The combined effect of Earth's rotations around the Sun and the Galactic Center is expected to produce an annual modulation of the dark matter particle interaction rate in terrestrial detectors [1], thereby offering a unique signature for directly probing dark matter particles and unveiling their true nature. The DAMA/LIBRA experiment claimed the detection of such a signature in their NaI detectors in the keV range [2,3]. The interpretation of this claim with the weakly interacting massive particle (WIMP) hypothesis is however currently facing challenges due to the null detection of WIMP-induced nuclear-recoil signals in other experiments [4][5][6][7][8][9][10][11][12][13][14][15]. Several experiments, such as ANAIS-112 [16] and COSINE-100 [17], have been making progress toward a model-independent test of the DAMA/LIBRA's claim adopting NaI detectors. Another approach to test this claim and possibly to reveal WIMP properties can be offered by searching for the modulation with other detectors which have different target materials, background sources, energy resolution, and experimental sites. Such results from xenon-based dark matter experiments are reported by XENON-100 [18], LUX [19], and XMASS [13] collaborations, though none of them have confirmed the positive claim above 1 keV electron recoil equivalent (keV ee ).
Dual-phase noble-liquid time projection chambers (TPCs) measure the scintillation and ionization signals from a particle interacting in the liquid. Such detectors were originally designed to discover and have led the search for WIMPs with masses above 10 GeV=c 2 . Moreover, in the last decade, they have also exhibited world-class sensitivity to light dark matter candidates exploiting only the ionization signal spectrum above a few detected ionization electrons (N e ) [20][21][22][23][24][25][26][27][28]. Among them, the DarkSide-50 detector, a liquid argon (LAr) TPC located underground at the Laboratori Nazionali del Gran Sasso (LNGS) [8,29,30], recently demonstrated an unprecedented sensitivity in this Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP 3 .
energy region [31][32][33][34]. This achievement was accomplished by looking for an event excess in the energy spectrum with respect to the background model above 0.06 keV ee . In this work, we report for the first time on the search for the annual rate modulation of events down to 0.04 keV ee , the lowest threshold ever achieved in a dark matter modulation search. The analysis relies on two approaches: the maximum likelihood fit and the Lomb-Scargle periodogram [35]. The results are also compared to the claim by the DAMA/LIBRA experiment assuming that the dark matter produces signals of the same electronrecoil-equivalent-energy in both NaI and LAr detectors.
The DarkSide-50 detector and associated apparatus are described in detail in Refs. [29,36,37]. Here we give a brief overview of the experimental apparatus.
DarkSide-50 consists of three nested detector systems, the LAr TPC, the neutron veto, and the cosmic muon veto. The TPC contains an active liquid target of ð46.4 AE 0.7Þ kg. It is housed in a stainless steel double-walled, vacuum-insulated cryostat, shielded by a 30 t boron-loaded liquid scintillator veto instrumented with 110 8-inch PMTs. The purpose of this is to actively tag neutrons in situ. A 1 kt water Čerenkov veto, equipped with 80 PMTs, surrounds the neutron veto to actively tag cosmic muons and to passively shield the TPC against external backgrounds [38].
Two arrays of 19 3-inch photomultiplier tubes (PMTs), located at the top and the bottom of the TPC, detect light pulses from scintillation (S1) induced by particle interactions in the liquid bulk. The same interactions generate ionization electrons, which are drifted through the LAr volume by a 200 V=cm electric field up to the top of the TPC. Then, they are extracted into the gas phase by a 2.8 kV=cm field and induce delayed photon pulses (S2) by electroluminescence under a 4.2 kV=cm field, as characterized in Ref. [39].
DarkSide-50 started taking data in April 2015 with a low-radioactivity LAr target, extracted from a deep underground source (UAr) [30], and concluded the operations in February 2018. We do not use a short period of time in July 2015 in which the inline argon purification getter was bypassed and an enhanced event rate was observed near the analysis threshold [24]. In addition, the first four months of data were contaminated by the cosmogenic 37 Ar isotope, with a half-life of 35.0 d [40], and were only used to calibrate the ionization response [41]. About 25% of the rest of the data taking was devoted to calibration campaigns with dissolved and external radioactive sources. The livetime used in this paper corresponds to 693.3 d.
