0711.4996v2 dark matter candidates 10 points

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[astro-ph]

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Dark Matter Candidates: A Ten-Point Test

Marco Taoso1,2, Gianfranco Bertone2, and Antonio Masiero11 INFN, Sezione di Padova, via Marzolo 8,Padova,35131,Italy and

2 Institut dAstrophysique de Paris, UMR 7095-CNRS,Universite Pierre et Marie Curie, 98 bis Boulevard Arago 75014, Paris, France

An extraordinarily rich zoo of non-baryonic Dark Matter candidates has been proposed over thelast three decades. Here we present a 10-point test that a new particle has to pass, in order to be

considered a viable DM candidate: I.) Does it match the appropriate relic density? II.) Is it cold?III.) Is it neutral? IV.) Is it consistent with BBN? V.) Does it leave stellar evolution unchanged?VI.) Is it compatible with constraints on self-interactions? VII.) Is it consistent with direct DMsearches? VIII.) Is it compatible with gamma-ray constraints? IX.) Is it compatible with otherastrophysical bounds? X.) Can it be probed experimentally?

INTRODUCTION

To identify the nature of Dark Matter is one of themost important open problems in modern cosmology. Al-though alternative explanations have been proposed interms of modified gravity, the discrepancies observed in

astrophysical systems ranging from galactic to cosmolog-ical scales appear to be better understood in terms ofa dark, yet undiscovered, matter component, roughly 6times more abundant than ordinary baryons in the Uni-verse (see Refs. [1, 2] for recent reviews).

The possible connection of this exciting problem withNew Physics beyond the Standard Model has promptedthe proliferation of Dark Matter candidates, that are cur-rently being searched for in an impressive array of accel-erator, direct and indirect detection experiments. As ourunderstanding of particle physics and astrophysics im-proves, we accumulate information that progressively re-duces the allowed regions in the DM particles parameterspace.

Here, we present a 10-point test that new particles haveto pass in order to be considered good DM candidates.We will work under the assumption that a single DMspecies dominates the DM relic density, while contribu-tion from other species is subdominant; it is straightfor-ward to generalize the discussion to the case of multi-component DM. Furthermore, we will consider a stan-dard CDM cosmological model, although we discussthe consequences of more general models, allowing forinstance a non-standard expansion history at the epochof DM freeze-out.

Each of the following ten points, that represent neces-saryconditions for a particle to be considered a good DMcandidate, will be discussed in a dedicated section, wherewe will review the literature on the subject and presentthe most recent results. In each section we will discusshow robust the constraints are, especially for those thatheavily rely on astrophysical quantities such as the localDM density and velocity distribution, or the extrapola-tion of DM profiles at the center of galactic halos, oftenaffected by large uncertainties.

A particle can be considered a good DM candidate onlyif a positive answer can be give to all the following points:

1. Does it match the appropriate relic density?

2. Is it cold?

3. Is it neutral?

4. Is it consistent with BBN?

5. Does it leave stellar evolution unchanged?

6. Is it compatible with constraints on self-interactions?

7. Is it consistent with direct DM searches?

8. Is it compatible with gamma-ray constraints?

9. Is it compatible with other astrophysical bounds?

10. Can it be probed experimentally?

The distinction between gamma-ray constraints andother astrophysical bounds, in points 8) and 9), is rather

artificial, and it simply reflects the privileged role of pho-tons in astrophysics, since they propagate along straightlines (unlike charged particles), and they can be detectedwith better sensitivity than, say, neutrinos. The fact ofconsidering gamma-ray photons is then due to the factthat the decay or annihilation of some of the most com-mon candidates falls in this energy range.

We also note that, strictly speaking, the last point isnot really a necessary condition, as DM particles couldwell be beyond the reach of current and upcoming tech-nology. However, measurable evidence is an essential stepof the modern scientific method, and a candidate thatcannot be probed, at least indirectly, would never be ac-cepted as the solution to the DM puzzle.

I. DOES IT MATCH THE APPROPRIATERELIC DENSITY?

The analysis of the Cosmic Microwave Background(CMB) anisotropies is a powerful tool to test cosmologi-cal models, and to extract the corresponding cosmologi-cal parameters. For instance, the angular position of thepeaks in the power spectrum of temperature anisotropies
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is a sensitive probe of the curvature of the Universe (seee.g. [3, 4] for a review and a more extended discussion).The power spectrum of CMB anisotropies is fitted withinthe Standard Cosmological Model with a number or freeparameters that depends onto the priors.The best fit of the three years WMAP data, with a 6parameters flat CDM model and a power-law spectrumof primordial fluctuations, gives [5]

bh2 = 0.0223+0.00070.0009 Mh

2 = 0.127+0.0070.013

for the abundance of baryons and matter, respectively.The normalized abundance i is defined as i = i/c,where c is the critical density, and the scaled Hubbleparameter h is defined as H0 100h km s1 Mpc1.A joint-likelihood analysis on a larger data-sets in-cluding, besides WMAP3, also small scale CMB ex-periments (BOOMERang, ACBAR, CBI and VSA),Large-Scale Structures (SDSS, 2dFGRS) and SuperNova(HST/GOODS, SNLS), further strengthens the con-straints to [6]

bh2

= 0.0220+0.0006

0.0008 Mh2

= 0.131+0.004

0.010.Note that the baryonic density is consistent with the de-termination from big bang nucleosynthesis [7]

0.017 < bh2 < 0.024 (95 % CL).

For a new particle to be considered a good DM can-didate, a production mechanism that reproduce the ap-propriate value of the relic density must exist. Moreover,to guarantee its stability, its lifetime must exceed thepresent age of the Universe. Taking in account the es-timates of the Hubble Space Telescope Key Project [8]and in agreement with the result derived by WMAP,

H0 = 723 (statistical)7 (systematic) km s1

Mpc

1

,we require a lifetime 4.3 1017 s.In many proposed extensions of the Standard Model

of particle physics, the stability of the DM particle isensured by imposing a symmetry that forbids the decayof DM into Standard Model particles. For example,R-parity in Supersymmetry models (SUSY) [9, 10],K-parity in Universal Extra Dimensions Models (UED)[11], and T-parity in Little Higgs Models [12], preventthe lightest new particle in the respective theories fromdecay (see for example Ref.[13] for a detailed discussionon SUSY DM and Ref.[14] for a review on UED DM).

Thermal relics

Among the best DM candidates, there is a class ofparticles called WIMPs (for weakly interacting massiveparticles), that are thermal relics and naturally achievethe appropriate relic density.

The scenario goes as follows: the WIMP is in thermo-dynamic equilibrium with the plasma in the early Uni-verse, and it decouples when its interaction rate drops

below the expansion rate of the Universe. For a non-relativistic particle at decoupling, the number densityover the entropy density remains frozen, i.e. the thermalrelic freezes-out. The evolution of the number density ofa generic species in the Universe, is described by thefollowing Boltzmann equation:

neq + 3Hn = annv n2 n2eq .

The second term in the l.h.s of the equation takes intoaccount the dilution of the number density due to theexpansion of the Universe. annv is the thermal averageof the annihilation cross section times velocity and it isparametrized with a non-relativistic expansion in powersofv2, as: annv = a + bv2+O(v4) a + 6b/x, withx m/T.

neq is the equilibrium density of WIMPs in the plasmaat temperature T and for a non-relativistic specie is given

by neq = g(mT2 )

3/2em

T , where g denotes the number ofdegrees of freedom of and m is the WIMP mass.

The Boltzmann equation can be solved integrating it

in two extreme regions, long before and long after theWIMP freeze-out (e.g. WIMP decoupling), and match-ing then the solutions. Skipping the calculation details,that can be reviewed e.g. in [15], the relic density todayfor a generic WIMP is [1]:

h2

1.07 109 GeV1MPl

xfgf

1

(a + 3b/xf)

3 1027 cm3s1annv . (1)

where gf counts the relativistic degrees of freedom atthe decoupling, MPl is the Planck mass and xf m/Tfwith Tf the freeze-out temperature. The last line is anorder of magnitude estimate and it shows that the relicabundance of a non relativistic decoupled specie strictlydepends on the annihilation cross section at freeze-out[13]. Furthermore, it has to be noticed that the annihi-lation cross section, for a particle of given mass, has amaximum, imposed by the partial wave unitarity of theS matrix, annvmax 1/m2 [35, 36]. Thus, with theuse of Eq. 1, the requirement Mh

2 1 implies the fol-lowing constraint on the mass of the DM particle, alsocalled unitarity bound [35]

mDM 340 TeV.

Applying the more stringent constraint, obtained byWMAP, the upper bound on mDM becomes:

mDM 120 TeV.

However, this constraint was derived under the as-sumption that particles were in thermal equilibrium inthe early universe, thus it applies only to thermal relics,and can be evaded by species which are non-thermallyproduced.


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0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

(1)

mass (TeV)

h2

LeptonsAll EW

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

0.1

0.2

0.3

0.4

0.5

(1)

mass (TeV)

h2

quarksgluons

Figure 1: Left: Relic Abundance ofB(1) in the UED model as a function of its mass after including no coannihilation (blackline), coannihilation with all leptons (blue) and all electroweak particles (red). For the cases with coannihilation, the solidand dashed lines are computed with a mass splitting = 0.01 and 0.05 respectively. Right: The same as in the left panelbut accounting for coannihilation of B(1) with all electroweak particles and quarks (blue line), and all level-one KK particles,including KK gluons (red line). Solid and dashed lines are for a mass splitting = 0.01 and 0.05 respectively. From Ref.[22].

