY con-figurations which could reproduce the signal butonly for large enough tanβ (typically above 10although SUSY points with smaller values canalso sometimes be found). More importantly, thecorresponding values of Ωχh2 are rather small,typically below 0.06 [34–36] although somewhatlarger values can also sometimes be found. Theseare clearly small values, well below the favoredrange 0.1 ∼< Ωχh2 ∼< 0.15. This is illustrated inFigure 2 [36].

However, one should remember that these re-sults have been obtained using commonly usedbut often rather uncertain values of several inputparameters. In addition to astrophysical ones, thenuclear physics and quark mass inputs in calcu-lating the scalar cross-section for the neutralino-nucleus elastic scattering are rather poorly de-termined, as mentioned above. The effect of thelatter has been recently re-analyzed in Ref. [37]

9

100 200

0.0001

Figure 2. A scan of SUSY points in the plane(mχ, ξ0.3σp) where ξ0.3 = ρχ/(0.3 GeV/cm3). Thelegend: circles: 0.1 < Ωχh2 < 0.15 (cosmologically fa-vored range), crosses: Ωχh2 > 0.25 (excluded), smallpoints: 0.02 < Ωχh2 < 0.25 (conservative range).The 2 − σ region (upper left) of DAMA is markedwith full thick dots.

and found to affect the overall scalar cross-sectionby a factor of ten or so.

It is worth presenting Figure 3 again with anoutlook for some expected limits (as claimed bythe respective groups) and compare them withpredictions of minimal SUSY obtained for verybroad ranges of SUSY parameters and neglect-ing nuclear input uncertainties mentioned above.The SUSY region is bounded from above by asomewhat arbitrary requirement Ωχh2 > 0.025.From below it is limited by a generous boundΩχh2 < 1. The SUSY points falling into the cur-rently expected range 0.1 ∼< Ωχh2 ∼< 0.15 (notindicated in the plane) form a sub-region reach-ing up to roughly a few times 10−6 pb.

It is clear that today’s experiments are nowonly reaching the sensitivity required to begin

101

102

103

10-48

10-46

10-44

10-42

10-40

WIMP Mass [GeV]

Cro

ss-s

ecti

on [

cm2 ]

(nor

mal

ised

to n

ucle

on)

Figure 3. The current and some future reach lim-its on the WIMP-proton spin-independent (scalar)cross-section compared with conservative predictionsfrom minimal SUSY (large shaded region). The leg-end is as follows: upper dot: Heidelberg-MoscowGe [30], solid: DAMA NaI [31], upper dash: CDMS1999 4 kg×day Ge with neutron background subtrac-tion [27]. Marked also are the 2− σ DAMA regions:solid: 15, 000 kg×day, filled: 20, 000 kg×day [24].Future reach of some experiments (as claimed bythe respective groups): lower dash: CDMS atSoudan, lower dot: CRESST. Some other experi-ments (e.g., Edelweiss, UKDMC-Xe, GENIUS) ex-pect to reach roughly similar sensitivities. (Source:http://cdms.berkeley.edu/limitplots/).

testing predictions coming from SUSY. What Ifind promising is that several experiments us-ing different detector materials and often differ-ent methods of [attempts at] distinguishing signalfrom background will explore a large fraction ofthe SUSY parameter space within the next fewyears. Especially reassuring would be an observa-tion of a positive signal in more than type of DMdetector, although many experimentalists wouldprobably remark that I am asking for too much.

10

Time will tell.

4. Axinos

Axinos are a natural prediction of the Peccei-Quinn solution to the strong CP-problem andSUSY. The axino is the fermionic partner of theaxion. Similarly to the axion, the axino couplesto ordinary matter with a very tiny coupling pro-portional to 1/fa where 109 − 1010 GeV ∼< fa ∼<1012 GeV.

It is plausible to consider the axino as the LSPsince its mass is basically a free parameter whichcan only be determined in specific models. As wehave seen above, the neutralino has been acceptedin the literature as a “canonical” candidate forthe LSP and dark matter. But with current LEPbounds between about 30 and 60 GeV (depend-ing on a SUSY model), it becomes increasinglyplausible that there may well be another SUSYparticle which will be lighter than the neutralino,and therefore a candidate for the LSP and darkmatter.

Primordial axinos decouple from the thermalsoup very early, around T ' fa, similarly to theaxions. The early study of Ragagopal, et al. [38]concluded that, in order to satisfy Ωh2 < 1, theprimordial axinos had to be light (∼< 2 keV), cor-responding to warm dark matter, unless inflationwould be invoked to dilute their abundance. Ineither case, one did not end up with axino as coldDM.