The data used in this analysis is acquired upon a hardware event trigger requiring a coincidence of two or more PMT signals above 0.6 photoelectron within 100 ns [36]. Selected events for further analysis in this dataset are required to be single-scatter, i.e., with a single S2 pulse. These events must also be isolated in time from the preceding events, following a veto of 20 ms after any event triggering the data acquisition system. Additional cuts are used to remove pile-up pulses, which are too close in time such that the pulse finder algorithm is unable to separate the clusters, and surface α events, characterized by a large S1 plus an anomalously low S2 because of absorption of the ionization electrons into the detector wall. Finally, we remove events reconstructed in the outer ∼7 cm thick cylindrical shell of the TPC, resulting in the 19.4 kg fiducial volume in the center. The low energy threshold for this analysis is defined in order to reject spurious electrons (SEs) [24,31]. These are considered to originate from ionization electrons trapped on impurities along the drift in LAr, and released with a certain delay, as will be the object of a paper in preparation. A full description of the selection criteria can be found in Ref. [31].
The time evolution of background events can be described by the combination of a set of decaying exponentials and a constant term. The latter component includes the radioactive backgrounds whose lifetime is much longer than the datataking period of about three years and is dominated by the β-decay of 39 Ar (268 yr [42]). The exponential components arise from the decays of 37 Ar (35.0 d [40]), 85 Kr (10.8 yr [43]), 54 Mn (312.1 d [43]), and 60 Co (5.27 yr [44]). The first two isotopes are intrinsically present in LAr, while the latter two are contaminants of the PMTs, and 60 Co is also present in the cryostat stainless steel. The latter two emit γand x-rays, which deposit energy in the LAr target. The background model is generated with the DarkSide-50 Geant4-based Monte Carlo [45] code. The model is built on data from an extensive material screening campaign to characterize the trace radioactivity content of every detector component. It also uses in situ measurements with DarkSide-50 [31] and incorporates the detector response model [41].
A crucial aspect for this analysis is the long-term stability of the detector performance, monitored by various sensors incorporated inside the cryogenic system, as well as by the recorded events from the TPC itself. The two parameters whose fluctuations may potentially have a high impact on the modulation search are the electric drift field, F, and the average number of detected S2 photons per ionization electron extracted in the gas phase, g 2 . The stability of F is monitored in situ via the stability of the edge of the drifttime distribution that corresponds to the very bottom of the TPC [39]. This is allowed by the fact that a large part of the events in DarkSide-50 come from the diffused isotopes of 39 Ar and 85 Kr. The maximum fluctuation of F was estimated to be less than 0.01%, too small to affect the ionization response. Based on the S2/S1 ratio for electronic recoil events above the region of interest (RoI) (½0.04; 20.0 keV ee ), g 2 varies at most by 0.5% over the whole data-taking period. The impact on the modulation signal searches described later from the measured instability is evaluated by pseudoexperiments. It is found that any possible bias on the result is smaller than the size of statistical fluctuations.
We also check the temporal evolution of other detector parameters, such as the liquid argon purity, pressure and temperature of the gaseous argon, PMT response to single photoelectron, and the condition of the inline filters to maintain pure argon. A systematic study on the stability of such parameters can be found in Ref. [37]. Throughout the work we find that the stabilities of most parameters are typically Oð0.1%Þ or less such that they do not affect the observed event rate. An exception is the liquid argon purity which continuously increases from O 2 equivalent contamination of 60 ppt (corresponding to the drift electron lifetime of 5 ms) to <15 ppt (>20 ms). A toy Monte Carlo study shows that such an increase cannot make any fake modulation signal, as the maximum electron drift time (376 μs) is much shorter than that level. Another exception is the temperature of a charcoal trap for radon removal which is put inside the gas circulation line to maintain purified liquid argon. The instability is observed at the level of 1%. Since we do not see any correlation between the temperature and the observed event rate in various energy ranges, and we do not find any way for the instability to affect the TPC observed event rate, we affirm that it does not influence the following analysis.
