An experiment to search for dark matter interactions using sodium iodide detectors

TL;DR

This paper reports initial results from the COSINE-100 experiment, which uses sodium iodide detectors to test DAMA's claimed dark matter signal, finding no evidence of the expected annual modulation and challenging DAMA's interpretation.

Contribution

The study provides a model-independent test of DAMA's dark matter claim using sodium iodide detectors, with initial data contradicting DAMA's reported modulation.

Findings

No excess events over background in initial data

Results challenge DAMA's annual modulation claim

Supports tension with other dark matter experiments

Abstract

Observations of galaxies and primordial radiation suggest that the Universe is made mostly of non-luminous dark matter. Several types of new fundamental particles have been proposed as candidates for dark matter such as weakly interacting massive particles (WIMPs) but no definitive signal has been seen despite concerted efforts by many collaborations. One exception is the much-debated claim by the DAMA collaboration of a statistically significant annual modulation in the event rate of their experiment with a period and phase consistent with that expected from WIMP dark matter. Several groups have been working to develop experiments with the aim of reproducing DAMA's results using the same target medium. Here we report results from the initial operation of the COSINE-100 experiment. COSINE-100 uses sodium iodide as the target medium-the same medium as DAMA-and is designed to carry out a model-independent test of DAMA's claim. Initial data based on the first 59.5 days indicate that there is no excess of events over the expected background, confirming that DAMA's annual modulation signal is in severe tension with results from other experiments under the assumption of dark matter having spin independent interactions and the Standard Halo Model. COSINE-100 is now taking data to study the presence of dark matter-induced annual modulation in the event rate of the sodium iodide detectors.

Equations

$$\mathcal{L}=\prod _i^{N_{ch}}\prod _j^{N_{bin}}\frac{{\mu }_{ij}^{n_{ij}}{e}^{-{\mu }_{ij}}}{n_{ij}!}\prod _k^{N_{bkg}}{e}^{-\frac{(x_k-{\alpha }_k{)}^2}{2{\sigma }_k^2}}\prod _l^{N_{syst}}{e}^{-\frac{x_l^2}{2{\sigma }_l^2}},$$

Full text

††thanks: Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA††thanks: High Energy Accelerator Research Organization (KEK), Ibaraki 319-1106, Japan††thanks: Center for Experimental Nuclear Physics and Astrophysics and Department of Physics, University of Washington, Seattle, WA 98195, USA††thanks: Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada

The COSINE-100 collaboration

An experiment to search for dark matter interactions using sodium iodide detectors

Govinda Adhikari

Department of Physics, Sejong University, Seoul 05006, Republic of Korea

  

Pushparaj Adhikari

Department of Physics, Sejong University, Seoul 05006, Republic of Korea

  

Estella Barbosa de Souza

Department of Physics, Yale University, New Haven, CT 06520, USA

  

Nelson Carlin

Physics Institute, University of São Paulo, 05508-090, São Paulo, Brazil

  

Seonho Choi

Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea

  

Mitra Djamal

Department of Physics, Bandung Institute of Technology, Bandung 40132, Indonesia

  

Anthony C. Ezeribe

Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

  

Chang Hyon Ha

changhyon.ha@gmail.com

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Insik Hahn

Department of Science Education, Ewha Womans University, Seoul 03760, Republic of Korea

  

Antonia J.F. Hubbard

Department of Physics, Yale University, New Haven, CT 06520, USA

  

Eunju Jeon

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Jay Hyun Jo

Department of Physics, Yale University, New Haven, CT 06520, USA

  

Hanwool Joo

Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea

  

Woon Gu Kang

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Woosik Kang

Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea

  

Matthew Kauer

Department of Physics and Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin-Madison, Madison, WI 53706, USA

  

Bonghee Kim

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Hyounggyu Kim

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Hongjoo Kim

Department of Physics, Kyungpook National University, Daegu 41566, Republic of Korea

  

Kyungwon Kim

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Nam Young Kim

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Sun Kee Kim

Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea

  

