Masaki Yamashita on Behalf of the XMASS Collaboration Kamioka Observatory, ICRR, the University of Tokyo

Annual modulation search by XMASS-I with 2.7 years of data Masaki Yamashita on behalf of the XMASS collaboration Kamioka observatory, ICRR, The University of Tokyo

•Introduction •Calibration and Analysis 232 km/s Sun •Modulation Result 30 km/s • WIMP search 60° Earth • Model independent search • Power spectrum •Conclusion and Summary

th 15 International Conference on Topics in Astroparticle and Underground Physics, TAUP2017Masaki Yamashita 1 Page 4 of 11 Eur. Phys. J. C (2013) 73:2648

Fig. 2 Experimental residual rate of the single-hit scintillation events measured by DAMA/LIBRA–phase1 in the (2–4), (2–5) and (2–6) keV energy intervals as a function of the time. The time scale is maintained the same of the previous DAMA papers for coherence. The data points present the experimental errors as vertical bars and the associated time bin width as week ending horizontal bars.The PRL 118, 101101 (2017) PHYSICAL REVIEW LETTERS 10 MARCH 2017 superimposed curves are the cosinusoidal functions Frequency [1/Days] 0.03 0.02 0.01 0.003 0.002 0.001 The maximum profiled likelihoods are denoted by L0 for behaviours A cos ω(t t0) with 30 P = 365 SS, (3-14) PE, MC the null hypothesis and L1 for the modulation hypothesis. aperiodT 2π 1yr,aphase− P = 450 ω 25 P = 750 The local test statistics (TS ) defined as 2 ln L =L and = = 2 (global) l − 0 1 t0 152.5day(June2nd)and 20 Null Hypothesis σ ð Þ l global test statistics (TSg) are constructed in the same way modulation= amplitudes, A, S T 15 1σ (global) as in Ref. [12] to quantify the significance of a modulation equal to the central values 10 obtained by best ﬁt on the data signature. A Monte Carlo (MC) simulation based on 5 Eq. (2), including all nuisance parameter variations, is points of the entire 0 30 40 50 60 100 200 300 400 1000 DAMA/LIBRA–phase1. The Period [Days] used to evaluate the asymptotic distributions of the test dashed vertical lines correspond statistics and to assess the sensitivity of the combined data to the maximum expected for FIG. 3. The expected mean (solid lines) and central 68.3% to event rate modulations. The average test statistics of the DM signal (June 2nd), while region (shaded bands) of test statistics as a function of period for three representative periods with the same amplitude as in the dotted vertical lines simulated data. Uncertainties on all parameters are taken into the run II only analysis [12] are shown in Fig. 3 for SS correspond to the minimum account. The horizontal global significance lines are derived from samples in the low-E range, which allows testing the annual the null hypothesis tests and shown here for comparison to modulation signature of 2.8σ therein. Results based on the Fig. 4. null hypothesis are overlaid in Fig. 3 for comparison. As the signal period increases, the resolution on the recon- Modulation Searches structed period decreases and approaches a characteristic i where ni and Nexp are the total number of observed and plateau above ∼750 day. As a result, the region of interest is expected events, respectively, and η is the uncertainty of the restricted from 25 to 750 day in the PL analysis. In the run motivation E. BARBOSA DE SOUZA et al. energy conversionPHYSICAL function. REVIEW Nuisance D 95, 032006 parameters (2017) are con- II-only analysis [12], this plateau became apparent at ∼500 strained by Gaussianπ penalty terms G, with the correspond- day. The sidelobes next to the peak at each period are due to where m and b are linear fit parameters, and A, x0, and t0 2 are annual modulation fit parameters. The period of the fit, ing uncertainties discussed above. The parameters of the time gaps between each run, verified by dedicated •DAMA/LIBRA NaI (Tl) result: modulation signal interest are P, A, and ϕ, while the other nuisance param- simulations. t0, is fixed to one year (365.15 days) in this analysis. 3π π Cosmogenically activated isotopes (such as 60Co and eters4 are profiledEur. out inPhys.J. the PL analysis. C(2013)4 73 The PL results for the low-E SS signal sample and the (9.3σ) 125I) and the broken 232Th and 238U-chains produce known DAMA/LIBRAtwo control samples are shown in Fig. 4. As the sensitivity changes in the event rate over time [34,36,46], though not and resolution increase by adding run I and run III data, the •No sign for SUSY particleenough at LHC to explain so the far. decrease at the ROI energies. Frequency [1/Days] rising significance for the signal sample at large periods Cosmogenically activated 3H provides a possible source 0.04 0.03 0.02 0.01 0.003 0.002 238 30 of the decrease [43]. The U surface contamination built Run II SS, (3-14) PE •No sign in direct detection for more than decade π 0 into the DM-Ice17 background model [36] is in equilib- 25 Run I - III 0 0.052σ (global) 0.1 0.15 0.2 P=365 238 210 20 7 rium; however, a broken U-chain at Pb would produce l

) 6 l S 2σ

S 5 with nuclear recoil signal.similar spectral features while introducing decreasing event T 15 1σ (global) 4 (T 3

rates. The decay in the data rate is consistent with a 10 ∆ - 2 1σ 3 238 1 XENON100 combination of H and the broken U-chain, though a 5 2π