We first perform a likelihood fit to search for annual modulation signal without constraining its phase. Since the observed events below 4 e -are contaminated by the SE background [31], of which a priori expectation is still missing, we define two ranges to be analyzed as ½4; 41 e - and ½41; 68 e -ranges, corresponding to ½0.06; 2.0 keV ee and ½2.0; 6.0 keV ee , respectively.
Figure 1 shows the measured time-dependent event rates for events with N e in the ½4; 41 e -1 and ½41; 68 e -1 ranges. The signal and backgrounds are modeled with
where l¼ ð 37 Ar; 85 Kr; 54 Mn; 60 CoÞ, A χ is the amplitude of the modulated term of the signal, ϕ the phase, and T the period fixed to 1 yr. The constant term C is the sum of the time-averaged signal component and long-lived backgrounds. The parameters τ l and A l correspond to the decay times and amplitudes, respectively, of the short-lived isotopes l. The background-only fits to data, by fixing A χ ¼ 0, are shown in Fig. 1 for the two ranges. The statistical significance of a possible modulated signal is assessed using the following binned likelihood with the bin width of 7 d,
The first term represents the Poisson probability of observing n i events in the i th time bin with respect to the expected ones, m i ðA χ ; ϕ; C; ΘÞ, evaluated with Eq. ( 1). In the fit, A χ , ϕ and C are left free to vary, while the other parameters are contained inside Θ, which represents the set of remaining nuisance parameters constrained by the Gaussian penalty terms in the last factor of Eq. ( 2). In the latter, θ 0 k and Δθ k represent the nominal central values and uncertainties, respectively, of the nuisance parameters and are listed in Table I. The nuisance parameters account for uncertainties on the fiducial volume of the TPC (which induces a 1.1% uncertainty on the event rate from 54 Mn and 60 Co in the PMTs and cryostat; and a 1.5% uncertainty on the other event rates, acting in a correlated way [31]) and on the activities of short-lived decays in the energy range of interest. These are obtained from the combination of the uncertainty on the measured rate (14%, 4.7%, 40%, 12% for 37 Ar, 85 Kr, 54 Mn, 60 Co, respectively [31]), with the uncertainty arising from the definition of the energy range due to the ionization response. In addition, the uncertainty on the 85 Kr activity is combined with the spectral FIG. 1. Temporal evolution of the observed event rates for ½3; 4 e -(corresponding to ½0.04; 0.06 keV ee ), 4; 41 e - (½0.06; 2.0 keV ee ), and ½41; 68 e -(½2.0; 6.0 keV ee ) ranges. The bin width is 7 d. The colored solid lines represent the background-only fit. The vertical dotted lines correspond to June 2nd, which is when the dark matter induced event rate has its maximum. The blue-shaded region corresponds to the first four months devoted to the detector calibration and is thus excluded from this analysis. interaction plus, on average, two subsequent ionization electron. The likelihood,
is the product of the Poisson probabilities in each of the ij-bins defined by the event time (i) and energy expressed in terms of number of electrons (j) given the signal amplitude, A j χ , and the constant background component, C j . The chosen bin width along the time axis corresponds to 7 d and the bin widths along the energy axis are 0.02 keV ee in the range ½0.04; 0.06 keV ee , 0.25 keV ee in the range ½0.06;1.0 keV ee , 1 keV ee in the range ½1.0;6.0 keV ee , and 2 keV ee in the range ½6.0; 20.0 keV ee The sample of events with 3 e -(½0.04; 0.06 keV ee ) is contaminated by SE's. To account for this background, we anchored its time variation to that of events below 3 e -, selected in coincidence with the previous event, largely dominated by SE. This approach is justified by the observation that the spectrum of events occurring in a 2 ms window from the previous event, which consists of more than 90% of SE's, is stable over time. The amplitude of the signal in each energy interval, A j χ , is assumed uncorrelated with the others. Nuisance parameters Θ, in Eq. ( 3) are the same as in Eq. ( 2), but account for energy spectral distortions of the background components as done in Ref. [31].
