Dark matter particles in the galactic halo

ISSN 1063-7788, Physics of Atomic Nuclei, 2009, Vol. 72, No. 12, pp. 20762088. c Pleiades Publishing, Ltd., 2009.

ELEMENTARY PARTICLES AND FIELDSTheory

Dark Matter Particles in the Galactic Halo*

R. Bernabei1)**, P. Belli1), F. Montecchia1), F. Nozzoli1), F. Cappella2),A. dAngelo2), A. Incicchitti2), D. Prosperi2), R. Cerulli3), C. J. Dai4),H. L. He4), H. H. Kuang4), J. M. Ma4), X. D. Sheng4), and Z. P. Ye4)

Received January 19, 2009

AbstractArguments on the investigation of the Dark Matter particles in the galactic halo are addressed.Recent results obtained by exploiting the annual modulation signature are summarized and the perspectivesare discussed.

PACS numbers: 29.40.Mc, 95.30.Cq, 95.35.+dDOI: 10.1134/S1063778809120114

1. INTRODUCTION

The problem of the existence of Dark Matter (DM)in our Universe dates back to the astrophysical ob-servations at the beginning of past century, but thepresence of DM in our Universe has been denitivelyaccepted by the scientic community only about 40years later, when two groups performed systematicmeasurements of the rotational velocities of celestialbodies in spiral galaxies. After the 1970 many otherobservations have further conrmed the presence ofDM in the Universe and, at present, the measure-ments are mainly devoted to the investigation of thequantity, of the distribution (from the cosmologicalscale down to the galactic one) and of the nature ofthe DM in the Universe. Measurements of the cos-mic microwave background temperature anisotropyby WMAP [1], analyzed in the framework of the BigBang cosmological scenario, support a density of theUniverse () equal to 1, further crediting that most ofthe Universe is dark. It has also been suggested fromobservations on the supernovae Ia at high red-shiftas standard candles that about 73% of might be inform of dark energy [2]; the argument is still underinvestigation and presents some problems on possi-ble theoretical interpretations. However, even in thisscenario (where the matter density in the Universewould be m 0.3 [1, 3], value also supported by

The text was submitted by the authors in English.1)Dipartimento di Fisica, Universita` di Roma Tor Vergataand INFN, Sezione di Roma Tor Vergata, I-00133 Rome,Italy.

2)Dipartimento di Fisica, Universita` di Roma La Sapienzaand INFN, Sezione di Roma, Italy.

3)Laboratori Nazionali del Gran Sasso, INFN, Assergi, Italy.4)IHEP, Chinese Academy, Beijing, China.**E-mail: [email protected]

observations on globular clusters) large space for DMparticles in the Universe exists. In fact, the luminousmatter can only account for a density 0.005 andthe baryonic DM for 0.04. On the other hand, thecontribution of DM particles relativistic at the decou-pling time (such as relic neutrinos) is also restrictedto be 0.01 by considerations on large scale structureformations [4]. Thus, most of the DM particles in theUniverse, relics from the Big Bang, were nonrelativis-tic at decoupling time. The detection of these particleshas motivated the development of the eld of theirdirect detection in underground activities (see later).The DM candidate particles have to be neutral, stableor quasi-stable (e.g., with a time decay of order ofthe age of the Universe) and have to weakly interactwith ordinary matter. These features are respected bythe axions, by a class of candidates named WIMPs(having phenomenology similar among them, but notidentical), by Light Dark Matter particles or parti-cles in the MeV scale, by the light ( keV mass)bosonic candidate (either with pseudoscalar or withscalar axion-like coupling), etc. Therefore possibleDM candidates range from heavy particles, such asneutralino or sneutrino from SUSY models, KaluzaKlein particles from theories with extra dimensions,mirror matter, heavy neutrinos, etc. . . . to lighter par-ticles such as keV-scale sterile neutrino, axino, grav-itino, moduli elds, majorons, familons, etc. . . . Justfor example we mention the case of the WIMP classof DM candidate particles, which can span from lowto high mass candidates with phenomenology welldierent from each other. In particular, many possiblescenarios exist for the WIMP interaction with ordi-nary matter: (i) mixed SI&SD (spin-independent andspin-dependent) coupling; (ii) dominant SI coupling;(iii) dominant SD coupling; (iv) preferred SI inelas-tic scattering; (v) dominant electron interaction, etc.

2076

DARK MATTER PARTICLES 2077

Therefore, following these interactions the nuclearand/or electron recoils can produce signals in suitabledetectors. In addition, electromagnetic contribution ispresent for WIMPs also in case the interaction withnuclei is assumed to be dominant since excitation ofbound electrons in scatterings on nuclei can occur(the well-known Migdal eect). Furthermore, thereexist also candidates, as light bosons, whose directdetection process in the target material is based onthe total conversion into electromagnetic radiation ofthe mass of the absorbed bosonic particle; thus, inthese processes the target nuclei recoil is negligibleand it is not involved in the detection process at all.Other candidates, as the Light Dark Matter particlesor particles in the MeV scale, can also produce sig-nals in the detector due to nuclear recoils and/or toinduced electromagnetic radiation. It is worth notingthat those signals, whose not negligible or even wholecontribution is of electromagnetic nature, cannot bedetected in all the other activitiessuch as those us-ing bolometer/ionization double read-out and thoseusing double phase liquid noble gases (see later)that apply rejection procedures of the electromagneticcomponent of the counting rate. Let us also note thatresults obtained with dierent target materials and/ordierent approaches cannot intrinsically be directlycompared among them even when considering thesame kind of candidate and of coupling, although ap-parently all the presentations generally refer to crosssection on nucleon. Phenomenological properties ofsome basic interaction mechanisms induced by DMparticles are discussed, for instance, in [513] and inliterature.