•Important to look for variety candidates. )] Table 3 Modulation amplitude, A, obtained by ﬁtting the single-hit the formula: A cos ω(t t0) with T ω 1yrandt0 152.5day 1 2 3 σ σ precise model requires further investigation. − = = = σ day

residual rate of the entire DAMA/LIBRA–phase1 (Fig. 2), and in- (June 2nd) as expected by the DM⋅ annual modulation signature. The 5 30 7 12 Expected Fig. 2 shows the Det-1 event rates for each energy bin π Run II MS, (3-14) PE π 2 cluding also the former DAMA/NaI data [22] for a total cumulative corresponding χ value of each fit and the confidence level (C.L.)DAMA/LIBRA are •WIMP-electron scattering 4 25 4 XENON100 before (top) and after (bottom) subtracting off the fitted tonne 10 Run I - III ⋅ exposure of 1.33 ton yr. It was obtained by fitting the data2 withσ (global) also reported P=365 linear component. To perform the modulation analysis,× a 20 Run I-III expected l 3π 8 – R. Bernabei et al. PRD, 77 02308 (2008), S phase from

likelihood minimization fits the event rate over time for T 15 2 Run II Energy interval DAMA/LIBRA–phase1 1σ (global) DAMA/NaI6 & DAMA/LIBRA–phase1DM halo – each energy bin with a sinusoid atop the linear background. 10 B.M. Roberts et al., PRL 116, 023201 (2016)(keV) WIMP:FIG. 3.(cpd/kg/keV) Allowed regions in amplitude (counts=day=keV=kg) vs (cpd/kg/keV) PRL 118 (2017) 101101 By varying the number of free parameters, a variety of 4 phase for annual5 modulation fits to the Det-1 4 6 keV data, models can be tested. For the 4–6 keV bin of Det-1, chi- – •Luminous dark matter 2–4 with contoursA (0 at.0167 (inner to0 outer).0022) 68%,7 95%,.6σ C.L. and 99% C.L (red). A (0.01792 0.0020) 9.0σ C.L. squared analysis produces χ2=d:o:f: p-value 86.11=87 =30 ± → = ± → The DAMA/LIBRA2 2–Run4 keV II 99% C.L.SS, (14-30) (blue) PE is also shown for 2 ð2 Þ¼ Nuclearχ /d.o.f. 52 .3Recoil/49 signal χ /d.o.f.Amplitude [events/(keV 0 87.1/86 – (0.51) for the null hypothesis, χ =d:o:f: p-value comparison. Phase25 of 0Run corresponds I - III to January 1st. The predicted 40 60 80 100 120 140 160 180 200 220 2 4 6 8 1012

= P=365 = B. Feldstein et al., PRD 82, 075019 (2010) ð Þ¼ 2σ (global) 86.03=86 (0.48) for an annual modulation2–5 (fixed one year A 20(0.0122 0.0016) 7.6σ C.L. A (0.0135 0.0015) Phase9.0σ [Days]C.L. -∆(TSl)

phase of al dark matter modulation signal under generic halo

=S ± → = ± → period) with the expected dark matter phase (fixed June 2nd models (June2 2nd) is indicated by the green line. 2 χ /T d.o.f.15 41.4/49 χ /d.o.f. 68.2/86 •Mirror Dark Matter 2 1σ (global) FIG. 5. The XENON100 best-fit black dot, and 68% (light red maximum), and χ =d:o:f: p-value 84.35=85 (0.50) for 10 = = Nuclear Recoil Energy [keVnr] ð 2–6Þ¼ A (0.0096 0.0013) 7.4σ C.L. A shaded(0.0110 region)5 0.0012 and10) 90%9.2 (greenσ15C.L. shaded20 region)25 confidence30 level – an annual modulation (fixed one year period) with floating = 5 ± → ] 0.05= ± →

R. Foot, Int. J. Mod. Pays. A 29, 126, (2014) ee phase. The other energy bins are similarly consistent with χ 2/d.o.f. 29.3/49 χ 2/d.o.f.contours70 as.4 a/86 function of amplitude and phase relative to January 0.06 DM-Ice17 Det-1 0.04 30= 40 50 60 100 200 300 400 1, 2011= for one year period. The corresponding runExpected II-only ± 1σ results the null hypothesis with p-values of 0.26 (6–8 keV), DM-Ice17 Det-2 • 0.03 Plasma Dark Matter 0.60 (8 10 keV), and 0.55 (10 20 keV), providing no Period [Days] [12] areXMASS-I overlaid with a black square and dashed lines. The phase – – 0.04 DAMA/LIBRA Expected ± 2σ – evidence for an annual modulation. DM-ICE 0.02is less constrained than in run II due to the smaller amplitude. The J. D. Clarke at el. axXiv1512.06471v FIG. 4. Test statistics as a function of modulation period for 0.01expected DAMA/LIBRA signal (cross, statistical uncertainty The best fit to the Det-1 4 6 keV bin has a modulation 0.02 – single scatters in the low-E region (top), multiple scatters in the only) and the phase expected from a standard DM halo (vertical amplitude of 0.05 0.03 counts=day=keV=kg and a maxi- 0 •The search can be also used for solarÆ related low-E region (middle) and single scatters in the high-E region dashed line) are shown for comparison. Top and side panels show mum on March 16th 42 days. DAMA has not published a 0 -0.01 (bottom). The phase is unconstrained. The previous run II-only −Δ TS1 as a function of phase0.8 and amplitude, respectively, floating phase best fitÆ for 4 6 keV, so a direct comparison is ð Þ – result [12] is overlaid for comparison. -0.02along with two-sided significance0.6 levels. physics, for instance, Kaluza Klein Axion search -0.02 not possible; however, across 2 6 keV, DAMA/LIBRA 0.4 – -0.03 observes a modulation amplitude of 0.011 0.001 and a Efficiency 0.2 -0.04 PRD 95 032006 (2017)

