DAMA/LIBRA results and perspectives

The DAMA/LIBRA experiment ($\sim$ 250 kg of highly radio-pure NaI(Tl)) is running deep underground at the Gran Sasso National Laboratory (LNGS) of the I.N.F.N. Here we briefly recall the results obtained in its first phase of measurements (DAMA/LIBRA--phase1, total exposure: 1.04 ton $\times$ yr). DAMA/LIBRA--phase1 and the former DAMA/NaI (cumulative exposure: $1.33$ ton $\times$ yr) give evidence at 9.3 $\sigma$ C.L. for the presence of DM particles in the galactic halo by exploiting the model-independent DM annual modulation signature. No systematic or side reaction able to mimic the exploited DM signature has been found or suggested by anyone over more than a decade. At present DAMA/LIBRA--phase2 is running with increased sensitivity.


Introduction
The DAMA project is based on the development and use of low background scintillators. The main experimental set-ups are: i) DAMA/NaI ( 100 kg of highly radiopure NaI(Tl)) that took data for 7 annual cycles and completed its data taking on July 2002 [1,2,3,4,5,6,7,8,9,10,11,12]; ii) DAMA/LXe, 6.5 kg liquid Kr-free Xenon enriched either in 129 Xe or in 136 Xe [13]; iii) DAMA/R&D, a facility dedicated to tests on prototypes and to perform experiments developing and using various kinds of low background crystal scintillators in order to investigate various rare processes [14]; iv) DAMA/Ge, where sample measurements are carried out and where dedicated measurements on rare events are performed [15]; v) the second generation DAMA/LIBRA set-up, 250 kg highly radiopure NaI(Tl)) [16,17,18,19] mainly devoted to the investigation of the presence of Dark Matter (DM) particles in the galactic halo. Profiting of the low background features of these set-ups, many rare processes have been studied.
The main apparatus, DAMA/LIBRA, is investigating the presence of Dark Matter particles in the galactic halo by exploiting the model independent DM annual modulation signature originally suggested in the mid 80's [20].
In fact, as a consequence of its annual revolution around the Sun, which is moving in the Galaxy traveling with respect to the Local Standard of Rest towards the star Vega near the constellation of Hercules, the Earth should be crossed by a larger flux of Dark Matter particles around ∼2 June (when the Earth orbital velocity is summed to the one of the solar system with respect to the Galaxy) and by a smaller one around ∼2 December (when the two velocities are subtracted). Thus, this signature has a specific origin with peculiarities not correlated with seasons. This DM annual modulation signature is very distinctive since the effect induced by DM particles must simultaneously satisfy all the following requirements: (1) the rate must contain a component modulated according to a cosine function; (2) with one year period; (3) with a phase that peaks roughly around ∼ 2nd June; (4) this modulation must be present only in a well-defined low energy range, where DM particles can induce signals; (5) it must be present only in those events where just a single detector, among all the available ones in the used set-up, actually "fires" (single-hit events), since the probability that DM particles experience multiple interactions is negligible; (6) the modulation amplitude in the region of maximal sensitivity has to be less about 7% in case of usually adopted halo distributions, but it may be significantly larger in case of some particular scenarios such as e.g. those in refs. [21,22]. Only systematic effects or side reactions able to simultaneously fulfil all the six requirements given above and to account for the whole observed modulation amplitude might mimic this DM signature; no one has been found or suggested. At present status of technology it is the only model independent signature available in direct Dark Matter investigation that can be effectively exploited.
The DAMA/LIBRA data released so far correspond to six annual cycles for an exposure of 0.87 ton×yr [17,18]. Considering these data together with those previously collected by DAMA/NaI over 7 annual cycles (0.29 ton×yr), the total exposure collected over 13 annual cycles is 1.17 ton×yr; this is orders of magnitude larger than the exposures typically collected in the field.