Summarizing, in the Standard Model of particlePhysics, no particle can be a suitable candidate asDM; thus, the eld of the direct detection of DMparticles in the galactic halo is investigating a newwindow beyond the Standard Model.

2. SIGNATURES FOR DM PARTICLESIN THE GALACTIC HALO

To obtain a reliable signature to point out thepresence of DM particles in the galactic halo, it isnecessary to follow a suitable model-independent ap-proach. In principle, three main possibilities exist;they are based on the correlation between the dis-tribution of the events, detected in a suitable under-ground setup, with the galactic motion of the Earth.

The rst one, which applies to WIMP/WIMP-like candidates, correlates the nuclear recoil direc-tion with that of the Earth velocity. This direction-ality signature is, however, dicult to exploit in thepractice mainly because of the technical dicultiesin reliably and eciently detecting the short recoiltrack. Few R&D attempts have been carried out so

WIMP mean

directionWIMP mean

directionN

Zenith

c

' axis

b

axis

42

35

13

AnthraceneLNGS

Fig. 1. Schematic representation of the experimentalapproach considered in [17] to investigate the correla-tion between the recoil direction and the Earth velocitydirection in the particular case of WIMP/WIMP-likeDM candidates by using anisotropic scintillators. Theanisotropic scintillator is placed ideally at LNGS withc axis in the vertical direction and b axis pointing tothe North. The area in the sky from which the WIMPsare preferentially expected is highlighted. (For detailssee [17].) Obviously, this approach is insensitive to DMcandidates whose detection does not invoke nuclear re-coils.

far such as, e.g., [14, 15], while a suggestionbasedon the possible use of anisotropic scintillatorswasoriginally proposed in [16] and revisited in [17]. As anexample, Fig. 1 shows a schematic representation ofthe experimental approach discussed in [17].

A second approach for WIMP/WIMP-like can-didates correlates the time occurrence of each eventwith the diurnal rotation of the Earth. In fact, a di-urnal variation of the low energy rate in WIMP directsearches can be expected during the sidereal day sincethe Earth shields a given detector with a variablethickness, eclipsing the WIMP wind [18]. However,this eect can be appreciable only for relatively highcross-section candidates and, therefore, it can onlytest a very limited range of halo density. For a recentexperimental result see, e.g., [19]. As an example,Fig. 2 shows the dependence of (the angle denedby the Earth velocity in the galactic frame with thevector joining the center of the Earth to the positionof the laboratory) on the sidereal time at the locationof the Gran Sasso National Laboratory (LNGS).

The third possibility, which is the only feasibleone at present and which is sensitive to wide rangesboth of DM candidates and of interactions, is theDM annual modulation signature. This signature ex-ploits the eect of the Earth revolution around theSun on the number of events induced by the DMparticles in a suitable low-background setup placeddeep underground. In fact, as a consequence of its

PHYSICS OF ATOMIC NUCLEI Vol. 72 No. 12 2009

2078 BERNABEI et al.

40

0 10

, deg

Sidereal time, h20

80

Fig. 2. Schematic description of the approach which cor-relates the time occurrence of each event with the diurnalrotation of the Earth. The angle (dened by the Earthvelocity in the galactic frame with the vector joining thecenter of the Earth to the position of the laboratory) as afunction of the sidereal time; here the case for the LNGSof the INFN is considered [19].

annual revolution, the Earth should be crossed by alarger ux of DM particles around 2 June (whenits rotational velocity is summed to the one of thesolar system with respect to the Galaxy) and by asmaller one around 2 December (when the two ve-locities are subtracted). This oers an ecient model-independent signature, able to test also a large in-terval of cross sections and of halo densities; it isnamed DM annual modulation signature and wasoriginally suggested in the middle of 1980 by [20].

The expected dierential rate as a function ofthe detected energy, dR/dE (see [713] for somedetailed discussions), depends on the DM particlevelocity distribution and on the Earths velocity inthe galactic frame, ve(t) (see Fig. 3). Projectingve(t) on the galactic plane, one can write: ve(t) =v + v cos cos (t t0). Here v is the Sunsvelocity with the respect to the galactic halo (v v0 + 12 km/s and v0 is the local velocity whose valueis in the range 170270 km/s [21, 22]); v = 30 km/sis the Earths orbital velocity around the Sun on aplane with inclination = 60 with the respect to thegalactic plane. Furthermore, = 2/T with T = 1 yrand roughly t0 2 June (when the Earths speedis at maximum). The Earths velocity can be con-veniently expressed in unit of v0: (t) = ve(t)/v0 =0 + cos (t t0), wheredepending on the as-sumed value of the local velocity0 = 1.041.07is the yearly average of and = 0.050.09.Since 0, the expected counting rate can beexpressed by the rst-order Taylor approximation:

dR

dE[(t)] =

dR

dE[0] (1)

+30 km/s

Earth

30 km/s

Sun

v

60

Fig. 3. Schematic view of the Earth motion around theSun.

