Dark Matter with DAMA/LIBRA and its perspectives

The existence of Dark Matter particles as a significant portion of the Universe’s total mass is suggested by theoretical reasoning at the galactic and larger scales as well as experimental data. This motivates the DAMA experiment’s efforts to investigate the presence of the Dark Matter particles in the galactic halo by utilizing a model-independent signature with an extremely radio-pure set-up underground. The long-standing, model-independent annual modulation effect at Gran Sasso seen by DAMA with several experimental set-ups is summarized in this paper, along with its perspectives. DAMA/LIBRA-phase2 set-up, ≃ 250 kg highly radio-pure NaI(Tl) further confirms the evidence of a signal that meets all the requirements of the model independent Dark Matter annual modulation signature at high C.L.; the combined exposure of DAMA/NaI and DAMA/LIBRA is 2.86 ton × yr over 22 independent annual cycles. The experiment is currently collecting data in the DAMA/LIBRA–phase2 empowered configuration with an even lower software energy threshold.


Introduction
The primary goal of the DAMA/LIBRA experiment [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and the first-generation DAMA/NaI [21,22] experiment is to use the Dark Matter (DM) annual modulation signature to study the presence of DM particles in the galactic halo (originally suggested in Ref. [23,24]).The highly radio-pure NaI(Tl) target-detectors that have been built [1,6,9,25] ensure sensitivity to a variety of DM candidates, interaction types, and astrophysical scenarios (see e.g.Ref. [18], and references therein).The Earth's revolution around the Sun, which is moving in the Galaxy, is the source of the DM annual modulation signature and its peculiar characteristics.As a result, the Earth should be crossed by a larger flux of DM particles around 2 June (when the projection of the Earth orbital velocity on the Sun velocity is maximum), and by a smaller flux around 2 December (when the two velocities are opposite).The DM annual modulation signature is very distinctive since the effect induced by DM particles must simultaneously satisfy all the following requirements: the rate must contain a component modulated according to a cosine function (1) with one year period (2) and a phase that peaks roughly 2 June (3); this modulation must only be found in a well-defined low energy range, where DM particle induced events can be present (4); it must apply only to those events in which just one detector of many actually "fires" (single-hit events), since the DM particle multi-interaction probability is negligible (5); the modulation amplitude in the region of maximal sensitivity must be ∼ 7% of the constant part of the signal for usually adopted halo distributions (6), but it can be larger in case of some proposed scenarios such as e.g.those reported in Ref. [18] (even up to 30%).Thus this signature has many peculiarities and can be used to test a wide range of parameters in a variety of astrophysical, nuclear, and particle physics scenarios.Only systematic effects or side reactions that can concurrently satisfy all the aforementioned requirements and account for the entire observed modulation amplitude can mimick this DM signature.
At the end of 2010 all the photomultipliers (PMTs) were replaced by Hamamatsu R6233MOD second generation PMTs, with higher quantum efficiency (Q.E.) and lower background compared to those used in phase1; they were created following a dedicated R&D effort within the company, and tests and selections were detailed in Refs.[6,25].The novel PMTs have Q.E. in the range of 36-44% at peak and in the range of 33-39% at 420 nm, the wavelength of NaI(Tl) emission.In 2011, the DAMA/LIBRA-phase2 experiment's commissioning was successfully completed, enabling the software energy threshold to be reached at 1 keV and the improvement of some detector properties, including energy resolution and acceptance efficiency close to the software energy threshold [6].Depending on the detector, the light response of the detectors during phase 2 typically ranges from 6 to 10 photoelectrons/keV.Energy calibration with X-rays/γ sources is routinely done under the same operating conditions down to a few keV (for details see e.g.Ref. [1].When averaging the data over lengthy periods, double coincidences caused by internal X-rays from 40 K -which are at ppt levels in the crystals -provide a calibration point at 3.2 keV that is close to the software energy threshold.Despite optimization being done for the lowest energy, the DAQ system captures both single-hit events (where only one of the detectors fires) and multiple-hit events (where more than one detector fires) up to the MeV region.