DAMA/LIBRA results
The DAMA/NaI set up and its performances are described in ref. [1,3,4,5], while for the DAMA/LIBRA set-up and its performances see refs. [16,18]. In particular, the software energy threshold of the experiments is 2 keV. Several analyses on the model-independent DM annual modulation signature have been performed [17,18]. Figure 1 shows the time behaviour of the experimental residual rates of the single-hit events collected by DAMA/NaI and by DAMA/LIBRA in the (2-6) keV energy interval [17,18].
The superimposed curve is the cosinusoidal function: A cos ω(t−t 0 ) with a period T = 2π ω = 1 yr, with a phase t 0 = 152.5 day (June 2 nd ), and modulation amplitude, A, obtained by best fit over the 13 annual cycles. The hypothesis of absence of modulation in the data can be discarded [17,18] and, when the period and the phase are released in the fit, values well compatible with those expected for a DM particle induced effect are obtained [18]. For example, in the cumulative (2)(3)(4)(5)(6) keV energy interval one gets: A = (0.0116 ± 0.0013) cpd/kg/keV, T = (0.999 ± 0.002) yr and t 0 = (146 ± 7) day. So, the analysis of the single-hit residual rate favours the presence of a modulated cosine-like behaviour with proper features at 8.9 σ C.L. [18].
The same data of figure 1 have also been investigated by a Fourier analysis, obtaining a clear peak corresponding to a period of 1 year [18]; this analysis in other energy regions shows only aliasing peaks instead. Moreover, in order to verify absence of annual modulation in other energy regions and, thus, to also verify the absence of any significant background modulation, the energy distribution in energy regions not of interest for DM detection has also been investigated. This allowed the exclusion of a background modulation in the whole energy spectrum at a level much lower than the effect found in the lowest energy region for the single-hit events [18]. A further relevant investigation has been done by applying the same hardware and software procedures, used to acquire and to analyse the single-hit residual rate, to the multiple-hits events in which  (2 -6) keV energy interval as a function of the time [4,5,17,18]. The zero of the time scale is January 1 st of the first year of data taking. The experimental points present the errors as vertical bars and the associated time bin width as horizontal bars. The superimposed curve is A cos ω(t − t 0 ) with period T = 2π ω = 1 yr, phase t 0 = 152.5 day (June 2 nd ) and modulation amplitude, A, equal to the central value obtained by best fit over the whole data. The dashed vertical lines correspond to the maximum expected for the DM signal (June 2 nd ), while the dotted vertical lines correspond to the minimum. See Refs. [17,18] and text. more than one detector "fires". In fact, since the probability that a DM particle interacts in more than one detector is negligible, a DM signal can be present just in the single-hit residual rate. Thus, this allows the study of the background behaviour in the same energy interval of the observed positive effect. The result of the analysis is reported in figure 2 where it is shown the residual rate of the single-hit events measured over the six DAMA/LIBRA annual cycles, as collected in a single annual cycle, together with the residual rates of the multiple-hits events, in the same (2-6) keV energy interval. A clear modulation is present in the single-hit events, while the fitted modulation amplitudes for the multiple-hits residual rate are well compatible with zero [18]. Similar results were previously obtained also for the DAMA/NaI case [5]. Thus, again evidence of annual modulation with proper features, as required by the DM annual modulation signature, is present in the single-hit residuals (events class to which the DM particle induced events belong), while it is absent in the multiple-hits residual rate (event class to which only background events belong). Since the same identical hardware and the same identical software procedures have been used to analyse the two classes of events, the obtained result offers an additional strong support for the presence of a DM particle component in the galactic halo further excluding any side effect either from hardware or from software procedures or from background.
The annual modulation present at low energy has also been analyzed by depicting the differential modulation amplitudes, S m , as a function of the energy; the S m is the modulation amplitude of the modulated part of the signal obtained by maximum likelihood method over the data, considering T = 1 yr and t 0 = 152.5 day.
The S m values are reported as function of the energy in figure 3. It can be inferred that a positive signal is present in the (2-6) keV energy interval, while S m values compatible with zero are present just above; in particular, the S m values in the (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) keV energy interval have random fluctuations around zero with χ 2 equal to 27.5 for 28 degrees of freedom. It has been also verified that the measured modulation amplitudes are statistically well distributed in all the crystals, in all the annual cycles and energy bins; these and other discussions can be found

