Dark Matter Candidates: A Ten-Point Test Marco Taoso1,2, Gianfranco Bertone2, and Antonio Masiero1 1 INFN, Sezione di Padova, via Marzolo 8,Padova,35131,Italy and 2 Institut d’Astrophysique de Paris, UMR 7095-CNRS, Université Pierre et Marie Curie, 98 bis Boulevard Arago 75014, Paris, France An extraordinarily rich zoo of non-baryonicDark Matter candidates has been proposed over the last 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 DM searches? VIII.) Is it compatible with gamma-ray constraints? IX.) Is it compatible with other astrophysical bounds? X.) Can it beprobed experimentally? 8 0 0 2 INTRODUCTION 1. Does it match the appropriate relic density? n 2. Is it cold? a To identify the nature of Dark Matter is one of the J mostimportantopenproblemsinmoderncosmology. Al- 3. Is it neutral? 5 though alternative explanations have been proposed in 2 terms of modified gravity, the discrepancies observed in 4. Is it consistent with BBN? astrophysicalsystemsrangingfromgalactictocosmolog- 5. Does it leave stellar evolution unchanged? ] h ical scales appear to be better understood in terms of p a dark, yet undiscovered, matter component, roughly 6 6. Is it compatible with constraints on self- - times more abundant than ordinary baryons in the Uni- interactions? o verse (see Refs. [1, 2] for recent reviews). r 7. Is it consistent with direct DM searches? t The possible connection of this exciting problem with s a New Physics beyond the Standard Model has prompted 8. Is it compatible with gamma-ray constraints? [ theproliferationofDarkMattercandidates,thatarecur- 2 rently being searchedfor in animpressive arrayof accel- 9. Is it compatible with other astrophysical bounds? v erator,directandindirectdetectionexperiments. Asour 10. Can it be probed experimentally? 6 understanding of particle physics and astrophysics im- 9 proves,weaccumulate informationthatprogressivelyre- The distinction between gamma-ray constraints and 9 duces the allowedregionsin the DM particles parameter 4 other astrophysical bounds, in points 8) and 9), is rather space. . artificial,anditsimplyreflectstheprivilegedroleofpho- 1 Here,wepresenta10-pointtestthatnewparticleshave tons in astrophysics,since they propagate along straight 1 to pass in order to be considered good DM candidates. lines(unlikechargedparticles),andtheycanbedetected 7 0 We will work under the assumption that a single DM with better sensitivity than, say, neutrinos. The fact of : species dominates the DM relic density, while contribu- considering gamma-ray photons is then due to the fact v tion from other species is subdominant; it is straightfor- that the decay or annihilation of some of the most com- i X ward to generalize the discussion to the case of multi- mon candidates falls in this energy range. r component DM. Furthermore, we will consider a stan- We also note that, strictly speaking, the last point is a dard ΛCDM cosmological model, although we discuss not really a necessary condition, as DM particles could the consequences of more general models, allowing for well be beyond the reach of current and upcoming tech- instance a non-standard expansion history at the epoch nology. However,measurableevidenceisanessentialstep of DM freeze-out. of the modern scientific method, and a candidate that Each of the following ten points, that represent neces- cannot be probed, at least indirectly, would never be ac- saryconditionsforaparticletobeconsideredagoodDM cepted as the solution to the DM puzzle. candidate,willbediscussedinadedicatedsection,where we will review the literature on the subject and present the most recent results. In each section we will discuss I. DOES IT MATCH THE APPROPRIATE how robust the constraints are, especially for those that RELIC DENSITY? heavily rely on astrophysicalquantities such as the local DM density and velocity distribution, or the extrapola- The analysis of the Cosmic Microwave Background tion of DM profiles at the center of galactic halos, often (CMB) anisotropies is a powerful tool to test cosmologi- affected by large uncertainties. cal models, and to extract the corresponding cosmologi- AparticlecanbeconsideredagoodDMcandidateonly calparameters. For instance,the angularpositionof the ifapositiveanswercanbegivetoallthefollowingpoints: peaksinthepowerspectrumoftemperatureanisotropies 2 is a sensitive probe of the curvature of the Universe (see below the expansion rate of the Universe. For a non- e.g. [3, 4] for a review and a more extended discussion). relativistic particle at decoupling, the number density ThepowerspectrumofCMBanisotropiesisfittedwithin overthe entropy density remains frozen,i.e. the thermal the StandardCosmologicalModel with a number or free relic freezes-out. The evolution of the number density of parameters that depends onto the priors. a generic species χ in the Universe, is described by the The best fit of the three years WMAP data, with a 6 following Boltzmann equation: parametersflatΛCDMmodelandapower-lawspectrum of primordial fluctuations, gives [5] n˙eq +3Hn=−hσannvi n2−n2eq . (cid:2) (cid:3) Ωbh2 =0.0223+−00..00000079 ΩMh2 =0.127+−00..000173 The second term in the l.h.s of the equation takes into account the dilution of the number density due to the for the abundance of baryons and matter, respectively. expansionoftheUniverse. σ v isthethermalaverage ann The normalized abundance Ω is defined as Ω = ρ /ρ , h i i i i c of the annihilation cross section times velocity and it is where ρ is the critical density, and the scaled Hubble c parametrizedwithanon-relativisticexpansioninpowers