The standard computation of the thermal relic abun-

dance discussed above presents three important excep-tions, as it has been shown, following previous ideas [16],by Griest and Seckel [17]. They take place for WIMPslying near a mass threshold, for annihilations near to apole in the cross section, or in presence of coannihila-tions. The last effect occur when a particle that sharesa quantum number with the WIMP, is nearly degeneratein mass with it. If the mass gap is low enough (roughly 10%) the coannihilation reactions, involving WIMPparticles, can control the WIMP abundance and lower orenhance it.Full relic density calculations, including all coannihila-tions, have been performed e.g. for the supersymmetric

neutralino, for which numerical codes such as DarkSUSY[18] and micrOMEGAs [19] are publicly available. Coan-nihilations have a dramatic effect on the relic density, andthey can lower it by a factor of up to several hundreds(see e.g. [20]).

Coannihilations are also important in UED models,where the relic density of the first excited state of the B,which may be the lightest Kaluza-Klein particle (LKP)and a viable DM candidate, may be enhanced or lowereddepending on the coannihilation channel [2123]. SeeFig.1.

Deviations from Standard Cosmology can substan-tially change the picture. For example, due to thepresence of scalar fields, the universe may undergo aperiod of much higher expansion rate and the relic abun-dance of a WIMP may result increased by several ordersof magnitude [24, 25]. Furthermore, the production ofentropy in the Universe after the WIMP decouplingmay dilute its abundance, e.g. due to out-of-equilibriumdecays of non-relativistic particles or to first-order phasetransitions [2629].

It is also possible that DM particles did not experience

the thermal history depicted above, and that they have

inherited the appropriate relic density through the de-cay of a more massive species, that has earlier decoupledfrom the thermal bath. This is e.g. the case for Super-Weakly Interacting Massive Particles (SWIMP), such asthe LSP gravitino in SUSY and the first excitation of thegraviton in UED, which are produced by late decays ofthe next-to lightest particles (NLSP/NLKP) in the re-spective theories [3033] and whose relic abundances aresimply the rescaled thermal relic densities of the NLPs:

SWIMP =mSWIMP

mNLPNLP.

Other production mechanisms may actually be con-

comitant for such candidates, such as the production atreheating after the end of the inflationary era (see e.g.[32, 34]. See also below for a brief discussion of gravitinoproduction).

Other production mechanisms

Very heavy DM candidates, such as the so-called wim-pzillas, have been proposed, with masses as large as1015 GeV, i.e. well above the unitarity limit (see e.g.[37] for a review). For mechanisms that produce thesesuper-massive particles with DM

1, departure from

thermal equilibrium is automatic [37], and the challengeis not to overproduce them. Several mechanisms havebeen proposed: for instance they could be created duringreheating after inflation, with masses a factor 103 largerthan the reheating temperature [38], or during a pre-heating stage, with masses up to the Grand Unificationscale (1015 GeV) [39] or even to the Planck Scale [40], oragain from bubble collisions if the inflation exit is realizedby a first-order transition [41]. Another very interestingmechanism is of gravitational nature: wimpzillas may be


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created by amplification of quantum fluctuations in thetransition between the inflationary regime and the mat-ter (radiation) dominated one, due to the nonadiabaticexpansion of the spacetime [42, 43]. This scenario canproduce particles with mass of the order of the inflatonmass and do not require couplings of wimpzillas with in-flaton or other particles.

These particles can be accomodated in existing theo-

retical frameworks. For instance, stable or metastablebound states called cryptons arise in M-theory, andother possibilities are contemplated in string theories[44]. Furthermore, messenger bosons in soft supersym-metry breaking models may be very massive and in pres-ence of accidental symmetries in the messengers sectors,might be stable [45].

Although wimpzillas have been invoked in top-downscenarios that seek to explain the origin of Ultra HighEnergy Cosmic Rays [43, 46, 47], this interpretation is to-day problematic because it predicts a large photon com-ponent in the UEHCRs spectrum, in disagreement withthe recent results of the Auger experiment [48].

Several production mechanisms can act together toproduce a given species, and its relic abundance receivescontributions from each of them. The calculationdepends on the details of the particle physics andcosmological models adopted. In the case of axions,i.e. light pseudoscalar particles introduced to solvethe Strong CP Problem, the production mechanismsin the early Universe are scattering in the hot thermalplasma and possibly radiation by topological defects likeaxion-strings. Another relevant production mechanismis the so-called misalignment: the axion field rollstowards its minimum, near the QCD epoch, and it endswith coherent oscillations that produce a Cold DarkMatter condensate. A lower bound on the axion masscan be inferred requiring that they do not overclose theUniverse, but the uncertainties in the calculation of theirproduction make the constraint rather weak (for recentreviews of axions see [50, 51]).

As mentioned before, gravitinos can be copiously emit-ted by the decay of the NLP in SUSY but they can alsobe produced, during reheating, by inelastic 22 scat-tering processes off particles in the thermal bath and insome scenarios they can act as Cold Dark Matter can-didates (e.g. [5257], see e.g. [58, 59] for more detailsand references on gravitino DM models). The efficiencyof the production depends on the reheating temperature

TR so the bound on DM translates into an upper limiton TR [34, 55, 60]. In addition to thermal production andlate decays of the NLSP, other non thermal and inflationmodel dependent contributions can arise and change con-siderably the predictions [61, 62].

Sterile neutrinos, which arise naturally in theoreticalframeworks [6366] or in the phenomenological MSM[67], have been proposed as a solution of the LSNDanomaly [68], as explanation of the high pulsar veloci-ties [69] and as Dark Matter candidates. Recently, the

MiniBoone collaboration has reported its first results, ex-cluding at 98% C.L. the two-neutrino appearance oscil-lation scheme obtained from LSND data [70]. The (3+1)scheme, involving one sterile neutrino specie, is excludedand also models with two or three sterile species are notviable because of the tension between appearance anddisappearance data [71].

Sterile neutrinos may be produced in the early Uni-

verse from collision oscillation conversions of active ther-mal neutrinos. Their momentum distribution is signifi-cantly distorted with respect to a thermal spectrum dueto the effects of quark-hadron transition, the modificationof the neutrino thermal potential caused by the presenceof thermal leptons and the heating of the coupled species(see e.g. [72] for precise computation of relic abundance).Moreover it has been proposed an enhanced resonantproduction, in presence of a lepton asymmetry in theearly universe significantly higher than the baryonic one[73, 74].

II. IS IT COLD?

The evolution of perturbations in the Universe de-pends on the microscopic properties of DM particles. Thestandard picture, widely accepted, is that after equality,when the Universe becomes Matter Dominated, the DMdensity perturbations begin to grow, and drive the os-cillations of the photon-baryonic fluid around the DMgravitational potential wells. Soon after recombination,baryons kinematically decouple from photons and remaintrapped in DM potential wells. Their density perturba-tions then grow to form the structures that we observetoday in the Universe (see for more details [4, 15]).

Hot Dark Matter

The imperfect coupling between baryons and pho-tons at recombination leads to a damping of small scaleanisotropies, also known as Silk damping [75]. A colli-sionless species, moving in the universe from higher tolower density regions, also tends to damp the fluctua-tions above its free-streaming scale. This a key propertyof Hot Dark Matter, which consists of species which arerelativistic at the time of structures formation and there-

fore lead to large damping scales [76].The prototype of HDM are Standard Model neutri-

nos: they were thermally produced in the early Uni-verse and they termodinamically decoupled again rela-tivistic at T 1 MeV, leading to a relic abundancetoday that depends on the sum of the flavor masses,m =

3i=1 mi :

h2 =

m90 eV

. (2)


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Their free-streeming length is [15]:

FS 20

30 eV

m

Mpc.

Hot DM models are today disfavored (see e.g. [77] fora more complete discussion). For instance, the powerspectrum of density perturbations should be suppressedbeyond the free-streaming length of HDM particles, thatfor neutrino masses in the eV range corresponds roughlyto the size of superclusters. Furthermore, HDM modelspredict a top-down hierarchy in the formation of struc-tures, with small structures forming by fragmentation oflarger ones, while observations show that galaxies areolder than superclusters.

Small amounts of HDM can still be tolerated, providedthat it is compatible with large scale structure and CMBdata. Assuming an adiabatic, scale-invariant and Gaus-sian power spectrum of primordial fluctuations, WMAPdata set an upper limit on the sum of light neutrinomasses [5] (or equivalently, through Eq. 2, on )

m < 2.11 eV (95 % CL).

The combination of data from WMAP, large scale struc-ture and small-scale CMB experiments, further strength-ens the constraint, but it also introduces potentially largesystematic effects [7881]. A significantly improved con-straint can been obtained combining Ly- forest, CMB,SuperNovae and Galaxy Clusters data [82, 83]:

m < 0.17 eV (95 % CL).

These limits can be applied to a generic hot DarkMatter candidate, e.g. to thermal axions [51, 84, 85] or

to hot sterile neutrinos [86].

Cold Dark Matter

The standard theory of structure formation thus re-quires that Dark Matter is cold, i.e. it is made of par-ticles that have become non-relativistic well before thematter domination era, and that can therefore clump onsmall scales. The prototype of cold DM candidates is thesupersymmetric neutralino, whose free-streaming lengthis such that only fluctuations roughly below the Earthmass scale are suppressed [87, 88]. CDM candidates canbe heavy thermal relics, such as the aforementioned neu-tralino, but also light species, non-thermally produced,like axions (see Sec. I for further comments and refer-ences).

N-body simulations of CDM Universe are in agree-ment with a wide range of observations, such as theabundance of clusters at z 1 and the galaxy-galaxycorrelation functions (see e.g. [89] for a review of CDM),making it a successful and widely accepted cosmologicalmodel.