Yeongduk Kim

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

Department of Physics, Sejong University, Seoul 05006, Republic of Korea

  

Yong-Hamb Kim

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

Korea Research Institute of Standards and Science, Daejeon 34113, Republic of Korea

  

Young Ju Ko

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Vitaly A. Kudryavtsev

Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

  

Hyun Su Lee

hyunsulee@ibs.re.kr

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Jaison Lee

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Jooyoung Lee

Department of Physics, Kyungpook National University, Daegu 41566, Republic of Korea

  

Moo Hyun Lee

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Douglas S. Leonard

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Warren A. Lynch

Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

  

Reina H. Maruyama

Department of Physics, Yale University, New Haven, CT 06520, USA

  

Frederic Mouton

Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

  

Stephen L. Olsen

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Byungju Park

IBS School, University of Science and Technology (UST), Daejeon 34113, Republic of Korea

  

Hyang Kyu Park

Department of Accelerator Science, Korea University, Sejong 30019, Republic of Korea

  

Hyeonseo Park

Korea Research Institute of Standards and Science, Daejeon 34113, Republic of Korea

  

Jungsic Park

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Kangsoon Park

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Walter C. Pettus

Department of Physics, Yale University, New Haven, CT 06520, USA

  

Hafizh Prihtiadi

Department of Physics, Bandung Institute of Technology, Bandung 40132, Indonesia

  

Sejin Ra

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Carsten Rott

Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea

  

Andrew Scarff

Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

  

Keon Ah Shin

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

  

Neil J.C. Spooner

Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

  

William G. Thompson

Department of Physics, Yale University, New Haven, CT 06520, USA

  

Liang Yang

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

  

Seok Hyun Yong

Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea

**Observations of galaxies and primordial radiation suggest that the Universe is made mostly of non-luminous dark matter Clowe et al. (2006); Ade et al. (2016). Several types of new fundamental particles have been proposed as candidates for dark matter Baer et al. (2015) such as weakly interacting massive particles (WIMPs) Lee and Weinberg (1977); Goodman and Witten (1985), but no definitive signal has been seen despite concerted efforts by many collaborations Battaglieri et al. (2017). One exception is the much-debated claim by the DAMA collaboration of a statistically significant annual modulation in the event rate of their experiment Bernabei et al. (1998, 2013, 2018) with a period and phase consistent with that expected from WIMP dark matter Savage et al. (2009); Baum, Freese, and Kelso (2018); Kang et al. (2018). Several groups have been working to develop experiments with the aim of reproducing DAMA’s results using the same target medium Barbosa de Souza et al. (2017); Amare et al. (2016); Fushimi et al. (2016); Xu et al. (2015); Adhikari et al. (2016). Here we report results from the initial operation of the COSINE-100 experiment Adhikari et al. (2018a, b). COSINE-100 uses sodium iodide as the target medium – the same medium as DAMA – and is designed to carry out a model-independent test of DAMA’s claim. Initial data based on the first 59.5 days indicate that there is no excess of events over the expected background, confirming that DAMA’s annual modulation signal is in severe tension with results from other experiments under the assumption of dark matter having spin independent interactions and the Standard Halo Model Tanabashi et al. (2018); Drukier, Freese, and Spergel (1986); Freese, Frieman, and Gould (1988); Lewin and Smith (1996). COSINE-100 is now taking data to study the presence of dark matter-induced annual modulation in the event rate of the sodium iodide detectors. **

COSINE-100 is located at the Yangyang Underground Laboratory in South Korea and began data taking in 2016. The experiment utilizes eight low-background thallium-doped sodium iodide crystals arranged in a 4$\times$2 array, giving a total target mass of 106 kg. Each crystal is coupled to two photomultiplier tubes (PMTs) to measure the amount of energy deposited in the crystal. The sodium iodide crystal assemblies are immersed in 2,200 L of liquid scintillator, which allows for the identification and subsequent reduction of radioactive backgrounds observed by the crystals Park et al. (2017). The liquid scintillator is surrounded by copper, lead, and plastic scintillator to reduce the background contribution from external radiation as well as cosmic-ray muons Prihtiadi et al. (2018) (Extended Data Fig. 1).