parameter h is defined as H0 ≡ 100h km s−1 Mpc−1. ofv2,as: σannv =a+b v2 + ( v4 ) a+6b/x,with A joint-likelihood analysis on a larger data-sets in- h i h i O h i ≃ x m/T. cluding, besides WMAP3, also small scale CMB ex- ≡ n istheequilibriumdensityofWIMPsintheplasma eq periments (BOOMERang, ACBAR, CBI and VSA), attemperatureTandforanon-relativisticspecieisgiven L(HarSgTe/-SGcOalOeDStSr,ucStuNrLesS)(,SDfuSrSt,h2erdFsGtrRenSg)tahnednsSutpheerNcoovna- byneq =g(m2πT)3/2e−mTχ, whereg denotes the numberof degrees of freedom of χ and m is the WIMP mass. straints to [6] χ The Boltzmann equation can be solved integrating it Ω h2 =0.0220+0.0006 Ω h2 =0.131+0.004. in two extreme regions, long before and long after the b −0.0008 M −0.010 WIMP freeze-out (e.g. WIMP decoupling), and match- Note that the baryonicdensity is consistentwith the de- ing then the solutions. Skipping the calculation details, termination from big bang nucleosynthesis [7] that can be reviewed e.g. in [15], the relic density today for a generic WIMP χ is [1]: 0.017<Ω h2 <0.024 (95 % CL). b 1.07 109 GeV−1 x 1 For a new particle to be considered a good DM can- Ω h2 ≈ × f χ didate, a production mechanism that reproduce the ap- MPl √g∗f (a+3b/xf) propriatevalueoftherelicdensitymustexist. Moreover, 3 10−27 cm3s−1 to guarantee its stability, its lifetime must exceed the ≈ × . (1) σ v ann present age of the Universe. Taking in account the es- h i timates of the Hubble Space Telescope Key Project [8] where g∗f counts the relativistic degrees of freedom at and in agreement with the result derived by WMAP, thedecoupling,M isthePlanckmassandx m /T H0 =72 3 (statistical) 7 (systematic) km s−1Mpc−1, with T the freezeP-olut temperature. The lasft ≡line χis anf we requir±e a lifetime τ &±4.3 1017 s. order off magnitude estimate and it shows that the relic × In many proposed extensions of the Standard Model abundance of a non relativistic decoupled specie strictly of particle physics, the stability of the DM particle is depends on the annihilation cross section at freeze-out ensured by imposing a symmetry that forbids the decay [13]. Furthermore, it has to be noticed that the annihi- of DM into Standard Model particles. For example, lation cross section, for a particle of given mass, has a R-parity in Supersymmetry models (SUSY) [9, 10], maximum, imposed by the partial wave unitarity of the K-parity in Universal Extra Dimensions Models (UED) S matrix, σ v 1/m2 [35, 36]. Thus, with the [11], and T-parity in Little Higgs Models [12], prevent use of Eq.h1,anthneirmeqaxuir∼ementχΩ h2 .1 implies the fol- M the lightest new particle in the respective theories from lowing constraint on the mass of the DM particle, also decay (see for example Ref.[13] for a detailed discussion called ”unitarity bound” [35] on SUSY DM and Ref.[14] for a review on UED DM). m .340 TeV. DM Applying the more stringent constraint, obtained by Thermal relics WMAP, the upper bound on m becomes: DM Among the best DM candidates, there is a class of m .120 TeV. DM particles called WIMPs (for weakly interacting massive particles), that are thermal relics and naturally achieve However, this constraint was derived under the as- the appropriate relic density. sumption that particles were in thermal equilibrium in The scenario goes as follows: the WIMP is in thermo- the early universe, thus it applies only to thermal relics, dynamic equilibrium with the plasma in the early Uni- and can be evaded by species which are non-thermally verse, and it decouples when its interaction rate drops produced. 3 γ γ quarks Leptons gluons All EW 0.5 0.5 0.4 0.4 2Ω h0.3 2Ω h0.3 0.2 0.2 0.1 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 γ(1) mass (TeV) γ(1) mass (TeV) Figure 1: Left: Relic Abundance of B(1) in the UED model as a function of its mass after including no coannihilation (black line), coannihilation with all leptons (blue) and all electroweak particles (red). For the cases with coannihilation, the solid and dashed lines are computed with a mass splitting δ = 0.01 and 0.05 respectively. Right: The same as in the left panel but 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 δ=0.01 and 0.05 respectively. From Ref.[22]. The standard computation of the thermal relic abun- the thermal history depicted above, and that they have dance discussed above presents three important excep- inherited the appropriate relic density through the de- tions,asithasbeenshown,followingpreviousideas[16], cayofamore massivespecies,thathas earlierdecoupled by Griest and Seckel [17]. They take place for WIMPs from the thermal bath. This is e.g. the case for Super- lying near a mass threshold, for annihilations near to a Weakly Interacting Massive Particles (SWIMP), such as pole in the cross section, or in presence of coannihila- theLSPgravitinoinSUSYandthefirstexcitationofthe tions. The last effect occur when a particle that shares graviton in UED, which are produced by late decays of aquantumnumberwiththe WIMP,isnearlydegenerate the next-to lightest particles (NLSP/NLKP) in the re- in mass with it. If the mass gap is low enough (roughly spective theories [30–33] and whose relic abundances are . 