However, the emergence of some discrepancies has leadsome authors to question the CDM model and to pro-pose alternative scenarios. For example, the number ofsatellite halos in Milky Way-sized galaxies, as predictedby simulations, exceeds the number of observed Dwarfgalaxies [90, 91]. Furthermore, the rotation curves oflow surface brightness (LSB) galaxies point to DM dis-tributions with constant density cores rather than the

cuspy profiles preferred by N-body simulations [9295].An additional problem arises when considering the an-gular momentum of dark matter halos: in simulationsgas cools at early time into small mass halos, leading tomassive low-angular momentum cores in conflict with theobserved exponential disks [96].

Several astrophysical processes have been invoked inorder to solve these problems, such as major mergersand astrophysical feedback[97]. The low efficiency of gascooling and star formation may decrease the number ofsatellites in Milky Way-sized galaxies [98100] and tidalstripping may have dramatically reduced the size of thesesubstructures or disrupted a fraction of them [102, 103].

Furthermore, new ultra-faint dwarf galaxies have beenrecently detected, alleviating the discrepancy betweenCDM predictions and observations [101]. It has also beenpointed out that the measurements of the LSB galaxiesrotation curves may suffer of observational biases, for ex-ample due to the fact that DM halos are triaxials ratherthan spherically symmetric [104]. Moreover, small devi-ations of the primordial power spectrum from scale in-variance, the presence of neutrinos [105] or astrophysicalprocesses [106, 107] can sensibly affect the halo profiles.Anyway, the lack of convincing explanations of the prob-lems discussed above leaves the door open to alternativesto the CDM scenario.

Warm Dark Matter

To alleviate these problems, Dark Matter candidateswith a strong elastic scattering cross section (SIDM)[108], or large annihilation cross sections [109] have beenproposed. It has also been suggested that Dark Matter iswarm, i.e. made of particles with velocity dispersion be-tween that of HDM and CDM particles. The larger free-streaming length of WDM, with respect to CDM, reducesthe power at small scales, suppressing the formation ofsmall structures [110, 111]. For instance, a WDM particlewith a mass of 1 keV and an abundance that matches thecorrect Dark Matter density, has a free-streaming lengthof order of galaxy scales FS 0.3 Mpc [112]. Measure-ments of the growth of structures in galaxy clusters andLy- forest can then be used to set a lower bound on themass of the WDM particle. Gravitinos in gauge-mediatedsupersymmetry breaking models might be warm DM can-didates, if they decouple when the number of degrees offreedom was much larger than at the neutrino decoupling[113]. However, explicit computations show that such alight thermal gravitino cannot account for all the DM


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[112].Another WDM candidate is the sterile neutrino, pro-

duced in the early Universe by oscillation conversion ofthermal active neutrinos, with a momentum distributionsignificantly suppressed and distorted from a thermalspectrum [67, 74, 114]. Its free-streaming scale is givenby (see e.g. [27])

FS 840 Kpc h11 KeV

ms< p/T >

3.15

,

where ms is the mass state associated to the sterile fla-vor eigenstate. < p/T > is the mean momentum overtemperature of the neutrino distribution and the ratio< p/T > /3.15 ranges from 1 for a thermal WDMparticle to 0.9, for a non-thermal sterile neutrinos dis-tribution.

The suppression of the power spectrum by a ther-mal WDM of a given mass mWDM, is identical to thatproduced by sterile neutrinos of mass ms derived by[112, 115]:

ms = 4.43 KeV

mWDM1 KeV4/3

0.25(0.7)

2

WDM

1/3.

This one-to-one correspondence allows to translate thebounds on sterile neutrinos to a generic thermal relic andviceversa.

A detailed analysis of the production of sterile neutri-nos and of the evolution of their perturbations, as wellas a comparison with the measured matter power spec-trum, have been performed in Refs. [112, 116119]). Theresulting lower limits on the mass of the WDM particlesstrongly depend on the dataset used in the analysis. Forexample, in [116], a combination of the SDSS 3D power-spectrum and SDSS Ly- forest allowed to constrain the

sterile neutrino mass to

ms 1.7 KeV (95 %CL),that translates in terms of a thermal WDM particle to

mWDM 0.50 KeV.The inclusion of high resolution Ly- data makes the

constraint even stronger, even if it has been pointed outthat they may suffer of large systematic uncertainties[112, 116].

More recently, very stringent bounds on the mass ofWDM particles have been obtained by different groups:[118]

ms 14 KeV (95 % CL) (mWDM 2.5 KeV)and [119]:

ms 28 KeV (2) (mWDM 4 KeV).The delay of the reionization of the Universe also sets

a constraint on the WDM mass [120122]. In the case ofsterile neutrinos, the X-rays produced by their decays canmodify the picture, enhancing the production of molecu-lar hydrogen and releasing heat in gas clouds [123125].

III. IS IT NEUTRAL?

Some extensions of the Standard Model of particlephysics predict the existence of new, stable, electricallycharged particles, such as the lightest messenger state ingauge-mediated supersymmetry breaking models [126] oreven the LSP in the R-parity conserving Minimal Super-symmetric Standard Model (MSSM).

Massive charged particles, independently on the con-text they emerge, have been proposed as Dark Mattercandidates by De Rujula et al and dubbed CHAMPs[127]. Evaluating their thermal relic abundance, withsimple assumptions on the annihilation cross sections,the authors found a viable mass range of 11000 TeV.They also pointed out that a positively charged particleX+ can capture an electron to form a bound state chem-ically similar to an heavy hydrogen atom. An X caninstead bind to an ++ particle and an electron, result-ing again in a heavy hydrogen-like atom, or alternativelyit can capture a proton to produce a bound state calledneutralCHAMP. The different behaviors of CHAMPs and

neutralCHAMPs lead to different bounds on their abun-dance. Note also that De Rujula et al. concluded thatX would emerge from Big Bang Nucleosynthesis pref-erentially in the form of neutralCHAMPs [127].

Galactogenesis models provide constraints on the DarkMatter interactions, in particular of CHAMPs. The en-ergy loss timescale in this case is in fact dominated byCoulomb scattering off protons, and it must be longerthan the dynamical timescale for galaxy formation. InRef. [127], the authors concluded that only CHAMPsheavier than 20 TeV are able to remain suspended inthe halo, and to be therefore rare on Earth. This es-timate disagree with that obtained by Dimopoulos et

al who found, for the same considerations, the limitMX > 105 TeV [128]. It has also been proposed that

shock accelerations in supernovae could eject CHAMPsfrom the disk and reinject them back to the halo or outof the galaxy [128]. The latter possibility is energeticallydisfavored, while in the former case, it may lead to adangerous heating of the disk.

One of the most stringent bounds on the CHAMPsabundance comes from searches of anomalous heavy wa-ter: CHAMPs, being chemically identical to heavy hy-drogen, can be trapped in oceans and lakes in the formof HXO. If one assumes, as in Ref. [127], that CHAMPsheavier than 20 TeV remain suspended in the Galactichalo and they provide the Galactic DM, taking an ac-

cumulation time of 3 109 yr, comparable with the ageof oceans, the abundance of CHAMPs in sea water ispredicted to be [129]:

nXnH

Earth

3 105

GeV

mX

Xh

2.

If instead CHAMPs are present in the Galactic disk,taking in account the density and velocity of the inter-stellar gas, mostly hydrogen, the expected concentration


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is [129]:

nXnH

Earth

6 105

GeV

mX

Xh

2.

All the searches of anomalous hydrogen in sea waterhave failed so that the abundance of CHAMPs, for massesin the range 100 GeV-1000 GeV is constrained to be

nXnH

Earth

1028 1029,

while it raises to (nX/nH) < 1020 for MX 10 TeV

(see [130] for a compilation of upper bounds of heavyhydrogen from sea water searches). As a result, CHAMPsas DM candidates are ruled out in the mass range MX 10 104 GeV.

NeutralCHAMPs would preferentially bind on Earthto nuclei to form anomalous heavy isotopes. Nullsearches for these elements, covering a variety of nuclearspecies, constrain the NeutralCHAMPs abundance to be< 1020

1016 for MX

100

1000 GeV [131] (for fur-

ther details see [130] and references therein). The authorsof Ref. [131], concluded that stable X Dark Matter inthe mass range 102 104 GeV is thus to be consideredunlikely.

CHAMPs are also constrained by balloon or satellitesexperiments for Cosmic Rays studies. Perl et al, taking inaccount data from different experiments [128, 133, 134],excluded CHAMPs as Galactic Dark Matter in the massrange 2.41035.6107 GeV and neutralCHAMPs for105 4 107 GeV [132]. The lower limit comes from therequirement that particles penetrate the solar wind andthe energy deposition is above the experimental thresh-old. The upper bound is obtained comparing the maxi-

mum CHAMP flux at the top of the atmosphere allowedby the CR experiments, with the local DM flux, which istypically assumed to be 107(GeV/MX) cm2s1.

In the atmosphere, a proton in a neutralCHAMP getsreplaced very quickly by a 14N atom, and the exchangeis followed by a MeV -ray emission from the excited14N X status. With the same argument explainedabove, the observational limits on -rays flux imply thatneutralCHAMPs should be heavier than 106 GeV if theyare to be the DM[128]. Further constraints on CHAMPscome from deep underground experiments. The re-sponses of scintillators to monopoles and CHAMPs areexpected to be similar, since they are both slowly mov-ing, highly ionizing and penetrating. In Ref. [132], theauthors applied the upper limit on monopole flux, ob-tained from MACRO experiment, to the CHAMP case,excluding the mass range 108 1020 GeV.