The data used in this analysis were acquired between 20 October 2016 and 19 December 2016 for a total exposure of 59.5 live days. During this two-month period, no significant environmental abnormality or unstable detector performance were observed. The analysis was performed with all eight crystals. Six of the crystals have light yields of about 15 photoelectrons/keV with analysis threshold of 2 keV. The other two crystals have lower light yields and require higher analysis thresholds of 4 keV and 8 keV respectively Adhikari et al. (2018a). Since their direct impact on the search is not substantial, we discuss the spectra of only six crystals in this Letter. When both PMTs on the same crystal register signals that are consistent with at least one photoelectron within 200 ns, that crystal is considered to have registered a “hit.” The outputs of all of the detector elements during 8 $\mu$s time windows surrounding the hit time are recorded.

A nucleus recoiling from a WIMP interaction is expected to produce a hit in a single crystal. A set of candidate events are selected by applying several criteria to reject backgrounds. Boosted Decision Trees (BDTs) Friedman (2001), i.e. multivariate machine learning algorithms, are used to characterize the pulse-shapes to discriminate PMT-induced noise events from radiation-induced events. Events that had hits in multiple crystals, liquid scintillator, or the muon detector are also rejected as multiple hit events. Although multiple-hit events are not used for the WIMP search, they are used to develop the event selection criteria, determine efficiencies, and model backgrounds.

Multiple-hit events recorded during the two week calibration campaign with the 60Co source provided a large sample of Compton scattering events where a $\gamma$-ray from the 60Co source scatters from an electron in one crystal and is detected in another crystal. The BDTs are trained for each detector using the multiple-hit events of the 60Co calibration data, weighted to match the energy spectrum of the expected background, and physics data for both signals and the PMT-induced noise (see Methods). The efficiencies of the selection requirements are first measured with the multiple-hit events from the 60Co source as shown in Fig. 1.

Multiple-hit events from $\rm{}^{40}K$ decay are produced when a 3 keV X-ray registers in one crystal and its accompanying 1460 keV $\gamma$-ray in another Adhikari et al. (2016). These occur throughout the data exposure time and provide independent, real-time energy calibrations and efficiency measurements in the 2–6 keV region of interest for the WIMP search. The efficiencies measured with the multiple-hit events that occur during the dark matter search exposure, including tagged 3 keV X-rays from the 40K, are in agreement with the measured efficiencies using the 60Co data. A specialized apparatus that has a monoenergetic 2.42 MeV neutron beam is used to measure the selection efficiencies of nuclear recoil events. This measurement was performed with a small test crystal that was cut from the same ingot as a crystal used for the COSINE-100 experiment. The efficiencies determined from the different methods are mutually consistent within a 5% level of uncertainty as shown in Fig. 1. The efficiency uncertainties are included as a systematic error.

The remaining dark matter search dataset predominantly originate from environmental $\gamma$ and $\beta$ radiations produced from the crystals themselves or the nearby surrounding materials. Sources include radioactive contaminants internal to the crystals or on their surfaces, external detector components, and cosmogenic activation Adhikari et al. (2018b). The background spectrum for each individual crystal is modeled using simulations based on the Geant4 toolkit Agostinelli et al. (2003). Multiple-hit events with measured energies between 2 and 2,000 keV and single-hit events between 6 and 2,000 keV are used in the modeling as described in detail elsewhere Adhikari et al. (2018b) (see also Methods). Single-hit events with energies below 6 keV are excluded to avoid a bias against dark matter signal events. Figure 2 shows the summed single-hit event spectrum between 2 and 20 keV for the six crystals compared with the simulated contributions from various sources. The data points in the 2–6 keV region of interest are within the error bands of the background model.

