DarkSide-50 532-day Dark Matter Search with Low-Radioactivity Argon
DarkSide Collaboration, P. Agnes, I. F. M. Albuquerque, T. Alexander, A. K. Alton, G. R. Araujo, M. Ave, H. O. Back, B. Baldin, G. Batignani, K. Biery, V. Bocci, G. Bonfini, W. Bonivento, B. Bottino, F. Budano, S. Bussino, M. Cadeddu, M. Cadoni, F. Calaprice, A. Caminata, N. Canci, A. Candela, M. Caravati, M. Cariello, M. Carlini, M. Carpinelli, S. Catalanotti, V. Cataudella, P. Cavalcante, S. Cavuoti, A. Chepurnov, C. Cicalò, A. G. Cocco, G. Covone, D. D'Angelo, M. D'Incecco, D. D'Urso, S. Davini, A. De Candia, S. De Cecco, M. De Deo, G. De Filippis, G. De Rosa, M. De Vincenzi, A. V. Derbin, A. Devoto, F. Di Eusanio, G. Di Pietro, C. Dionisi, M. Downing, E. Edkins, A. Empl, A. Fan, G. Fiorillo, R. S. Fitzpatrick, K. Fomenko, D. Franco, F. Gabriele, C. Galbiati, C. Ghiano, S. Giagu, C. Giganti, G. K. Giovanetti, O. Gorchakov, A. M. Goretti, F. Granato, M. Gromov, M. Guan, Y. Guardincerri, M. Gulino, B. R. Hackett, K. Herner, B. Hosseini, D. Hughes, P. Humble, E. V. Hungerford, An. Ianni, V. Ippolito, I. James, T. N. Johnson, K. Keeter, C. L. Kendziora, I. Kochanek, G. Koh, D. Korablev, G. Korga, A. Kubankin, M. Kuss, M. La Commara, M. Lai, X. Li, M. Lissia, G. Longo, Y. Ma, A. A. Machado, I. N. Machulin, A. Mandarano, L. Mapelli, S. M. Mari, et al. (75 additional authors not shown)
DDarkSide-50 532-day Dark Matter Search with Low-Radioactivity Argon
P. Agnes, I.F.M. Albuquerque, T. Alexander, A.K. Alton, G.R. Araujo, M. Ave, H.O. Back, B. Baldin,
5, a
G. Batignani,
6, 7
K. Biery, V. Bocci, G. Bonfini, W. Bonivento, B. Bottino,
11, 12
F. Budano,
13, 14
S. Bussino,
13, 14
M. Cadeddu,
15, 10
M. Cadoni,
15, 10
F. Calaprice, A. Caminata, N. Canci,
1, 9
A. Candela, M. Caravati,
15, 10
M. Cariello, M. Carlini, M. Carpinelli,
17, 18
S. Catalanotti,
19, 20
V. Cataudella,
19, 20
P. Cavalcante,
21, 9
S. Cavuoti,
19, 20
A. Chepurnov, C. Cical`o, A.G. Cocco, G. Covone,
19, 20
D. D’Angelo,
23, 24
M. D’Incecco, D. D’Urso,
17, 18
S. Davini, A. De Candia,
19, 20
S. De Cecco,
8, 25
M. De Deo, G. De Filippis,
19, 20
G. De Rosa,
19, 20
M. De Vincenzi,
13, 14
A.V. Derbin, A. Devoto,
15, 10
F. Di Eusanio, G. Di Pietro,
9, 24
C. Dionisi,
8, 25
M. Downing, E. Edkins, A. Empl, A. Fan, G. Fiorillo,
19, 20
R.S. Fitzpatrick,
16, b
K. Fomenko, D. Franco, F. Gabriele, C. Galbiati,
16, 32
C. Ghiano, S. Giagu,
8, 25
C. Giganti, G.K. Giovanetti, O. Gorchakov, A.M. Goretti, F. Granato, M. Gromov, M. Guan, Y. Guardincerri,
5, c
M. Gulino,
36, 18
B.R. Hackett, K. Herner, B. Hosseini, D. Hughes, P. Humble, E.V. Hungerford, An. Ianni,
16, 9
V. Ippolito, I. James,
13, 14
T.N. Johnson, K. Keeter, C.L. Kendziora, I. Kochanek, G. Koh, D. Korablev, G. Korga,
1, 9
A. Kubankin, M. Kuss, M. La Commara,
19, 20
M. Lai,
15, 10
X. Li, M. Lissia, G. Longo,
19, 20
Y. Ma, A.A. Machado, I.N. Machulin,
41, 42
A. Mandarano,
32, 9
L. Mapelli, S.M. Mari,
13, 14
J. Maricic, C.J. Martoff, A. Messina,
8, 25
P.D. Meyers,
16, d
R. Milincic, A. Monte, M. Morrocchi, B.J. Mount, V.N. Muratova, P. Musico, A. Navrer Agasson, A.O. Nozdrina,
41, 42
A. Oleinik, M. Orsini, F. Ortica,
43, 44
L. Pagani, M. Pallavicini,
11, 12
L. Pandola, E. Pantic, E. Paoloni,
6, 7
K. Pelczar, N. Pelliccia,
43, 44
A. Pocar, S. Pordes, S.S. Poudel, D.A. Pugachev, H. Qian, F. Ragusa,
23, 24
M. Razeti, A. Razeto, B. Reinhold, A.L. Renshaw, M. Rescigno, Q. Riffard, A. Romani,
43, 44
B. Rossi, N. Rossi, D. Sablone,
16, 9
O. Samoylov, W. Sands, S. Sanfilippo,
14, 13
C. Savarese,
32, 9
B. Schlitzer, E. Segreto, D.A. Semenov, A. Shchagin, A. Sheshukov, P.N. Singh, M.D. Skorokhvatov,
41, 42
O. Smirnov, A. Sotnikov, C. Stanford, S. Stracka, Y. Suvorov,
19, 20, 29
R. Tartaglia, G. Testera, A. Tonazzo, P. Trinchese,
19, 20
E.V. Unzhakov, M. Verducci,
8, 25
A. Vishneva, B. Vogelaar, M. Wada, T.J. Waldrop, H. Wang, Y. Wang, A.W. Watson, S. Westerdale,
45, e
M.M. Wojcik, X. Xiang, X. Xiao, C. Yang, Z. Ye, C. Zhu, and G. Zuzel (The DarkSide Collaboration) Department of Physics, University of Houston, Houston, TX 77204, USA Instituto de F´ısica, Universidade de S˜ao Paulo, S˜ao Paulo 05508-090, Brazil Pacific Northwest National Laboratory, Richland, WA 99352, USA Physics Department, Augustana University, Sioux Falls, SD 57197, USA Fermi National Accelerator Laboratory, Batavia, IL 60510, USA INFN Pisa, Pisa 56127, Italy Physics Department, Universit`a degli Studi di Pisa, Pisa 56127, Italy INFN Sezione di Roma, Roma 00185, Italy INFN Laboratori Nazionali del Gran Sasso, Assergi (AQ) 67100, Italy INFN Cagliari, Cagliari 09042, Italy Physics Department, Universit`a degli Studi di Genova, Genova 16146, Italy INFN Genova, Genova 16146, Italy INFN Roma Tre, Roma 00146, Italy Mathematics and Physics Department, Universit`a degli Studi Roma Tre, Roma 00146, Italy Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy Physics Department, Princeton University, Princeton, NJ 08544, USA Chemistry and Pharmacy Department, Universit`a degli Studi di Sassari, Sassari 07100, Italy INFN Laboratori Nazionali del Sud, Catania 95123, Italy Physics Department, Universit`a degli Studi “Federico II” di Napoli, Napoli 80126, Italy INFN Napoli, Napoli 80126, Italy Virginia Tech, Blacksburg, VA 24061, USA Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119234, Russia Physics Department, Universit`a degli Studi di Milano, Milano 20133, Italy INFN Milano, Milano 20133, Italy Physics Department, Sapienza Universit`a di Roma, Roma 00185, Italy Saint Petersburg Nuclear Physics Institute, Gatchina 188350, Russia a r X i v : . [ a s t r o - ph . C O ] N ov Amherst Center for Fundamental Interactions and PhysicsDepartment, University of Massachusetts, Amherst, MA 01003, USA Department of Physics and Astronomy, University of Hawai’i, Honolulu, HI 96822, USA Physics and Astronomy Department, University of California, Los Angeles, CA 90095, USA Joint Institute for Nuclear Research, Dubna 141980, Russia APC, Universit´e Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, USPC, Paris 75205, France Gran Sasso Science Institute, L’Aquila 67100, Italy LPNHE, CNRS/IN2P3, Sorbonne Universit´e, Universit´e Paris Diderot, Paris 75252, France Physics Department, Temple University, Philadelphia, PA 19122, USA Institute of High Energy Physics, Beijing 100049, China Engineering and Architecture Faculty, Universit`a di Enna Kore, Enna 94100, Italy Department of Physics, University of California, Davis, CA 95616, USA School of Natural Sciences, Black Hills State University, Spearfish, SD 57799, USA Radiation Physics Laboratory, Belgorod National Research University, Belgorod 308007, Russia Physics Institute, Universidade Estadual de Campinas, Campinas 13083, Brazil National Research Centre Kurchatov Institute, Moscow 123182, Russia National Research Nuclear University MEPhI, Moscow 115409, Russia Chemistry, Biology and Biotechnology Department, Universit`a degli Studi di Perugia, Perugia 06123, Italy INFN Perugia, Perugia 06123, Italy Department of Physics, Carleton University, Ottawa, ON K1S 5B6, Canada M. Smoluchowski Institute of Physics, Jagiellonian University, 30-348 Krakow, Poland (Dated: November 21, 2018)The DarkSide-50 direct-detection dark matter experiment is a dual-phase argon time projectionchamber operating at Laboratori Nazionali del Gran Sasso. This paper reports on the blind analysisof a (16 660 ± . × − cm (3 . × − cm ,3 . × − cm ) for a WIMP mass of 100 GeV /c (1 TeV /c , 10 TeV /c ). PACS numbers: 29.40.Gx, 95.35.+d, 95.30.Cq, 95.55.Vj