Further constraints come from stellar evolution, in par-ticular it has been shown that CHAMPs can disrupt aneutron star in a short timescale, falling into its centerand producing a Black Hole. This argument excludesCHAMPs with masses 102 1016 GeV [135]. In addi-tion, the properties of diffuse interstellar clouds constrainthe interactions of halo particles with atomic hydrogen:

Figure 2: Exclusion plot for CHAMPs (solid lines) and Neu-tralCHAMPs (dotted lines). See text for more details.

the rate of energy deposition due to collisions must besmaller than the cooling rate, for clouds in equilibrium.It results that CHAMPs with masses below 106 GeV areruled out because, for these particles, the expected crosssection with hydrogen is higher than the maximum al-lowed value [136].

The various constraints on CHAMPs that we havediscussed are summarized in Fig. 2. Even if the boundsare not completely model-independent, the combinationof them basically rules out CHAMPs as DM.

The above limits apply to particles with integer elec-tric charge, but theoretical frameworks have been pro-posed where particles with fractionary electric charge ex-ist, also known as milli-charged particles [137142]. For

example, adding a new unbroken U(1)

gauge group, thephoton and paraphoton can mix, and particles chargedunder U(1)

can have a small coupling with photons [137].Moreover, realistic extensions of SM motivated by stringtheory exist, that naturally implement this mechanism[139].

Constraints on mass and charge of milli-charged parti-cles come from a variety of observations, and in Fig. 3 weshow the excluded regions in the parameter space (mq,), with = q/e, obtained by Davison et al. [143].

Milli-charged particles can also affect CMBanisotropies, and for this reason WMAP data canseverely constrain their cosmological abundance, at least

in some regions of the milli-charged particle parameterspace [144].

Furthermore, searches of neutrino magnetic momentwith reactor experiments exclude Dark Matter particleswith q > 105e, for masses mq 1 keV [145].

The result of the PVLAS collaboration [146] have beententatively interpreted in terms of milli-charged particleswith masses mq 0.1 eV and fractional electric charge 106 [139, 140, 148], but the experimental result wasnot confirmed after an upgrade of the PVLAS apparatus


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Figure 3: Excluded regions in the mass-charge plane formilli-charged particles. The constraints are relative to: RD

plasmon decay in red giants; WD plasmon decay in whitedwarfs; BBN big bang Nucleosynthesis; SN Supernova 1987A;AC accelerator experiments; SLAC SLAC millicharged par-ticle search; L Lamb Shift; Op invisible decay of ortho-positronium; DM Dark Matter searches. From Ref. [143].

[147].

Light milli-charged particles may largely affect sub eVCosmology. In particular, processes such as qqcan distort the CMB energy spectrum, which has beenmeasured with high sensitivity by FIRAS. A detailedanalysis has been performed in Ref. [149] and the au-thors reported the conservative upper bound 107,

for m 1 eV, excluding in this way also the lightmilli-charged particles proposed in Ref. [139, 140, 148].

In principle, DM particles could have a SU(3)c charge.For example, colored candidates are naturally pre-dicted in SUSY models if the LSP is a squark [150] ora gluino [151, 152], or in gauge mediated SUSY break-ing models, where messengers can be colored and stable[153], or in mirror models [154]. These heavy partons,after the deconfinement temperature, T 180 MeV, aresurrounded by a QCD cloud and confined inside hadronsforming a color neutral bound state [155]. These particlescan be actively searched for by underground experiments,

indirect detection experiments or through the search ofrare anomalous isotopes.

Since the proposal that DM might interact stronglywith ordinary matter (SIMP), regardless of the natureof the interaction [127, 128, 156], many candidates havebeen put forward, but also many constraints on the scat-tering cross section off nuclei, N.

For example, the SIMPs interactions with baryons maydisrupt the disk of spiral galaxies [156, 157]. Moreover,they may dissociate the light elements produced during

Figure 4: Excluded regions in the SIMP mass versus SIMP-

nucleon cross section plane. The Violet area is excluded by theEarths heat argument. See Ref.[165] and references therein.

Big Bang Nucleosynthesis, while SIMPs collisions withCosmic Rays can produce an observable -ray flux [158].The scattering of SIMPs off baryons also produces sub-stantial distortion of CMB anisotropies and of the largescale structure power spectrum [159]. The SIMPs abun-dance for the mass range 1 103 GeV, is also con-strained by searches in terrestrial samples of gold andiron [160].

Atmospheric and satellite experiments, originally in-tended for other purposes, have been used to investigatehigh DM cross sections with baryonic matter. In par-ticular, the results of the X-ray Quantum Calorimeterexperiment (XQC) allow to rule out a large portion ofthe SIMP parameter space (M, N), as discussed inRefs. [161, 162] and (more recently and with substantialchanges with respect to previous analyses) in Ref. [163].

Complementary constraints are obtained by under-ground experiments, which are sensitive to DM particleswith small interactions. In fact, they are able to detectSIDM particles if their interactions with ordinary matterare high enough to trigger a nuclear recoil in the detectorbut at the same time low enough to allow the particles to

penetrate the Earth crust to the detector [164]. Recently,Mack et al. have analyzed the effect of SIMP annihila-tions on Earth, showing that a substantial heating of theEarths core may occur, if the capture rate is efficient[165]. This argument rules out the regions of the param-eter space lying between astrophysical and undergrounddetector constraints.

To summarize the constraints on the SIMP scenario,Fig. 4 shows the excluded areas in the SIMP parameterspace. The bounds leave no room for SIMPs as Dark


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Matter candidates in a very large mass range. Sincethe neutron-neutron scattering cross section is of order1025 1024 cm2 and the expected value for coloredDark Matter candidates is not far from this range ( seee.g. [166]), DM particles are thus unlikely to bring colorcharge.

However, these constraints can be evaded by very mas-sive composite dark matter candidates. For example

macroscopically large nuggets of ordinary light quarksand/or antiquarks, with masses in the range m 10201033 GeV, can behave as collisionless cold dark matter,without contradicting observations [167].

IV. IS IT CONSISTENT WITH BBN?

Big Bang Nucleosynthesis (BBN) is one of the mostimpressive successes of the Big Bang Cosmology (See [7,168] for reviews). It predicts the abundances of lightelements produced in the first 3 minutes after the BigBang, in agreement with the observations over a range

spanning nine order of magnitudes.The model is based on a set of coupled Boltzmann

equations relating the number densities of protons, neu-trons and light elements, through a network of nuclearchemical reactions. The weak interactions maintain theneutron-proton ratio to its equilibrium value until thefreeze-out, that occurs at roughly 0.7 MeV. Later, nearlyall neutrons are captured in the nuclei producing princi-pally the most stable element 4He. Smaller amount of2H,3H, and 7Li are synthesized but the production of heav-ier elements is suppressed by the large Coulomb barriers.Looking for astrophysical environments with low metal-licity, it is possible to infer the primordial abundance of

light elements in order to test the predictions of BBN.In the framework of the Standard Model, BBN dependsonly on the baryon to photon ratio , and observationsof the abundance of different elements agree with predic-tions in the range [7]

4.7 1010 6.5 (95% CL).

The agreement between predictions and measurements isa powerful success of the model and it is remarkable thatthe inferred abundance of baryons quoted above is alsoconsistent with the estimate of CMB experiments likeWMAP [5]. BBN also provides a test of physics beyondthe Standard Model, and it also constraints deviationsfrom Standard Cosmology. In fact, the primordial abun-dance of4He is proportional to the ratio n/p and its valueis related to the freeze-out temperature of the weak in-teractions and it is therefore sensitive to the expansionrate at that time.

Since H g1/2 T2, an increase of the relativistic de-grees of freedom g with respect to the SM value leads toa faster expansion rate, thus to an earlier freeze out of theneutron to proton ratio and consequently to a higher 4Heabundance (and in general it also affects the abundance

of the other light elements). At T 1 MeV, the relativis-tic species in the Standard Model are photons, electronsand neutrinos so with N neutrino family g = 5.5 +

7

4N

and for N = 3 this gives 43/4.New relativistic particles can be accounted for through

the introduction of an effective number of neutrinos:

74 (N 3) =

i=extra bgi

TiT4

+ 78

i=extra fgi

TiT4

,

where Ti parametrizes the energy density of the rela-tivistic species and b (f) stands for bosons (fermions).

A likelihood analysis, taking and N as free param-eters, and based on the abundance of 4He and 2H, con-strains the effective number of neutrinos to be [169]:

1.8 < N < 4.5 (95% CL).

Assuming the value of inferred by CMB experiments,the limit is further strengthened to [169]:

2.2 < N < 4.4 (95% CL).

These bounds on N can be applied to new species af-fecting the expansion rate during nucleosynthesis, such asgravitons [170], neutrinos with only right-handed inter-actions [169] or millicharged particles [143]. For a largeclass of supergravity models with a light gravitino, therequirement N < 4 rules out gravitino masses below 1eV [171]. However, particles coupled to photons or toneutrinos during BBN, with masses in MeV range, havea non trivial impact on BBN, that cannot be accountedfor with an equivalent number of light neutrinos [172].

For instance, it has been suggested that MeV Dark

Matter, with masses in the range 4-10 MeV and coupledwith the electromagnetic plasma, can lower the heliumand deuterium abundances, contrary to what one naivelyexpects, and it can therefore improve the agreement be-tween the predicted and measured 4He abundance [173].