Several sources of systematic uncertainties were identified and included in this analysis. The largest uncertainties are those associated with the efficiency, which include statistical errors in the efficiency determination with the 60Co calibration and systematic errors derived from the independent cross-checks. Uncertainties in the energy resolution and nonlinear responses of the sodium iodide crystals Swiderski (2013) affect the shapes of the background and signal spectra. These are studied using tagged 3 keV X-rays from internal 40K and 59.5 keV $\gamma$-rays from an external 241Am source. Different models for 210Pb decays Adhikari et al. (2018b) and variations of the levels of external Uranium and Thorium decay-chain contaminants are also accounted for, as are effects of event rate variations and possible distortions in the shapes of the background model components (see Methods).

We used the simulated data to determine the contributions of dark matter-induced nuclear recoils to the measured energy spectra. Samples of WIMP-sodium and WIMP-iodine spin independent scattering events were generated for 18 different WIMP masses, ranging from $5~{}\mathrm{GeV}/{\rm c}^{2}$ to $10,000~{}\mathrm{GeV}/{\rm c}^{2}$ using the standard WIMP halo model with the same parameters that were used for the WIMP interpretation of the DAMA/LIBRA-phase1 signal Savage et al. (2009). These events were then processed through the detector simulation and the output events were subjected to the same selection criteria that were applied to the data.

To search for evidence of dark matter-induced events, binned, maximum likelihood fits to the measured single-hit energy spectra between 2 and 20 keV were performed for each of the 18 WIMP masses. The Bayesian Analysis Toolkit Caldwell, Kollár, and Kröninger (2009) was used with Probability Density Functions (PDFs) that were based on shapes of the simulated WIMP signal spectra and the various components of the background model. Uniform priors were used for the signals and Gaussian priors for the background, with means and uncertainties for each background component set at the values determined from the model fitted to the data Adhikari et al. (2018b). The systematic uncertainties are included in the fit as nuisance parameters with Gaussian priors. To be conservative in the assignment of systematic uncertainties, the maximum allowed distortions of the PDF shapes within their uncertainties are considered. The possibility of correlated rate and shape uncertainties as well as the uncorrelated bin by bin statistical uncertainties are also considered (see Methods). To calculate the expected 90% confidence level upper limits on WIMP-nucleon scattering cross sections, we performed 1,000 simulated experiments with the expected backgrounds and no additional dark matter signal.

Data were fit to each of the 18 WIMP masses. An example of a maximum likelihood fit with a $10~{}\mathrm{GeV}/{\rm c}^{2}$ WIMP signal is presented in Fig. 3 (see also Extended Data Fig. 5). The summed event spectrum for the six crystals is shown together with the best-fit result. For comparison, the expected signal for a $10~{}\mathrm{GeV}/{\rm c}^{2}$ WIMP with a spin independent cross section of $2.35\times 10^{-40}$cm2, the central value of the DAMA/LIBRA-phase1 signal interpreted as a WIMP-sodium interaction, is overlaid in red. No excess of events that could be attributed to Standard Halo WIMP interactions are found in the 18 WIMP masses considered. The posterior probabilities of signal were consistent with zero in all cases and 90% confidence level limits are determined. Figure 4 shows the 3$\sigma$ contours of the allowed WIMP mass and cross section values that are associated with the DAMA/LIBRA-phase1 signal Savage et al. (2009) together with the 90% confidence level upper limits from the COSINE-100 data.

Despite the strong evidence for its existence, the identity of dark matter remains a mystery. COSINE-100, a new sodium iodine-based experiment designed to resolve the long-standing controversy between DAMA collaboration’s claim for detection of dark matter and the null results from many other experiments, is now taking data at the Yangyang Underground Laboratory. Several years of data will be necessary to fully confirm or refute DAMA’s annual modulation results. However, the first 59.5 days of background data show that the annual modulation signal observed by DAMA is inconsistent with spin independent interaction between WIMPs and sodium or iodine in the context of the Standard Halo Model.