+

(dR

dE

)=0

cos (t t0).

Averaging this expression in a kth energy interval oneobtains:

Sk[(t)] = Sk[0] +[Sk

]0

(2)

cos (t t0) = S0,k + Sm,k cos(t t0);the contribution from the highest order terms isless than 0.1%. Hence, S0 and Sm are the time-independent expected counting rate and the modu-lation amplitude, respectively; the k index points outthat the average has been made in the kth energyinterval. The DM annual modulation signature is verydistinctive since it must simultaneously satisfy all thefollowing requirements: (i) the rate must contain acomponent modulated according to a cosine function;(ii) with one year period; (iii) a phase that peaksroughly around 2 June; (iv) this modulation mustonly be found in a well-dened low-energy range,where DM particle induced events can be present;(v) it must apply only to those events in which just onedetector of many actually res (single-hit events),since the DM particle multi-interaction probabilityis negligible; (vi) the modulation amplitude in theregion of maximal sensitivity must be 7% for usuallyadopted halo distributions, but it can be larger in caseof some possible scenarios such as, e.g., those in [6,23]. Only systematic eects able to full these sixrequirements and to account for the whole observedmodulation amplitude could mimic this signature;thus, no other eect investigated so far in the eld ofrare processes oers a so stringent and unambiguoussignature. With the present technology, the annualmodulation signature remains the main signatureof the DM particles signal. It is worth noting thathighly radiopure set-ups are necessary since noapproach for rejection of electromagnetic background



can be applied contemporaneously to the data bothbecause: (i) all similar approaches have in every casea statistical nature (this will aect the investigationof the DM annual modulation signature) and well-known side processes inducing recoils as well; (ii) theexperiment will be insensitive to the many possibleDM candidates, which give part or all the signal inelectromagnetic form. On the other hand, as known,the annual modulation analysis acts itself as a veryecient background rejection.

The corollary questions related to the exact natureof the DM particle(s) (detected by means of the DMannual modulation signature) and to the astrophys-ical, nuclear, and particle Physics scenarios requiresubsequent model-dependent corollary analyses, asthose performed, e.g., in [713, 24]. On the otherhand, one should stress that it does not exist anyapproach in direct and indirect DM searches whichcan oer information on the nature of the candidateindependently of assumed astrophysical, nuclear, andparticle Physics scenarios.

Present Experimental Results on the DM AnnualModulation Signature

Highly radiopure NaI(Tl) scintillators oer manycompetitive features to eectively investigate the DMannual modulation signature, such as, e.g.: (i) high-duty cycle; (ii) well-known technology; (iii) largemasses; (iv) no safety problems; (v) the lowest costwith the respect to every other considered technique;(vi) necessity of a relatively small underground space;(vii) reachable high radiopurity by material selectionsand protocols, by chemical/physical purications,etc.; (viii) feasibility of well-controlled operationalconditions and monitoring; (ix) feasibility of routinecalibrations down to few keV in the same conditionsas the production runs; (x) high light response (thatis, a keV threshold is reachable); (xi) absence of thenecessity of repurication or cooling down/warmingup procedures (implying high reproducibility, highstability, etc.); (xii) absence of microphonic noiseand an eective noise rejection at threshold (timedecay of NaI(Tl) pulses is hundreds ns, while thatof noise pulses is tens ns); (xiii) wide sensitivityto both high and low mass DM candidates and tomany dierent interaction types and astrophysical,nuclear and particle Physics scenario; (xiv) possibilityto eectively investigate the DM annual modulationsignature in all the needed aspects; (xv) possibilityto achieve signicant results on several other rareprocesses, etc.

However, neither commercial low backgroundNaI(Tl) detectors nor NaI(Tl) detectors grown withold technology (even after revision) can reliablyreach the needed sensitivity. Thus, devoted R&D

must be realized selecting all the involved materialsand procedures.5)

These arguments motivated the development anduse of highly radiopure NaI(Tl) scintillators for theDAMA/NaI and DAMA/LIBRA target-detectors;their competitivity is based on the reached intrinsicradiopurity, on the large sensitivity to many of theDM candidates, of the interaction types and of as-trophysical, nuclear and particle Physics scenarios,to the granularity of the setups, to the data taking upto the MeV scale (even though the optimization ismade for the lowest energy region), to the full controlof the running conditions, etc.

The rst generation DAMA/NaI [7, 8, 25, 26] andthe second generation DAMA/LIBRA [27, 28] set-ps are part of the DAMA project6), and they were andare located deep underground in the LNGS of INFN,whose main features have been reported, e.g., in [3336]. The DAMA project is mainly based on the devel-opment and use of low-background scintillators [713, 2428, 3740]. In particular, they have the mainaim to perform a direct detection of DM particlesin the galactic halo through the model-independentannual modulation signature.