In addition, the predictions of BBN can be danger-ously modified by the decays of particles during or afterBBN. For example, radiative dacays induce electromag-netic showers and the subsequent photon-photon pro-cesses can destroy the light elements. In the early stagesof BBN, t < 102 sec, hadronic decays may modify theinterconversion of protons and neutrons, increasing then/p ratio and consequently enhancing the 4He and 2Habundance. The opposite effect occur for late hadronicdacays, t > 102 sec, when the energetic hadrons triggerthe 4He dissociation.

Accurate calculations, with the use of BBN codes, re-strict the primordial abundance of the decaying particle,depending on its lifetime, mass and hadronic branchingratio [174178]. These results can be applied for instanceto NLSP gravitinos: BBN requires an upper limit tothe reheating temperature, which controls the primordialgravitino abundance, and in some cases the restrictionscould lead troubles to thermal leptogenesis and inflation


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models [175, 177]. The difficulties can be circumventedfor example in the case of a heavy gravitino, which decayswell before BBN [179, 180].

Alternatively, the gravitino could be stable and playthe role of Dark Matter. In this case, the NLSP parti-cle is typically long-lived, because of the extremely weakinteractions of gravitino, and its late decays can affectBBN. Moreover, it has been pointed out that if the long-

lived particles are charged, e.g the stau, they can formbound states with light elements, potentially overproduc-ing 6Li and 7Li [181185]. However, these elements canalso be destroyed, alleviating the severe bounds on theCHAMPs abundance during BBN.

A neutralino NLSP is excluded [186188], while sneu-trino NLSP poorly affects BBN [189]. A stop NLSP isviable in some regions of the parameter space [190].

We note that these BBN bounds can be circumventedif the NLSP abundance is diluted due to a significantentropy production [191].

V. DOES IT LEAVE STELLAR EVOLUTIONUNCHANGED?

Stellar evolution provides a powerful tool to constrainparticle physics, providing bounds that are often com-plementary to those arising from accelerator, direct andindirect Dark Matter searches.

If Weakly interacting particles are light, they may beproduced in the hot plasma in the interior of stars, and ifthey escape without further interactions, they representan energy loss channel for the star, possibly modifyingthe stellar evolution. Such particles may also be detectedon Earth, as was the case for neutrinos from SN 1987A,

or they can be indirectly searched for through their decayproducts. Here we describe the most important observa-tional consequences (see Refs. [192, 193] for extensivereviews).

Stars as the Sun can be described as self-gravitatinggas in hydrostatic equilibrium, such that the gas pres-sure equilibrates the gravitational force. A significantenergy loss produces a contraction of the system and anincrease of the burning rate of the stellar fuel, reducingthe lifetime of the star and enhancing the neutrino flux.Moreover, exotic energy losses would modify the soundspeed profile, which is accurately measured in the interiorof the Sun by means of helioseismic measurements.

Globular Clusters are alternative interesting probes ofstellar evolution models because they are gravitationallybound systems of up to a million stars, formed at thesame time, with the same chemical composition and dif-fering only for their masses. The ignition of helium inRed Giant stars is sensitive to the temperature and den-sity of the helium core, and any energy loss channel in-evitably tends to delay it, resulting in more massive coresand producing observational consequences, such as an en-hancement of star brightness. Therefore, observations ofRed Giants in Globular Clusters allow to derive an up-

per limit on the energy loss rate of the helium plasma, ,[192]:

10 erg g1s1 at T 108 K, 2 105g cm3,

where the value of temperature and density are appropri-ate for Red Giant cores. In Horizontal Branch stars, en-ergy losses speed up the helium burning rate, decreasing

their lifetimes, that can be measured by number countingin Globular Clusters. This argument provides anotherbound on [192]:

10 erg g1s1 at T 0.7108 K, 0.6104g cm3.

In addition, the cooling rate of White Dwarfs, inferredby their luminosity functions, is in agreement with thepredictions and therefore any new cooling channel has tobe subdominant.

It is remarkable that the total number of neutrino de-tected from SN 1987A, their energy and their time distri-bution, is in agreement with expectations from the stan-dard model which describes the core collapse of a star.

Any further energy loss mechanism reduces the durationof the neutrino burst and can in principle spoil the successof the model, leading therefore to the following bound on [192]:

1019 erg g1s1 at T = 30 MeV, = 31014g cm3.

All the arguments listed above provide upper limitsto any additional energy loss rate and can be appliedto constrain, for instance, the neutrino properties, thegraviton emission in theories with extra dimensions, aswell as models with right-handed neutrinos, sterile neu-trinos, milli-charged particles, axions and other pseu-

doscalar particles. For instance, updated limits on axionsfrom stars are reviewed in Ref. [194] and the implicationsof light Dark Matter or sterile neutrino Dark Matter onSupernovae core collapse are discussed in Ref. [195, 196].More details and references for other particle physics sce-narios can be found in [192, 193].

As we have seen in Sec.III, the most restrictive boundson the fractional charge of keV milli-charged particlescome from stellar physics, as it was shown in Fig.3.

The bounds discussed above apply to particles that areproduced in the core of stars and that escape withoutlosing energy, thanks to their weak interactions. How-ever, if the particles interact strongly, they undergo mul-tiple scattering, providing a mechanism for energy trans-port, in competition with photons, electrons or convec-tion. This effect has been studied for keV-mass scalarsproduced in the Sun, Horizontal Branch stars and RedGiants, constraining the interactions of these particles[197, 198].

Moreover, the energy transport channel, provided bythe WIMPs trapped in the Sun, may cool its interior anddecrease the neutrino flux. This idea was proposed inthe past as a solution of the solar neutrino problem andWIMPs with masses and cross sections suitable for this


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purpose (m 4 10 GeV 1036 cm2) were calledcosmions [199201].

Stars in which the heat transport is dominated by coreconvection may be dramatically affected by WIMPs inthe case of effective transport of energy. In fact, in thiscase, the convection is suppressed, and the core is notreplenished with nuclear fuel from outer regions, lead-ing to a reduced stellar lifetime and a modification of its

evolution [202, 203]. As a consequence, main sequencestars would present an anomalous mass-to-luminosity re-lation and Horizontal Branch stars would develop ther-mal pulses [203205]. However, taking in account the cur-rent limits on the WIMP-nucleon cross section inferredfrom direct searches, these effects seems to be hardly de-tectable for the Sun [206, 207].

Dark Matter annihilations may provide an importantsource of energy, which, for stars orbiting in high DarkMatter density regions, can even be comparable or over-whelm that originated by nuclear reactions. This sce-nario has been investigated, in the case of main sequencestars, in Ref.[208] and more recently, by means of nu-

merical simulations, in Ref.[209, 210]. The most pro-nounced effects are on low-mass stars and the authors inRef.[209, 210] have proposed that these WIMP burnerscould be found in regions where a recent star formationis inhibited, looking for populations of stars appearingoddly younger then higher mass ones. Although appar-ently young stars have been detected in the inner regionsof Andromeda and of our own galaxy, it is difficult tointerpret these observations in terms of WIMP burners.WIMP annihilations could also enhance the luminosity ofWhite Dwarfs and neutron stars, as it has been observedin [211213].

The effect of DM decays and annihilations on the for-mation of first structures have been investigated for light

DM candidates [125, 214]. Recently, it has been pointedout that even standard DM candidates, such as the neu-tralino, may substantially modify the evolution of Pop-ulation III stars, which may even be supported by DMannihilations rather than nuclear reactions, during partof their evolution [215].

VI. IS IT COMPATIBLE WITH CONSTRAINTSON SELF-INTERACTIONS?

The collisionless and cold nature of Dark Matter, hasbeen questioned during the last decade, because of ap-parent discrepancies between the results of CDM simu-lations and observations. Two remarkable problems, asmentioned in Sec. II, are the conflict between the cuspyDM halos predicted by N-body simulations and the con-stant core profiles inferred by LSB and dwarfs [92, 93] andthe excess of substructures in CDM halo with respect tothe observed number of galaxy satellites [90, 91].

Although astrophysical explanations exist for the ob-served discrepancies, [98, 99, 104107], many attemptshave been made to modify the properties of DM parti-

cles in order to reproduce the appropriate astrophysicalphenomenology. A possible solution is that DM is warmrather than cold, as mentioned before. Alternatively,DM might be self-interacting (SIDM), as proposed bySpergel and Steinhardt, with large scattering cross sec-tion (and small enough annihilations cross sections, inorder to be consistent with the bounds from indirect de-tection) [108]. The net effect, under these assumptions,

is that the central cusp reduces to an almost constantcore. Moreover, subhalos can be destroyed by interac-tions with the surrounding halo particles, because theyare excessively heated or because particles are scatteredout of the them [108, 161]. Suitable SIDM candidatesinclude Q-balls [108, 216], a quark-gluino bound state[161, 217] and scalar gauge singlets coupled with Higgsfield [218].

Semi-analytical calculations and N-body simulationshave been developed to study the effect of SIDM inter-actions on halo structures, especially for what concernsthe formation of flat cores. Different solutions are ob-tained, depending on the ratio between the mean free

path of the Dark Matter particle (mfp ( /m)1

,with n the number density and /m the scattering crosssection per unit mass of the SIDM) and the virial ra-dius of the halo. A cross section per unit mass in therange /m 0.5 5cm2g1 was found to correctly re-produce the observed profile of galaxies [219222]. Morerecently, Ahn and Shapiro have found a much highervalue, /m 200cm2g1, as the best fit to LSB rota-tion curves [223].