Author Information

Contributions Y.D.K., H.S.L., R.H.M., and N.J.C.S. conceived the COSINE-100 experiment. Its design and installation were led by K.S.P. and C.H. and carried out by members of the COSINE-100 collaboration. Operation and maintenance were organized by C.H. with the support from on-site crews, W.G.K., B.H.K., and S.H.Y. J.L., J.S.P., J.H.J., G.A., P.A., H.P., C.H, W.G.T., E.B.S., H.S.L., and K.W.K. contributed in data acquisition, production, and verification. H.W.J., H.P., and K.W.K. provided nuclear recoil data. P.A., G.A., J.S.P., K.W.K., H.P., N.Y.K., and C.H. performed source calibrations. H.K., N.Y.K., C.H., and H.S.L. developed slow control framework. J.H.J. and W.G.T. developed data monitoring package. N.Y.K., J.Y.L., and Y.J.K. provided radiopurity of detector materials. G.A., J.S.P., and N.Y.K produced the liquid scintillator. Background simulations were performed by F.M., E.J.J., P.A., W.G.T., and E.B.S. C.H. and P.A analyzed data and the simulated data. This manuscript and plots were produced by C.H. and H.S.L., and edited by R.H.M., S.L.O, N.J.C.S., and other members of the collaboration. All authors have participated in online shift and approved the manuscript. Authors are alphabetically listed by their last names.

Competing interests The authors declare no competing interests.

Correspondence and requests for materials should be addressed to C.H. and H.S.L.

Fig.1 Event selection efficiency. A variety of methods are used to evaluate event selection efficiencies. The statistical error bands (68% confidence interval) of the event selection efficiencies determined from the 60Co calibration data are shown as green shaded regions and are compared with efficiencies determined from multiple-hit events (red diamond), internal 40K coincidence events (black square), and the nuclear recoil calibration data (blue circle) for one of the crystals. Horizontal error bars depict the data bin width. Vertical error bars are 68% confidence intervals.

Fig.2 Measured and simulated energy spectra. Summed energy spectrum for the six crystals (black filled circles shown with 68% confidence level error bars) and the expected background (blue line) are compared. Contributions to the background from internal radionuclide contaminations (primarily 210Pb and 40K), 210Pb on the surface of the crystals and nearby materials, cosmogenic activation (mostly 109Cd and 3H), and external backgrounds (mostly 238U and 232Th) are indicated. The green (yellow) bands are the 68% (95%) confidence level intervals for the background model.

Fig.3 Fit results for a 10 GeV/c2 WIMP mass. The data points (black filled circles shown with 68% confidence level error bars) show the summed energy spectra from the six crystals and the solid blue line shows the result for the $10~{}\mathrm{GeV}/{\rm c}^{2}$ WIMP mass fit. The expected signal excess above background for a $10~{}\mathrm{GeV}/{\rm c}^{2}$ WIMP mass and a spin independent WIMP-nucleon cross section of 2.35$\times$10*-40cm2* is shown as a solid red line. The green (yellow) bands are the 68% (95%) confidence level intervals for the background model. The lower panel shows the data-best fit residuals normalized to the best fit. Here the bands of systematic uncertainty and the expected DAMA/LIBRA-phase1 signal spectrum are shown.

Fig.4 Exclusion limits on the WIMP-nucleon spin independent cross section. The observed (filled circles with black solid line) 90% confidence level exclusion limits on the WIMP-nucleon spin independent cross section from the first 59.5 days data of COSINE-100 are shown together with the 65% and 95% probability bands for the expected 90% confidence level limit assuming the background-only hypothesis. The limits are compared with a WIMP interpretation of DAMA/LIBRA-phase1 of 3$\sigma$ allowed region for the WIMP-sodium (red-dot-contour) and the WIMP-iodine (blue-dot-contour) scattering hypothesis Savage et al. (2009). The limits from NAIAD Alner et al. (2005), the only other sodium iodide based experiment to set a competitive limit, are shown in magenta.