Despite much evidence from astronomy for darkmatter (DM), years of laboratory and indirectsearches have yielded no experimental evidence forDM that is not contradicted by other experiments.Weakly Interacting Massive Particles (WIMPs) re-main a promising candidate for DM, but directsearches are being pushed to probe lower WIMP-nuclear interaction cross sections and to lower( <
10 GeV /c ) and higher ( > /c ) DM masses.Probing lower cross sections requires higher sensi-tivity and hence larger exposures (target mass × runtime), and also, as importantly, more efficientbackground discrimination. This issue is espe-cially acute for spin-independent scattering for DMmasses above 10 GeV /c , where current limits on theWIMP-nucleon cross section are < − cm , reach-ing as low as 4 . × − cm at 30 GeV /c [1].Liquid argon Time Projection Chambers(LAr TPCs) share the scalability and 3D positionreconstruction of liquid xenon TPCs. Moreover, a Present address: Raleigh, NC 27613-3313, USA b University of Michigan, Ann Arbor, Michagan. c Deceased. d [email protected] e Currently at Carleton University, Ottawa, Canada.
LAr TPCs have powerful pulse shape discrimination(PSD) in the scintillation channel that separatesthe nuclear recoils (NR) expected from WIMPscattering from the electron recoil (ER) eventsfrom the dominant β - and γ -induced backgrounds.Exploiting this PSD, the single-phase DEAP-3600LAr scintillation detector has recently reportedthe best available DM-nucleon cross section limitusing an Ar target, 1 . × − cm at a DM massof 100 GeV /c , from an initial 9.87 tonne-dayexposure [2].In this paper, we report results from a 532.4-live-day exposure of DarkSide-50, a LAr TPC with anactive mass of (46 . ± .
7) kg of low-radioactivity ar-gon from underground sources (UAr) deployed in aliquid-scintillator veto (LSV) for neutron and γ -rayrejection and a water Cherenkov veto (WCV) forshielding and muon detection. We report here themost sensitive result to date with an argon targetand demonstrate the effectiveness of this combina-tion of detectors in rejecting a broad range of back-grounds. This paper describes the techniques devel-oped for a blind analysis of the 532.4-live-day dataset, which required detailed prediction of the back-ground and deployment of new rejection methods. FIG. 1. The DarkSide-50 TPC. Reproduced from [4]under [6].
I. THE DARKSIDE-50 DETECTORS
The DarkSide-50 experiment is located in Hall Cof the Gran Sasso National Laboratory (LNGS) inItaly, at a depth of 3800 m.w.e. [3].The DarkSide-50 DM detector is a two-phase (liq-uid and gas) argon TPC, described in Ref. [4] andshown schematically in Fig. 1. Briefly, a cylindri-cal volume containing UAr is viewed through fused-silica windows by top and bottom arrays of 19 3 (cid:48)(cid:48)
Hamamatsu R11065 photomultiplier tubes (PMTs).The windows are coated with Indium-Tin-Oxide(ITO) which acts as the cathode (bottom) and anode(top) of the TPC. The PMTs operate immersed inLAr and are fitted with cryogenic preamplifiers [5].The pre-amplifiers allow operation at reduced PMTgain, taming breakdown issues in these PMTs.LAr is boiled to form a 1 cm-thick gas pocket un-der the anode window. A grid 4 . / cm drift re-gion in the main active volume from a higher-fieldextraction region.The side wall of the active LAr volume is a Teflonreflector. The inner surfaces of the Teflon reflectorand the windows are coated with tetraphenylbutadi-ene (TPB), which shifts the 128 nm argon scintilla-tion light to 420 nm, allowing transmission throughthe windows and detection by the PMTs.Interactions in the active volume result in ER orNR events which produce primary scintillation (S1)as well as ionization in the LAr. Ionization elec-trons surviving recombination at the event site aredrifted to the liquid-gas interface, where the extrac-tion field injects them into the gas region. In thegas, the electric field is large enough to cause the electrons to produce a second signal (S2) by gas pro-portional scintillation. S1 and S2 are both measuredwith the PMT arrays. S1 (or, for higher resolution,a linear combination of S1 and S2) measures energy;the drift time ( t drift ), the time between the detectionof S1 and S2, measures the vertical ( z ) location ofthe event; and the pattern of S2 on the PMT arraysmeasures the x and y coordinates of the event.The DarkSide-50 veto system is described in de-tail in Ref. [7]. The LSV is filled with 30 t of bo-rated liquid scintillator that detects neutrons viaboth prompt signals from thermalization and de-layed signals from capture products. It detects neu-trons producing NR in the LAr TPC with extremelyhigh efficiency (see Sec. V C) and also detects abouta third of the γ -rays giving ER in the TPC. TheLSV is surrounded by the 1 kt WCV, which pro-vides shielding for the LSV and a veto for cosmicray muons. Radioactive calibration sources for thecharacterization of the TPC and LSV are deployedthrough the WCV and LSV to the side of the cryo-stat using an articulated arm described in Ref. [8].Under normal running conditions for the WIMPsearch, all three detectors are read out upon a trig-ger from the TPC that requires at least two PMTsabove a threshold of 0 . .
05 Hz of pulser-generatedtriggers, which provides an unbiased sample of detec-tor baselines and signals. Timestamps are recordedwith the data from each detector to allow later syn-chronization.
II. DATA DESCRIPTION ANDCALIBRATION
Data are recorded from the TPC and both vetoeswith each trigger. TPC data contains the waveformsfrom the 38 PMTs, digitized at 250 MHz withoutzero suppression [5]. The digitized waveforms areacquired in a single 440 µ s window, beginning 5 µ sbefore the trigger time and long enough to includeS1 and S2, given the maximum electron drift time of376 µ s. Data from each PMT in both vetoes are digi-tized at 1 .