The DAMA/LIBRA-phase2 results
The details of the annual cycles of DAMA/LIBRA-phase2 are reported in Ref. [18,19].The first annual cycle was dedicated to the commissioning and to the optimizations towards the achievement of the 1 keV software energy threshold [6].Thus, the considered annual cycles of DAMA/LIBRA-phase2 released so far are eight (exposure of 1.53 ton×yr); when considering also the former DAMA/NaI and DAMA/LIBRA-phase1, the exposure is 2.86 ton×yr.The duty cycle of the DAMA/LIBRA-phase2 experiment is high, ranging between 76% and 86%.The routine calibrations and, in particular, the data collection for the acceptance windows efficiency mainly affect it.
Residual rates versus time for 1 keV energy threshold are reported in Ref. [19].The former DAMA/LIBRA-phase1 and the new DAMA/LIBRA-phase2 residual rates of the single-hit scintillation events are reported in Fig. 1.The energy interval is from 2 keV, the software energy threshold of DAMA/LIBRA-phase1, up to 6 keV.The data of Fig. 1 and those of DAMA/NaI have been fitted with the function: A cos ω(t − t 0 ), considering a period T = 2π ω = 1 yr and a phase t 0 = 152.5 day (June 2 nd ) as expected by the DM annual modulation signature.The obtained χ 2 /d.o.f. is 130/155 and the modulation amplitude A = (0.00996 ± 0.00074) cpd/kg/keV is obtained.When the period and the phase are kept free in the fitting procedure, the achieved C.L. for the full exposure (2.86 ton×yr) is 13.7σ; the modulation amplitude of the single-hit scintillation events is: (0.01014 ± 0.00074) cpd/kg/keV, the measured phase is (142.4 ± 4.2) days and the measured period is (0.99834 ± 0.00067) yr, all these values are well in agreement with those expected for DM particles.
Absence of any significant background modulation in the energy spectrum has also been verified in the present data taking for energy regions not of interest for DM [2][3][4][5]9,15,16,18,19].It is worth noting that the obtained results account of whatever kind of background and, in addition, no background process able to mimic the DM annual modulation signature (that is able to simultaneously satisfy all the peculiarities of the signature and to account for the measured modulation amplitude) is available (see also discussions e.g. in Ref. [1-5, 7, 8, 15, 16, 18-20]).
A further relevant investigation on DAMA/LIBRA-phase2 data has been performed by applying the same hardware and software procedures, used to acquire and to analyze the singlehit residual rate, to the multiple-hit one.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, the comparison of the results of the single-hit events with those of the multiple-hit ones corresponds to compare the cases of DM particles beam-on and beam-off.This procedure also allows an additional test of the background behaviour in the same energy interval where the positive effect is observed.While a clear modulation, satisfying all the peculiarities of the DM annual modulation signature, is present in the single-hit events, the fitted modulation amplitude for the multiple-hit residual rate is well compatible with zero [19].Since the same identical hardware and the same identical software procedures have been used to analyze 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.
The single-hit residuals have also been investigated by a Fourier analysis [5].A clear peak corresponding to a period of 1 year is evident in the low energy intervals; the same analysis in the (6)(7)(8)(9)(10)(11)(12)(13)(14) keV energy region shows only aliasing peaks instead.Neither other structure at different frequencies has been observed.
The annual modulation present at low energy can also be pointed out by depicting the energy dependence of the modulation amplitude, S m (E), obtained by maximum likelihood method considering fixed period and phase: T =1 yr and t 0 = 152.5 day.The modulation amplitudes for the whole data sets: DAMA/NaI, DAMA/LIBRA-phase1 and DAMA/LIBRA-phase2 (total exposure 2.86 ton×yr) are plotted in Fig. 2; the data below 2 keV refer only to the DAMA/LIBRA-phase2 exposure (1.53 ton×yr).It can be inferred that positive signal is present in the (1-6) keV energy interval (a new data point below 1 keV has been added, see later), while S m values compatible with zero are present just above.All this confirms the previous analyses.The test of the hypothesis that the S m values in the (6-14) keV energy interval have random fluctuations around zero yields χ 2 /d.o.f.equal to 20.3/16 (P-value = 21%).It has been verified that the observed annual modulation effect is well distributed in all the 25 detectors.In particular, the modulation amplitudes S m integrated in the range (2-6) keV for each of the 25 detectors for the DAMA/LIBRA-phase1 and DAMA/LIBRA-phase2 periods have random fluctuations around the weighted averaged value confirmed by the χ 2 analysis.Thus, the hypothesis that the signal is well distributed over all the 25 detectors is accepted.
To test the hypothesis that the modulation amplitudes calculated for each DAMA/LIBRA-phase1 and DAMA/LIBRA-phase2 annual cycle are compatible and normally fluctuating around their mean values, the χ 2 test and the run test have been used.This analysis confirms that the data collected in all the annual cycles with DAMA/LIBRA-phase1 and phase2 are statistically compatible and can be considered together [19].
Let us, finally, release the assumption of the phase t 0 = 152.5 day in the procedure to evaluate the modulation amplitudes.In this case the signal can be alternatively written as: For signals induced by DM particles one should expect: i) Z m ∼ 0 (because of the orthogonality between the cosine and the sine functions); ii) S m Y m ; iii) t * t 0 = 152.5 day.These conditions hold for most of the dark halo models; however, slight differences can be expected in case of possible contributions from non-thermalized DM components (see e.g.Ref. [18] and references therein).
Considering cumulatively the data of DAMA/NaI, DAMA/LIBRA-phase1 and DAMA/LIBRA-phase2 the obtained 2σ contours in the plane (S m , Z m ) for the (2-6) keV and (6-14) keV energy intervals are shown in Fig. 3-left while in Fig. 3-right the obtained 2σ contours in the plane (Y m , t * ) are depicted.Moreover, Fig. 3 also shows only for DAMA/LIBRA-phase2 the 2σ contours in the (1-6) keV energy interval.The best fit values are reported in Ref. [19].
Setting S m = 0 in eq. ( 1), the Z m values have also been determined by using the same procedure for DAMA/NaI, DAMA/LIBRA-phase1 and phase2 data sets; they are expected to No systematic or side processes able to mimic the signature, i.e. able to simultaneously satisfy all the many peculiarities of the signature and to account for the whole measured modulation amplitude, has been found or suggested by anyone throughout some decades thus far (for details see e.g.Ref. [1-5, 7, 8, 15-22]).In particular, arguments related to any possible role of some natural periodical phenomena have been discussed and quantitatively demonstrated to be unable to mimic the signature (see references; e.g.Refs.[7,8]).
Finally, let us cite the detailed analyses of Ref. [18,20], quantitatively confuting the claims of Refs.[26,27] that the DAMA annual modulation result might be mimicked by the adopted analysis procedure.In particular, the arguments reported in Ref. [18,20] already showed that any possible effect in DAMA/ LIBRA due either to long-term time-varying background or to any odd behavior of the rate, increasing with time, is negligible.
Thus, on the basis of the exploited signature, the model independent DAMA results give evidence at 13.7σ C.L. (over 22 independent annual cycles and in various experimental configurations) for the presence of DM particles in the galactic halo.
The DAMA model independent evidence is compatible with a wide set of astrophysical, nuclear and particle physics scenarios for high and low mass candidates inducing nuclear recoil and/or electromagnetic radiation, as also shown in various literature.Moreover, both the negative results and all the possible positive hints, achieved so-far in the field, can be compatible with the DAMA model independent DM annual modulation results in many scenarios considering also the existing experimental and theoretical uncertainties; the same holds for indirect approaches.For a discussion see e.g.Ref. [5,18] and references therein.