Amplitude[events/day/kg/keV -0.04 0 Æ Phys Lett. B (2016)2720 2 4 6 8 10 best-fit phase of May 24th 7 days [9]. A log-likelihood 101101-5 Energy[keV ] (7/26 by Ichimura) ee 0 2 4E. 6Barbosa 8 10 de Souza 12 14 et 16al. 18 20 Æ Amplitude (counts / day keV kg) Modulation -0.05 analysis comparing annual modulations of each amplitude 0 1 2 3 4 5 6 7 8 Energy (keV) and phase to the best fit shows that the data from DM-Ice17 Energy[keV ] Masaki Yamashitaee 2 are consistent with the null hypothesis (see Fig. 3). The FIG. 4. Amplitude of modulation vs energy showing maximum limitations of this detector are also apparent as the likelihood fits for DAMA [9] (blue) and DM-Ice17 rates DAMA/LIBRA 99% C.L. contour is indistinguishable [Det-1 (red) and Det-2 (green)]. The linear backgrounds under- from the null hypothesis at the 68% C.L. lying the event rate and the modulation amplitude are free Modulation fits with fixed period of one year and fixed parameters in these fits, with period and phase forced to that phase of 152.5 days are consistent with zero amplitude (see of an expected dark matter signal (1 year and 152.5 days, Fig. 4). The best-fit modulation amplitudes across the entire respectively). Horizontal error bars represent the width of the ROI can be combined to set limits in the WIMP parameter energy bins used for the analysis. Vertical error bars are 1σ error on the binned modulation fit amplitudes. Æ space assuming a standard halo model with WIMP density of 0.3 GeV=c2, disk rotation speed of 220 km=s, Earth orbital speed of 29.8 km=s, and galactic escape velocity of particular WIMP candidates as described in [10]. Best-fit 650 km=s. An exclusion limit (see Fig. 5) is produced via a contours for the full DAMA/LIBRA-phase1 run [9] log-likelihood analysis of the observed binned modulation were produced along with the DM-Ice17 exclusion limit amplitudes, with predicted modulation amplitudes for for comparison, based on the methodology from [11].

032006-4 Interaction nuclear recoil electronic recoil

fast neutron -U/Th/40K etc background WIMP (SUSY, KK …)

Masaki Yamashita 3 Interaction electronic recoil •If the signal is not a nuclear recoil. nuclear recoil

•axial vector interaction •photon emission from excited DM (Luminous dark matter) •…. •Axion like particle can not be candidate because σ ~1/v , dm fux ~ v. •DAMA/LIBRA vs LXe •Energy deposit ~ 3 keV energy deposit. (from DAMA/LIBRA)

•Event rate is similar for Xe(z=54) and fast neutron -U/Th/40K etc background Iodine (z=53) WIMP -WIMP-electron -Super WIMP (bosonic) (SUSY, KK …) -Axion/Axion like particle •modulation analysis is not depend on -Mirror DM the halo model. -Luminous DM …

Masaki Yamashita 4 XMASS experiment

• Kamioka Observatory in Japan (2700 m.w.e) • Single phase LXe scintillation detector (832 kg) • 642 low radioactive Hex PMT (R10789) • φ10 m x 10 m Water Cherenkov active muon veto

Masaki Yamashita 5 Calibration system OFHC copper rod and source stepping motor on the tank top

guide pipe

OFHC copper rod

moved along z−axis Flange for Detectorsource exchange calibration -Innergate valve calibration is for energy calibration.

Figure 5: Calibration system on top of the tank. Source placedontheedgeofthecopper

rod is inserted into the ID and can be moved along the z axis.

26 2012/12/21

SUS 0.21 side) (KRISS 68 122 57 - Co (4)

SUS 0.17 485 59.5 241 - Am (3)

brass 5 800 88 25, 22, 109 - Cd (2)

brass 5 350 5.9 55 - Fe (1)

material Outer [mm] Dia. [Hz] Intensity ] keV [ energy

5 5

Table 7: Calibration sources and energies. The 8 keV (*1) in the 109Cd and 59.3 keV (*2) Gate 57 in the Co source are Kα X-rays from the copper and tungsten, respectively, used for ~5m valve

source housing. 0 3 0 3 Isotopes Energy [keV] Shape

55 Fe 5.9 cylinder Cosource

1.65, 57

109Cd 8(*1), 22, 58, 88 cylinder Am 241 for

241

Am 17.8, 59.5 thin cylinder 13 φ 20

Co 59.3(*2), 122 thin cylinder Co 5.9keV g 57 L-shell 137Cs 662 cylinder X-ray

Theses sources were made by KRISS by made were sources Theses Xe atom 0.21mm

sources made by Korean group Masaki Yamashita 6 Sources 3.

21 ① Power cut Energy calibration and stability ② Purifcation work • Energy calibration 1.65 - 122 keVee ③ continuous gas • High Photoelectron Yield ~15 PE/keV @122 keV recirculation • Low energy threshold: 1.0 keVee (4.8 keVnr) (15PE/keV) Run1 Run2 Evaluated absorption length 4-30 m, scatter ~52cm • 17 2013. Dec 31 ① 2015. Jan 01 2016. Jan 01 • Run1: Std ± 2.4% , Run2 Std ± 0.5% ② K. Abe et al. / Nuclear Instruments and Methods in Physics16 Research A 716 (2013) 78–85 85 ③ energy and vertices for 122 keV gamma rays are reproduced well 1 real data 15

byNPE/122 the MC. 0.8 simulation (MC) ± 2.4% ± 0.5%

0.6 14. Conclusion

0.4 57Co The30 construction of the XMASS detector was completed in 15PE/keV September 2010 and commissioning runs were conducted from