The DAMA/NaI setup and its performances aredescribed in [7, 8, 25, 26], while DAMA/LIBRA setupand its performances in [27]. Here we just remindthat: (i) the detectors responses range from 5.5 to7.5 photoelectrons/keV; (ii) the hardware threshold ofeach PMT is at single photoelectron (each detector isequipped with two low background photomultipliersworking in coincidence); (iii) energy calibrations withX-rays/ sources are regularly carried out down tofew keV; (iv) the energy threshold of the experimentis 2 keV. The DAMA/NaI experiment collected anexposure of 0.29 ton yr over seven annual cycles [7,8, 26], while DAMA/LIBRA has released so far anexposure of 0.53 ton yr collected over four annualcycles [28]; thus, the total exposure of the two exper-iments is 0.82 ton yr, which is orders of magnitudelarger than the exposure typically collected in the eld.

5)We remark that the low-background technique requires verylong and accurate work for the selection of low radioactivematerials by sample measurements with HPGe detectors(placed deep underground in suitable hard shields) and/orby mass spectrometer analyses. Thus, these measurementsare often dicult experiments themselves, depending on therequired level of radiopurity.

6)We remind that DAMA is also composed by several otherlow-background setups, such as: (i) DAMA/LXe (6.5 kgpure liquid xenon scintillator) [29, 30]; (ii) DAMA/R&D,setup devoted to tests on prototypes and small-scale exper-iments [31]; (iii) DAMA/Ge detector for sample measure-ments [32].



0.04

500

DAMA/NaI (0.29 ton yr)

Time, d1500

0.08

2500 3500 4500

0

26 keV

0.08

0.04

(target mass = 87.3 kg)DAMA/LIBRA (0.53 ton yr)

(target mass = 232.8 kg)

0.04


0.08

0

25 keV

0.08

0.04



0.04


0.08

0

24 keV

0.08

0.04



Residuals, cpd/(kg keV)

Fig. 4. Experimental model-independent residual rate of the single-hit scintillation events, measured by DAMA/NaI andDAMA/LIBRA in the (24), (25), and (26)-keV energy intervals as a function of the time. The zero of the time scaleis January 1 of the rst year of data taking of DAMA/NaI. The experimental points present the errors as vertical barsand the associated time bin width as horizontal bars. The superimposed curves are the cosinusoidal functions behaviorsA cos (t t0) with a period T = 2/ = 1 yr, with a phase t0 = 152.5 d (June 2), and with modulation amplitudes,A, equal to the central values obtained by best t over the whole data, that is: 0.0215 0.0026, 0.0176 0.0020, and0.0129 0.0016 cpd/(kg keV) for the (24), (25), and (26)-keV energy intervals, respectively. The dashed vertical linescorrespond to the maximum of the signal (June 2), while the dotted vertical lines correspond to the minimum. The totalexposure is 0.82 ton yr. (For details see [28].)

Several analyses on the model-independent in-vestigation of the DM annual modulation signaturehave been performed (see [28] and references therein);here just few arguments are reminded. In particular,Fig. 4 shows the time behavior of the experimen-tal residual rates for single-hit events collected byDAMA/NaI and by DAMA/LIBRA in the (24),(25), and (26)-keV energy intervals. The super-imposed curves represent the cosinusoidal functionsbehaviors A cos (t t0) with a period T = 2/ =1 yr and with a phase t0 = 152.5 d (June 2), whilethe modulation amplitudes, A, have been obtainedby best t over the DAMA/NaI and DAMA/LIBRAdata. When the period and the phase parameters arereleased in the t, values well compatible with those

expected for a DM particle induced eect are ob-tained [28]. Summarizing, the cumulative analysis ofthe single-hit residual rate favors the presence of amodulated cosine-like behavior with proper featuresat 8.2 C.L. [28].

The same data of Fig. 4 have also been investi-gated by a Fourier analysis and clear peaks corre-sponding to a period of 1 year have been found inthe (26)-keV energy interval [28]. For comparisonthe power spectrum of the (614)-keV energy inter-val has also been investigated; it shows instead onlyaliasing peaks. Similar result is obtained by compar-ing the single-hit residuals in the (26)- and (614)-keV energy intervals; in fact, a clear modulationis present in the lowest energy interval, while it isabsent just above [28]. Moreover, in order to verify



0.02

0.04

0

0.04

0.02

25 keV

0.02

250Time, d

350

0.04

450 550 650

0

0.04

0.02

26 keV

0.02

0.04

0

0.04

0.02

24 keVResiduals, cpd/(kg keV)

Fig. 5. Experimental residual rates over the four DAMA/LIBRA annual cycles for single-hit events (open circles) (class ofevents to which DM events belong) and for multiple-hits events (lled triangles) (class of events to which DM events donot belong), in the energy regions 24, 25, and 26 keV, respectively. They have been obtained by considering for eachclass of events the data as collected in a single annual cycle and by using in both cases the same identical hardware and thesame identical software procedures. The initial time of the scale is taken on August 7. The experimental points present theerrors as vertical bars and the associated time bin width as horizontal bars (see [28]). Analogous results were obtained for theDAMA/NaI data [8].

absence of annual modulation in other energy regionsand, thus, to also verify the absence of any signicantbackground modulation, the energy distribution mea-sured during the data taking periods in energy regionsnot of interest for DM detection has also been inves-tigated. In fact, the background in the lowest energyregion is essentially due to Compton electrons, X-rays and/or Auger electrons, muon induced events,etc., which are strictly correlated with the eventsin the higher energy part of the spectrum. Thus, ifa modulation detected in the lowest energy regionwould be due to a modulation of the background(rather than to a signal), an equal or larger modula-tion in the higher energy regions should be present.The performed analyses have allowed to exclude thepresence of a background modulation in the wholeenergy spectrum at a level much lower than the eectfound in the lowest energy region for the single-hitevents [28].

