Final model independent result of DAMA/LIBRA–phase1
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Abstract
The results obtained with the total exposure of 1.04 ton × yr collected by DAMA/LIBRA–phase1 deep underground at the Gran Sasso National Laboratory (LNGS) of the I.N.F.N. during 7 annual cycles (i.e. adding a further 0.17 ton × yr exposure) are presented. The DAMA/LIBRA–phase1 data give evidence for the presence of Dark Matter (DM) particles in the galactic halo, on the basis of the exploited model independent DM annual modulation signature by using highly radio-pure NaI(Tl) target, at 7.5σ C.L. Including also the first generation DAMA/NaI experiment (cumulative exposure 1.33 ton × yr, corresponding to 14 annual cycles), the C.L. is 9.3σ and the modulation amplitude of the single-hit events in the (2–6) keV energy interval is: (0.0112±0.0012) cpd/kg/keV; the measured phase is (144±7) days and the measured period is (0.998±0.002) yr, values well in agreement with those expected for DM particles. No systematic or side reaction able to mimic the exploited DM signature has been found or suggested by anyone over more than a decade.
1 Introduction
The present DAMA/LIBRA [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] experiment, as the former DAMA/NaI [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], has the main aim to investigate the presence of DM particles in the galactic halo by exploiting the model independent DM annual modulation signature (originally suggested in Refs. [41, 42]). Moreover, the developed highly radio-pure NaI(Tl) target-detectors [1] assure sensitivity to a wide range of DM candidates, interaction types and astrophysical scenarios.
As a consequence of the Earth’s revolution around the Sun, which is moving in the Galaxy 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 DM particles around ≃2 June and by a smaller one around ≃2 December.^{1} In the former case the Earth orbital velocity is summed to the one of the solar system with respect to the Galaxy, while in the latter the two velocities are subtracted. 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 % for usually adopted halo distributions (6), but it can be larger in case of some possible scenarios such as e.g. those in Refs. [43, 44, 45, 46, 47] (even up to ≃30 %). Thus this signature is model independent, very effective and, in addition, it allows to test a large interval of cross sections and of halo densities.
This DM signature might be mimiced only by systematic effects or side reactions able to account for the whole observed modulation amplitude and to simultaneously satisfy all the requirements given above. No one is available [1, 2, 3, 6, 7, 21, 22, 23].
The data of the former DAMA/NaI setup (0.29 ton × yr) and, later, those of the first 6 annual cycles of DAMA/LIBRA (0.87 ton × yr) have already given positive model independent evidence for the presence of DM particles in the galactic halo with high confidence level on the basis of the exploited DM annual modulation signature [2, 3, 7, 22].
In this paper the final model independent result of DAMA/LIBRA–phase1, obtained by including in the analysis also the data collected during the last seventh annual cycle of operation, is presented. The total exposure of DAMA/LIBRA–phase1 is: 1.04 ton × yr; when including also that of the first generation DAMA/NaI experiment it is 1.33 ton × yr, corresponding to 14 annual cycles.
2 The results
Exposures of the 7 annual cycles of DAMA/LIBRA–phase1. Here α=〈cos^{2}ω(t−t_{0})〉 is the mean value of the squared cosine, and β=〈cosω(t−t_{0})〉 is the mean value of the cosine (the averages are taken over the live time of the data taking and t_{0}=152.5 day, i.e. June 2nd); thus, (α−β^{2}) indicates the variance of the cosine (i.e. it is 0.5 for a detector being operational evenly throughout the year). During the first five annual cycles a detector was out of trigger; it was recovered in the 2008 upgrade [3]
Period | Mass (kg) | Exposure (kg×day) | (α−β^{2}) | |
---|---|---|---|---|
DAMA/LIBRA-1 | Sept. 9, 2003–July 21, 2004 | 232.8 | 51405 | 0.562 |
DAMA/LIBRA-2 | July 21, 2004–Oct. 28, 2005 | 232.8 | 52597 | 0.467 |
DAMA/LIBRA-3 | Oct. 28, 2005–July 18, 2006 | 232.8 | 39445 | 0.591 |
DAMA/LIBRA-4 | July 19, 2006–July 17, 2007 | 232.8 | 49377 | 0.541 |
DAMA/LIBRA-5 | July 17, 2007–Aug. 29, 2008 | 232.8 | 66105 | 0.468 |
DAMA/LIBRA-6 | Nov. 12, 2008–Sept. 1, 2009 | 242.5 | 58768 | 0.519 |
DAMA/LIBRA-7 | Sep. 1, 2009–Sept. 8, 2010 | 242.5 | 62098 | 0.515 |
DAMA/LIBRA–phase1 | Sept. 9, 2003–Sept. 8, 2010 | 379795 ≃ 1.04 ton × yr | 0.518 | |
DAMA/NaI + DAMA/LIBRA–phase1: | 1.33 ton × yr |
The total number of events collected for the energy calibrations during the entire DAMA/LIBRA–phase1 is about 9.6×10^{7}, while about 3.5×10^{6} events/keV have been collected for the evaluation of the acceptance window efficiency for noise rejection near energy threshold [1].