10%) the coannihilation reactions, involving WIMP simply the rescaled thermal relic densities of the NLPs: particles,cancontroltheWIMPabundanceandloweror mSWIMP enhance it. ΩSWIMP = ΩNLP. mNLP Full relic density calculations, including all coannihilations, have been performed e.g. for the supersymmetric Other production mechanisms may actually be con- neutralino,forwhichnumericalcodessuchasDarkSUSY comitant for such candidates, such as the production at [18]andmicrOMEGAs[19]arepubliclyavailable. Coan- reheating after the end of the inflationary era (see e.g. nihilationshaveadramaticeffectontherelicdensity,and [32,34]. See alsobelow fora briefdiscussionofgravitino they can lower it by a factor of up to several hundreds production). (see e.g. [20]). Coannihilations are also important in UED models, where the relic density of the firstexcited state of the B, which may be the lightest Kaluza-Klein particle (LKP) Other production mechanisms andaviableDMcandidate,maybe enhancedorlowered depending on the coannihilation channel [21–23]. See VeryheavyDMcandidates,suchasthe so-calledwim- Fig.1. pzillas, have been proposed, with masses as large as 1015 GeV, i.e. well above the unitarity limit (see e.g. Deviations from Standard Cosmology can substan- [37] for a review). For mechanisms that produce these tially change the picture. For example, due to the super-massive particles with Ω 1, departure from DM ∼ presence of scalar fields, the universe may undergo a thermal equilibrium is automatic [37], and the challenge periodofmuchhigherexpansionrateandthe relicabun- is not to overproduce them. Several mechanisms have dance of a WIMP may result increasedby severalorders beenproposed: forinstancetheycouldbecreatedduring of magnitude [24, 25]. Furthermore, the production of reheating after inflation, with masses a factor 103 larger entropy in the Universe after the WIMP decoupling than the reheating temperature [38], or during a pre- may dilute its abundance, e.g. due to out-of-equilibrium heating stage, with masses up to the Grand Unification decaysof non-relativisticparticles or to first-orderphase scale(1015 GeV) [39] orevento the PlanckScale [40], or transitions [26–29]. againfrombubblecollisionsiftheinflationexitisrealized by a first-order transition [41]. Another very interesting ItisalsopossiblethatDMparticlesdidnotexperience mechanismis ofgravitationalnature: wimpzillas maybe 4 created by amplification of quantum fluctuations in the MiniBoonecollaborationhasreporteditsfirstresults,ex- transition between the inflationary regime and the mat- cluding at 98% C.L. the two-neutrino appearance oscil- ter (radiation) dominated one, due to the nonadiabatic lationschemeobtainedfromLSNDdata[70]. The(3+1) expansion of the spacetime [42, 43]. This scenario can scheme,involvingone sterile neutrino specie, is excluded produce particles with mass of the order of the inflaton and also models with two or three sterile species are not mass and do not requirecouplings of wimpzillas with in- viable because of the tension between appearance and flaton or other particles. disappearance data [71]. These particles can be accomodated in existing theo- Sterile neutrinos may be produced in the early Uni- retical frameworks. For instance, stable or metastable versefromcollisionoscillationconversionsofactivether- bound states called cryptons arise in M-theory, and mal neutrinos. Their momentum distribution is signifi- other possibilities are contemplated in string theories cantly distorted with respect to a thermal spectrum due [44]. Furthermore, messenger bosons in soft supersym- totheeffectsofquark-hadrontransition,themodification metrybreakingmodelsmaybeverymassiveandinpres- ofthe neutrino thermalpotentialcausedby the presence ence of accidental symmetries in the messengers sectors, ofthermalleptonsandtheheatingofthecoupledspecies might be stable [45]. (seee.g. [72]forprecisecomputationofrelicabundance). Although wimpzillas have been invoked in top-down Moreover it has been proposed an enhanced resonant scenarios that seek to explain the origin of Ultra High production, in presence of a lepton asymmetry in the EnergyCosmicRays[43,46,47],thisinterpretationisto- early universe significantly higher than the baryonic one day problematic because it predicts a large photon com- [73, 74]. ponent in the UEHCRs spectrum, in disagreement with the recent results of the Auger experiment [48]. Several production mechanisms can act together to II. IS IT COLD? produce a given species, and its relic abundance receives contributions from each of them. The calculation The evolution of perturbations in the Universe de- depends on the details of the particle physics and pendsonthemicroscopicpropertiesofDMparticles. The cosmological models adopted. In the case of axions, standard picture, widely accepted, is that after equality, i.e. light pseudoscalar particles introduced to solve when the Universe becomes Matter Dominated, the DM the Strong CP Problem, the production mechanisms density perturbations begin to grow, and drive the os- in the early Universe are scattering in the hot thermal cillations of the photon-baryonic fluid around the DM plasma and possibly radiationby topologicaldefects like gravitational potential wells. Soon after recombination, axion-strings. Another relevant production mechanism baryonskinematicallydecouplefromphotonsandremain is the so-called misalignment: the axion field rolls trapped in DM potential wells. Their density perturba- towards its minimum, near the QCD epoch, and it ends tions then grow to form the structures that we observe with coherent oscillations that produce a Cold Dark today in the Universe (see for more details [4, 15]). Matter condensate. A lower bound on the axion mass can be inferred requiring that they do not overclose the Universe,buttheuncertaintiesinthecalculationoftheir production make the constraint rather weak (for recent Hot Dark