A further relevant investigation has been doneby applying the same hardware and software proce-

dures, used to acquire and to analyze the single-hit residual rate, to the multiple-hits one. In fact,since the probability that a DM particle interacts inmore than one detector is negligible, a DM signalcan be present just in the single-hit residual rate.Thus, this allows the test of the background behaviorin the same energy interval of the observed posi-tive eect. In particular, Fig. 5 shows the residualrates of the single-hit events measured over the fourDAMA/LIBRA annual cycles, as collected in a sin-gle annual cycle, together with the residual rates ofthe multiple-hits events, in the considered energyintervals. A clear modulation is present in the single-hit events, while the tted modulation amplitudesfor the multiple-hits residual rate are well com-patible with zero: (0.0004 0.0008), (0.0005 0.0007), and(0.0004 0.0006) cpd/(kg keV) in theenergy regions 24, 25, and 26 keV, respectively.Similar results were previously obtained also for theDAMA/NaI case [8]. Thus, again evidence of an-nual modulation with proper features as required by



0.025

0 4

S

m

,

k

, cpd/(kg keV)

Energy, keV8

0.050

12 16 200.025

0

Fig. 6. Energy distribution of the Sm,k variable for the total exposure of DAMA/NaI and DAMA/LIBRA: 0.82 ton yr. A clearmodulation is present in the lowest energy region, while Sm,k values compatible with zero are present just above. In fact, theSm,k values in the (620)-keV energy interval have random uctuations around zero with 2/d.o.f. = 24.4/28 (see [28]).

the DM annual modulation signature is present inthe single-hit residuals (events class to which theDM particle induced events belong), while it is ab-sent in the multiple-hits residual rate (event classto which only background events belong). Since thesame identical hardware and the same identical soft-ware procedures have been used to analyze the twoclasses of events, the obtained result oers an addi-tional strong support for the presence of a DM parti-cle component in the galactic halo further excludingany side eect either from hardware or from softwareprocedures or from background.

The annual modulation present at low energy hasalso been shown by depicting the dierential modu-lation amplitudes, Sm,k values, as a function of theenergy; the Sm,k is the modulation amplitude of themodulated part of the signal (see above) obtained bymaximum-likelihood method over the data, consider-ing T = 1 yr and t0 = 152.5 d. In Fig. 6 the measuredSm,k for the total exposure (0.82 ton yr, DAMA/NaIand DAMA/LIBRA) are reported as function of theenergy. It can be inferred that positive signal is presentin the (26)-keV energy interval, while Sm,k valuescompatible with zero are present just above. In fact,the Sm,k values in the (620)-keV energy intervalhave random uctuations around zero with 2 = 24.4for 28 degrees of freedom. All this conrms the otheranalyses.

It has also been veried that the measured modu-lation amplitudes are statistically well distributed inall the crystals, in all the annual cycles and in theenergy bins; these and other discussions can be foundin [28].

It is also interesting the result of the analysisperformed by releasing the assumption of the phaset0 = 152.5 d in the maximum-likelihood procedureto evaluate the modulation amplitudes from thedata of the seven annual cycles of DAMA/NaIand the four annual cycles of DAMA/LIBRA. Inthis case alternatively the signal has been written

as: S0,k + Sm,k cos (t t0) + Zm,k sin(t t0) =S0,k + Ym,k cos (t t). Obviously, for signals in-duced by DM particles one would expect: (i) Zm,k 0(because of the orthogonality between the cosine andthe sine functions); (ii) Sm,k Ym,k; (iii) t t0 =152.5 d. In fact, these conditions hold for most of thedark halo models; however, it is worth noting thatslight dierences can be expected in case of possiblecontributions from nonthermalized DM components,such as, e.g., the SagDEG stream [24] and thecaustics [41].

Figure 7a shows the 2 contours in the plane(Sm, Zm) for the (26) keV and (614) keV en-ergy intervals and Figure 7b shows, instead, thosein the plane (Ym, t). The best-t values for the(26) keV energy interval are (1 errors):Sm = 0.0122 0.0016 cpd/(kg keV),Zm = (0.0019 0.0017) cpd/(kg keV),Ym = 0.0123 0.0016 cpd/(kg keV),t = 144.0 7.5 d; while for the (614)-keV energyinterval are: Sm = 0.0005 0.0010 cpd/(kg keV),Zm = 0.0011 0.0012 cpd/(kg keV), Ym = 0.00120.0011 cpd/(kg keV), and obviously not determined(see Fig. 7). These results conrm those achieved byother kinds of analyses. In particular, a modulationamplitude is present in the lower energy intervals andthe period and the phase agree with those expected forDM induced signals. For more discussions see [28].