25 GHz and zero suppressed with a thresh-old of ∼ .
25 PE. Veto data are recorded in a 200 µ swindow beginning 10 . µ s before the initiating TPCtrigger [9]. A. Reconstruction
Low-level reconstruction of TPC events followsthe steps described in Ref. [4]. The digitized PMTwaveforms that make up the raw data are analyzedusing darkart , a code based on the Fermi NationalAccelerator Laboratory art framework [10], whichidentifies pulses with area (cid:38)
10 PE in the acquisitionwindow. Timing and integral information are cal-culated for each pulse. While pulse-finding is doneon the veto data, the WIMP search uses only in-tegrals over pre-specified regions of interest (ROI),described in V A 4.Of particular interest is the TPC PSD parameter f , defined as the fraction of S1 light detected inthe first 90 ns of a pulse. This parameter allows verystrong pulse shape discrimination between NR andER [11], as demonstrated in practice in our previouswork [4].In the current analysis, we perform radial fiducial-ization using transverse ( x - y ) reconstruction. Wedid not do so in previous DarkSide-50 analyses,as reconstruction of the x - y position of events inDarkSide-50 proved to be very difficult [12, 13]. Thisis believed to be due to the proximity of the topPMTs to the S2-emission region, which limits chargesharing among the 3 (cid:48)(cid:48) PMTs. The ( x - y ) positionreconstruction algorithm used here [12] starts withmaps constructed from Monte Carlo events of thesimulated light response for each PMT vs. the trueposition. Atmospheric argon data [4], dominated byuniformly-distributed Ar decays, are used to it-erate the maps to account for features in data notmodeled in the Monte Carlo. For a given event in thedata, the algorithm compares the measured patternof S2 light with the maps, finding the position thatgives the best agreement. The position resolutionis estimated to be about 0 . Bi-
Po decays. These events weredistributed across the full volume and had an S2signal size of about 20 × PE. In the absence ofany internal calibration sources with known location,we found no reliable way to calibrate the resolutionvs. the absolute position. We discuss how we dealtwith this situation to estimate the rejection and ac-ceptance of the radial cut in Secs. V E and V F.After reconstruction, data are stored in a ROOTformat [14]. This is summarized in a secondary out-put called SLAD (for SLim Analysis Data), withevent and pulse information for further study by an-alyzers. Separate SLAD are made for the TPC andveto data. These are then matched event-by-eventusing the timestamps in each data stream.
B. Calibration
The single-photoelectron (SPE) response of eachPMT in the TPC and vetoes is determined by inject-ing low-light-level laser pulses into the detector vol-umes via optical fibers. The SPE means and widths are determined in the TPC and vetoes as describedin [4, 9, 15].The S1 light yield is measured using m Kr intro-duced into the recirculating argon [16]. The m Krdecays to Kr in two sequential transitions, wherethe second transition has a mean-life of 222 ns andthus is usually reconstructed as part of S1. This pro-vides a monoenergetic signal in the TPC that is alsoused to calibrate the S1 signal z -dependence and theS2 signal radial dependence as described in [4, 17].The zero-field UAr photoelectron yield at the TPCcenter, measured at the 41 . m Kr peak, is(8 . ± .
2) PE / keV. m Kr campaigns taken at var-ious times during the running period indicate thatit remained stable within ∼ . γ -ray lines fromtrace radioactivity in detector components. Theselines at higher energies consist of multiple Comp-ton scattering events, requiring special techniquesto deal with events with multiple S2 pulses [18].We construct the nuclear recoil energy scale fromthe S1 signal using the photoelectron yield of NRsof known energy measured in the SCENE experi-ment [20, 21], via the procedure described in Ref. [4].Briefly, SCENE measures the ratio of NR yield at200 V / cm to that of m Kr at zero field. Our zero-field photoelectron yield for m Kr then gives the NRPE yield vs. S1 in DarkSide-50. We assume constantNR PE yield above the highest SCENE-measuredenergy, 57 . nr .Initial operations of DarkSide-50 with atmo-spheric argon (AAr) [4] provided a large sampleof Ar β decays. This data set of uniformly-distributed, single-sited ER events is used as ourprimary calibration of f (see Sec. V E).Coincident γ rays from Co decays in the cryo-stat steel are used to determine the LSV light yieldand to measure the time-offset between the TPC andLSV signals. Cosmic-ray muons align the timing ofthe WCV with the other detectors.
AmBe neutron calibrations are used to deter-mine the f distribution for NR. AmBe NR can-didates are selected by requiring a single-sited TPCevent in prompt coincidence with an LSV signal con-sistent with a 4 . γ ray from the source. The f distributions for each S1 bin in this data sampleare fitted with an analytic model based on a modi-fied ratio-of-two-Gaussians treatment [22, 23]. Thisanalytic model is used only for calculating the ac-ceptance of the final f vs. S1 WIMP search box(see Sec. V F). AmBe calibrations are used to establish theheavily-quenched visible energy of the neutron cap-tures on B that give the LSV its high efficiency forcaptures [7]. Coincident γ rays preclude the use of AmBe for calibrating the prompt neutron ther-malization signal in the LSV. For this we use an Am C source [24] with a thin degrader that re-duces the α energy below that needed to reach thelowest excited state of O. With lead shielding toabsorb the
Am x-rays, this results in a neutronsource very low in coincident γ rays, allowing studyof isolated neutrons (see Sec. V C). C. Data Set
The data set reported in this paper consists of532 . ∼ m Kr,
AmBe, and Am C, last-ing a few days to a few weeks), data were takencontinuously in DM-search mode, and running con-ditions were very uniform throughout this period.Data were usually divided into runs of 6-hour dura-tion.The trigger rate varied from 1 . . . γ raysfrom detector materials and Kr and residual Arin the UAr [17].Blinded data (see Sec. IV) were checked run-by-run for hardware and software issues that warrantedrun removal. The main causes were oscillationsin veto-channel front end electronics (34 . . ∼
10 min duration), in-dividual TPC PMTs breaking down or emittinglight, and other causes. After eliminating theseruns, the total livetime of the data set was545 . . . ± .
5) kg (see Sec. V F), the exposure reportedhere is (16 660 ± S1 [PE]30000 35000 40000 45000
Events / [250 PE]
DataPo Rn Po Energy [MeV]4 4.5 5 5.5 6 6.5
FIG. 2. α spectrum. The events are selected by requir-ing the first pulse to be alpha-like (0 . < f < . z -dependence of the light yield [25]. The Rn and
Popeaks are fitted with Gaussian+exponential functions,and the energy scale at the top of the plot is set by the
Po peak [26]. The
Po is fitted with a Crystal Ballfunction, the shape of which suggests that the
Po ison the surface beneath the TPB.
III. BACKGROUND SOURCES ANDMITIGATION
Processes that provide backgrounds to the DMsearch fall into two main categories. The first cate-gory consists of α decays and neutrons, which yieldNR or NR-like signals strongly resembling DM scat-ters. The second category consists of ER-inducingprocesses, primarily β decays and γ -ray interactions,that, although more copious, are suppressed by thepowerful PSD in LAr. In this section we describethe major background categories and our mitigationstrategies. The background rejection levels achievedand the levels of background expected in the finalsample after all cuts are given in Sec. V. A. α Decays
For α decays in the active LAr, or on or very nearsurfaces touching it, both the α itself and the re-coiling daughter nuclide give NR-like f . Given thehighly radiopure materials selected for constructionof the TPC, the α emitters of interest are primarilyradon daughters either deposited on detector sur-faces during fabrication and assembly or introducedinto the circulating LAr during the experiment.We have seen and studied both surface and bulk-LAr α events in DarkSide-50 [26], with an energyspectrum shown in Fig. 2. The measured spe-cific activities of Rn and
Po in the LAr are(2 . ± . µ Bq / kg and (1 . ± . µ Bq / kg, re-spectively [26]. α decays in the bulk LAr give sharppeaks in S1 which are far outside the DM NR en-ergy range, leaving surface events to contend withas background.The major source of surface background is Pb-supported
Po decays. With the full-energy Po α ’s outside the DM-search energy range, the poten-tial background sources are either α ’s degraded inenergy or events with the daughter Pb atom re-coiling directly into the LAr. The broad lineshapeof the
Po signals identified in Ref. [26] and shownin Fig. 2 gives clear evidence for degraded α events.The recoiling atoms alone would not produce enoughlight in the LAr to be a background, but simultane-ous α scintillation in the TPB can boost the eventinto the DM search region [27].Surface events on the cathode and grid are easilyrejected by drift time cuts ( z fiducialization). Theobserved rate of Po α ’s on the ∼ . side reflec-tor is (2 . ± .