Events (normalized) 0.2 @122keV October 2010 to June 2012.Absorption (light) 0 The20 XMASS detector is the world's largest (ton scale) single- 0 500 1000 1500 2000 2500 phase liquid xenon detector for dark matter searches. The key idea total nPEs forAbs.(m) BG10 reduction is self-shielding using vertex reconstruction. The position and energy resolution along the z-axis inside the detector Fig. 7. Observed n PE spectrum using the 57Co source at z 0 cm (red dots). ¼ Simulated spectrum is shown as blue histogram. (For interpretation of the references were measured with radioactive sources and are well reproduced to color in this figure caption, the reader is referred to the web version of this article.) by MC. The observed position and energy resolution for 122 keV 1.65keV 5.9keV gamma rays are 1.0 cm at z 720 cm and 4% (rms) at z 0 cm, 1.02 ¼ ¼ 1.21 respectively. Ahighlightyield,14:771:2PE=keV, was obtained owing to the 10-1 Data large photocoverage (462%)andsmallamountofimpuritiesinthe 1.1 yield 1.00 -2 10 MC liquidR xenon. This was achieved by careful control of dust and radon during construction and purification by liquid collection and filling 10-3 55Fe 1 with0.98 purified gas. The concentrations of radon (8:270:5mBq=835 kg 222 Ryield 0.6% 220 10-4 for Rn and o0:28 mBq=835 kg for Rn) and krypton (o2:7 ppt) in liquid xenon are also the lowest among liquid xenon detectors 0.9 0 10 20 30 40 50 60 70 80 90 100 for dark matter0 searches. 200 400 600 800 Day from 2014. Jan. 1 0.8 PE Masaki Yamashita 7 Acknowledgments Calibration data/ Simulation 0.7 We gratefully acknowledge the co-operation of Kamioka Fitted Mining and Smelting Company. This work was supported by 0.6 the Japanese Ministry of Education, Culture, Sports, Science and 0 20 40 60 80 100 120 Technology, Grant-in-Aid for Scientific Research, and partly sup- Electron equivalent energy [keVee] ported by the National Research Foundation of Korea Grant funded Fig. 8. Comparison of energy scales in calibration data and MC. by the Korean Government (NRF-2011-220-C00006).

References

[1] Y. Suzuki, arXiv:hep-ph/0008296. [2] K.G. Begeman, A.H. Broeils, R.H. Sanders, Monthly Notices of the Royal Astronomical Society 249 (1991) 523; J. Dunkley, et al., Astrophysical Journal Supplement 180 (2009) 306; R.A. Knop, et al., Astrophysical Journal 598 (2003) 102; S.W. Allen, et al., Monthly Notices of the Royal Astronomical Society 334 (2002) L11; M. Tegmark, et al., Physical Review D 69 (2004) 103501. [3] H.C. Cheng, et al., Physical Review Letters 89 (2002) 211301; A. Birkedal-Hansen, J.G. Wacker, Physical Review D 69 (2004) 065022; A. Bottino, et al., Physical Review D 69 (2004) 037302; J. Ellis, et al., Physical Review D 71 (2005) 095007. [4] K. Ueshima, et al., the XMASS Collaboration, Nuclear Instruments and Methods in Physics Research Section A 659 (2011) 161. [5] M. Laubenstein, G. Heusser, Applied Radiation and Isotopes 67 (2009) 750. [6] K. Abe, et al., the XMASS Collaboration, Astroparticle Physics 31 (2009) 290. [7] K. Abe, et al., the XMASS Collaboration, Nuclear Instruments and Methods in Physics Research Section A 661 (2012) 50. [8] I. Lawson, B. Cleveland, in: the Proceedings of the Low Radioactivity Techni- ques, LRT2010, AIP Conference Proceedings, Sudbury, Canada, 28–29 August 2010, pp. 68–77. [9] Y. Takeuchi, et al., Nuclear Instruments and Methods in Physics Research Section A 421 (1999) 334. [10] H. Ikeda, et al., Nuclear Instruments and Methods in Physics Research Section A 320 (1992) 310; S. Fukuda, et al., Nuclear Instruments and Methods in Physics Research Section A 501 (2003) 418. Fig. 9. Energy spectra reconstructed using the 57Co source at z 0cm(upper)and [11] K. Abe, et al., the XMASS Collaboration, Physics Letters B 719 (2013) 78–82. ¼ vertex distributions reconstructed using the same source at z −40, −30,…,40cm [12] K. Abe, et al., the XMASS Collaboration arXiv:1212.6153. ¼ (lower). [13] S. Agostinelli, et al., Nuclear Instruments and Methods in Physics Research Section A 506 (2003) 250. vertices for various 57Co source positions. The observed position [14] T. Doke, et al., in: the Proceedings of the International Workshop on Technique and Application of Xenon Detectors, Xenon01, World Scientiﬁc, the University resolution (rms) is 1.4 cm at z 0 cm and 1.0 cm at z 720 cm for ¼ ¼ of Tokyo, Japan, 3–4 December 2001, pp. 17–27. 122 keV gamma rays. The distributions of the reconstructed [15] Y. Endo, et al., JSAP: The 72th Autumn Meeting, 2011, 30a-T-8. Annual Modulation search -Run 1 was reported in Phys Lett. B (2016)272. - Data set 2013/11/20 - 2016/07/20 (800.0 live days) XMASS (1.82 ton x year) ⇔ DAMA/LIBRA (1.33 ton x year) -Quality cut + Likelihood analysis based on Sphericity, Aplanality, Maximum/Total PE 3

Date Live time [day] Exposure [ton year] PEyieldstability(57Co) · Run1 Nov/20/2013-Mar/31/2015 387.8 0.884 2.4% ± Run2 Apr/1/2015-Jul/20/2016 412.2 0.940 0.5% ± Total 800.0 1.82 #~20 days live time was recovered after PLB2016 in Run1 103