2-6 keV
Time (day) Residuals (cpd/kg/keV) Figure 2. Experimental residual rates over the six DAMA/LIBRA annual cycles for single-hit events (open circles) (class of events to which DM events belong) and for multiple-hit events (filled triangles) (class of events to which DM events do not belong). They have been obtained by considering for each class of events the data as collected in a single annual cycle and by using in both cases the same identical hardware and the same identical software procedures. The initial time of the figure is taken on August 7 th . The experimental points present the errors as vertical bars and the associated time bin width as horizontal bars [17,18]. See text. in ref. [18]. Other interesting results have been obtained by analysing the data introducing a   [17,18].
sine-like modulation in the maximum likelihood procedure. In this case alternatively the signal can be written as: S 0,k + S m,k cos ω(t − t 0 ) + Z m,k sin ω(t − t 0 ) = S 0,k + Y m,k cos ω(t − t * ), where S 0,k , S m,k and Z m,k are the constant part, the cosine-like and sine-like modulation amplitudes of the signal in k-th energy interval. Obviously, for signals induced by DM particles one would expect: i) Z m,k ∼ 0 (because of the orthogonality between the cosine and the sine functions); ii) S m,k Y m,k ; iii) t * t 0 = 152.5 day. In fact, these conditions hold for most of the dark halo models; however, it is worth noting that slight differences in the phase could be expected in case of possible contributions from non-thermalized DM components, such as e.g. the SagDEG stream [7] and the caustics [23]. The 2σ contours in the plane (S m , Z m ) for the (2-6) keV and (6)(7)(8)(9)(10)(11)(12)(13)(14) keV energy intervals and those in the plane (Y m , t * ) are reported in figure 4 [18]. The best fit values for the (2-6) keV energy interval are (1σ errors): S m = (0.0111 ± 0.0013) cpd/kg/keV; Z m = −(0.0004 ± 0.0014) cpd/kg/keV; Y m = (0.0111 ± 0.0013) cpd/kg/keV; t * = (150.5 ± 7.0) day; while for the (6)(7)(8)(9)(10)(11)(12)(13)(14) keV energy interval are: S m = −(0.0001 ± 0.0008) cpd/kg/keV; Z m = (0.0002 ± 0.0005) cpd/kg/keV; Y m = −(0.0001 ± 0.0008) cpd/kg/keV and t * obviously not determined. These results confirm those achieved by other kinds of analyses. In particular, a modulation amplitude is present in the single-hit events of the lower energy intervals and the period and the phase agree with those expected for DM induced signals [18].  Both the data of DAMA/LIBRA and of DAMA/NaI fulfil all the requirements of the DM annual modulation signature.
Sometimes naive statements were put forwards as the fact that in nature several phenomena may show some kind of periodicity. It is worth noting that the point is whether they might mimic the annual modulation signature in DAMA/LIBRA (and former DAMA/NaI), i.e. whether they might be not only quantitatively able to account for the observed modulation amplitude but also able to contemporaneously satisfy all the requirements of the DM annual modulation signature; the same is also for side reactions.
Careful investigations on absence of any significant systematics or side reaction have been quantitatively carried out (see e.g. ref. [4,5,16,17,18,24], and refs therein). No systematics or side reactions able to mimic the signature (that is, able to account for the measured modulation amplitude and simultaneously satisfy all the requirements of the signature) has been found or suggested by anyone over more than a decade.