01) mBq / m . Section V B discussesseveral characteristics of surface events, beyond theirradial location, that allow them to be rejected. B. Neutrons
Individual elastic scatters of neutrons in theLAr are indistinguishable from DM-induced scat-ters, making these a critical background. Consider-able efforts in DarkSide-50 were devoted to reducingand suppressing neutron background, most notablystringent materials selection and the development ofthe veto system.Neutrons are produced by cosmic-ray muons in-teracting in the rock and other materials surround-ing the experiment (cosmogenic) and by trace ra-dioactivity of detector materials (radiogenic). Manyneutron-induced events can be rejected because, un-like DM particles, the neutrons are very likely tointeract multiple times in our detectors. Multipleinteractions in a single TPC event are detected byresolving multiple S2 pulses. Both cosmogenic andradiogenic neutrons leaving WIMP-like signatures inthe TPC also leave signals in the LSV with highprobability, allowing them to be rejected with highefficiency. (See Sec. V C for details.) Additional re-jection in the TPC comes from fiducialization (againdue to the relatively short neutron interaction lengthin LAr), and from requiring S1 to lie in the WIMPsearch range. The WCV gives additional rejectionof cosmogenic events.Radiogenic neutrons come from spontaneous fis-sion of
U and from ( α , n ) interactions, where the α ’s come from uranium and thorium chain activity.In DarkSide-50, the spontaneous fission events areeasily rejected due to the high LSV efficiency forneutrons and moderate efficiency for γ rays, com-bined with the average neutron multiplicity for U spontaneous fission of 2.01 and the high γ -ray mul-tiplicity. This leaves ( α , n ) as the main source ofpotential radiogenic neutron background.Our ( α , n ) calculations [28], normalized to the as-sayed construction materials activities described inSec. III D, indicate that the dominant sources ofneutron production in the TPC and cryostat arethe PMTs and a viton o-ring in the outer cryostatflange. For neutrons that reach the TPC and givesingle-scatter NR-like events in the fiducial volume,Geant4-based Monte Carlo simulations (G4DS) [29]indicate that the o-ring contribution is negligible,and the PMTs, specifically the borosilicate-glass“stem” and the ceramic plates that hold the dyn-odes, are the source of >
90 % of the radiogenic neu-tron background in the TPC. C. β Decays and γ Rays
The WCV and LSV provide efficient passiveshielding against β ’s and γ rays originating outsidethe TPC cryostat, leaving the cryostat and TPCcomponents (including the LAr) as the only im-portant sources of β/γ -induced background. Ar-gon derived from the atmosphere (AAr) contains ∼ / kg of cosmic-ray produced Ar activity [30,31]. Ar is a β emitter and dominated the trig-ger rate and background in DarkSide-50 when itwas filled with AAr [4]. The DarkSide collaborationhas identified, extracted, and purified argon fromunderground sources (UAr) [32–34] that has only(0 . ± .
11) mBq / kg of Ar activity [17]. The useof UAr drastically reduces the ER background inDarkSide-50. Even including the 1 . ± . / kgof Kr found in the current DarkSide-50 UAr fill [17,corrected for the 15.5-y mean life], the dominantsource of ER background is Compton scatters of γ rays from the TPC and cryostat.PSD via f is the major rejector of γ -inducedER. In Ref. [4] we showed that PSD with f re-jected the single-sited ER events from Ar decay toa level of one in 1 . × . Unlike the ER events from Ar, γ -induced events are often multi-sited and arenot uniformly distributed, so requiring single-scatterevents and fiducializing give additional suppression.Many γ -induced events in the TPC are in promptcoincidence with additional interactions in the LSV,giving further rejection.The fundamental limitation on PSD removingsingle-sited ER scintillation events is at low energies,where photoelectron statistics limit rejection. How-ever, among γ -ray-induced events, there are somein which a γ ray multiple-Compton scatters, scat-tering once in the active LAr and also in a nearbyCherenkov radiator such as the Teflon reflector orthe fused silica windows of the TPC or PMTs. Theall-prompt Cherenkov light adds to the prompt com-ponent of the normal ER-like S1 and can give aNR-like f . As discussed in Sec. V E, these mixedscintillation+Cherenkov events, hints of which hadalready appeared in Ref. [17], prove to be the dom-inant background in the experiment. D. Determination of Activities in DetectorMaterials
The γ -ray- and neutron-induced backgroundsoriginate primarily in the trace radioactivity of de-tector components. The DarkSide collaboration car-ried out an extensive program of assays to select ra-diopure materials and to understand their residualactivities. Our background estimates are based ona radioactivity model that starts with the resultsof the assays. However, due to a late-developingneed to use R11065 PMTs instead of the plannedlower-activity R11065-20s, we do not have assays ofthe PMTs installed in DarkSide-50, but rather onlya single measurement of three R11065s from earlyproduction batches.For this reason, activities in the PMTs are esti-mated by fitting spectra generated by Monte Carlofrom activities in various detector locations to a re-constructed TPC energy spectrum [18, 35]. Sincethe actual construction materials used for the cryo-stat components (stainless steel body, flanges, nuts,bolts, pipes/feedthroughs, Viton o-ring, multi-layerinsulation) were assayed, their respective activitiesin the fitting process are fixed to the assayed values.The Ar and Kr in the LAr are fixed to their val-ues as reported in [17], with the Kr corrected forits decay since that measurement.We consider the activities of these isotopes in thePMTs: Co, K, Th,
U, and
U (allow-ing secular equilibrium to be broken, with
Ra asthe top of the lower chain). The main hosts of ra-dioactivity in the PMTs are the borosilicate glassstem at the back of the PMT, the ceramic insu-lators supporting the dynodes, and the Kovar cas-ing. Comparing the results of assays of the ceramicinsulators, a Kovar casing, and various versions ofwhole R11065 PMTs, the fraction of each activityin each PMT component was inferred, and we fitthe summed PMT activities keeping these fractionsfixed.The fit is done iteratively, estimating the PMTactivities by taking advantage of certain high-energy γ rays unique to individual decay chains. Th ac-tivity in the PMTs is estimated first by fitting the2.6 MeV
Tl peak, where the contribution fromthe other decay chains is low.
Th activity is then
Energy [keV]0 500 1000 1500 2000 2500 3000
Events / [2 keV] Th CryoK Co U
238 up U U Kr Ar TotalDATA
FIG. 3. Measured γ -ray spectrum in the TPC (darkgreen) with the total from the fit (dark blue) includingcryostat activity (light blue) fixed to assayed values andfitted PMT activities (see legend). The energy scale isthe combined S1-S2 ER energy scale (see Sec. II B). fixed at the fitted best value, and the U lowerchain ( U low ) activity is estimated by fitting the1.76 MeV Bi peak, and so on. The
U and the
U upper chain ( U up ) activities are fitted withone free parameter to preserve their natural abun-dance ratio. The activity estimates from this proce-dure are presented in Table I and the resulting en-ergy spectrum is shown in Fig. 3. We note that leav-ing Kr and Ar free in the fit along with
U and U up returns significantly different rate estimatesfor these four decay chains; however, switching be-tween the rates so-obtained and those presented inTable I has no impact on the predicted backgroundin the WIMP search region. Note as well that, whilethe WIMP-search region is far to the left in Fig. 3,the thorium and lower uranium chains, fitted to theright side of the plot, are the main contributors toCherenkov radiation, from electrons scattered by thehigh energy γ rays, and neutrons, produced by highenergy α ’s.The uncertainty on the PMT background activityfrom a given chain is estimated by propagating theuncertainty on the measured cryostat activity in thatchain. (The uncertainties from the fit are negligible.)In particular, the uncertainties on Co, K, Th,and U low , the main contributors to Cherenkovbackground due to their high energy γ rays, are es-timated to be < IV. BLINDING SCHEME
We performed a blind analysis on the 532.4-live-day data set. This means that candidate selec-tion/background rejection was designed, and thebackground surviving cuts was estimated, withoutknowledge of the number or properties of events inthe final search region.Blindness was imposed by a “Blinding Module”
TABLE I. TPC component activities, estimated by fit-ting Th PMT , U lowPMT , K PMT , and Co PMT in se-quence, followed by U PMT and U upPMT while Krand Ar are fixed at their measured rates as reportedin [17]. Cryostat activities are fixed at their measuredrates from assays and summed across all cryostat loca-tions. PMT activities are summed across all locationswithin the PMTs and across all 38 PMTs. For compari-son, we show the assayed activities for 3 R11065 PMTs(scaled to 38 PMTs), which have an estimated additionalsystematic uncertainty of about 25%.Source PMTs [Bq] Cryostat [Bq]fitted assayed assayed
Th 0.277 ± ± ± K 2.74 ± ± +0 . − . Co 0.15 ± ± ± U low ± ± +0 . − . U up ± ± +0 . − . U 0.19 ± ± +0 . − . Liquid Argon Activity [mBq/kg] Kr 1 . ± . Ar 0.7 ± in SLAD. An unblinded SLAD was produced firstand kept in a protected directory. Then the SLADprogram operated on it with the Blinding Moduleto produce the blinded, analyzer’s version. Blindedevents appear in the output files, but with all TPCdata except the event ID, timestamps, and the live-time associated with the event set to −
1. In theinitial blinding, used through most of the analysis,details of two categories of events were hidden fromusers. The first category consisted of events with S1and f falling within the “blinding box”, shown inFig. 4 superimposed on the published data set fromRef. [17] before any analysis cuts. The blinding boxwas designed to be larger than any expected finalWIMP-search box and to be just above the main ERband. It was applied to all events, even those thatfailed major analysis cuts (e.g., single-pulse events,events with multiple S2’s, etc.). The second categoryconsisted of events randomly chosen with a proba-bility of 2 × − . The random fraction was chosento have enough fluctuations to obscure the count-ing of possible candidate events in the final analysisstages, where it was anticipated that the number ofcandidates would be small or zero when final cutswere applied.Besides the events outside the blinding box, opendata available to analyzers included the large AArdata set [4], the initial 70.9-live-day UAr dataset [17], laser calibration data, and all data fromcampaigns with calibration sources present. Duringthe analysis, we opened sections of the blinded dataoutside of the WIMP search region to provide sam-ples enriched in particular backgrounds for study,and later, when the background predictions weremature, to test the predictions. Several such test f FIG. 4. f vs. S1 showing the blinding box (red) appliedto the Ref. [17] data set. regions, described below, were studied before the fi-nal box opening. V. BACKGROUND ESTIMATION ANDREJECTION
The goal of the blind analysis is to design a set ofcriteria that rejects background to a pre-determinedlevel without prior inspection of events in the finalsearch region (the “box”), which itself must be de-signed as part of the analysis procedure. We choose0.1 event of expected background as an acceptablelevel, giving a <
10% Poisson probability of seeingone or more background events in the search box.