2 1. ID trigger 0.8 10 TABLE I. Summary of XMASS-IID Trigger data exposures and PE yield stability established by the 57Co calibration. 2. Timing cut Timing cut Efﬁciency 10 3. CherenkovCherenkov cut cut 0.6

Likelihood Efficiency 1 4. Likelihood The standard deviation of PE yield during the Run10.4 were into account with those calibrations using a non-linearity 10-1

Rate [counts/day/kg/keVee] 2.4%. It changed gradually from the beginning of the model from Doke et al. [21]. In this work, the energy 0.2 10-2 Run± 1, however, suddenly dropped at the power failure scale below below 5.9 keV was measured by the escape -3 55 10 0 0 2 on4 17,6 August8 2014,10 12 thus,14 the16 detector18 20 was cooled0 by X-ray5 peak in10 the Fe calibraion15 and20its mean energy Energy[keV ] Energy [keV ] ee the liquid nitrogen through the coolingee coil attached to is 1.65 keV.Thedi↵erence of lightMasaki yield Yamashita at8 this energy the inner vessel. Later, sharp PE yield changes was seen was about 5% smaller than previous work. The light again when the two pulse tube refrigerators for the detec- yield at 1.65 keV was 40% smaller than that of 122 keV tor was swapped for a maintenance work from December with an uncertainty of 10%. 2) keVnr denotes the nuclear 2014 to February 2015. According to the XMASS MC recoil energy which is estimated from the light yield at study with 57Co calibration data, those change can be 122 keV by using non-linearity response measurement at explained by the scintillation light absorption length in zero electric field in [22]. The energy threshold in this LXe. The absolute absorption length varied from about work corresponds to 1.0 keVee or 4.8 keVnr. 4 m to 30 m. We think that the gaseous impurity such as water, nitrogen and oxygen caused these changes. In- deed, by recovering xenon gas from refrigerator, the PE yield was recovered and the good stability was achieved III. DATA ANALYSIS after staring the gas circulation with a getter purifier in March 2015. The fluctuation of PE yield was 0.5% A. Data Selection ± in Run 2. The relative intrinsic light yield (Ryield)of LXe scintillator stayed at 0.6% and 0.3% in Run1 ± ± Before retrieving time variation information from data, and Run2 ,respectively. similar events reduction was perform to reduce back-

Run1 Run2 ground mainly from Cherenkov light from PMT windows 17 and events near the detector wall as described in [2] as 2013. Dec 31 2015. Jan 01 2016. Jan 01 standard cuts. Events with 4 or more PMT hits in a 16 200 ns coincidence timing window without a muon veto 15 NPE/122 were initially selected as a‘ID Trigger’. A ‘Timing cut’ was applied by rejecting events occurring within 10 ms 30 from the previous event and having a variance in their 20 hit timings of greater than 100 ns. This cut avoid events

Abs.(m) 10 caused by afterpulses of bright events induced by, for ex- ample, high energy gamma-rays or alpha particles. A 1.02 ‘Cherenkov cut’ removed events which produce light pre-

yield 1.00

R dominantly from Cherenkov emission, in particular from 40 0.98 the beta decays of K in the PMT photocathode[6]. Fi- 0 200 400 600 800 nally, we construct likelihood function to remove back- Day from 2014. Jan. 1 ground events that occurred in front of PMT window or near the detector wall based on PE hits pattern in one FIG. 2. PE yield was monitored by 122 keV gamma rays from event. a 57Co source . The relative intrinsic scintillation light yield (Ryield) was obtained by comparing to calibration data with the XMASS MC by considering optical parameters such as L = f (S(q)) f (A(q)) f (M(q)) (1) absorption and scattering length. sph ⇥ apl ⇥ max

Here, we deﬁne two di↵erent energy scales:1) keVee where q(q1,...,q642) is a number of PE for all 642 PMTs represents an electron equivalent energy incorporating all in one event. S(q), A(q), M(q) are the parameters based the gamma-ray calibrations in the energy range between on the q for the sphericity, aplanality and maximum PE, 55 109 241 57 1.65 keV and 122 keV from Fe, Cd, Am and Co respectively. fsph, fapl and fmax are the probability den- sources by inserting sources into the sensitive volume of sity functions based on those parameters and they will the detector. The non-linearity of energy scale was taken be described in more detail later. 5 6

1.1 1-2 keVee 0.05 1-2 keVee +sigma 1.05 s as the signal amplitude Ai () and unmodulated1 compo- per0 limit on the WIMP-nucleon cross section is shown s 0.95 0.05 41 2 nent Ci (). in Fig. 7. The exclusion-1sigma upper limit of 1.9 10 cm at The expected modulation amplitudes0.9 become a func- 8 GeV/c2 was obtained. To evaluate the⇥ sensitivity of 1.1 2-6 keVee 2-6 keVee 0.05 2-6 keVee +sigma tion of the WIMP mass Ai(m) as1.05 the WIMP mass m WIMP-nucleon cross section, we carried out a statisti- determines the recoil energy spectrum.1 The expected cal0 test by applying the same analysis to 10,000 dummy rate in a bin then becomes: 0.95 samples0.05 with the same-1sigma statistical and systematic errors 0.9 Error Size 1 as data but without modulation by the same procedure tj + 2 tj 1.1 6-20 keVee 6