As it can be inferred from Table 1, the duty cycle of the experiment is high; the routine calibrations and, in particular, those related with the acceptance windows efficiency mainly affect it. The further improvement of the duty cycle in the last two annual cycles is mainly due to the improved performances of the new transient digitizers and DAQ system installed at fall 2008 before the start of the sixth annual cycle [3].
The same procedures previously adopted [1, 2, 3, 7] have been exploited also in the analysis of the data of the seventh annual cycle and several analyses on the model-independent investigation of the DM annual modulation signature have been performed.
χ^{2} test of absence of modulation in the entire DAMA/LIBRA–phase1 data. The P-values are also shown. A null modulation amplitude is discarded
Energy interval (keV) | DAMA/LIBRA–phase1 (7 annual cycles) | ||
---|---|---|---|
2–4 | χ^{2}/d.o.f.=111.2/50 | → | P=1.5×10^{−6} |
2–5 | χ^{2}/d.o.f.=98.5/50 | → | P=5.2×10^{−5} |
2–6 | χ^{2}/d.o.f.=83.1/50 | → | P=2.2×10^{−3} |
Modulation amplitude, A, obtained by fitting the single-hit residual rate of the entire DAMA/LIBRA–phase1 (Fig. 2), and including also the former DAMA/NaI data [22] for a total cumulative exposure of 1.33 ton × yr. It was obtained by fitting the data with the formula: Acosω(t−t_{0}) with \(T = \frac{2\pi}{\omega} = 1\) yr and t_{0}=152.5 day (June 2nd) as expected by the DM annual modulation signature. The corresponding χ^{2} value of each fit and the confidence level (C.L.) are also reported
Energy interval (keV) | DAMA/LIBRA–phase1 (cpd/kg/keV) | DAMA/NaI & DAMA/LIBRA–phase1 (cpd/kg/keV) |
---|---|---|
2–4 | A=(0.0167±0.0022)→7.6σ C.L. | A=(0.0179±0.0020)→9.0σ C.L. |
χ^{2}/d.o.f.=52.3/49 | χ^{2}/d.o.f.=87.1/86 | |
2–5 | A=(0.0122±0.0016)→7.6σ C.L. | A=(0.0135±0.0015)→9.0σ C.L. |
χ^{2}/d.o.f.=41.4/49 | χ^{2}/d.o.f.=68.2/86 | |
2–6 | A=(0.0096±0.0013)→7.4σ C.L. | A=(0.0110±0.0012)→9.2σ C.L. |
χ^{2}/d.o.f.=29.3/49 | χ^{2}/d.o.f.=70.4/86 |
Modulation amplitude (A), period (\(T = \frac{2\pi}{\omega}\)) and phase (t_{0}), obtained by fitting, with the formula: Acosω(t−t_{0}), the single-hit residual rate of the entire DAMA/LIBRA–phase1, and including also the former DAMA/NaI data. The results are well compatible with expectations for a signal in the DM annual modulation signature
A (cpd/kg/keV) | \(T = \frac{2\pi}{\omega}\) (yr) | t_{0} (days) | C.L. | |
---|---|---|---|---|
DAMA/LIBRA–phase1 | ||||
2–4 keV | (0.0178±0.0022) | (0.996±0.002) | 134±7 | 8.1σ |
2–5 keV | (0.0127±0.0016) | (0.996±0.002) | 137±8 | 7.9σ |
2–6 keV | (0.0097±0.0013) | (0.998±0.002) | 144±8 | 7.5σ |
DAMA/NaI & DAMA/LIBRA–phase1 | ||||
2–4 keV | (0.0190±0.0020) | (0.996±0.002) | 134±6 | 9.5σ |