A. Event selection
As in earlier DarkSide-50 analyses, the initially-dominant ER background and the power of LAr PSDsuggest an analysis structured around the f vs. S1distribution. We thus choose the design of the f vs. S1 box as the final analysis step, after allother cuts are defined.We began with the set of analysis cuts developedfor earlier analyses [4, 17]. Some of these cuts weremodified for this analysis, and some new ones weredeveloped – the new or modified cuts are indicatedwith asterisks. We introduce all the cuts here withbrief descriptions; the full set is listed in the accep-tance table, Table V. The motivations for some ofthe cuts will be elaborated on in the sections de-scribing the relevant backgrounds.
1. Event quality cuts
AllChan : data are present for all TPC channels inthe event.
Baseline : baselines for the digitized waveforms aresuccessfully found in all TPC channels.
VetoPresent : the event has GPS-timestamp-matchedveto data.
TimePrev* : the event occurs at least 400 µ s afterthe end of the inhibit window of the previous trigger(that is, at least 1 .
21 ms after the previous trigger).This removes events that triggered on an S2 whoseS1 occurred during the inhibit window.
2. Basic TPC event cuts
These cuts are designed to ensure that passingevents are single-scatter events that triggered on S1and have a single valid S2.
S1start : the first pulse occurs at trigger time.
Npulse : there is a second pulse, presumed to be S2.A third pulse is allowed only if its timing is consis-tent with the small tertiary pulses produced whenS2 light photoionizes the TPC cathode.
S1sat : the first pulse does not saturate the digitizers.
MinS2uncorr* : the second pulse is required to be ≥
200 PE before position-based corrections, the ap-proximate threshold for successful reconstruction ofthe event’s radial position. For reference, the uncor-rected S2’s of interest in this analysis are >
400 PE.
S2f90 : the second pulse has f < xyRecon : the x - y reconstruction algorithm success-fully derives transverse coordinates of the event fromS2. MinS2/S1 : a more refined S2 cut that removes eventswith unphysically small S2/S1. The cut is set to re-move events in the lowest 1% of the S2/S1 distribu-tion of
AmBe NRs.
3. Surface background cuts
These cuts were all developed for the current anal-ysis [26]. They are described in Sec. V B.
LongS1tail* : removes events with S1 with a longtail, consistent with laboratory measurements of α -induced scintillation in TPB wavelength shifter. MaxS2/S1* : removes events in the highest 1% of theS2/S1 distribution of
AmBe NRs. This cut tar-gets the “Type 2” surface background with uncorre-lated S1 and S2 described in Sec. V B. This can alsobe a powerful discriminant between NR and ER andis the basis of WIMP discrimination in LXe TPCs.In LAr TPC’s it is effective against high-energy ERs,but it is not effective at low S1, where further rejec-tion is most needed.
S2LEshape* : removes events in which the shape ofthe leading edge of the second pulse is not consistentwith the shape of a true S2 pulse [36].
S1TBA* : removes events with a z location deter-mined from the S1 top-bottom asymmetry that isnot consistent with the z location determined fromS2 via t drift .
4. Neutron background cuts
The neutron veto cuts are essentially unchangedfrom the first UAr analysis [7, 17].
LSVprompt : rejects events with > LSVdelayed : rejects events with > µ s after a TPCtrigger. This interval can be compared to the cap-ture lifetime of 22 µ s in the boron-loaded liquid scin-tillator. The long acquisition window and searchinterval allow us to veto efficiently via the emitted γ rays even when the neutron captures in TPC ma-terials with long capture lifetimes. LSVpre : rejects events with > − . µ s before a TPC interac-tion. CosmicMu : rejects events with a WCV signal >
400 PE or an LSV signal > µ s acquisition window. This vetoscosmic-ray muons or their showers and thus cosmo-genic neutrons. CosmoActiv* : a“cosmic ray activation veto” is ap-plied if a TPC event occurs within 0.6 s (shorter thanin previous analyses) following a triggered event fail-ing the
CosmicMu cut. This removes some delayedneutrons produced by cosmic-ray-activated isotopesin the detectors.
5. ER background cuts
PSD via f is the primary discriminant againstER backgrounds and is used to define the finalWIMP search box via the procedure discussed inSec. V E. We found in this analysis that scintilla-tion+Cherenkov events dominated the tail of the f distribution near the WIMP search region. Theythus determined the search box needed to reduce thetotal background to < tdrift : vertical fiducialization via the time betweenS1 and S2 ( t drift ) is effective against γ rays from thePMTs, their primary source. We use the same ver-tical fiducialization as in the previous analyses, re-moving 40 µ s of drift time ( ∼ s] m Drift time [
FIG. 5. Radial cut (red) shown on events in the ini-tial blinding box shown in Fig. 4. All event qualitycuts (Sec. V A 1), all basic cuts (Sec. V A 2) through
MinS2uncorr , and vertical fiducialization via t drift havebeen applied. bottom of the active volume. Though the ER back-ground determined the location of the cut, it is alsoclearly important for surface background, notablyserving to eliminate α decays occurring on the TPCcathode and grid. S1pMaxFrac* : for “S1 prompt maximum fraction”,removes events with S1 too concentrated in any onePMT. These events are likely to have interactionsgiving Cherenkov light in the fused silica PMT andTPC windows. A variant of this cut was used inpast analyses, but it was modified for the currentanalysis to use only prompt light, boosting its ef-fectiveness as a Cherenkov discriminant. This cutis extremely effective against fused silica Cherenkov,leaving scintillation+Cherenkov in the Teflon reflec-tor as the main surviving ER background.