About interpretation
In literature it is present a rich and plenteous variety of theoretical patterns that are stimulating and intriguing to interpret in model dependent ways the results coming from different experiments on dark matter investigation. Anyhow, it is worth noting that DAMA has firstly a model independent result due to the exploitation of a DM signature with specific peculiarities.
About the interpretation of this model independent result in terms of a possible DM candidate and in order to consider a comparative overview with measurements by other experiments, it is important to refresh that there is neither an unique reference theoretical model of interpretation, nor a single set of assumptions for parameters in astrophysical, nuclear and particle Physics. In addition often comparisons are not performed in a fully consistent way. So every model dependent analysis chooses a model framework by fixing many parameters and assumptions, but many uncertainties are still present. Uncertainties are present on the models about the nature of the candidate particle, on the interaction coupling, on the form factors for each target material, on spin factors, on the scaling laws, on the nuclear Physics framework, on the dark halo model and related parameters, on possible galactic streams and so on. Uncertainties can also exist in some cases on some experimental aspects as: marginal exposures, poorly known detector response, extrapolated energy threshold, extrapolated energy scale, extrapolated energy resolution, definition of a fiducial volume, possible non-uniformity of some detector response, not regular and/or suitable calibration procedures, on quenching factors, and on stability of the operating conditions, etc.. In addition, in some cases, there are significant uncertainties on subtraction/rejection procedures when applied and on the stability of all the selected acceptance windows and related quantities. All these aspects can affect results and comparisons at various extent, precluding the comparisons from an universal value. The obtained DAMA model independent evidence is compatible with a wide set of scenarios regarding the nature of the DM candidate and related astrophysical, nuclear and particle Physics. For examples some given scenarios and parameters are discussed e.g. in Refs. [2,4,5,6,7,8,9,10,11] and in Appendix A of Ref. [17]. Further large literature is available on the topics [25]; other possibilities are open and we just recall the recent paper [26] on the case of a light-mass Dark Matter candidate particle interacting with the detector nuclei by coherent elastic process; comparison with recent possible positive hint [27] is also given.
It is worth noting that no other experiment exists, whose result can be directly compared in a model-independent way with those by DAMA/NaI and DAMA/LIBRA. Moreover, concerning those activities claiming model dependent exclusion under some largely arbitrary assumptions (see for example discussions in [4,5,17,28,29]) and generally using marginal exposures, it is worth noting that often important critical points exist in some of their experimental aspects (energy threshold, energy scale, multiple selection procedures, non uniformity of the detectors response, absence of suitable periodical calibrations in the same running conditions and in the claimed low energy region, stabilities, etc.); in addition existing experimental and theoretical uncertainties are not considered.
Similar considerations hold for the indirect detection searches, in fact also in this case no direct model-independent comparison can be performed between the results obtained in direct and indirect activities, since it does not exist a biunivocal correspondence between the observables in the two kinds of experiments. Moreover, these searches are restricted to some DM candidates and scenarios and their results are strongly model dependent. Anyhow, measurements published up to now are not in conflict with the effect observed by DAMA experiments.

Upgrades and perspectives
A first upgrade of the DAMA/LIBRA set-up was performed in September 2008.
A further and more important upgrade has been performed in the end of 2010 (see figure  5). In fact, all the PMTs have been replaced with new ones with higher quantum efficiency; this will allow the lowering of the software energy threshold and, hence, the improvement of the performance and of the sensitivity also for deeper corollary information on the nature of the DM candidate particle(s) and on the various related astrophysical, nuclear and particle Physics scenarios. Since January 2011 the DAMA/LIBRA experiment is again in data taking in the new configuration. Further improvements are foreseen with new preamplifiers and trigger modules realised to further implement the low energy studies. In the future DAMA/LIBRA will also continue its study on several other rare processes [19] as also the former DAMA/NaI apparatus did [12].

Conclusion
The positive evidence for the presence of DM particles in the galactic halo is now supported at 8.9σ C.L. (on a cumulative exposure of 1.17 ton×yr i.e. 13 annual cycles of DAMA/NaI and DAMA/LIBRA). An update of corollary analyses in some of the many possible scenarios for DM candidates, interactions, halo models, nuclear/atomic properties, etc. is in progress as well as analyses/data taking to investigate other rare processes. The last upgrade in fall 2010 was successfully concluded, while further improvements are planned. The strictly quality control allows DAMA/LIBRA to be still the highest radiopure set-up in the field with the largest exposed sensitive mass, the full control of running conditions, the largest duty-cycle and an exposure orders of magnitude larger than any other activity in the field.