Methods

The COSINE-100 experiment is located 700 m below the surface at the Yangyang Underground Laboratory in eastern Korea. A cut-out view of the detector is shown in Extended Data Fig. 1. It is comprised of an array of eight sodium iodide “NaI(Tl)” scintillating crystals (total mass 106 kg) immersed in 2,200 L of liquid scintillator contained in an acrylic box that is surrounded by copper and lead shielding. Plastic scintillators surround the entire apparatus to detect cosmic-ray muons that penetrate the apparatus. External radiation is attenuated by the lead, copper and liquid scintillator shields and signals from the liquid scintillator and muon detectors are used to identify background events that are induced by radiation sources in or near the crystals and cosmic-ray muons. More details about the experimental site, including the fluxes of cosmic-ray muons and neutrons, and data acquisition system can be found elsewhere Adhikari et al. (2018a); Prihtiadi et al. (2018); Adhikari et al. (2018).

event selection

Pulse shapes from the detector are recorded when both PMTs on a crystal record signals that correspond to at least one single photoelectron within 200 ns. In the offline analysis, events are rejected if they occur within 30 ms of a signal from any of the surrounding muon detectors or if there is a signal in the liquid scintillator within 4 $\mu$s. Events with and without accompanying hit crystals in an $8\mu$s time window are classified as multiple-hit and single-hit, respectively. Events are further classified according to their energy: 2–70 keV are low energy and 70–2,000 keV are high energy.

Extended Data Figure 2 (panel a)) shows an averaged waveform for radiation-induced scintillation light signals in the NaI(Tl) crystal detectors, where the characteristic 250 ns NaI(Tl) scintillation light decay time is evident. In contrast, PMT noise pulses, which are considerably more frequent, decay faster, with decay times ranging between 20 ns and 50 ns, as shown in panel b). Some detectors intermittently produce events that have both slow-rise and decay-times as shown in the figure’s panel c). These are attributed to PMT discharges.

Boosted Decision Trees (BDTs) are used to separate signal from noise events. The fast PMT noise-induced events are efficiently removed by a BDT that is based on the amplitude-weighted average time of a signal, the ratios of the leading-edge and trailing-edge charge sums relative to total charge, and the balance of deposited energies between the two PMTs. This is trained with a sample of signal-rich, energy-weighted, multiple-hit events from the 60Co calibration campaign, and single-hit events in the WIMP-search data sample, which are mostly triggered by PMT noise. A second boosted decision tree (BDTA) that includes weighted higher-order time moments is effective at eliminating discharge events. Extended Data Figure 3 shows two-dimensional scatter plots of the BDT vs BDTA outputs for two separate crystals, one with and the other without PMT discharge signals. Events that are above and to the right of the dashed red lines in the figure are retained.

background modeling

The primary background components of the crystal energy spectra are from internal 238U, 232Th, 40K and 210Pb contaminations in the bulk material of the crystal, plus additional 210Pb on the surfaces of the crystal and its reflecting wrapping foil, caused by exposure to atmospheric Radon during the crystals’ encapsulation Adhikari et al. (2018b). In addition, we considered background from external sources such as 238U, 232Th and 40K contaminations in the PMTs, liquid scintillator, and the bulk material of the surrounding shields. The modeling of these contributions used starting values that were based on radioassay results from an underground, high-purity Ge detector Sala et al. (2016). The modeling of contributions from cosmogenic activity in the crystals was guided by measured surface production rates in NaI(Tl) Pettus (2015) and the above- and below-ground histories of each individual crystal.

In 10.7% of 40K decays, a $\sim$3 keV K-shell X-ray (or Auger electron) is produced in coincidence with a 1460 keV $\gamma$-ray. Since this results in a peaking background in the WIMP search region of interest (ROI), it is of particular concern. However, in the COSINE-100 detector, about 80% of these 3 keV X-rays are tagged by the detection of its accompanying 1460 keV $\gamma$-ray in one of the other crystals or in the liquid scintillator and, thus, can be vetoed. The measured rate for these tagged events is used to establish the contribution of untagged 3 keV 40K-induced events to the background in the single-hit spectrum’s ROI in each crystal.