S1NLL* : squeezes further rejection from the S1 PMTpattern, targeting the multi-sited nature of scintil-lation+Teflon Cherenkov events. The pattern of S1light on the PMT arrays is required to be consistentwith the reconstructed x - y position via a negative-log-likelihood comparison to templates derived fromAAr data (dominated by single-sited Ar β decays). RadialFid* : a radial fiducial cut. The radial cutis a drift-time-dependent radial contour chosen toreject a fixed fraction of G4DS-simulated scintilla-tion+Teflon Cherenkov events (see Sec. V E) in eachdrift time bin. The final cut varies from ∼
23 mmfrom the wall at the top and bottom of the TPC to ∼ γ rays, includ-ing mixed scintillation+Cherenkov events) are seento be concentrated near the top and sides of the de-tector as expected. Despite the limitations of the re-construction algorithm, the concentration of eventsand the impact of the cut are clear. B. Surface events
Alphas coming from isotopes embedded in detec-tor surfaces exhibit a degraded energy spectrum andcan fall within the energy and f regions of inter-est, as can the recoiling nucleus in an α decay [27].We find that the S2 signal for surface events inDarkSide-50 is heavily suppressed, possibly due toloss of drifting electrons very close to the side reflec-tor of the TPC. Few surface events have an S2 thatis large enough to pass analysis cuts, with the ma-jority having no discernible S2 pulse. We call these“S1-only” events.We therefore consider two cases for a surface decayto become a background event. Type 1: the rare caseof a surface event with a true S2 that passes analysiscuts. Type 2: an S1-only event that happens to oc-cur before an uncorrelated “S2-only” event such thatthe combination appears to be a regular event withone S1 and one S2. We estimate the backgroundrates of these two cases separately.Type 1: In the open data with S1 >
600 PE, sur-face events only pass S2 analysis cuts at energies farabove the region of interest (S1 >
20 000 PE) due tothe low electron collection efficiency along the sidewall, with an acceptance that declines with decreas-ing S1. Extrapolating this effect into the WIMPsearch region and applying it to the observed rate ofS1-only events, we estimate that < LongS1tail , that accepts 99% of
AmBeNR events. Applying the cut to a sample of surfacedecays obtained in Ref. [37] results in a rejectionfactor of more than 100, giving an expectation of < RadialFid and
MinS2uncorr cuts, which isdifficult to estimate and not included in the back-ground estimate.Type 2: True S2-only events are rare, but appar-ent S2-only events are present in the form of ordinaryevents near the top of the detector. In these events,S1 and S2 can be so close in time ( t drift (cid:46) µ s) thatthey are not resolved by our reconstruction. Thereal or apparent S2-only events and S1-only surfaceevents are uncorrelated and of constant rate, allow-ing the use of Poisson statistics to predict the ex-1 TABLE II. Neutron veto efficiencies for Am C sourcedata. Errors are statistical. The prompt cut targetsneutron thermalization; the delayed cut neutron capture.Prompt cut only Delayed cut only Combined0 . ± . . ± . . ± . pected number of S1+S2 pileup background events.We mitigate Type 2 background by imposing threeadditional requirements on the apparent S2 signal.The first is the maximum S2/S1 cut, MaxS2/S1 ,which removes events with S2/S1 larger than 99%of
AmBe NR events of the same S1. This cuttargets S1-only events with an accidental S2 eitheraugmented by an unresolved S1 or simply uncorre-lated with S1. The second,
S2LEshape , removes un-resolved S1 and S2 by requiring that the apparent S2pulse have the ∼ µ s risetime of a true S2 pulse [36]rather than the few-ns risetime of S1. This S2 shapecut is applied via the ratio of the integrals of thefirst 90 ns and first 1 µ s of the S2 pulse. The third, S1TBA , removes events with S1 and S2 pulses thatoriginate from different positions. We require thatthe z positions inferred from the top-bottom asym-metry in the detected S1 light and from t drift differby no more than 3 σ , as determined from uniform Ar events from AAr. These last two cuts are eachdesigned to have >
99% acceptance for nuclear re-coils. After application of these additional cuts, weexpect 0 . ± . C. Radiogenic neutrons
The estimate of radiogenic neutron backgroundstarts with a direct measurement of the LSV ef-ficiency for detecting neutrons that leave WIMP-like signatures in the TPC. We do this with the Am C source (see Sec. II B) deployed just out-side the TPC cryostat. Am C calibration dataare taken in the same trigger configuration as nor-mal WIMP-search data, with the TPC triggeringboth vetoes. The standard WIMP analysis is runto find NR candidates in a preliminary version ofthe f vs. S1 WIMP-search box. The neutron vetoefficiency is then calculated as the fraction of TPCNR candidates that fail the standard WIMP-searchLSV cuts described in Sec. V A 4. From a sample ofabout 25,000 events that pass TPC NR cuts, we findthe veto efficiencies shown in Table II. Radiogenic-neutron background events differ from Am C-neutron events in their origin point and energy spec-trum, but Monte-Carlo simulations indicate a higher veto efficiency for radiogenic events; we do not applythat correction here.One of the test regions opened prior to the fi-
S1 [PE]100 150 200 250 300 350 400 450 500 f RadiogenicCosmogenicFission candidate50% NR acceptance
FIG. 6. Neutron candidates in the Veto Prompt Tagsample. The closed curve is the final WIMP-search box,and the dashed curve is the 50% NR contour, aroundwhich neutron-induced events should be distributed. nal unblinding was the “Veto Prompt Tag” (VPT)sample, which unblinded any event that failed the
LSVprompt cut. The high neutron efficiency of theprompt cut allows radiogenic neutron events to becounted directly in the VPT sample. The narrowintegration window of the LSV-prompt cut meansthat, even with its 1 PE threshold, the accidentaltagging rate is <
1% (see Table V). Thus the VPTtag accidentally accepts practically no real WIMPevents, and γ -induced events are the only back-ground to a neutron count using the VPT sample.To get a sample of confirmed neutron events fromthe VPT sample, we use a modified version of theLSV-delayed cut. The modification is needed fortwo reasons: the sliding window used for the LSV-delayed cut overlaps the LSV-prompt window (al-beit with a higher threshold), and the LSV has ahigh rate of PMT afterpulses, so the delayed regionis heavily populated by afterpulses from the promptsignal. The modified LSV-delayed cut uses LSVcluster-finding [7] to identify veto hits. To countas a likely neutron capture signal, the cluster is re-quired to be >
200 ns after the veto prompt time, tohave the number of PMTs contributing to the clus-ter greater than that expected for afterpulses, and tohave an integral >
100 PE, which includes the α + γ capture peak for B [7] and captures on H and C.The neutron efficiency for this restricted capture sig-nal is calculated from Am C data to be ∼ B α -only capture peak and events from the α + γ capture peak in which the γ ray escapes intothe cryostat. (None of these complications or effi-ciency losses apply to the actual neutron vetoing inthe WIMP search, which is done with simple inte-grals over regions-of-interest – see Sec. V A 4.)The selected neutron candidate events are shownin Fig. 6, where we label neutron candidates thatfail the CosmicMu cut as “Cosmogenic”, and a spec-tacular event with three neutron capture signals as2“Fission”. There is one observed radiogenic ( α , n )neutron in the WIMP-search region in the VPTsample. With an acceptance of 0.79 for the neu-tron counting and a veto efficiency greater than (cid:15) dataAmC = 0 . ± . < .
005 events, with 100 % sta-tistical error.
D. Cosmogenic Neutrons
The rate of cosmogenic neutron background isestimated via simulation using FLUKA (version2011.2c) [38, 39]. The simulation is carried out inmultiple steps. In the first and most time-consumingstep, cosmic-ray muons are started 7 m above theceiling of LNGS Hall C and propagated through the7 m of rock. The muon and any produced secon-daries are stopped and stored when they reach theceiling of Hall C [40]. The stored events are restartedand propagated onto the WCV and are only pro-cessed further if there are no muons entering thewater tank with energy > > . γ -ray or another neutron. None of these 7 eventshave TPC energy deposits in our WIMP-search re-gion.If we take a 90% CL upper limit of 2.3 of 1388events reaching the TPC passing the veto cuts andtake the 7 (neutron+ ≤ . < . ∼ E. Electron Recoil Backgrounds
With the PSD performance demonstrated in theAAr run of DarkSide-50 [4] and the reduced ratefrom the use of UAr [17], the most tenaciousER background is mixed scintillation+Cherenkov events. To estimate ER background surviving cuts,a data/MC hybrid model was developed, which in-corporates our GEANT4 simulation to model the γ -ray kinematics and Cherenkov radiation while draw-ing f from the AAr data.A very large sample of Monte Carlo simulatedevents, equivalent to about 90 live-years of data, wasgenerated. Statistics this large were needed to en-sure that 0.05 events of ER background in our expo-sure would be represented by at least 3 Monte Carloevents. This was chosen so that, based on the 68%C.L. interval constructed in [41], the statistical un-certainty on the background prediction would be nomore than a factor of two. Events were generatedrepresenting the decay chains and TPC componentslisted in Table I. These were later normalized to theactivities in that Table and the accumulated live-time of the WIMP-search data. To save on compu-tation time, S1 photons for individual LAr scattersare typically generated but not tracked. However,for events with Cherenkov radiation, all photons –including those from LAr scintillation, if there is anaccompanying scatter in the LAr – are generated andtracked using optical parameters tuned on data [29].Cherenkov light can be generated in the fusedsilica PMT windows, the fused silica TPC win-dows, and the Teflon reflectors surrounding the ac-tive LAr volume. The optical parameters affectingthe Cherenkov radiation and collection are adjustedto match the observed “pure Cherenkov” eventsin data, which are easily identified as single-pulseevents with f ≈ . Na source deployed next to the TPC cryostat. Themodeling of the generation of Cherenkov photonsand their collection by the PMTs was subsequentlyvalidated against pure Cherenkov events from theopen UAr data set and from the
Am-Be cali-bration data, and the scintillation+Cherenkov back-ground model was frozen.The model constructs the f of a simulatedmultiple-scatter event from the f ’s of its compo-nent scatters. Energy depositions in the LAr witha vertical separation < .