The measured event rate with 3 e -is shown in Fig. 1, together with the fitted background model including the SE component. Figure 4 shows the best-fitted amplitude as a function of the energy, together with the 1-and 2-σ significance coverages, as derived with background-only Monte Carlo datasets. The χ 2 =NDF for the best-fitted amplitude is 2275.9=2055. The results from DAMA/ LIBRA [3], COSINE-100 [17], and XMASS [13] are also shown. In contrast to our approach, the DAMA/LIBRA looked at each energy bin independently and measured the amplitude by looking at the residuals of a yearly averaged event rate.
Finally, a Lomb-Scargle periodogram analysis is performed on the temporal evolution of the event rate to look for sinusoidal signals with any period, including the one expected from dark matter. The analysis is applied to the data residuals, after the subtraction of the best-fitted background model determined for each energy range independently from each other [i.e., Eq. (1) but A χ is fixed to 0], as shown with the red and blue lines in Fig. 1. The uncertainty from the background fit is propagated to the data errors. To assess the significance of the sinusoidal signals, we calculate the false alarm probability which is defined as the probability for a Gaussian noise background to produce a peak of the observed amplitude. In this work, the bootstrap method [35] is adopted for the calculation. FIG. 2. Best fit parameters in the phase versus amplitude space from the likelihood analysis with the fixed period of 1 yr. The vertical dotted line represents the phase of the dark matter signal expected from the standard halo model. The horizontal dashhatched line corresponds to the estimated biases in the fit, extracted from pseudo experiments. Also shown are the results from other experiments using NaI(Tl) crystal scintillators (DAMA/LIBRA [3], COSINE-100 [17], and ANAIS-112 [16]) and liquid xenon TPC (XENON100 [18] and LUX [19]). FIG. 3. Distributions of the best-fit amplitude for backgroundonly pseudo datasets. The vertical red line is the mean of the amplitude obtained by the fit, while the blue vertical line corresponds to ffiffiffiffiffiffiffi ffi π=2 p σ where σ 2 is the variance of the amplitude obtained by the fit fixing the phase.
The sensitivity of this analysis is evaluated by applying the Lomb-Scargle analysis over 1000 pseudo experiments where an annual modulation signal has been injected. A median of 1σ significance for the false alarm probability is obtained with the addition of 0.03 counts=ðd kg keVÞ. The analysis of the data does not identify any significant modulation, scanning periods up to 800 d, as shown in Fig. 5. For the period of 1 yr for instance, the significance is lower than 0.01σ for both ranges.
We searched for an event rate modulation in the DarkSide-50 data between 0.06 and 6.0 keV ee without assuming a specific dark matter signal model. In none of the two analyzed ranges of ½0.06; 2.0 keV ee and ½2; 6 keV ee , a modulation signal was observed within the sensitivity. Also, a search is performed taking into account the background energy spectrum, which also failed to observe a significant modulation amplitude in the range ½0.04; 20.0 keV ee . This is the first search for a dark matter-induced modulation signal in the sub-keV region. Unfortunately, the significance of this result is not sufficient to confirm or reject the DAMA/LIBRA's positive observation in ½0.75; 6.0 keV ee .
The stability of the DarkSide-50 detector over nearly three years of operation, the accuracy of the background model, and the low-energy threshold achieved demonstrate the competitiveness of the dual-phase LAr-TPC technology in searching for modulation signals. This result is therefore promising in view of future massive dual-phase liquid argon experiments [53][54][55], expected to reach much larger exposures and even lower background levels.
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