Relative Efficiency 6-20 keVee Correlated error size ex b 1.05 b of0.05 [2]. At first, the+si time-averagedgma energy spectrum was Ri,j(↵, )= ✏i (↵) (Bit + Ci ) 1 1 · s 0 tjas the2 t signalj amplitude Ai () and unmodulated compo-obtainedper limit from on the the WIMP-nucleon observed data. cross Then, section we is shown performed Z s ✓ 0.95 41 2 nent Ci (). a toy0.05 in Monte Fig. 7. The Carlo exclusion-1si simulationgma upper limit to simulate of 1.9 10 time cm variationat s s 0.9s (t t0) 2 ⇥ The expected modulation amplitudes0 200 400 become600 a800 func- 8 GeV/c was obtained. To evaluate the sensitivity of + n ✏ (↵) C ()+A (0) cos200 2⇡ 400 600 800dt, of event0 rate200 400 of background600 800 at each energy bin assum- · i · i i T tion of the WIMP mass Ai(m) asDay thefrom 2014. WIMP Jan. 1 mass◆ ming theWIMP-nucleon sameDay from live 2014. cross timeJan. 1 section, as data we and carried including out a statisti- systematic determines the recoil energy spectrum. The(4) expected cal test by applying the same analysis to 10,000 dummy rate in a bin then becomes: uncertainties.samples with The the same1 statisticaland 2 and bands systematic in Fig. errors 7 out- FIG. 5. Relative eciencies for both signal (cross) andb background (circle) by normalizing± the overall± eciency at an absorption t + 1 t line theas data expected but without 90% modulation C.L. upper by limit the same band procedure for the no- where n is the WIMP-nucleonj 2 j cross section, ✏i (↵) and s length of 8 m forex di↵erent energy rangesb (left). Sizeb of correlated uncertaintiesof [2]. At first, due to the the time-averaged position dependence energy spectrum or background was ✏ (↵) are the relativeRi,j(↵, )= eciency for✏i background(↵) (Bit + Ci and) sig- modulation hypothesis using the dummy samples. The i model are also shown witht 11t (right).· Their changes are also normalizedobtained at fromsame the absorption observed length. data. Then, we performed Z j ±2 j ✓ result excludes the 3 DAMA/LIBRA allowed region as nal, respectively. The background component was de- a toy Monte Carlo simulation to simulate time variation s s s b (t t0) interpreted in [9]. scribed by the linear function,+ n ✏ (B↵) forC slope()+A and() cosC 2con-⇡ dt, of event rate of background at each energy bin assum- · i i · i i i T s ◆ ing the same live time as data and including systematic stant[2]. for As the the background time dependence in i-th bin. of theAi PE()represents yield a↵ects (4) each time-bin were then further divided into energy-bins s uncertainties. The 1 and 2 bands in Fig. 7 out- an amplitudethe eciency and ofCi the() cuts, for unmodulated we evaluate component the absorption for (Ebins) with a width± of 0.5 keV± ee.A’pullterm’method b line the expected 90% C.L. upper limit band for±1 the σ expected no- signallength in i dependence-th bin.where To ofn obtainis the the relative WIMP-nucleon the WIMP-nucleon cut eciencies cross section, through cross✏i (↵) andwas usedXe100-S2 to fit all energy- and time-bins simultaneously s modulation hypothesis using the dummy samples.±2 σ Theexpected sectionXMASS the data MC.✏i (↵ Towas) are evaluate fitted the relative in relative the eciency energy eciencies for range background for of 1.0- both and sig-to treat the correlated errorsDAMA/LIBRA(2012 above. Kopp) nal, respectively. The background component was de- result excludes the 3 DAMA/LIBRA allowed region as 20 keVsignalee. and We background, assume a thestandard energy spherical range 1–20 isothermal keVee wasb interpreted in [9]. scribed by the linear function, Bi for slope and Ci con- divided into 3 energy bins: 1–2 keV , 2–6 keV sand 6–20 XMASS2013 galactic halo modelstant for with the background the mostee in probablei-th bin. eeA speedi ()represents of s CDMS-Si v0=220keVee km/s,. We normalizean the amplitude Earth’s the and velocity overallCi () e for relativeciency unmodulated at to an the component absorp- dark for CoGeNTIV. RESULTS(2013) AND DISCUSSION ±1 σ expected tion length ofsignal 8 m in andi-th the bin. relative To obtain eciencies the WIMP-nucleon in the 1–20 cross Xe100-S2 matter distribution of vE = 232+15 sin2⇡(t t0)/T km/s, XMASS 2016DAMA/LIBRA(2012 Kopp) ±2 σ expected keVee changessection from the4% data to was +10% fitted for in the the wall energy events range and of 1.0- and a galactic20 escape keV . velocity We assume of v aesc standard= 544 spherical km/s [25], isothermal We performed two analyses, one assuming WIMP in- about 3% to +4%ee for the uniform events3 over the rel- XMASS(This work) a local dark mattergalactic density halo model of 0.3 with GeV/cm the most, probable following speed ofteractions andLUX the otherXENON1T independent of anyXMASS2013 specific dark evant absorption range as shown in Fig.5 (left). The er- CDMS-Si [14]. In the analysis,v0=220 km/s, the the signal Earth’s e velocityciencies relative for to each the darkmatterFitting model.CoGeNT (2013) Hereafter time we variation call the former case data the ror of thesematter eciencies distribution were ofalsovE evaluated= 232+15 sin2 based⇡(t ont0)/T thekm/s, WIMP mass are estimated from57 Monte Carlo simulation WIMP analysis andXMASS the 2016 latter a model independent anal- PE yield measurementand a galactic by escapeCo velocity calibration of vesc and= 544 the km/s ra- [25],• of uniformly distributed nuclear recoil events in the liquid ysis.2D fitting energy and XMASS(Thistime bins work) with the systematic errors from PE yield stability, Decay time, Leff dioactive backgrounda local dark model matter uncertainty. density of 0.3 We GeV/cm found3, that following xenon volume. LUX XENON1T the primary[14]. radioactive In the analysis, background the signal came e fromciencies Al seal for each•Relative efficiency differences were taken into account for each period based on PE yield. for PMT windowWIMP and mass secondary are estimated gamma from Monte rays from Carlo PMT simulation 6 2014. Janof uniformly2015. distributed Jan nuclear2016. recoil Jan events in the liquid•The efficiency was normalized @ 8 m absorption length.(same as PLB2016) body in low energy and the background study was de- FIG. 7. (Color online)A. Limits WIMP on the search spin-independent elastic ]