Matter reviews of axions see [50, 51]). The imperfect coupling between baryons and pho- Asmentionedbefore,gravitinoscanbecopiouslyemit- tons at recombination leads to a damping of small scale ted by the decay of the NLP in SUSY but they can also anisotropies, also known as Silk damping [75]. A colli- be produced, during reheating, by inelastic 2 2 scat- → sionless species, moving in the universe from higher to tering processes off particles in the thermal bath and in lower density regions, also tends to damp the fluctua- some scenarios they can act as Cold Dark Matter can- tions above its free-streaming scale. This a key property didates (e.g. [52–57], see e.g. [58, 59] for more details of Hot Dark Matter, which consists of species which are and references on gravitino DM models). The efficiency relativisticatthetimeofstructuresformationandthere- of the production depends on the reheating temperature fore lead to large damping scales [76]. T so the bound on Ω translates into an upper limit R DM The prototype of HDM are Standard Model neutri- onT [34,55,60]. Inadditiontothermalproductionand R nos: they were thermally produced in the early Uni- latedecaysoftheNLSP,othernonthermalandinflation verse and they termodinamically decoupled again rela- modeldependentcontributionscanariseandchangecon- tivistic at T 1 MeV, leading to a relic abundance siderably the predictions [61, 62]. ∼ today that depends on the sum of the flavor masses, Sterile neutrinos, which arise naturally in theoretical 3 m = m : frameworks [63–66] or in the phenomenological νMSM ν i=1 νi P [67], have been proposed as a solution of the LSND anomaly [68], as explanation of the high pulsar veloci- m ties [69] and as Dark Matter candidates. Recently, the Ωνh2 = ν . (2) 90 eV 5 Their free-streeming length is [15]: However,theemergenceofsomediscrepancieshaslead some authors to question the CDM model and to pro- 30 eV pose alternative scenarios. For example, the number of λ 20 Mpc. FS ∼ (cid:18) mν (cid:19) satellite halos in Milky Way-sized galaxies, as predicted by simulations, exceeds the number of observed Dwarf Hot DM models are today disfavored (see e.g. [77] for galaxies [90, 91]. Furthermore, the rotation curves of a more complete discussion). For instance, the power low surface brightness (LSB) galaxies point to DM dis- spectrum of density perturbations should be suppressed tributions with constant density cores rather than the beyondthe free-streaminglengthofHDM particles,that cuspy profiles preferred by N-body simulations [92–95]. for neutrino masses in the eV range correspondsroughly An additional problem arises when considering the an- to the size of superclusters. Furthermore, HDM models gular momentum of dark matter halos: in simulations predict a top-down hierarchy in the formation of struc- gas cools at early time into small mass halos, leading to tures, with small structures forming by fragmentationof massivelow-angularmomentumcoresinconflictwiththe larger ones, while observations show that galaxies are observed exponential disks [96]. older than superclusters. Several astrophysical processes have been invoked in SmallamountsofHDMcanstillbetolerated,provided order to solve these problems, such as major mergers thatitiscompatiblewithlargescalestructureandCMB and astrophysicalfeedback[97]. The low efficiency of gas data. Assuming an adiabatic, scale-invariant and Gaus- cooling and star formation may decrease the number of sian power spectrum of primordial fluctuations, WMAP satellites in Milky Way-sized galaxies [98–100] and tidal data set an upper limit on the sum of light neutrino strippingmayhavedramaticallyreducedthesizeofthese masses [5] (or equivalently, through Eq. 2, on Ω ) ν substructures or disrupted a fraction of them [102, 103]. Furthermore, new ultra-faint dwarf galaxies have been m <2.11 eV (95 % CL). ν recently detected, alleviating the discrepancy between X CDMpredictionsandobservations[101]. Ithasalsobeen The combinationofdata from WMAP, largescale struc- pointed out that the measurements of the LSB galaxies tureandsmall-scaleCMBexperiments,furtherstrength- rotationcurvesmaysufferofobservationalbiases,forex- enstheconstraint,butitalsointroducespotentiallylarge ample due to the fact that DM halos are triaxials rather systematic effects [78–81]. A significantly improved con- than spherically symmetric [104]. Moreover, small devi- straint can been obtained combining Ly-α forest, CMB, ations of the primordial power spectrum from scale in- SuperNovae and Galaxy Clusters data [82, 83]: variance,the presence ofneutrinos [105] or astrophysical processes [106, 107] can sensibly affect the halo profiles. m <0.17 eV (95 % CL). ν Anyway,thelackofconvincingexplanationsofthe prob- X lemsdiscussedaboveleavesthedooropentoalternatives These limits can be applied to a generic hot Dark to the CDM scenario. Matter candidate, e.g. to thermal axions [51, 84, 85] or to hot sterile neutrinos [86]. Warm Dark Matter Cold Dark Matter To alleviate these problems, Dark Matter candidates with a strong elastic scattering cross section (SIDM) The standard theory of structure formation thus re- [108], or largeannihilationcrosssections[109] havebeen quires that Dark Matter is cold, i.e. it is made of par- proposed. IthasalsobeensuggestedthatDarkMatteris ticles that have become non-relativistic well before the warm, i.e. made of particles with velocity dispersion be- matter domination era, and that can therefore clump on tweenthat of HDM and CDM particles. The largerfree- smallscales. TheprototypeofcoldDMcandidatesisthe