Perspectives, comparisons and conclusions
An increase in the exposure in the lowest energy bin and a further lowering of the software energy threshold are required to further increase the experimental sensitivity of DAMA/LIBRA and to disentangle some of the numerous possible astrophysical, nuclear, and particle physics scenarios in the investigation on the DM candidate particle(s).This is accomplished by running DAMA/LIBRA-phase2 and upgrading the experimental setup, aiming to drop the software energy threshold below 1 keV with high acceptance efficiency.
First, specific efforts have been made to reduce the software energy threshold in the DAMA/LIBRA-phase2 data that have previously been gathered, using the same method as before and with special studies on the efficiencies.As a result, Fig. 2 shows a new data point for the modulation amplitude as a function of energy down to 0.75 keV.Below 1 keV, a modulation is also noticeable.This early result shows the need to upgrade the hardware in order to decrease the software energy threshold and improve the statistics in the first energy bin.
A dedicated hardware upgrade of DAMA/LIBRA-phase2 was done.Downsized low background new concept preamplifiers and miniaturized HV dividers mounted on the same socket were installed in all of the PMTs.The use of 14-bit digitizers with increased vertical resolution was the key factor in the electronic chain's improvement.A reduced software energy threshold and a high acceptance efficiency are the main goals of this improvement, which seeks to increase experimental sensitivity.The experiment is currently running in this new configuration, DAMA/LIBRA-phase2 empowered, and new results are foreseen in the near future.

Figure 1 .
Figure 1.Experimental residual rate of the single-hit scintillation events measured by DAMA/LIBRA-phase1 and DAMA/LIBRA-phase2 in the (2-6) keV energy intervals as a function of the time.The superimposed curve is the cosinusoidal functional forms A cos ω(t − t 0 ) with a period T = 2π ω = 1 yr, a phase t 0 = 152.5 day (June 2 nd ) and modulation amplitude, A, equal to the central value obtained by best fit. Figure reused from [19].

Figure 2 .
Figure 2. Modulation amplitudes, S m , as function of the energy in keV(ee) for the whole data sets: DAMA/NaI, DAMA/LIBRA-phase1 and DAMA/LIBRA-phase2 (total exposure 2.86 ton×yr) above 2 keV; below 2 keV only the DAMA/LIBRA-phase2 exposure (1.53 ton × yr) is available and used.A clear modulation is present in the lowest energy region, while S m values compatible with zero are present just above.This figure is being reused from [19].

Figure 3 .
Figure 3. 2σ contours in the plane (S m , Z m ) (left) and in the plane (Y m , t * ) (right) for: i) DAMA/NaI, DAMA/LIBRA-phase1 and DAMA/LIBRA-phase2 in the (2-6) keV and (6-14)keV energy intervals (light areas, green on-line); ii) only DAMA/LIBRA-phase2 in the (1-6) keV energy interval (dark areas, blue on-line).The contours have been obtained by the maximum likelihood method.A modulation amplitude is present in the lower energy intervals and the phase agrees with that expected for DM induced signals.Figures reused from[19].