65 mm (motivated by stud-ies using our electronics simulation) are merged tomodel our S2 two-pulse resolution. Figure 7 showsthat f for unresolved multiple-scatter events ishigher than that of single-scatters with the same S1,since mean ER f increases with decreasing S1. Weestimate that unresolved multiple-scatters are 3% ofER events with 100 < S1 <
180 PE (the regionwhere this is estimated to have the most impact).With a targeted background level of < . f0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ] Events / [0.01 f - Single-ScatterUnresolved Multi-ScatterScint. + Fused-Silica Cheren.Scint. + Teflon Cheren.(after S1pMaxFrac cut)Scint. + Fused-Silica Cheren.(after S1pMaxFrac cut)Scint. + Teflon Cheren.
FIG. 7. Modeled f profiles of single-scatter, unresolvedmultiple-scatter, scintillation+fused silica Cherenkov,and scintillation+Teflon Cherenkov 2-pulse events with100 < S1 <
180 PE. Decay chains and activities in the vari-ous detector locations in Table I are used. It is clear thatthe
S1pMaxFrac cut is very effective on high f eventswith a FS Cherenkov component (blue), hence the mostproblematic background comes from Teflon Cherenkov. tions far out in the tail of the ER f distribution.For this analysis, we do not extrapolate using ananalytic model fit to data. Instead, we use our high-statistics AAr data set [4], which is dominated byuniformly distributed, single-sited ERs from Ar β -decays, as the f probability distribution func-tion. In particular, modeled single-scatter events inthe LAr ( Ar and Kr β -decays and single Comp-ton scatters of γ rays) draw directly from the AAr f vs. S1 distribution, unresolved multiple Comp-ton scatter events draw multiple times, and scintil-lation+Cherenkov events have their scintillation S1and f augmented with the Cherenkov light pre-dicted by the G4DS model, treating the Cherenkovradiation as entirely prompt. The available AArstatistics, which represent about 15 years-worth ofsingle-scatter events in UAr running, are sufficient,given the randomization that occurs when the scin-tillation f ’s are combined with Cherenkov light.ER background with Cherenkov light radiated inthe fused silica PMT and TPC windows results inabnormally large amounts of light concentrated inindividual PMTs. As shown in Fig. 7, the S1 promptmaximum fraction cut, S1pMaxFrac , is very effectiveagainst fused-silica Cherenkov, leaving Cherenkov inthe Teflon, primarily the cylindrical side wall of theTPC, as the dominant ER background.Attempts to find cuts effective against scintilla-tion+Teflon Cherenkov events were only modestlysuccessful. A major motivation for introducing a ra-dial fiducial cut was its observed impact on high- f events in the open data, as discussed below.Some cuts are difficult or impossible to apply tomodeled events, so their impact in the search regionis hard to estimate. These include cuts based on S2,which was too costly in computation time to fully f0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 ] Events / [0.004 f - Ar Data VPTModel VPT
FIG. 8. f for events with 100 < S1 <
180 PE compar-ing single-scatter ER data ( Ar), VPT data passing allmajor cuts, notably
S1pMaxFrac , and simulated VPTevents using the f model including Cherenkov light.The normalization of the simulation is absolute, usingthe activities in Table I and the 532 . simulate in the large Monte Carlo sample, and cutsbased on detector foibles like the surface backgroundcuts discussed in Sec. V B. Although they are appliedto the data, we do not include potential rejectionfrom the S2/S1 cut, the NLL cut, and the surfacebackground cuts in our ER background estimate.Final testing of the model was carried out by un-blinding various test samples. These samples are oftwo types. The first type consists of samples cre-ated by inverting an established analysis cut, givingevents already tagged as background. The secondtype consists of regions with small WIMP accep-tance, outside any plausible final f vs. S1 box, butinside our (initially generous) blinding box.The first of these tests uses the Veto Prompt Tagsample described in Sec. V C. The number of neu-trons in this sample was found to be small, and theyare identified and removed. While the VPT allows usto look in the WIMP search region without compro-mising blindness, the statistics are low. We insteadtest the model in pre-defined regions near the searchregion with higher statistics, still dominated by scin-tillation+Teflon Cherenkov events. Agreement innumber of events between the data and model inthese regions is within two statistical standard devi-ations. Figure 8 shows the data-model agreement inthe f spectrum.In the final tests, we open two regions in the f vs. S1 plot, regions A and B in Fig. 9, af-ter applying the LSVprompt cut and all the TPCcuts other than the radial, NLL, S2/S1, and sur-face background cuts. From the model, we ex-pect these regions to be dominated by scintilla-tion+Teflon Cherenkov events. Table III shows thedata-model comparisons for the two test regions,with the model normalized to the data livetime. Thefirst to be opened was region A. As can be seen inTable III, the data and model in region A disagree4 f AB S1 [PE]50 100 150 200 250 f - - - AB FIG. 9. f vs. S1 for events (top: data, bottom: model)passing all modeled cuts (see text). Overlaid on the plotare the two final test regions (dashed red), the remain-ing blinded region (solid red, and of course hidden inthe data plot), and, for reference, NR 90% and 99% ac-ceptance contours (dashed black) and the final WIMPsearch box (solid black). Note: in the bottom plot, thehigh Monte Carlo statistics means that individual eventshave very small weights after normalization to data live-time, as reflected in the color axis of the plot. at about the three-standard-deviation level statisti-cally.Region B was designed and opened shortly afterobserving the data/model discrepancy in region A tosupplement the available data statistics. As can beseen in Table III, the observed and predicted regionB event counts are in agreement, albeit with poorstatistics.We choose to combine the statistics in regions Aand B, and interpret the observed discrepancy be-tween the data and model—a factor of 1.5—as ameasure of the model’s systematic error. Accord-ingly, we scale the model’s output up by the samefactor when making our ER background prediction.The observed data events in regions A and B arealso used to estimate the rejection of our radial fidu-cialization. After the remaining cuts not used in Ta-ble III are applied, there are 30 events, of which 13survive the radial cut. From this a rejection factorof (2.3 ± . / . TABLE III. Observed and predicted event counts in testregions A and B, shown in Fig. 9. Note that while themodel is normalized to the same livetime as the data,the model has vastly higher statistics, and thus negligiblestatistical errors. Region A Region Bevents eventsData 24 9Model 13.3 8.7 edge of the WIMP box at S1=460 PE. The pres-ence of pure Cherenkov events in the data suggeststhat having a search box extending all the way to f = 1, as in past analyses, is unnecessarily risky,so we choose to put the upper edge of the box at f = 0 .