streaminglengthofWDM,withrespecttoCDM,reduces supersymmetric neutralino, whose free-streaming length the power at small scales, suppressing the formation of is such that only fluctuations roughly below the Earth smallstructures[110,111]. Forinstance,aWDMparticle mass scale are suppressed [87, 88]. CDM candidates can withamassof1keVandanabundancethatmatchesthe be heavythermalrelics,suchasthe aforementionedneu- correctDark Matter density, has a free-streaminglength tralino, but also light species, non-thermally produced, of order of galaxy scales λ 0.3 Mpc [112]. Measure- FS ∼ like axions (see Sec. I for further comments and refer- ments of the growth of structures in galaxy clusters and ences). Ly-αforestcanthenbeusedtosetalowerboundonthe N-body simulations of ΛCDM Universe are in agree- massoftheWDMparticle. Gravitinosingauge-mediated ment with a wide range of observations, such as the supersymmetrybreakingmodelsmightbewarmDMcan- abundance of clusters at z 1 and the galaxy-galaxy didates, if they decouple when the number of degrees of ≤ correlationfunctions (see e.g. [89]forareview ofCDM), freedomwasmuchlargerthanattheneutrinodecoupling making it a successful and widely accepted cosmological [113]. However, explicit computations show that such a model. light thermal gravitino cannot account for all the DM 6 [112]. III. IS IT NEUTRAL? Another WDM candidate is the sterile neutrino, produced in the early Universe by oscillation conversion of Some extensions of the Standard Model of particle thermalactiveneutrinos,with a momentumdistribution physics predict the existence of new, stable, electrically significantly suppressed and distorted from a thermal chargedparticles, such as the lightestmessenger state in spectrum [67, 74, 114]. Its free-streaming scale is given gauge-mediatedsupersymmetrybreakingmodels[126]or by (see e.g. [27]) eventhe LSP inthe R-parityconservingMinimalSuper- symmetric Standard Model (MSSM). λFS ≈840 Kpc h−1 1 KeV

, Massive charged particles, independently on the con- (cid:18) m (cid:19)(cid:18) 3.15 (cid:19) s text they emerge, have been proposed as Dark Matter where ms is the mass state associated to the sterile fla- candidates by De Ru´jula et al and dubbed CHAMPs vor eigenstate. < p/T > is the mean momentum over [127]. Evaluating their thermal relic abundance, with temperature of the neutrino distribution and the ratio simple assumptions on the annihilation cross sections, < p/T > /3.15 ranges from ≈ 1 for a thermal WDM theauthorsfoundaviablemassrangeof 1 1000 TeV. particle to ≈0.9, for a non-thermalsterile neutrinos dis- They also pointed out that a positively c∼har−ged particle tribution. X+ cancaptureanelectrontoformaboundstatechem- The suppression of the power spectrum by a ther- ically similar to an heavy hydrogen atom. An X− can mal WDM of a given mass mWDM, is identical to that instead bind to an α++ particle and an electron, result- produced by sterile neutrinos of mass ms derived by ingagaininaheavyhydrogen-likeatom,oralternatively [112, 115]: it can capture a proton to produce a bound state called neutralCHAMP.ThedifferentbehaviorsofCHAMPsand mWDM 4/3 0.25(0.7)2 1/3 neutralCHAMPs lead to different bounds on their abun- m =4.43 KeV . s (cid:16) 1 KeV (cid:17) (cid:18) ΩWDM (cid:19) dance. Note also that De Ru´jula et al. concluded that X− would emerge from Big Bang Nucleosynthesis pref- This one-to-one correspondence allows to translate the erentially in the form of neutralCHAMPs [127]. boundsonsterileneutrinostoagenericthermalrelicand GalactogenesismodelsprovideconstraintsontheDark viceversa. Matter interactions, in particular of CHAMPs. The en- A detailed analysis of the production of sterile neutri- ergy loss timescale in this case is in fact dominated by nos and of the evolution of their perturbations, as well Coulomb scattering off protons, and it must be longer as a comparison with the measured matter power spec- than the dynamical timescale for galaxy formation. In trum,havebeenperformedinRefs.[112,116–119]). The Ref. [127], the authors concluded that only CHAMPs resulting lower limits on the mass of the WDM particles heavier than 20 TeV are able to remain suspended in strongly depend on the dataset used in the analysis. For the halo, and to be therefore rare on Earth. This es- example, in [116], a combination of the SDSS 3D power- timate disagree with that obtained by Dimopoulos et spectrum andSDSS Ly-α forestallowedto constrainthe al who found, for the same considerations, the limit sterile neutrino mass to M > 105 TeV [128]. It has also been proposed that X m 1.7 KeV (95 %CL), shock accelerations in supernovae could eject CHAMPs s ≥ from the disk and reinject them back to the halo or out that translates in terms of a thermal WDM particle to ofthe galaxy[128]. The latter possibility is energetically m 0.50 KeV. disfavored, while in the former case, it may lead to a WDM ≥ dangerous heating of the disk. The inclusion of high resolution Ly-α data makes the One of the most stringent bounds on the CHAMPs constraint even stronger, even if it has been pointed out abundance comes from searches of anomalous heavy wa- that they may suffer of large systematic uncertainties ter: CHAMPs, being chemically identical to heavy hy- [112, 116]. drogen, can be trapped in oceans and lakes in the form More recently, very stringent bounds on the mass of of HXO. If one assumes, as in Ref. [127], that CHAMPs WDM particles have been obtained by different groups: heavier than 20 TeV remain suspended in the Galactic [118] halo and they provide