However, it has recently been shown [3] thatthe axino can be a plausible cold dark matter can-didate, and that its relic density can naturally beof order the critical density. The axino can beproduced as a non-thermal relic in the decays ofheavier SUSY particles. Because its coupling isso much weaker, superparticles first cascade de-cay to the next lightest SUSY partner (NLSP)for which the most natural candidate would bethe neutralino. The neutralino then freezes outfrom thermal equilibrium at Tf ' mχ/20. If itwere the LSP, its co-moving number density af-ter freeze-out would remain nearly constant. Inthe scenario of Covi et al. (CKR) [3], the neu-tralino, after decoupling from the thermal equi-librium, subsequently decays into the axino via,

e.g., the process

χ → aγ (11)

as shown in Fig. 1 in Ref. [3]. This process wasalready considered early on in Ref. [39] (see alsoRef. [38]) in the limit of a photino NLSP and onlyfor both the photino and axino masses assumedto be very low, m

γ≤ 1 GeV and m

a≤ 300 eV,

the former case now excluded by experiment. Inthat case, the photino lifetime was typically muchlarger than 1 second thus normally causing de-struction of primordial deuterium from Big Bangnucleosynthesis (BBN) by the energetic photon.Avoiding this led to lower bounds on the massof the photino, as a function of fa, in the MeVrange [39].

Because both the NLSP neutralino and theCKR axino are both massive (GeV mass range),the decay (11) is now typically very fast. In thetheoretically most favored case of a nearly purebino, [11,15] the neutralino lifetime can be writ-ten as

τ ' 3.3×10−2s(

fa/(NCaY Y )1011 GeV

)2 (100 GeV

mχ

)3

(12)

where the factor NCaY Y is of order one. Onecan see that it is not difficult to ensure thatthe decay takes place well before 1 second inorder for avoid problems with destroying suc-cessful predictions of Big Bang nucleosynthesis.The axino number density is equal to that of theNLSP neutralino. Therefore its relic abundanceis Ω

ah2 =

(m

a/mχ

)Ωχh2. The axinos are ini-

tially relativistic but, by the time of matter dom-inance they become red-shifted by the expansionand become cold DM.

There are other possible production mecha-nisms and cosmological scenarios for massive ax-inos.6 Even if the primordial population of axi-nos is inflated away (which would happen if thereheating temperature Treh fa), they can beregenerated from thermal background processesat high enough Treh.

6For a recent comprehensive study, see [40].

11

5. Conclusions

Looking for the invisible is not easy but is cer-tainly worthwhile. The discovery of dark matterwill not only resolve the mystery of its nature butis also likely to provide us with much informationabout the particle physics beyond the StandardModel. What I find most encouraging is that wehave a very good chance of fully testing the neu-tralino as a WIMP by the end of the decade. De-tecting other candidates, like the axino, will bethe task for the more distant future.

Note Added:

After the Conference both the DAMAand CDMS Collaborations published new re-sults. Based on the combined statistics of57, 986 kg×day of data collected in a NaI detec-tor since November ’96, the DAMA Collaborationreported [41] a statistically significant (4 σ CL)effect which it interprets as being caused by aWIMP annual modulation signal.

The CDMS experiment using germanium andsilicon crystals at Stanford published [42] a newlimit on scalar WIMP-proton cross section. Thenew result is based on the total of 10.6 kg×day ofdata collected a current shallow site (17 mwe) atStanford during 1999. A powerful event-by-eventdiscrimination method allows CDMS to reach asensitivity matching that of DAMA with only lessthan 0.2% of DAMA’s statistics.

The new 90% CL CDMS limit excludes mostof the signal region claimed by DAMA. In par-ticular, it fully rules out the previous 2 σ regionbased on the combined data of 19, 511 kg×dayfrom runs I and II [24] and the new 3 σ region atmore than 84% CL.

An updated compilation of these andother data can be found on the Web:http://cdms.berkeley.edu/limitplots/.)

REFERENCES

1. E. Kolb and M. Turner, The Early Universe,(Addison-Wesley, New York, 1989).

2. P. Sikivie, in the Proceedings.

3. L. Covi, L. Roszkowski and J.E. Kim, Phys.Rev. Lett. 82, 4180 (1999) (hep-ph/9905212).

4. Super-Kamiokande Collaboration,Y. Fukuda, et al., Phys. Lett. B433, 9(1998); Phys. Lett. B436, 33 (1998); Phys.Rev. Lett. 81, 1562 (1998).