Several constraints exist on SIDM interactions. Forinstance, Gnedin and Ostriker have shown that, for0.3 /m 104 cm2g1, galactic halos in clusterswould evaporate in a timescale shorter than an Hubbletime [224]. Following the suggestion of Furlanetto andLoeb [225], Natarajan et al. compared the predictedtruncation radii of SIDM halos with those of observedgalactic halos in clusters, inferred by gravitational lens-ing, excluding /m > 42 cm2g1 [226].

An upper limit of /m < 0.1 cm2g1, has been ob-tained by Arabadjis et al. comparing the results of simu-lations with the profile of the cluster MS 1358+62 [227].Hennawi and Ostriker ruled out /m 0.02 cm2g1,pointing out that the supermassive black holes at thecenter of galaxies would be more massive than observed[228]. The evidence of ellipticity in DM halos hasbeen used to rule out /m > 0.02 cm2g1 because self-interactions tend to produce more spherical halos [229].

The limits reported above rule out the range of cross sec-tions required to explain the mass profiles of galaxies,although the underlying simpliying assumptions and in-complete statistics suggest to take them with a grain ofsalt (see e.g. [223, 231]).

More robust results are obtained from the analysis ofthe 1E 0657-56 cluster of galaxies [230], which actuallyconsists of a bullet-like gas sub-cluster, exiting the coreof the main cluster at high velocity, v 4700 Km s1.The combination of optical and X-ray images with the


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weak lensing map, shows that the centroid of the colli-sionless subcluster galaxies is ahead of the subcluster gasdistribution and coincident with that of the Dark Mat-ter clump. This cluster not only provides a robust visualevidence for Dark Matter, but it is also provides a probeof its collisionless nature.

The subcluster DM halo would be dragged by the mainhalo in presence of DM self-interactions, leadig to an off-

set between the galaxies centroid and the total mass peakinferred through weak lensing measurents. Moreover, themeasured high merger velocity implies that eventual dragforces, due to DM collisions, are small. Finally, the massto light ratio of the subcluster is in agreement with thatobserved in other clusters and in the main cluster, whileSIDM would tend to scatter out the particles from thesubcluster.

Markevitch et al. found that the latter argumentprovides the most restrictive limit to the self interac-tion cross section, /m < 1 cm2g1 [231]. Makinguse of more recent observations and more accurate N-body simulations, this bound has been slightly improved,/m < 0.7 cm2g1 [232]. Since this constraint assumesan identical mass-to light ratio of cluster and subclus-ter before the merger, a more robust limit is inferred bythe absence of an offset between galaxies and total masspeaks, which implies /m < 1.25 cm2g1 [232]. Almostthe full range of cross sections needed to solve the discrep-ancies emerged in CDM models, /m 0.5 5cm2g1,is ruled out, thus disfavoring SIDM.

It has been suggested that the scattering cross sectionmight be velocity dependent, thus smaller on average inclusters than in galaxies (e.g. [221, 224, 228, 233]). Apossible functional form is

= 100 Km s1

vrela

.

In order to avoid a fast evaporation of the cluster ora core collapse, the parameters are restricted to be: = 0.5 1 cm2g1 and a = 0.5 1 [224, 228], and sim-ulations have confirmed that in this range, predictionsmatch the observed flat cores [221]. However, observa-tions of the LSB galaxy NGC 5963 seem to require aneffective cross section per unit mass /m < 0.2cm2g1,in the low velocity regime 150 km s1, at odds withthe quoted range [234].

In addition to the bounds presented above, that con-strain the cross section per unit mass, additional limitscome from the unitary of the scattering matrix [35, 36].This argument provides upper bounds on the total crosssection and inelastic cross section. In the low energyregime, taking in account the range of SIDM elasticcross sections needed to the reproduce the observed haloprofile, the constraint on the total cross section can beturned into an upper bound on the SIDM mass: m < 12GeV [36]. Possible exceptions to unitarity bounds havebeen discussed in Refs. [35, 36].

Self-annihilating DM has also been proposed to solvethe cold dark matter cusp crisis [109] This scenario is

however ruled out by the comparison of the neutrino fluxfrom the Galactic center with the measured rate of (at-mospheric) neutrinos, i.e. the least detectable among thefinal states produced in DM annihilations [235]. For themass range 101 105 GeV, annv has to be less thanroughly 1021 cm3s1.

VII. IS IT CONSISTENT WITH DIRECT DMSEARCHES?

Direct DM searches aim at detecting DM particlesthrough the measurement of nuclear recoils produced byDM scattering. Despite the large DM flux expected atEarth, 105(100 GeV/mDM) cm2s1 assuming alocal density of 0 0.3 GeVcm3 and mean velocityof v 220 km s1, the weakness of WIMP interactionswith nuclei makes direct detection challenging (see e.g.[236] for a review of direct searches).

The coupling between a WIMP and a nucleon receivescontributions from both scalar (spin independent) andvector (spin dependent) interactions. The cross sectionfor spin independent (SI) coupling with a nucleus (N)cross section is coherently enhanced with respect to thecase of single nucleons:

SIN A2(Mred(N, M)/Mred(p, N))2SIpwhere A is the atomic number and Mred is the reducedmass of the system WIMP () - nucleus (proton) [237].

Although heavy nuclei are used in current DM di-rect detection experiments, the results are often givenin terms of scattering cross section off protons in orderto allow easy comparison between different experimen-tal settings, involving different target materials. For spin

dependent (SD) couplings, there is no coherent enhance-ment, and the cross section is determined by unpairedneutrons or protons in the target nucleus. For this rea-son, SI interactions usually dominate the cross section incurrent experiments, which exploit heavy nuclei. How-ever, in region of parameter space where scalar couplingis suppressed, spin dependent couplings may representthe leading contribution to the direct detection event rate[238, 239].

The signature of DM elastic scattering off nuclei arenuclear recoils, characterised by an exponential recoilspectrum with typical energies ofO(10) keV or less, forWIMP masses between 1 and 100 GeV (see for more de-tails e.g. [13]). In the case of inelastic scattering off nucleior orbital electrons, the recoil is followed by a decay pho-ton from the excited state [240, 241]. However, the natu-ral radioactivity background makes the detection of thissignal very problematic. Current experiments exploit avariety of detection techniques, focusing on signals suchas scintillation, phonons, ionization or a combination ofthem, as well as a variety of targets, e.g. NaI, Ge, Si andXe.

In order to discriminate a DM signal against the natu-ral background, some experiments have been searching


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070514082101

http://dmtools.brown.edu/Gaitskell,Mandic,Filippini

101

102

103

10-44

10-43

10-42

10-41

10-40

WIMP Mass [GeV]

Cross-section[cm

2](normalisedtonucleon)

Figure 5: Upper limits on the spin independent WIMP-nucleon cross section, versus WIMP mass. The blue dashed(points) line is the Ge (Si) CDMS bound [250]. The dark red,pink, green and dark blue curves are the experimental lim-its respectively from EDELWEISS [253], CRESST 2004 [254],ZEPLIN II (Jan. 2007) [255] and WARP [256]. The lowest redsolid line shows the first results from XENON 10 [251]. Thered shaded region is the parameter space favored by DAMAexperiment [247]. Supersymmetric models allow the filled re-gions colored: pink [257], green [258], dark red [259] and blue[260]. This figure has been obtained with the use of the inter-face at http://dendera.berkeley.edu/plotter/entryform.html.

for an annual modulation of the measured event rate

[242]. In fact, the Earth rotation around the Sun is ex-pected to produce a modulation of the relative velocityof DM particles given by

vE = 220 Km/s {1.05 + 0.07 cos[2(t tm)]/1 year}where tm is approximatively the begin of June. The vari-ation of the WIMP flux is actually small 7%, so that alarge number of events has to be collected and thereforea large detector is needed.

In 1998, the DAMA collaboration obtained evidencefor a modulation of the event rate, that was later con-firmed with a confidence level of 6.3 (see [243] for arecent discussion).

If interpreted in terms of a SI scattering of a WIMPoff NaI, and further assuming an isothermal sphereDM halo, with a characteristic velocity of the Maxwell-Boltzmann distribution of v0 = 270 Kms

1, with a lo-cal DM density of = 0.3 GeV cm3, and with a slope r2, the DAMA result is compatible with the de-tection of a DM particle with a mass around 50 GeVand a WIMP-nucleons scattering cross section of order1041 1042 cm2.

Other experiments, such as CDMS and EDELWEISS,

have explored the region of parameter space allowedby the DAMA modulation signal, finding null results[244, 245]. The comparison between the DAMA annualmodulation and the other mentioned experiments is how-ever model-dependent. Taking into account astrophysi-cal uncertainties, the DAMA allowed region is sensiblyincreased, with masses extending up to 250 GeV andspin independent WIMP-proton cross section down to

1043

cm2

[246248]. Nevertheless, null searches of re-cent experiments make the most nave interpretation ofthe DAMA signal problematic [249251].

It should be stressed, however, that the DAMA signalshould not be dismissed without further investigation,especially in view of the fact that theoretical scenarios(despite exotic) exist where an interpretation in termsof DM appears not to be in conflict with other existingexperiments [269] (see also references therein).

The upper bounds on the WIMP spin-independentcoupling inferred by several experiments are summarizedin Fig. 5. The most stringent result (as of November2007) was obtained by the XENON collaboration. The

limits on SD cross section are far weaker and the bestconstraints, plotted in Fig. 6, come from CDMS [239],NAIAD [262], Super-Kamiokande [266] and KIMS [267].A better sensitivity to spin dependent couplings is ex-pected for the COUPP experiment, a heavy liquid bub-ble chamber under development in the NuMi gallery atFermilab [268].