the Galactic DM, taking an ac- cumulation time of 3 109 yr, comparable with the age m 14 KeV (95 % CL) (m 2.5 KeV) s WDM × ≥ ≥ of oceans, the abundance of CHAMPs in sea water is and [119]: predicted to be [129]: m 28 KeV (2σ) (m 4 KeV). s ≥ WDM ≥ nX 3 10−5 GeV Ω h2. X The delay of the reionization of the Universe also sets (cid:18)n (cid:19) ∼ × (cid:18)m (cid:19) H Earth X a constraintonthe WDM mass [120–122]. In the caseof sterileneutrinos,theX-raysproducedbytheirdecayscan If instead CHAMPs are present in the Galactic disk, modify the picture,enhancing the productionofmolecu- taking in account the density and velocity of the inter- lar hydrogen and releasing heat in gas clouds [123–125]. stellar gas, mostly hydrogen,the expected concentration 7 is [129]: n GeV X 6 10−5 Ω h2. X (cid:18)n (cid:19) ∼ × (cid:18)m (cid:19) H Earth X All the searches of anomalous hydrogen in sea water havefailedsothattheabundanceofCHAMPs,formasses in the range 100 GeV-1000 GeV is constrained to be n X 10−28 10−29, (cid:18)n (cid:19) ∼ − H Earth while it raises to (n /n ) < 10−20 for M 10 TeV X H X ∼ (see [130] for a compilation of upper bounds of heavy hydrogenfromseawatersearches). Asaresult,CHAMPs asDMcandidatesareruledoutinthemassrangeM X 10 104 GeV. ∼ Figure 2: Exclusion plot for CHAMPs (solid lines) and Neu- − NeutralCHAMPs would preferentially bind on Earth tralCHAMPs (dotted lines). Seetext for more details. to nuclei to form anomalous heavy isotopes. Null searches for these elements, covering a variety of nuclear species, constrainthe NeutralCHAMPs abundance to be the rate of energy deposition due to collisions must be <10−20 10−16forM 100 1000GeV[131](forfur- X smaller than the cooling rate, for clouds in equilibrium. − ∼ − therdetailssee[130]andreferencestherein). Theauthors It resultsthat CHAMPs with massesbelow 106 GeV are of Ref. [131], concluded that stable X− Dark Matter in ruled out because, for these particles, the expected cross the mass range 102 104 GeV is thus to be considered section with hydrogen is higher than the maximum al- − unlikely. lowed value [136]. CHAMPs are also constrained by balloon or satellites The various constraints on CHAMPs that we have experimentsforCosmicRaysstudies. Perletal,takingin discussed are summarized in Fig. 2. Even if the bounds account data from different experiments [128, 133, 134], are not completely model-independent, the combination excluded CHAMPs as Galactic Dark Matter in the mass of them basically rules out CHAMPs as DM. range2.4 103 5.6 107 GeVandneutralCHAMPsfor 105 4 ×107 G−eV[1×32]. The lowerlimit comesfromthe − × The above limits apply to particles with integer elec- requirement that particles penetrate the solar wind and tric charge, but theoretical frameworks have been pro- the energy deposition is above the experimental thresh- posedwhereparticleswithfractionaryelectricchargeex- old. The upper bound is obtained comparing the maxi- ist, also known as milli-charged particles [137–142]. For mum CHAMP flux atthe topof the atmosphere allowed ′ example,adding a new unbrokenU(1) gaugegroup,the bythe CRexperiments,with the localDMflux, whichis typically assumed to be φ 107(GeV/MX) cm−2s−1. photon and′ paraphoton can mix, and particles charged ∼ underU(1) canhaveasmallcouplingwithphotons[137]. In the atmosphere, a proton in a neutralCHAMP gets replaced very quickly by a 14N atom, and the exchange Moreover,realistic extensions of SM motivatedby string theory exist, that naturally implement this mechanism is followed by a MeV γ-ray emission from the excited 14NX− status. With the same argument explained [139]. Constraintsonmassandchargeofmilli-chargedparti- above,the observationallimits on γ-raysflux imply that neutralCHAMPsshouldbe heavierthan106 GeVifthey clescomefromavarietyofobservations,andinFig. 3we show the excluded regions in the parameter space (m , are to be the DM[128]. Further constraintsonCHAMPs q ǫ), with ǫ=q/e, obtained by Davison et al. [143]. come from deep underground experiments. The re- sponses of scintillators to monopoles and CHAMPs are Milli-charged particles can also affect CMB expected to be similar, since they are both slowly mov- anisotropies, and for this reason WMAP data can ing, highly ionizing and penetrating. In Ref. [132], the severelyconstraintheir cosmologicalabundance,atleast authors applied the upper limit on monopole flux, ob- in some regions of the milli-charged particle parameter tained from MACRO experiment, to the CHAMP case, space [144]. excluding the mass range 108 1020 GeV. Furthermore, searches of neutrino magnetic moment − Furtherconstraintscomefromstellarevolution,inpar- with reactor experiments exclude Dark Matter particles ticular it has been shown that CHAMPs can disrupt a with q >10−5e, for masses mq .1 keV [145]. neutron star in a short timescale, falling into its center TheresultofthePVLAScollaboration[146]havebeen and producing a Black Hole. This argument excludes tentativelyinterpretedintermsofmilli-chargedparticles CHAMPs with masses 102 1016 GeV [135]. In addi- with masses m 0.1 eV and fractional electric charge q tion,thepropertiesofdiffuse−interstellarcloudsconstrain ǫ 10−6 [139,14∼0,148],buttheexperimentalresultwas ∼ the interactions of halo particles with atomic hydrogen: notconfirmedafteranupgradeofthe PVLASapparatus 8 Figure 3: Excluded regions in the mass-charge plane for milli-charged particles. The constraints are relative to: RD Figure 4: Excluded regions in the SIMP mass versus SIMP- plasmon decay in red giants; WD plasmon decay in white nucleoncrosssectionplane. TheVioletareaisexcludedbythe dwarfs;BBNbigbangNucleosynthesis;SNSupernova1987A; Earth’s heat argument. See Ref.