Extended Data Figure 4 shows the results of the model fits to the data for the four categories of events (single-hit and multiple-hit events in low and high energy), with $1\sigma$ and $2\sigma$ uncertainty bands indicated in green and yellow, respectively Adhikari et al. (2018b). All four distributions were fit simultaneously. To avoid biasing the WIMP search, the 2 to 6 keV region of the low-energy, single-hit spectrum (panel a) in the figure) is not included in the fitting. The fit model indicates that the main contributions in the 2–6 keV ROI are from internal 40K and 210Pb, and cosmogenic 109Cd and 3H. The 109Cd contribution was independently confirmed by a time-dependent analysis.

systematic uncertainties

The analysis results are limited by the systematic uncertainties. Errors in the selection efficiency, the energy resolution, the energy scale and background modeling technique translate into uncertainties in the shapes of the signal and background component PDFs that are used in the likelihood fit and affect the results. These quantities are allowed to vary within their errors in the likelihood as nuisance parameters. Of these, the systematic errors associated with the efficiencies have the largest effects on the results. Uncertainties in the efficiencies are determined by the statistical errors from the multiple-hit 60Co source data efficiency measurements and their stability has been verified with independent datasets shown in Fig. 1. The efficiency systematic that maximally covers the statistical errors in the region of interest mimics the shape of a WIMP signal.

For most of the energy range, the resolutions and scales are well measured with internal radioactive peaks and external calibrations. However, since external source measurements are impractical for energies below 10 keV, the resolution and scale values for these energies are determined with the samples of tagged 3 keV X-rays from the internal 40K contamination. For these, statistical errors dominate and are taken as the systematic spread from these quantities. We used changes that occur in the background model when the simulation is done with different locations of the U/Th contamination in the PMTs, and alternative Geant4 methods for X-ray production of 210Pb as the systematic error from this source. The inclusion of the total systematic uncertainties degrades the sensitivity by a factor of 2.3.

WIMP extraction Bayesian fit

A Bayesian analysis with a likelihood formulated in Eq. 1 was performed and this fitter, more computationally demanding than the background modeling fits, was run with the WIMP search data (low-energy single-hit spectrum) between 2 and 20 keV. The function that is maximized has the form

[TABLE]

where, $N_{ch}$ is the number of crystals, $N_{bin}$ is the number of bins in each histogram, $N_{bkg}$ is the number of background components, $N_{syst}$ is the number of systematic nuisance parameters, $n_{ij}$ is the number of observed counts and $\mu_{ij}$ is the total model expectation by summing all $N_{bkg}$ background components and a WIMP signal component after application of a shape change due to $N_{syst}$ systematic effects. In the first product of Gaussians, $x_{k}$ is the value of the $k^{th}$ background component, $\alpha_{k}$ is the mean value and $\sigma_{k}$ is its 68% error. The second product of Gaussians $x_{l}$ is the $l^{th}$ systematic parameter and $\sigma_{l}$ is its error.

To avoid biasing the WIMP search, the fitter was developed and tested with simulated event samples. All eight crystals are fit simultaneously with a common WIMP signal model for each assumed WIMP mass and with fits performed for 18 different WIMP masses between 5 GeV/c2 and 10,000 GeV/c2. The shapes of the WIMP signal energy spectra are determined from simulations based on the standard WIMP halo model with parameters taken from Ref. 10. To relate the simulated WIMP signals, which are caused by nuclear recoils, to our energy scale, which is calibrated with electron recoils, we use the same NaI(Tl) quenching factors that were used in interpretations of the DAMA/LIBRA-phase1 signal, (QNa=0.3 and QI=0.09) (Quenching factors are the ratio of scintillation-light energy determinations for nuclear- and electron recoils of the same energy).

We use Gaussian priors for the normalizations of the background components and the systematic nuisance parameters for efficiencies, the energy resolutions, and the energy scales. The initial values for the background component normalizations are taken from the above-described fits that do not use the single-hit events in the 2–6 keV ROI. The final fit values for all nuisance parameters are within $\pm 1\sigma$ of their initial values.