In comparison, the theoretical predictions of neutralinoelastic scattering off nucleons, for different SUSY scenar-ios, show that current direct searches have begun to ex-plore a relevant portion of the parameter space, whileimproved sensitivities are needed to perform a completescan [270, 271].

Direct detection constraints exclude the left-handedsneutrino in the MSSM as dominant Dark Matter com-ponent. However, the right-handed sneutrino, in exten-sions of the MSSM, is a viable Dark Matter candidate,compatible with direct searches [272, 273].

VIII. IS IT COMPATIBLE WITH GAMMA-RAYCONSTRAINTS?

Aside from direct and accelerator searches, one maysearch for DM through the detection of its annihilationproducts, such as photons, anti-matter and neutrinos.

In particular, since the energy scale of the annihila-tion photons is set by the DM mass, and since someof the most studied DM candidates, such as the su-persymmetric neutralino and the LKP in UED models,are expected to lie in mass in GeV-TeV region, exoticgamma-ray sources are among the primary targets of in-direct searches (see e.g. [274] for a review about DMsearches though gamma-ray astrophysics). Significantemissions at other wavelengths is however predicted inmost cases, due to the interactions of the annihilationproducts with ambient photons or magnetic fields, mak-


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Figure 6: Upper limits on spin-dependent WIMP cross section as a function of the WIMP mass, in the case of a pure neutron(proton) and proton (left) coupling. The blue solid (dashed) line is the Ge (Si) CDMS bound [239]. The blue dotted line isthe CDMS limit with an alternative form factor [239]. The light red, cyan, magenta and red curves are the experimental limitsrespectively from EDELWEISS [265], PICASSO [263], NAIAD 2005 [262] and ZEPLIN I [264]. The dark green shaded regionshows the parameter space favored by DAMA experiments [261]. Finally the green points represent the CRESST results [261],the black crosses stand for Super-Kamiokande [266] and the black circles for KIMS 2007 [267]. The figures have been obtainedwith the use of the interface at http://dendera.berkeley.edu/plotter/entryform.html.

ing multi-wavelength searches possible. Emission at dif-ferent energy scales has also been discussed in the contextof other DM candidates, e.g. X-rays from the decay ofsterile neutrinos (see Sec.IX).

The gamma-ray flux from WIMP annihilations in a

DM halo depends on the particle physics parameters aswell as on cosmological quantities, such as the profile ofDM halos. More precisely, the gamma-ray flux at earth(if the WIMP is not its own antiparticle a factor 1/2 mustbe added) is given by

(, E) =annv8m2

dNdE

l.o.s.

ds2(r(s, )),

where m and annv are respectively the mass and thecross section annihilation times relative velocity of theDM particle. From Eq. 1 in Sec. I it follows that, tomatch the correct DM density, it is necessary for a coldthermal relic annv

1026 cm3s1, although this value

is just indicative because, for instance, coannihilationscan substantially modify the picture, plus the cross sec-tion in the non relativistic limit may substantially differfrom the one at decoupling (e.g. in the case of p-wave

annihilations).dNdE is the photon spectrum from DM an-

nihilations, that depends on the nature of DM candidate.Finally, the last term in the equation is the integrationalong the line of sight of the dark matter density squared.The quadratic dependence on , suggests that ideal tar-gets of indirect searches are regions where the DM den-

sity is strongly enhanced such as the Galactic center (e.g.[275281, 299]), halo substructures (e.g. [282287]) andthe core of external galaxies (e.g. [288291]). Prospectsfor detecting gamma-rays have been discussed also foroverdensities in DM halos called caustics (e.g. [292296]).

Much steeper profiles, called spikes, may form due to adi-abatic growth of black holes, for example around the Su-per Massive black hole at the Galactic center (see e.g.[297299] for a discussion about the prospect for detect-ing DM annihilation gamma-rays in this scenario). Al-though in this case the spike is likely disrupted by astro-physical processes [297, 300, 301], a moderate enhance-ment, called crest, may form again due to gravitationalinteractions with the observed stellar cusp [302]. Morepromising targets may be mini-spikes around intermedi-ate massive black holes, since they are not affected bydynamical processes that tend to lower the density en-hancement [303, 304].

Although conclusive evidence for Dark Matter annihi-lations has not been obtained so far, gamma-ray experi-ments have nonetheless provided a wide range of obser-vations that can be used as upper bounds of gamma-rayfluxes from DM annihilations, in order to constrain exist-ing DM scenarios. In particular observations in the softgamma-ray energy band, between roughly 50 keV and 1MeV, have been performed by the Osse experiments [310]and more recently by INTEGRAL in the range 20-8000keV (see [311, 312]). All-sky observations have been per-formed by COMPTEL in the energy range 3 MeV - 30


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produced e.g. by neutralino or LKP annihilations vialoop-diagrams with or Z as final states (see e.g.[278, 323, 348350]) or also in models with scalar darkmatter [351, 352]. A number of alternative strategieshave been proposed over the years, see e.g. Ref. [353] fora recent review.

IX. IS IT COMPATIBLE WITH OTHERASTROPHYSICAL BOUNDS?

Neutrinos

Neutrinos can be produced in DM annihilations ei-ther directly or via the decay of other annihilation prod-ucts, and may be detected with high-energy neutrino tele-scopes, that measure the Cherenkov light emitted by sec-ondary muons propagating in water or ice.

The Sun and the Earth have been proposed as tar-gets for indirect DM searches, since a large number ofWIMPs could accumulate in their interior, releasing a

large number of neutrinos. The neutrino flux depends onthe capture rate of WIMPs in the Sun or in the Earth,thus on the elastic cross section of these particles.

The spin-dependent cross section is far less constrainedthan the spin-independent one (see Sec.VI) Since in theEarth the abundance of nuclei with odd atomic num-bers is very small, the capture rate is dominated by thestrongly constrained spin independent coupling, contraryto what happens in the Sun. The prospects for detectingneutrinos from the center of the Earth are therefore notparticularly promising, at least for current and upcom-ing experiments [355]. The null searches of AMANDAhave been used to derive an upper limit on neutrino flux

from WIMP annihilations, for example in the frameworkof neutralino Dark Matter [356]. In the framework ofMSSM, however, the most optimistic neutralino scenar-ios will be probed by kilometer size neutrino telescopessuch as IceCube [357].

The prospects for detecting neutrinos from the annihi-lation of Kaluza-Klein Dark Matter in the Sun are morepromising, because of its large axial coupling, and theannihilations ofB1 particles to neutrino and tau leptonspairs, respectively forbidden and subdominant in the caseof neutralino, dominate the neutrino spectrum, produc-ing a large number of high energy neutrinos. The eventrate in kilometer scale detectors is expected between 0.5and 10 events per year [359].

The Galactic Center (GC), a well studied site forgamma-ray DM searches, offers instead poor prospectsfor detecting Dark Matter annihilations though neutri-nos. An upper limit on neutrino flux from GC, in thecase of neutralino Dark Matter, has been obtained byrequiring that the associated gamma-ray emission wouldnot exceed the flux measured by EGRET [360]. Unfor-tunately this bound is below the sensitivity of presentand upcoming experiments, such as ANTARES, unlessextreme scenarios are considered.

The prospects for detecting neutrinos from so-calledmini-spikes around Intermediate Mass Black Holes (seethe discussion in Sec. VIII) appear more promising. Thestrong enhancement of the DM density around these ob-

jects induces a substantial boost of the DM annihila-tion rate, leading to neutrino fluxes within the reach ofANTARES and IceCube [361].

A combination of data from different neutrino tele-

scopes can already be used to set an upper bound on thetotal DM annihilation cross section in the non-relativisticlimit, for WIMP masses between 100 MeV and 105 GeV,which is stronger than the unitarity bound. [235].

Antimatter

Indirect searches of Dark Matter can be performedby looking at an exotic contribution in the spectra ofpositrons and antiprotons in cosmic-ray fluxes. Thesecharged messengers, contrary to gamma-rays and neutri-nos, do not provide information on the location of their

source because of the interaction with the interstellarmagnetic fields.

Positrons in cosmic-rays mostly originate from the de-cay of charged pions and kaons produced in cosmic-rayinteractions with interstellar gas. Analytic treatmentsand numerical codes have been developed to describe thepropagation of cosmic rays, and to compute the amountof secondary cosmic rays, including positrons, producedby collisions of primary particles with the interstellarmedium (see e.g. [368] for a review about the cosmic-ray propagation in the Galaxy). The measurement ofthe positron fraction, i.e. the ratio of the positron fluxover the sum of the positron and electron fluxes, provides

an interesting tool to search for exotic positron sourcesin a region of a few Kpc from us.In 1994, the HEAT experiment has observed an excess

of the positron fraction, with respect to standard prop-agation models, at energies beyond 7 GeV [369]. Thisresult has been subsequently confirmed by further mea-surements obtained by HEAT [370] and recently by re-analysis of the AMS-01 data [371, 372]. WIMP annihila-tions have been proposed to explain this enhancement, inparticular in the framework of supersymmetry [373380]and Kaluza-Klein Dark Matter [379, 381]. The spectralshape of the positron excess can be well reproduced byLSP annihilation models but a very high annihilation rateis necessary to match the correct normalization, requiringtherefore unnaturally large amounts of local dark mattersubstructures [378]. Instead, a modest boost factor isneeded for Kaluza-Klein Dark Matter, due to their largeannihilation rate to charged leptons, that leads to a largernumber, and harder spectrum, of positrons [379, 381].