Both the data of the rst four annual cycles ofDAMA/LIBRA and of the seven cycles of DAMA/NaIfull all the requirements of the DM annual modula-tion signature.

As previously done for DAMA/NaI [7, 8], carefulinvestigations on absence of any signicant system-atics or side reaction eect in DAMA/LIBRA havebeen quantitatively carried out and reported in detailsin [28].

In particular, in order to continuously monitorthe running conditions, several pieces of information



0.01

0.03 0.02

Z

m

, cpd/(kg keV)

S

m

, cpd/(kg keV)0.02

0.03

00.03

0.01 0.030.01

(

a

)

0

0.02

0.01

0.02

614 keV

26 keV

120

0.04 0.02

t

*

, d

Y

m

, cpd/(kg keV)0.02

240

0 0.04

(

b

)

200

160

80

614 keV

26 keV

Fig. 7. 2 contours in the plane (Sm, Zm) (a) and in the plane (Ym, t) (b) for the (26)- and (614)-keV energy intervals.The contours have been obtained by the maximum-likelihood method, considering the seven annual cycles of DAMA/NaI andthe four annual cycles of DAMA/LIBRA all together. A modulation amplitude is present in the lower energy intervals and theperiod and the phase agree with those expected for DM induced signals (see [28]).

are acquired with the production data and quanti-tatively analyzed. No modulation has been found inany possible source of systematics or side reactionsfor DAMA/LIBRA as well; thus, cautious upperlimits (90% C.L.) on the possible contributions tothe DAMA/LIBRA measured modulation amplitudehave been estimated and summarized in the table. Itis important to stress that no source of systematicsor side reactions able to mimic the signaturethatis able to account for the measured modulationamplitude and contemporaneously satisfy all therequirements of the signature7)has been found orsuggested by anyone over more than a decade. Fordetailed quantitative discussions on all the relatedtopics and for results see [28] and references therein.

Summarizing, DAMA/LIBRA has conrmed thepresence of an annual modulation satysfying all therequirements of the DM annual modulation signa-ture, as previously pointed out by DAMA/NaI; inparticular, the evidence for the presence of DM par-ticles in the galactic halo is cumulatively supported at8.2 C.L.

7)It is worth noting that, e.g., the DM annual modulation isnotas often naively saida seasonal variation and itis not a wintersummer eect. In fact, the DM annualmodulation is not related to the relative Sun position, but it isrelated to the Earth velocity in the galactic frame. Moreover,the phase of the DM annual modulation (roughly 2 June) iswell dierent than those of other physical quantities (such astemperature of atmosphere, pressure, other meteorologicalparameters, cosmic ray ux, . . . ) that are correlated withseasons.

As regards the corollary investigation on the na-ture of the DM candidate particle and related astro-physical, nuclear, and particle Physics scenarios, ithas been shown that the result can be compatiblewith a wide set of possibilities (see, e.g., [713] andin literature) on the basis of the DAMA/NaI result(many others are open). Obviously, this is also thecase when the DAMA/NaI and DAMA/LIBRA dataare considered all together (see, e.g., [28]); an updat-ing of previous corollary investigations and some newones are in progress. Finally, it is worth noting thatan increase of the exposure and a possible loweringof the energy threshold below 2 keV will improve thediscrimination capability among dierent astrophysi-cal, nuclear, and particle Physics scenarios.

3. COMPARISON WITH OTHERAPPROACHES

3.1. Direct Detection

As already mentioned, no other experiment, whoseresult can be directly compared in a model indepen-dent way with those of DAMA/NaI andDAMA/LIBRA, is available so far in the eld of DMdirect detection.

However, some unjustied claims for contradic-tion have been made by some activities, whichalthough started in the early 1990s have releasedso far marginal exposures with the respect to themany years of existence and to the several used de-tectors as well as by some recent ones which shouldbe more properly considered still at R&D stage. All



Summary of the results obtained by investigating all possible sources of systematics and side reactions in the data ofthe DAMA/LIBRA four annual cycles. (None able to give a modulation amplitude dierent from zero has been found;thus cautious upper limits (90% C.L.) on the possible contributions to the measured modulation amplitude have beencalculated and are shown here; for details see [28]. Analogous results were obtained for DAMA/NaI [7, 8].)

Source Main comment (also see [27])Cautious upper

limit, cpd/(kg keV)(90% C.L.)

Radon Sealed Cu box in HP nitrogen atmosphere, threefold level of sealing


eld of Physics a comparison would requirein everycasee.g., a deep investigation of the radiopurity ofall the part of the dierent setups, of their specicperformances in all the aspects, of the detailed pro-cedures used by each one, etc.

In conclusion, those claims for contradiction haveintrinsically no robust scientic bases.

3.2. Indirect Detection

Some of the DM candidate particles, via theirannihilation either in the celestial bodies (such asEarth and Sun) or in the galactic halo, could giverise to high-energy neutrinos, positrons, antiprotons,and gammas. Therefore, they could be indirectlydetected by looking either for upgoing muonsproduced by in underground, underwater orunder-ice detectors or for antimatter and gammasin the space. However, it is worth to remark thatno direct model independent comparison can beperformed between the results obtained in direct andindirect searches.