84, which is approximately the contour thatexcludes 1% of NR. At high S1, the backgroundstudies support a lower f boundary than used inprevious analyses – we fix it along a curve thatour latest calculations show to be approximatelythe 99% NR acceptance contour. At low S1, thebox’s lower boundary is determined by the desiredtotal predicted background in the box (0.1 events inour case), and in particular, the ER backgrounds.With near-final estimates of the other backgroundsin hand, we allocated 0.08 background events tothe ER backgrounds; the corresponding lower boxboundary is drawn according to this requirement.In previous DarkSide analyses [4, 17], analyticalmodels of f fluctuations were fit to data in binsof S1, and the resulting functions were used to seta boundary that admitted equal background in eachbin. Adding Cherenkov light to the mix invalidatesthat procedure. We use the ER background modeldescribed above for this purpose, but we do not haveadequate Monte Carlo statistics for bin-by-bin as-sessment. Instead, the determination of the bound-ary is done in two steps. 1) The rough shape of theboundary is determined where Monte Carlo statis-tics are available, by finding the f that gives 0.07leakage events in each 5 PE bin, about 14 timesthe final target background. A polynomial is fit tothese points. 2) The fitted curve is translated up-ward in f until the box defined by its intersectionwith the other bounds contains ≤ ±
50% by the construction in [41]. This is thedominant uncertainty on the predicted ER and to-tal background estimates.
F. Background Summary and Cut Acceptance
A summary of the predicted backgrounds surviv-ing all cuts in the full exposure is given in Table IV.The acceptance for each cut in the analysis ex-5
TABLE IV. Predicted backgrounds surviving allcuts. The ER background includes the scintilla-tion+Cherenkov background. The f vs. S1 search boxis defined to give 0.08 ± < . ± . < . < . ± . ± . cept the fiducial cuts and the final f vs. S1 WIMPsearch box is given in Table V [35]. With the excep-tion of purely accidental losses such as those fromthe veto cuts, acceptances are measured with NRevents from the AmBe calibration data, correctedfor spatial non-uniformity when necessary. Severalof the cuts have non-negligible S1 dependence. Inthese cases, the full S1-dependent acceptance (seeFig. 10) is used to calculate the sensitivity of theanalysis, and the Table-V entry is an average value.The impact of the fiducial cuts on sensitivity arecounted in the fiducial mass. The effect of the tdrift cut, unchanged from previous analyses, is calculatedfrom the geometry and drift velocity. The accep-tance of the
RadialFid cut (see Fig. 5) requires spe-cial treatment because of our lack of an absolute cal-ibration for the x - y reconstruction and because it isin principle S1 dependent via the S2-dependent x - y resolution. We use the fact that Ar events are uni-formly distributed like WIMP scatters and
AmBeevents have NR S2/S1 like WIMP scatters to de-termine the acceptance in two steps. 1) The cut’sacceptance vs. S2 is estimated using Ar events inour AAr data, which are uniformly distributed. 2)Acceptance vs. NR S1 is then estimated by usingS2/S1 as measured in our
AmBe data to look upacceptance in the corresponding AAr S2 bin. Av-eraged over S1 in the WIMP selection region, theacceptance of this cut (after the drift time fiducial-ization) is 0 . ± . . ± .
5) kg, with most of the uncertainty comingfrom the uncertainty in the thermal contraction ofthe Teflon reflector.The f acceptance vs. S1 is determined from the f parametrization as described in Sec. II B. Fig-ure 10 shows acceptance vs. S1 for the analysis cuts.Having designed a box to achieve our backgroundtarget using cuts with understood acceptance, weproceeded to unblinding. TABLE V. Summary of cuts and their respective impacton livetime and WIMP acceptance. The average accep-tance of S1-dependent cuts are presented; acceptances > f cuts. Events sur-viving after each cut were tabulated after unblinding.Cut Livetime(cumulative) AllChan
Baseline
TimePrev
VetoPresent
CosmoActiv
S1start S1sat
Npulse tdrift (fiducial mass) 191
S1pMaxFrac
MinS2uncorr xyRecon
S2f90
MinS2/S1
MaxS2/S1
S2LEshape
S1TBA
LongS1tail
S1NLL
RadialFid (fiducial mass) 2
CosmicMu
LSVprompt
LSVdelayed
LSVpre . ± .
001 (stat) +0 . − . (syst) S1 [PE]0 50 100 150 200 250 300 350 400 450
NR Acceptance ] nr Energy [keV0 20 40 60 80 100 120 140 160 180 200
Total cut acceptance NR Acceptance fOverall NR Acceptance FIG. 10. Acceptance vs. S1. The NR Energy scale atthe top comes from the cross-calibration with SCENEdescribed in Sec. II B.
VI. UNBLINDING
Unblinding consisted of changing the access per-missions of the open SLAD (see Sec. IV), the blindedversions of which had been used for the background6 f ] nr Energy [keV0 20 40 60 80 100 120 140 160 180 200
FIG. 11. Observed events in the f vs. S1 plane sur-viving all cuts in the energy region of interest. The solidblue outline indicates the DM search region. The 1%,50%, and 99% f acceptance contours for nuclear re-coils, as derived from fits to our AmBe calibrationdata, are shown as the dashed lines. predictions, and running the analysis code applyingall cuts to it. Figure 11 shows f vs. S1 after allanalysis cuts. With the analysis cuts applied andthe data fully unblinded, no events are observed inthe pre-defined DM search region.After unblinding, we tabulated events survivingeach cut, as shown in Table V. The order that thecuts were applied is not meaningful – the ordershown in the table was chosen to be informative.Each of the last two events in Table V was cut byboth the prompt and delayed veto cuts. They arethe events in the box in Fig. 6 labeled “Radiogenic”and “Fission candidate”. VII. WIMP SENSITIVITY AND LIMIT
A limit on spin-independent DM-nucleon scat-tering is derived assuming the standard isothermalWIMP halo model, with v escape = 544 km / sec [42], v = 220 km / sec [42], v Earth = 232 km / sec [43], and ρ DM = 0 . / ( c cm ) [44]. The background-and signal-free result is consistent with up to 2 . . × − cm (3 . × − cm ,3 . × − cm ) for 100 GeV /c (1 TeV /c ,10 TeV /c ) DM particles. The minimum upperlimit is 1 . × − cm at 126 GeV /c . Figure 12compares this limit to those obtained by otherexperiments.Figure 13 demonstrates available improvements inbackground rejection, which we do not use in thisanalysis. If we require S2/S1 lower than the medianvalue for nuclear recoils and also radial fiducializa-tion to about 8 cm from the wall ( r <
10 cm), we ob-tain an even greater separation between the eventssurviving the selection and the previously defined ] WIMP mass [TeV/c - -
10 1 10 ] [cm SI s WIMP-nucleon - - - - - - L U X ( 2 0 1 7 )P A N D A X - I I ( 2 0 1 7 ) X E N O N 1 T ( 2 0 1 8 )W A R P ( 2 0 0 7 )
D a r k S i d e - 5 0 ( 2 0 1 5 )
D E A P - 3 6 0 0 ( 2 0 1 7 )
DarkSide-50 (2018)
FIG. 12. Spin-independent DM-nucleon cross section90 % C.L. exclusion limits from the analysis detailedin this paper, compared to our previous result [17]and selected results from other experiments using ar-gon (WARP [45], DEAP-3600 [2]) and xenon (LUX [46],XENON1T [1], PandaX-II [47]).
DM search region. In a multi-tonne detector [48],these cuts would provide exceptional background re-jection at the cost of an affordable loss in detectionefficiency. f ] nr Energy [keV0 20 40 60 80 100 120 140 160 180 200
FIG. 13. Distribution of events in the f vs S1 planethat survive all analysis cuts and that in addition survivetightened radial and S2/S1 cuts (see text for details). ACKNOWLEDGMENTS
The DarkSide Collaboration offers its profoundgratitude to the LNGS and its staff for their in-valuable technical and logistical support. We alsothank the Fermilab Particle Physics, Scientific, andCore Computing Divisions. Construction and oper-ation of the DarkSide-50 detector was supported bythe U.S. National Science Foundation (NSF) (GrantsPHY-0919363, PHY-1004072, PHY-1004054, PHY-1242585, PHY-1314483, PHY-1314501, PHY-1314507, PHY-1352795, PHY-1622415, and associ-ated collaborative grants PHY-1211308 and PHY-71455351), the Italian Istituto Nazionale di Fisica Nu-cleare, the U.S. Department of Energy (ContractsDE-FG02-91ER40671, DE-AC02-07CH11359, andDE-AC05-76RL01830), the Russian Science Foun-dation (Grant 16-12-10369), the Polish NCN (GrantUMO-2014/15/B/ST2/02561) and the Foundationfor Polish Science (Grant Team2016-2/17). 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