The measurements of the positron fraction performedby several experiments, including AMS-01, CAPRICEand HEAT are in agreement with each other but thelarge uncertainties, as shown in Fig.8, do not allow todraw definitive conclusions on the nature of the GeV ex-


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Figure 8: Left: Positron fraction as a function of energy. Shown are the theoretical calculations for pure secondary production(solid and dashed lines) and for pure primary production from neutralino (m=336 GeV) annihilations (dotted line). Redcircles (squares) show a projection of the Pamela measurements after three years of data taking with (without) a neutralinocontribution. Right: Energy spectrum of anti-protons. Shown are the theoretical prediction for secondary (solid and dashedlines) and primary production from neutralino (m=964 GeV) annihilations (dotted line). From Ref.[382].

cess. However, the situation may be clarified soon thanksthe larger positron statistics that will be obtained by thePAMELA satellite [382], which was launched in June2006, and the AMS-02 experiment [383], which shouldbe launched in the near future.

Dark Matter annihilations in the galactic halo mayproduce antiprotons and the possible imprint on cosmicrays measurements, both at low and high energies, hasbeen extensively studied [384390]. However the datacollected by several experiments, in particular BESS,CAPRICE and BESS-Polar, agree with the calculations

of the positron production by cosmic rays, showing noevidence for primary antiprotons [391] (Fig.8 shows datafrom recent experiments and also theoretical calculationsfor pure secondary/primary antiproton production). Fur-thermore, these results cannot be easily translated intoconstraints on DM candidates, due to the large uncer-tainties on the antiproton flux induced by the propaga-tion parameters [384, 385]. Much more data will soonbe available thanks to Bess-Polar, PAMELA and AMS-02, in particular at high energies, where the contribu-tion from DM annihilations might be dominant for heavyenough WIMPs [390].

Despite the uncertainties in the propagation models,the study of anti-matter fluxes can sometimes providea useful diagnostic tool for specific DM scenarios. Forinstance, Bergstrom et al. have investigated the DMannihilation model of Ref.[392], proposed to explain theEGRET excess of the diffuse galactic gamma ray back-ground, by computing the associated primary antiprotonflux from WIMP annihilations. They were then able torule out the scenario since the anti-proton flux was foundto grossly exceed the measured anti-proton flux [393].The model of Ref.[392] might still be made compatible

with observations allowing for an anisotropic diffusion ofcosmic rays [394].

Multi-wavelength approach and X-Rays emission

More in general, a multi-messenger, multi-wavelengthanalysis provides more robust results than the simpler fit-the-bump approach. For example, when interpreting theorigin of a gamma-ray source, one may study the associ-

ated synchrotron, bremsstrahlung and Inverse Comptonemission, produced by electrons and positrons inevitablyproduced along with gamma-rays in DM annihilations.These signals can in principle extend over a wide rangeof wavelengths, all the way from radio to gamma-rays.The limited field of view of radio and X-ray experimentsmakes it easier to perform multi-wavelength studies ofa restricted number of candidate sources, such as theGalactic center [299, 395, 396] galaxy clusters [397, 398],and dwarf galaxies [399, 400]. Radio and X-ray observa-tions are powerful techniques to search for WIMP anni-hilations and they can provide constraints even more re-strictive than those inferred from gamma-rays [396, 400].

X-ray observations provide useful constraints also onDM candidates other than WIMPs. For example, sterileneutrinos (see Sec. II) can decay into active neutrinos and photons with energies in the X band: s + ,E = ms/2. Therefore, X-rays observations constrain thesterile neutrino mass ms and their mixing angle with ac-tive neutrinos. Assuming then a production mechanism(see e.g. [72]), these limits can be turned into an up-per bound on the particle mass. The observation of thecosmic X-ray background requires ms < 8.9 keV (95 %C.L.) [401], but more stringent constraints are obtained


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from individual objects, such as galaxies or clusters ofgalaxies. For example the XMM-Newton observations ofVirgo A impose m < 10.6 keV (95 % C.L.) [402] and ananalysis of the Virgo and Coma cluster data further re-strict the bound to m < 6.3 keV (95 % C.L.) [402, 403].A significant improvement has been obtained from X-ray observations of the Andromeda Galaxy: m < 3.5keV (95 % C.L.) [404]. These results, combined with the

lower limit on the sterile neutrino mass inferred by mea-surements of small scale clustering (see Sec. II), rule outsterile neutrinos in this scenario as the dominant DarkMatter component, constraining their fraction on the to-tal Dark Matter amount to be fs 0.7 at the 2 level[405].

However, sterile neutrinos remain viable for alternativeproduction mechanisms, such as Higgs decays in modelswith an extended Higgs sector [406], or a resonant pro-duction in presence of a very large lepton asymmetry inthe Universe, L >> 1010 [73, 74].

X. CAN IT BE PROBED EXPERIMENTALLY?

The last requirement for a particle to be a good DMcandidate, is that such particle can be probed experimen-tally, in the sense that it can be directly detected or thatconvincing evidence for it, or for the theoretical scenarioit arises from, can be obtained with present or futureexperiments. The nature of this requirement is differentfrom that of the nine other conditions discussed above,where we have essentially required that DM scenarios arenot in conflict with existing experiments and observa-tions. Here we add the requirement of discoverability,that reflects our prejudice on what can be considered agood theory in science.

A. Probing SuperWimps

DM particles may interact far less than weakly, andthey could evade all conventional dark matter searches.For example, the supersymmetric gravitino, which onlycouples gravitationally, has been proposed as a well mo-tivated Dark-Matter candidate. The LKP graviton inUED, axions and axinos are other examples of super-weakly interacting massive particles (or super-WIMPs),i.e. Dark Matter candidates that can be extremely diffi-cult or impossible to observe in direct and indirect DarkMatter searches because of their very suppressed inter-actions [30, 410, 411].

However, the next to lightest supersymmetric particle(NLSP) could be long-lived, for example the stau NLSPlifetime is of order 106 sec, for gravitino masses of 10GeV [412]. If the NLSP is a neutralino, this scenariomay have an interesting collider signature, similar to thecase of neutralino LSP, because the decays of the NLSPneutralino may occur outside the detector. In this case,the sparticle spectrum may allow the discrimination be-

tween gravitino and neutralino LSP through the analysisof selected decay channels [413], or spins [414], even ifthis programme may be challenging for the LHC.

A stau NSLP scenario, as possibly realized in super-gravity models [413], offers a more promising opportunityto uncover gravitino Dark Matter models at colliders.The charged NLSP particle particle would have distinc-tive time-of-flight and energy-loss signatures that might

enable to reconstruct its mass with high accuracy, at alevel of per cent or even smaller [413, 415, 416]. A stauwould be produced at the end of every supersymmetriccascade and being strongly ionizing, if it is sufficientlyslow moving, it may be stopped inside the detector orin a surrounding water tank or calorimeter detector. Inparticular, it has been suggested that up to O(103) andO(104) charged NLSP can be trapped per year at LHCand ILC respectively, by placing a 10 Kton trap aroundthe detector [412, 416, 417].

Collecting a large number of stau, it would be possibleto measure the stau lifetime and kinematically determinethe gravitino mass, from the dominant decay + g.The measurements of gravitino and stau masses would al-low to compute the stau lifetime predicted by the super-gravity model and if it matches the experimental value,one would obtained a strong evidence for supergravityand for gravitino LSP [412, 414, 417].

Detailed simulations have been performed to study thegravitino Dark Matter scenario at LHC and ILC (e.g.[413, 415, 418]). In particular, at ILC, with an integratedluminosity of 200 fb1 at

s = 420 GeV, thousands of

stau will be stopped within the hadron calorimeter, al-lowing a reconstruction of the gravitino mass with anaccuracy of few GeV and a determination of the Planckmass, for a test of supergravity predictions, at a level of10 % [418].

As discussed in Sec.IV, for NLSP and gravitino massesin the GeV range, BBN bounds severely constrain thecase of neutralino and stau NLSP, while a sneutrinoNLSP is perfectly viable. In the latter case, the NLSPdecay is invisible, but the predicted small sneutrino-staumass splitting may produce interesting collider signa-tures, with soft jets or leptons in the final states [419].Finally, models of gravitino DM with broken R-parity,may also be searched for in accelerators [420422], butalso through indirect detection [423, 424].

Axinos

Axinos appear in supersymmetric models implement-ing the Peccei-Quinn mechanism for solving the strongCP problem, and correspond to the fermionic superpart-ner of the axion. Their mass ranges between the eVand the GeV scale, and they can be efficiently producedthrough thermal and non-thermal processes in the earlyUniverse under the form of cold, warm or even hot Darkmatter (see e.g. Refs. [410, 425427] and referencestherein).


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In particular, axinos cold Dark Matter is achieved formasses m 100 keV and for low reheating temperaturesTR 106 GeV, in contrast with gravitino CDM that canallow for higher values ofTR, such as TR 1010 GeV formg 1 TeV.

Axino couplings are suppressed by the inverse of thePeccei-Quinn breaking scale, fa 109 GeV, and there-fore these particles are extremely weakly interacting. As

a consequence, similarly to the case of gravitino LSP, thelifetime of the NLSP can be long, and the strong boundsfrom Big Bang Nucleosynthesis avoided [427].

The direct production of axinos at colliders is stronglysuppressed but they can be profusely produced by thedecays of the NLSP particles. As in the case of gravitino,a large number of sleptons NLSP could be collected, inorder to measure the NLSP lifetime and to reconstructthe axino mass and the Peccei-Quinn scale fa (see [426]and references therein).

However, the problem may arise of discriminating be-tween axino and gravitino LSP models. For instance, astau NLSP with a lifetime within the range 0.01 s - 10

0711.4996v2 dark matter candidates 10 points

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