In the case of upgoing muons in terrestrial de-tectors, the expected ux is the key quantity. How-ever, several sources of uncertainties are present inthe related estimates (and, therefore, in the obtainedresults) such as, e.g., the assumption that a steadystate has been reached in the considered celestialbody and the estimate and subtraction of the exist-ing competing processes, oered by the atmosphericneutrinos. Model dependent analyses with a simi-lar approach have been carried out by large exper-iments deep underground such as, e.g., MACROand Super-Kamiokande. In particular, the case of theneutralino candidate in MSSM has been discussedin [44], showing that their model dependent resultswere not in conict with the DAMA result.

As we mentioned, the annihilation of the DM par-ticles in the galactic halo could also produce antimat-ter particles and gammas. The antimatter searcheshave to be carried out outside the atmosphere, i.e. onballoons or satellites. In particular, the DM particlesannihilation would result in an excess of antiprotonsor of positrons over an estimated background arisingfrom other possible sources. The estimate and sub-traction of such a background together with the inu-ence of the Earth and of the galactic magnetic eld onthese particles play a crucial role on the possibility ofa reliable extraction of a signal. However, at presentthe excess of positrons with energy 520 GeVsuggested by [46] and by other experimentshasbeen conrmed at least up to 70 GeV by the rstdata of the PAMELA experiment [45]. If these resultsare interpreted in terms of annihilation of some DarkMatter candidate particles, this gives rise to results

not in conict with the eect observed by DAMA (seealso [46]).

As regards the possibility to detect s from DMparticles annihilation in the galactic halo, experi-ments in space are planned. In particular, the experi-ment GLAST is in orbit since June 2008. However,at present it is dicult to estimate the possibilitiesof the space experiments considering, e.g., the back-ground level, the uncertainties in its reliable estimateand subtraction as well as the smallness of the ex-pected signal (even more, if a subdominant compo-nent would be present) when properly calculated withrescaling procedure. However, the presence of a excess from the center of the Galaxy in the EGRETdata [47] has already been suggested. This excessmatches with a possible DM particles annihilation inthe galactic halo and is not in conict with the DAMAmodel independent results.

4. TOWARD THE FUTURE

The large merits of highly radiopure NaI(Tl) havebeen demonstrated in the practice by the DAMA set-ups which have been/are the highest radiopure setupsavailable in the eld, have eectively pursued a model-independent approach to investigate the presence ofDM particles in the galactic halo collecting exposuresseveral orders of magnitude larger than those usuallyavailable in the eld and have obtained and/or are inprogress to obtain many other complementary or by-product results.

The highly radiopure DAMA NaI(Tl) setups arepowerful tools for the investigation on the DM particlecomponent in the galactic halo having all the intrinsicmerits already mentioned and large exposed mass, ahigh overall radiopurity, a high duty-cycle and partic-ular performances. In 1996 DAMA proposed to INFNto realize a ton setup [40] and a new R&D project forhighly radiopure NaI(Tl) detectors was funded at thattime and carried out for several years in order to realizeDAMA/LIBRA, as an intermediate step.

The collection of a much larger exposure will allowto further investigate the model independent evidencewith an increased sensitivity. Moreover, it will also of-fer an increased sensitivity to improve corollary questson the nature of the candidate particle, trying to dis-entangle at least among some of the many dierentpossible astrophysical, nuclear, and particle Physicsmodels as well as to investigate other new possiblescenarios.

In the following some of the many topicsnot yetwell known at present and which can aect whatevercorollary model dependent interpretation of exper-iment and/or model dependent comparison amongdierent experimental resultswill be addressed.



1. The velocity and spatial distribution of theDM particles in the galactic halo. It has beenshown that the naive description of the galactic haloas an isothermal halo is an unphysical and nonreal-istic approximation which signicantly aects modeldependent evaluations (exclusion plots, allowed re-gions, etc.) and comparisons. Other modelings (notexhaustive at all), many of them based on N-bodiessimulations, have been considered in literature andsome of them have been discussed at some extentin [7, 48] and references therein. Some of these mod-els can be signicantly discriminated when largerexposure (larger mass and/or much longer runningtime) will be available.

2. The eects induced on the DM particles dis-tribution in the galactic halo by contributionsfrom satellite galaxies tidal streams. It has beenpointed out [23] that contributions to the DM parti-cles in the galactic halo should be expected from tidalstreams from the Sagittarius Dwarf elliptical Galaxy.Considering that this Galaxy was undiscovered until1994 and considering Galaxy formation theories, onehas to expect that also other satellite galaxies do existand contribute as well. In particular, the Canis Majorsatellite Galaxy has been pointed out as reported in2003 in [49]; it can, in principle, play a very signicantrole being close to our galactic plane. Some debateon these arguments is present in literature. Anyhow,at present, the best way to investigate the presence ofa stream contribution is to determine in accurate waythe phase of the annual modulation, t0, as a functionof the energy; in fact, for a given halo model t0 wouldbe expected to be (slightly) dierent from 152.5 d andto vary with energy [24].

3. The eects induced on the DM particles dis-tribution in the galactic halo by the existence ofcaustics. It has been shown that the continuous infallof DM particles in the galactic gravitational eld canform caustic surfaces and discrete streams in the DMparticles halo [41]. The phenomenology to point out asimilar scenario is analogous to that in the previousitem.