[165] and references therein. AC accelerator experiments; SLAC SLAC millicharged particle search; L Lamb Shift; Op invisible decay of ortho- positronium; DMDark Matter searches. From Ref. [143]. Big Bang Nucleosynthesis, while SIMPs collisions with Cosmic Rayscanproduce anobservableγ-rayflux [158]. [147]. The scattering of SIMPs off baryons also produces sub- Lightmilli-chargedparticles maylargelyaffect subeV stantial distortion of CMB anisotropies and of the large Cosmology. In particular, processes such as γγ qq¯ scale structure power spectrum [159]. The SIMPs abun- can distort the CMB energy spectrum, which has→been dance for the mass range 1 103 GeV, is also con- ∼ − measured with high sensitivity by FIRAS. A detailed strained by searches in terrestrial samples of gold and analysis has been performed in Ref. [149] and the au- iron [160]. thors reported the conservative upper bound ǫ . 10−7, Atmospheric and satellite experiments, originally in- for m . 1 eV, excluding in this way also the light tended for other purposes, have been used to investigate milli-charged particles proposed in Ref. [139, 140, 148]. high DM cross sections with baryonic matter. In particular, the results of the X-ray Quantum Calorimeter Inprinciple,DMparticlescouldhaveaSU(3) charge. experiment (XQC) allow to rule out a large portion of c For example, ”colored” candidates are naturally pre- the SIMP parameter space (Mχ, σχN), as discussed in dicted in SUSY models if the LSP is a squark [150] or Refs. [161, 162] and (more recently and with substantial a gluino [151, 152], or in gauge mediated SUSY break- changes with respect to previous analyses) in Ref. [163]. ing models, where messengers can be colored and stable Complementary constraints are obtained by under- [153], or in mirror models [154]. These ”heavy partons”, groundexperiments, which are sensitive to DM particles after the deconfinement temperature, T 180 MeV, are with small interactions. In fact, they are able to detect ∼ surroundedby aQCDcloudandconfinedinside hadrons SIDMparticlesiftheirinteractionswithordinarymatter formingacolorneutralboundstate[155]. Theseparticles arehighenoughtotriggeranuclearrecoilinthedetector canbeactivelysearchedforbyundergroundexperiments, butatthesametimelowenoughtoallowtheparticlesto indirect detection experiments or through the search of penetratetheEarthcrusttothedetector[164]. Recently, rare anomalous isotopes. Mack et al. have analyzed the effect of SIMP annihila- Since the proposal that DM might interact strongly tionsonEarth,showingthatasubstantialheatingofthe with ordinary matter (SIMP), regardless of the nature Earth’s core may occur, if the capture rate is efficient of the interaction [127, 128, 156], many candidates have [165]. This argumentrules outthe regionsof the param- beenputforward,butalsomanyconstraintsonthescat- eter space lying between astrophysical and underground tering cross section off nuclei, σ . detector constraints. χN Forexample,theSIMPsinteractionswithbaryonsmay To summarize the constraints on the SIMP scenario, disrupt the disk of spiral galaxies [156, 157]. Moreover, Fig. 4 shows the excluded areas in the SIMP parameter they may dissociate the light elements produced during space. The bounds leave no room for SIMPs as Dark 9 Matter candidates in a very large mass range. Since oftheotherlightelements). AtT 1MeV,therelativis- ∼ the neutron-neutron scattering cross section is of order tic species in the Standard Model are photons, electrons 10−25 − 10−24 cm2 and the expected value for colored andneutrinossowithNν neutrinofamilyg∗ =5.5+47Nν Dark Matter candidates is not far from this range ( see and for N =3 this gives 43/4. ν e.g. [166]), DM particles are thus unlikely to bring color Newrelativisticparticlescanbeaccountedforthrough charge. the introduction of an effective number of neutrinos: However,theseconstraintscanbeevadedbyverymas- sive composite dark matter candidates. For example 4 4 7 T 7 T macroscopically large nuggets of ordinary light quarks i i (N 3)= g + g , and/orantiquarks,with masses in the rangem 1020 4 ν− i(cid:18)T (cid:19) 8 i(cid:18)T (cid:19) 1033 GeV, can behave as collisionless cold dark∼matte−r, i=eXxtra b i=eXxtra f without contradicting observations [167]. where T parametrizes the energy density of the rela- i tivistic species and b (f) stands for bosons (fermions). A likelihood analysis, taking η and N as free param- ν IV. IS IT CONSISTENT WITH BBN? eters, and based on the abundance of 4He and 2H, con- strains the effective number of neutrinos to be [169]: Big Bang Nucleosynthesis (BBN) is one of the most 1.8 102 sec, when the energetic hadrons trigger danceof4Heisproportionaltotheration/panditsvalue the 4He dissociation. is related to the freeze-out temperature of the weak in- Accurate calculations, with the use of BBN codes, re- teractions and it is therefore sensitive to the expansion strictthe primordialabundance ofthe decaying particle, rate at that time. depending on its lifetime, mass and hadronic branching Since H g∗1/2T2, an increase of the relativistic de- ratio[174–178]. Theseresultscanbeappliedforinstance ∝ greesoffreedomg∗ withrespecttotheSMvalueleadsto to NLSP gravitinos: BBN requires an upper limit to afasterexpansionrate,thustoanearlierfreezeoutofthe thereheatingtemperature,whichcontrolstheprimordial neutrontoprotonratioandconsequentlytoahigher4He gravitino abundance, and in some cases the restrictions abundance (and in general it also affects the abundance could lead troubles to thermal leptogenesis and inflation 10 models [175, 177]. The difficulties can be circumvented per limit onthe energylossrate ofthe heliumplasma,ǫ, forexampleinthecaseofaheavygravitino,whichdecays [192]: well before BBN [179, 180]. Alternatively, the gravitino could be stable and play ǫ.10 erg g−1s−1 at T 108 K, ρ 2 105g cm−3, ≈ ≈ × the role of Dark Matter. In this case, the NLSP particle is typically long-lived,because of the extremely weak wherethevalueoftemperatureanddensityareappropri- interactions of gravitino, and its late decays can affect ate for Red Giant cores. In Horizontal Branch stars, en- BBN.Moreover,ithasbeenpointedoutthatifthe long- ergy losses speed up the helium burning rate, decreasing lived particles are charged, e.g the stau, they can form theirlifetimes,thatcanbemeasuredbynumbercounting boundstateswithlightelements,potentiallyoverproduc- in Globular Clusters. This argument provides another ing 6Li and 7Li [181–185]. However, these elements can bound on ǫ [192]: also be destroyed, alleviating the severe bounds on the ǫ.10 erg g−1s−1 at T 0.7 108 K, ρ 0.6 104g cm−3. CHAMPs abundance during BBN. ≈ × ≈ × A neutralino NLSP is excluded [186–188], while sneu- Inaddition,the coolingrateofWhite Dwarfs,inferred trino NLSP poorly affects BBN [189]. A stop NLSP is by their luminosity functions, is in agreement with the viable in some regions of the parameter space [190]. predictionsandthereforeanynewcoolingchannelhasto We note that these BBN bounds can be circumvented be subdominant. if the NLSP abundance is diluted due to a significant It is remarkable that the total number of neutrino de- entropy production [191]. tectedfromSN1987A,theirenergyandtheirtimedistri- bution, is in agreementwith expectations fromthe standard model which describes the core collapse of a star. V. DOES IT LEAVE STELLAR EVOLUTION Any further energy loss mechanismreduces the duration UNCHANGED? oftheneutrinoburstandcaninprinciplespoilthesuccess ofthemodel,leadingthereforetothefollowingboundon Stellar evolution provides a powerful tool to constrain ǫ [192]: particle physics, providing bounds that are often complementary to those arising from accelerator, direct and ǫ.1019 erg g−1s−1 at T=30 MeV, ρ=3 1014g cm−3. indirect Dark Matter searches. × If Weakly interacting particles are light, they may be All the arguments listed above provide upper limits producedinthehotplasmaintheinteriorofstars,andif to any additional energy loss rate and can be applied they escape without further interactions, they represent to constrain, for instance, the neutrino properties, the an energy loss channel for the star, possibly modifying graviton emission in theories with extra dimensions, as thestellarevolution. Suchparticlesmayalsobedetected well as models with right-handed neutrinos, sterile neu- on Earth, as was the case for neutrinos from SN 1987A, trinos, milli-charged particles, axions and other pseu- ortheycanbeindirectlysearchedforthroughtheirdecay doscalarparticles. Forinstance,updatedlimitsonaxions products. Here we describe the most importantobserva- fromstarsarereviewedinRef.[194]andtheimplications tional consequences (see Refs. [192, 193] for extensive of light Dark Matter or sterile neutrino Dark Matter on reviews). SupernovaecorecollapsearediscussedinRef. [195,196]. Stars as the Sun can be described as self-gravitating Moredetailsandreferencesforotherparticlephysicssce- gas in hydrostatic equilibrium, such that the gas pres- narios can be found in [192, 193]. sure equilibrates the gravitational force. A significant AswehaveseeninSec.III,themostrestrictivebounds energy loss produces a contraction of the system and an on the fractional charge of keV milli-chargedparticles ∼ increase of the burning rate of the stellar fuel, reducing come from stellar physics, as it was shown in Fig.3. the lifetime of the star and enhancing the neutrino flux. Theboundsdiscussedaboveapplytoparticlesthatare Moreover, exotic energy losses would modify the sound produced in the core of stars and that escape without speedprofile,whichisaccuratelymeasuredintheinterior losing energy, thanks to their weak interactions. How- of the Sun by means of helioseismic measurements. ever,ifthe particlesinteractstrongly,they undergomul- Globular Clusters are alternative interesting probes of tiplescattering,providingamechanismforenergytrans- stellar evolution models because they are gravitationally port, in competition with photons, electrons or convec- bound systems of up to a million stars, formed at the tion. This effect has been studied for keV-mass scalars same time, with the same chemical composition and dif- produced in the Sun, Horizontal Branch stars and Red fering only for their masses. The ignition of helium in Giants, constraining the interactions of these particles Red Giant stars is sensitive to the temperature and den- [197, 198]. sity of the helium core, and any energy loss channel in- Moreover, the energy transport channel, provided by evitablytendstodelayit,resultinginmoremassivecores theWIMPstrappedintheSun,maycoolitsinteriorand andproducingobservationalconsequences,suchasanen- decrease the neutrino flux. This idea was proposed in hancement of star brightness. Therefore,observations of the past as a solution of the solar neutrino problem and Red Giants in Globular Clusters allow to derive an up- WIMPs with masses and cross sections suitable for this

Dark Matter Candidates: A Ten-Point Test

Similar Dark Matter Candidates: A Ten-Point Test