ee xenon volume. V ke •These errors are correlateds with both energy and time bins and treated by pull term method. 0.8 g/ WIMP-nucleon cross section as a function of WIMP mass. k scribed in/ [24] including high energy region.1.0-1.5 In keVee Fig.5 as the signal amplitude A () and unmodulated compo- per limit on the WIMP-nucleon cross section is shown ay i d / s t 2014. Jan 2015. Jan 2016. Jan 2 n The solids line shows the XMASS 90% C.L.pull exclusion term from 41 2 (right) showsou their uncertainty as a function of a time nentIn theC case(). of the WIMP analysis, deﬁned as: in Fig. 7. Therelative exclusion efﬁciency upper limit of 1.9 10alpha:cm Uncertaintyat for pull term

[c FIG. 7.i (Color online) Limits on the spin-independent elastic ate

0.7 ] R 2 ⇥ ee WIMP case: V the annual modulation analysis. The 1 and 2 bands normalized normalized ke e] period from January 2014. Note that these errors af- The expected modulation amplitudes become a func- 8 GeV/c was obtained. To evaluate the sensitivity of

0.8 g/ WIMP-nucleon cross section as a function of WIMP mass. k / 1.0-1.5 keVee ± ± e ay d / s t representE thet expected 90% exclusion distributions.Nsys Limits as 1.1

n bins bins V fects count rate of ﬁnal data samples and are correlated tionThe of solid the line WIMP showsdata mass the XMASSA ex(m 90%) as C.L. the2 WIMPexclusion mass from m WIMP-nucleon cross section, we carried out a statisti- ou i [c (R R (↵, )) e 0.4 i,j i,j 1-2 keVee 0.05 1-2 keVee +sigma 0.7 ate 2 2 2 R k 1.5-2.0 keVee well asthe allowed annual modulation regions from analysis. other The searches1 and based2 onbands counting 1.05 between energye] bins and time period bins. As we nor- determines= the recoil energy2 spectrum.±2 + ↵ The± + expectedi , cal test by applying the same analysis to 10,000 dummy e g/ represent the expected(stat) 90% exclusion+ (sys) distributions. Limits as 0 V method are also shown [3,i,j 4, 6, 9–11].i,j k rate ini a binj then becomes: ! samples1 with the same statisticalb: and systematic errors e / malized the relative0.4 eciency and the size of these errors ε wall events

0.35 k well as allowed regions from other searches based on counting y 1.5-2.0 keVee X X X a g/ 1 (3) as data0.95 but without modulation by the same0.05 procedure at absorption length of 8m in the analysis, the relative method are alsotj shown+ t [3,j 4, 6, 9–11]. Decay k s: -1sigma d 2 / ε uniform events / 0.35 data ex +2.0 y ex b b 0.25eciency and the correlated error size became one at 170 where R , R , (stat) and (sys) time(2.7are data,-1.5 ns)of [2].0.9 At ﬁrst, the time-averaged energy spectrum was a R (↵, )= ✏ (↵) (B t + C ) ts i,j i,j i,j i i,j i i i,j d 2.0-2.5 keVee 1 n / tj tj · and Leff uncertaintyobtained from the observed data. Then, we performed days. This is the0.25 dominant systematic uncertainty in the expected event rate,2 statistical and systematic error, re- 1.1 ts Z ✓ 2-6 keVee

ou 2.0-2.5 keVee n 2-6 keVee B. Model Independent Search a toy Monte Carlo simulation to simulate time0.05 variation +sigma

c 2-6 keVee present0.2 analysis. The second largest contribution comes spectively, of the i-th energy and j-th time(t bin.t0) The 1.05 [ s s s ou B. Model Independent Search c 0.2 + n ✏ C ()+A () cos 2⇡ dt,