5. D.J.H. Chung, E.W. Kolb, and A. Riotto,Phys. Rev. Lett. 81, 4048 (1998).

6. H. Baer, K. Cheung and J.F. Gunion,Phys.Rev. D59 (1999) 075002 (hep-ph/9806361).

7. A. Mafi and S. Raby, hep-ph/9912436.8. For a detailed discussion and references, see

J. Primack, in the Proceedings.9. G. Jungman, M. Kamionkowski, K. Griest,

Phys. Rep. 267, 195 (1996).10. L. Roszkowski, in the Proceedings of the 2nd

Rencontres du Vietnam, Eds. Nguyen vanHieu and J. Tran Thanh Van, Editions Fron-tiers 1996.

11. L. Roszkowski, Phys. Lett. B 262, 59(1991); see also J. Ellis, D.V. Nanopoulos,L. Roszkowski, and D.N. Schramm, Phys.Lett. B245, 251 (1990).

12. K. Griest and D. Seckel, Phys. Rev. D 43(1991) 3191; M. Drees and M. Nojiri, Phys.Rev. D 47 (1993) 376; S. Mizuta and M. Ya-maguchi, Phys. Lett. B 298 (1993) 120.

13. M. Drees, M. Nojiri, D.P. Roy, Y. Yamada,Phys. Rev. D 56 (1997) 276.

14. R.G. Roberts and L. Roszkowski, Phys. Lett.B 309 (1993) 329.

15. G.L. Kane, C. Kolda, L. Roszkowski, andJ. Wells, Phys. Rev. D49, 6173 (1994).

16. K. Griest and L. Roszkowski, Phys. Rev. D46 (1992) 3309.

17. J. Ellis, T. Falk, and K. Olive, Phys.Lett.B444 367-372 (1998); J. Ellis, T. Falk,K. Olive, and M. Srednicki, hep-ph/9905481.

18. See, e.g., B. Moore, et al., Ap. J. Lett.499, 5 (1998); Y.P. Jing and Y. Suto, astro-ph/9909478.

19. A. Morales, in the Proceedings.20. P. Gondolo and J. Silk, Phys. Rev. Lett. 83,

1719 (1999) (astro-ph/9906391).21. H. Baer and M. Brhlik, Phys. Rev. D 57

(1998) 567.22. A. Drukier, K. Freese, and D. Spergel, Phys.

12

Rev. D 33 (1986) 3495.23. K. Freese, J. Frieman, and A. Gould, Phys.

Rev. D 37 (1988) 3388.24. R. Bernabei, et al. (The DAMA Collabora-

tion), Phys. Lett. B450, 448 (1999).25. R. Bernabei, et al. (The DAMA Collabora-

tion), Phys. Lett. B424, 195 (1998).26. G. Gerbier, et al., Astropart. Phys. 11, (1999)

287.27. R. Gaitskell, in the Proceedings.28. P. F. Smith, et al., Physics Reports 307

(1998) 275.29. D. Abriola, et al., Astropart. Phys.10, (1999)

133 (astro-ph/9809018).30. L. Baudis, et al., Phys. Rev. D59, 022001

(1999).31. R. Bernabei, et al., Phys. Lett. B 389 (1996)

757.32. M. Brhlik and L. Roszkowski, Phys. Lett.

B464, 303 (1999) (hep-ph/9903468).33. P. Belli, et al., Phys.Rev. D61, 023512 (2000)

(hep-ph/9903501).34. A. Bottino, F. Donato, N. Fornengo, S.

Scopel, Phys. Rev. D59, 095004 (1999).35. P. Nath and R. Arnowitt, Phys. Rev. D60,

044002 (1999) (hep-ph/9902237)36. Work in progress.37. A. Bottino, F. Donato, N. Fornengo and S.

Scopel, hep-ph/9909228.38. K. Ragagopal, M.S. Turner, and F. Wilczek,

Nucl. Phys. B358, 447 (1991).39. J.E. Kim, A. Masiero, and D.V. Nanopoulos,

Phys. Lett. B139, 346 (1984).40. L. Covi, L. Roszkowski, H.-B. Kim and

J.E. Kim, hep-ph/0101009.41. R. Bernabei, et al. (The DAMA Collab-

oration), INFN/AE-00/01 (February 2000),Phys. Lett. B480, 23 (2000).

42. The CDMS Collaboration, Phys. Rev. Lett.84, 5699 (2000) (astro-ph/0002471).