2–5 keV | (0.0140±0.0015) | (0.996±0.002) | 140±6 | 9.3σ |
2–6 keV | (0.0112±0.0012) | (0.998±0.002) | 144±7 | 9.3σ |
Modulation amplitudes obtained by fitting the time behaviour of R_{90} for the seven annual cycles of DAMA/LIBRA–phase1, including a term with a cosine function having phase and period as expected for a DM signal. The obtained amplitudes are compatible with zero, and absolutely incompatible (≃100σ) with modulation amplitudes of tens cpd/kg (see text)
Period | \(A_{R_{90}}\) (cpd/kg) | Period | \(A_{R_{90}}\) (cpd/kg) |
---|---|---|---|
DAMA/LIBRA-1 | −(0.05±0.19) | DAMA/LIBRA-5 | (0.20±0.18) |
DAMA/LIBRA-2 | −(0.12±0.19) | DAMA/LIBRA-6 | −(0.20±0.16) |
DAMA/LIBRA-3 | −(0.13±0.18) | DAMA/LIBRA-7 | −(0.28±0.18) |
DAMA/LIBRA-4 | (0.15±0.17) |
As in Refs. [2, 3, 7], the annual modulation present at low energy can also be pointed out by depicting—as a function of the energy—the modulation amplitude, S_{m,k}, obtained by maximum likelihood method over the data considering T=1 yr and t_{0}=152.5 day. For such purpose the likelihood function of the single-hit experimental data in the kth energy bin is defined as: \(\mathbf{L}_{\mathbf{k}} = \boldsymbol{\varPi}_{ij} e^{-\mu_{ijk}} (\mu_{ijk}^{N_{ijk}} / N_{ijk}!)\), where N_{ijk} is the number of events collected in the ith time interval (hereafter 1 day), by the jth detector and in the kth energy bin. N_{ijk} follows a Poisson’s distribution with expectation value μ_{ijk}=[b_{jk}+S_{ik}]M_{j}Δt_{i}ΔEϵ_{jk}. The b_{jk} are the background contributions, M_{j} is the mass of the jth detector, Δt_{i} is the detector running time during the ith time interval, ΔE is the chosen energy bin, ϵ_{jk} is the overall efficiency. Moreover, the signal can be written as S_{ik}=S_{0,k}+S_{m,k}⋅cosω(t_{i}−t_{0}), where S_{0,k} is the constant part of the signal and S_{m,k} is the modulation amplitude. The usual procedure is to minimize the function y_{k}=−2ln(L_{k})−const for each energy bin; the free parameters of the fit are the (b_{jk}+S_{0,k}) contributions and the S_{m,k} parameter. Hereafter, the index k is omitted for simplicity.
Among further additional tests, the analysis of the modulation amplitudes as a function of the energy separately for the nine inner detectors and the remaining external ones has been carried out for the entire DAMA/LIBRA–phase1. The obtained values are fully in agreement; in fact, the hypothesis that the two sets of modulation amplitudes as a function of the energy belong to same distribution has been verified by χ^{2} test, obtaining: χ^{2}/d.o.f.=3.9/4 and 8.9/8 for the energy intervals (2–4) and (2–6) keV, respectively (ΔE=0.5 keV). This shows that the effect is also well shared between inner and outer detectors.