4. The detection of possible solar wakes. Asan additional verication of the possible presence ofcontributions from streams of DM particles in ourgalactic halo, it can be investigated also the gravita-tional focusing eect of the Sun on the DM particleof a stream. In fact, one should expect two kinds ofenhancements in the DM particles ow: one namedspike, which gives an enhancement of DM particledensity along a line collinear with the direction of theincoming stream and of the Sun, and another, namedskirt, which gives a larger DM particle density ona surface of cone whose opening angle depends onthe stream velocity [41]. Thus, such a possibility can

be investigated with high sensitivity through second-order timeenergy correlation analyses.

5. The investigation of possible diurnal eects.Beyond the diurnal variation expected only in caseof high cross section WIMP/WIMP-like candidates(see [19] and references therein), also other sideraldaily eect can be considered.

In particular, a very interesting eect, which holdsfor a wide range of DM candidates, isin principlethe diurnal modulation due to the Earth rotation ve-locity contribution. In fact, considering a detector onthe Earth surface at the latitude , the velocity of thedetector in the galactic frame can be written as:

vd(t) = v + v cos cos(t t0) (3)+ vrot cos sin cos (t td).

Here, vrot 0.46 km/s is the Earth rotational velocityat the equator, 42 is the angle beetwen the Earthaxis and the DM ux (approximatively the Cygnusconstellation declination), = 2/ds (where ds is 1sidereal day), and td is a phase depending on detectorlongitude. Applying a Taylor expansionas alreadydone in Eqs. (1) and (2)the expected signal count-ing rate in a given kth energy bin can be written as:

Sk[(t)] Sk[0] (4)

+[Sk

]0

( cos(t t0) + cos (t td)) ,

where =vrot cos sin

v0. The interest in this second-

order signature is that the ratio Rdy of this diurnalmodulation amplitude over the annual modulationamplitude is a fully model independent constant;considering the LNGS latitude ( 42.5) one has:

Rdy =

=

vrot cos sin v cos

0.015. (5)

This signature can allow a powerful decoupling fromthe models. However, considering that the annualmodulation amplitude observed in DAMA in the (26)-keV energy interval is roughly0.013 cpd/(kg keV) [28], the expected diurnal mod-ulation amplitude is 2 104 cpd/(kg keV); thisamplitude can be relevantly investigated only whena much larger exposure will be available (e.g., manyyears of running of DAMA/1 ton).

6. The study of possible structures as clumpi-ness with small scale size. Possible structures asclumpiness with small scale size could, in principle,be investigated by exploiting a large exposure andsearching for distinctive peculiarities in the time dis-tribution of the data.



7. The coupling(s) of the DM particle with the23Na and 127I and its nature. As mentioned, sev-eral large uncertainties are linked to the coupling(s)between the DM particle and the target-nuclei. Asuitably large exposure will allow to better constrainthe related aspects.

8. The scaling laws and cross sections. Atpresent just simple scaling laws are used to scaleall the nuclear cross sections to a common nucleoncross section; however, the use of these simple scalinglaws is a large source of uncertainties in modeldependent results and comparisons. For example, ithas been pointed out [50] that, even for the neutralinocandidate, these assumptions (which hold in the caseof model with one-nucleon current) are arbitrarywhen two-nucleon current with pion exchange areintroduced. Thus, the presence of two target-nucleiin the NaI(Tl) detectors could in principle oer aprobe for possible more rened or new nuclear cross-section scaling laws by collecting larger exposuresand increasing the knowledge on the related aspects.

At present a third-generation R&D eort towardthe possible highly radiopure NaI(Tl) ton setup hasbeen funded and the DAMA Collaboration has al-ready performed various related works.

Finally, it is worth noting that ultra-low-backgroundNaI(Tl) scintillators can also oer the possibil-ity to achieve signicant results on several otherrare processes as already done, e.g., by the formerDAMA/NaI apparatus such as [3840]: (i) possibleviolation of Pauli exclusion principle in 127I and in23Na; (ii) electron stability; (iii) charge nonconservingprocesses; (iv) search for solar axions; (v) searchfor exotic matter; (vi) search for spontaneous tran-sition of nuclei to a superdense state; (vii) searchfor spontaneous emission of heavy clusters in 127I;(viii) search for possible nucleon, di-nucleon andtri-nucleon decays into invisible channels with newapproach, etc.

5. CONCLUSIONS

Dark Matter is a very intriguing eld of Physics onwhich eorts are in progress since about a century.Many experimental evidences have allowed to betterdene the problem and to clarify various related as-pects. Highly radiopure NaI(Tl) DAMA setups haveinvestigated the aspects related to the presence ofDM particles in the galactic halo by exploiting theDM annual modulation signature, achieving a modelindependent evidence at 8.2 C.L.

The collection of larger exposures (withDAMA/LIBRA or with the possible DAMA/1 ton,which is at R&D stage) will allow to signicantlyinvestigate several open aspects on the nature of

the candidate particle(s) and on the various relatedastrophysical, nuclear, and particle Physics as wellas to investigate with high sensitivity other DMfeatures and second order eects. In particular, futureperspectives have also been discussed in this paper atsome extent.

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Dark matter particles in the galactic halo