Best fit values for the (2–6) and (6–14) keV energy intervals (1σ errors) for S_{m} versus Z_{m} and Y_{m} versus t^{∗}, considering the cumulative exposure of DAMA/NaI and DAMA/LIBRA–phase1. See also Fig. 11
E (keV) | S_{m} (cpd/kg/keV) | Z_{m} (cpd/kg/keV) | Y_{m} (cpd/kg/keV) | t^{∗} (day) |
---|---|---|---|---|
2–6 | (0.0106±0.0012) | −(0.0006±0.0012) | (0.0107±0.0012) | (149.5±7.0) |
6–14 | (0.0001±0.0007) | (0.0000±0.0005) | (0.0001±0.0008) | undefined |
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. This has already been deeply investigated in Refs. [1, 2, 3] and references therein; the arguments and the quantitative conclusions, presented there, also apply to the entire DAMA/LIBRA–phase1 data. Additional arguments can be found in Refs. [6, 7, 54, 55, 56, 57, 58, 59, 60].
In conclusion, the model-independent DAMA results give evidence (at 9.3σ C.L. over 14 independent annual cycles) for the presence of DM particles in the galactic halo.
In order to perform corollary investigation on the nature of the DM particles, model-dependent analyses are necessary;^{3} thus, many theoretical and experimental parameters and models are possible and many hypotheses must also be exploited. In particular, the DAMA model-independent evidence is compatible with a wide set of astrophysical, nuclear and particle physics scenarios as also shown in literature. Moreover, both the negative results and all the possible positive hints, achieved so-far in the field, are largely 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. [7] and references therein.
Finally, in order to increase the experimental sensitivity of DAMA/LIBRA and to disentangle—in the corollary investigation on the candidate particle(s)—at least some of the many possible astrophysical, nuclear and particle Physics scenarios [7], the decreasing of the software energy threshold has been pursued. Thus, at end of 2010 all the PMTs have been replaced with new ones having higher quantum efficiency [5]; then, the DAMA/LIBRA–phase2 is started.
3 Conclusions
The data of the new DAMA/LIBRA-7 annual cycle have further confirmed a peculiar annual modulation of the single-hit events in the (2–6) keV energy region satisfying all the many requirements of the DM annual modulation signature; the cumulative exposure by the former DAMA/NaI and DAMA/LIBRA–phase1 is 1.33 ton × yr.
In fact, as required by the DM annual modulation signature: (1) the single-hit events show a clear cosine-like modulation as expected for the DM signal; (2) the measured period is equal to (0.998±0.002) yr well compatible with the 1 yr period as expected for the DM signal; (3) the measured phase (144±7) days is compatible with the roughly ≃152.5 days expected for the DM signal; (4) the modulation is present only in the low energy (2–6) keV interval and not in other higher energy regions, consistently with expectation for the DM signal; (5) the modulation is present only in the single-hit events, while it is absent in the multiple-hit ones as expected for the DM signal; (6) the measured modulation amplitude in NaI(Tl) of the single-hit events in the (2–6) keV energy interval is: (0.0112±0.0012) cpd/kg/keV (9.3 σ C.L.). No systematic or side processes able to simultaneously satisfy all the many peculiarities of the signature and to account for the whole measured modulation amplitude is available.
DAMA/LIBRA is continuously running in its new configuration (named DAMA/LIBRA–phase2) with a lower software energy threshold aiming to improve the knowledge on corollary aspects regarding the signal and on second order effects as discussed e.g. in Ref. [7].
Footnotes
- 1.
Thus, the DM annual modulation signature has a different origin and peculiarities than the seasons on the Earth and than effects correlated with seasons (consider the expected value of the phase as well as the other requirements listed below).
- 2.
In fact, the background in the lowest energy region is essentially due to “Compton” electrons, X-rays and/or Auger electrons, muon induced events, etc., which are strictly correlated with the events in the higher energy region of the spectrum. Thus, if a modulation detected in the lowest energy region were due to a modulation of the background (rather than to a signal), an equal or larger modulation in the higher energy regions should be present.
- 3.
It is worth noting that it does not exist in direct and indirect DM detection experiments approaches which can offer such information independently on assumed models.
Notes
Acknowledgements
It is a pleasure to thank Mr. A. Bussolotti and A. Mattei for their qualified technical work.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
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