e i i i of event rate of background at each energy bin assum- [

time is denoted as the number of days from January 1, from a gain instability of the waveform digitizers (CAEN · · T 1 0 e at ◆ ing the same live time asb: data and including systematic at ε wall events R V1751) between April 2014 and September 2014 due to a 2014. A penalty term ↵ represents the size of the rela- For the model independent analysis, the expected (4) 0.95 0.15 R 0.05 0.15 2.5-3.0 keVee For the model independent analysis, the expectedpull term uncertainties. The 1 and 2 bands in Fig. 7 out- -1sigma di↵erent calibration method of the digitizers used in that2.5-3.0 keVee tive eciency error and it is common for all fitted energy εs:uniform events Modeleventevent rate Independent rate was was estimated estimated case: as: as: 0.9 ± ± Error Size b line the expected 90% C.L. upper limit band for the no- 0.10period. This e0.10↵ect contributes an uncertainty of 0.3% bins,where therefore,n is the the WIMP-nucleon size of error changes cross section, simultaneously✏i (↵) and s EbinsEbinstbinstbins datadata exex2 2 modulation1.1 hypothesis using the dummy samples. The ✏ (↵) are the relative e((RRciencyi,j R forRi,j) background) and sig- 6-20 keVee to the energy scale. Other0 e↵200ects from400 LED600 calibration,800 1000duringi 2 fit2 procedure. ↵=1(i,j 1) correspondsi,j to2 12 ( 1) Relative Efficiency 6-20 keVee Correlated error size 0 200 400 600 800 1000 = + ↵ , (5) 1.05 0.05 +sigma Day from Jan/2014 nal, respectively.= The(stat) background22 +(sys) component2 2 + ↵ was, de-(5) result excludes the 3 DAMA/LIBRA allowed region as trigger threshold stability,Day from timing Jan/2014 calibration were negli- correlated systematici j error(stat) oni,j the+ expected(sys)i,j ! event rate in i,j i,j ! b interpreted1 in [11]. scribed byi X thejX linear function, B for slope and C con- 0 gible. Day from Jan/2014that energyX binX as shown in Fig. 5.i Other pull-termsi i εb:wall events Day from Jan/2014 s 0.95 stant for the1 background in i-th bin. A ()represents FIG. 6. (Color online) Observed count rate as a functionare parameterstj + fortj systematical uncertaintyi of expected s: 0.05 2 s (t t0) ε uniform events -1sigma FIG. 6. (Colorof online) time in Observedthe 1.0 - 3.0 count keVee energy rate as range a function after correcting an amplitudeex 1 and Cs (s) for unmodulatedb componentb for 0.9 To retrieve the annual modulation amplitude from the WIMPRi,j = signaltj + 2 simulation.tj ✏iiAi cos Here, 2⇡ two+ systematical✏i (↵)(Bit + C uncer-i ) dt, relative eciency (see text). The black error bars show the 1 (tT t0) 0 200 400 600 800 ±1 σ expected exsignal in tij-th2 t bin.j s Tos obtain the WIMP-nucleonb crossb Xe100-S2 of timedata, in the the least 1.0 - squares 3.0 keV methodee energy for range the time-binned after correcting data Rtainties,= scintillationZ ✓✏ A ecosciency 2⇡ for nuclear+ ✏ recoil(↵)(B andit +◆ theC ) dt, 0 200 400 600 800 0 200 400 600 800 statistical uncertainty of the count rate. The solid curves i,j i i i (6) i DAMA/LIBRA(2012 Kopp) ±2 σ expected relative eciency (see text). The black error bars show the section the1 data was fitted in theT energy range of 1.0- Day from 2014. Jan. 1 Day from 2014. Jan.Masaki 1 Yamashita 9 was used. The data set was divided into 63 time-bins time constanttj 2 t ofj nuclear recoil are considered. Valuation represent the best fit result for model independent analysis whereZ the free parameters✓ Ci and Ai were the unmodu- ◆ statistical(t ) with uncertainty roughlybefore total of 15 e the daysciency count of correction. real rate. time The each. solid The curves data in of20 the keV expectedee. We signal assume simulation a standard with spherical are calculated isothermal(6) bins lated event rate and the modulation amplitude,i respec- XMASS2013 represent the best fit result for model independent analysis wheregalactic the free halo parameters model withC thei and mostAi probablewere the speed unmodu- of tively. t0 and T were the phase and period of the mod- CDMS-Si before total eciency correction. v =220 km/s, the Earth’s velocity relative to the dark CoGeNT (2013) As we found no significant signal, the 90% C.L. up-lated0ulation, event and ratetj andand thetj modulationwas the time-bin’s amplitude, center and respec- matter distribution of vE = 232+15 sin2⇡(t t0)/T km/s, tively. t0 and T were the phase and period of the mod- XMASS 2016 and a galactic escape velocity of vesc = 544 km/s [26], As we found no significant signal, the 90% C.L. up- ulation, and tj and tj was the time-bin’s3 center and XMASS(This work) a local dark matter density of 0.3 GeV/cm , following LUX XENON1T [16]. In the analysis, the signal eciencies for each WIMP mass are estimated from Monte Carlo simulation of uniformly distributed nuclear recoil events in the liquid xenon volume.

2014. Jan 2015. Jan 2016. Jan FIG. 7. (Color online) Limits on the spin-independent elastic ] ee V ke

0.8 g/ WIMP-nucleon cross section as a function of WIMP mass. k / 1.0-1.5 keVee ay d / s t n The solid line shows the XMASS 90% C.L. exclusion from ou [c

0.7 ate R the annual modulation analysis. The 1 and 2 bands e] ± ± e represent the expected 90% exclusion distributions. Limits as V

e 0.4

k 1.5-2.0 keVee well as allowed regions from other searches based on counting

g/ method are also shown [3, 4, 6, 11–13]. k / 0.35 y a d / 0.25 ts 2.0-2.5 keVee n

ou B. Model Independent Search

c 0.2 [

e at

R 0.15 For the model independent analysis, the expected 2.5-3.0 keVee event rate was estimated as: 0.10 Ebins tbins (Rdata Rex )2 0 200 400 600 800 1000 2 = i,j i,j + ↵2, (5) Day from Jan/2014 (stat)2 + (sys)2 i j i,j i,j ! Day from Jan/2014 X X 1 FIG. 6. (Color online) Observed count rate as a function tj + tj 2 (t t0) of time in the 1.0 - 3.0 keVee energy range after correcting ex s s b b Ri,j = ✏i Ai cos 2⇡ + ✏i (↵)(Bit + Ci ) dt, relative eciency (see text). The black error bars show the t 1 t T Z j 2 j ✓ ◆ statistical uncertainty of the count rate. The solid curves (6) represent the best ﬁt result for model independent analysis where the free parameters Ci and Ai were the unmodu- before total eciency correction. lated event rate and the modulation amplitude, respectively. t0 and T were the phase and period of the mod- As we found no signiﬁcant signal, the 90% C.L. up- ulation, and tj and tj was the time-bin’s center and WIMP case

•Assuming WIMP(standard halo model) ±1 σ expected •Lewin and Smith (1996, APP) Xe100-S2 DAMA/LIBRA(2012 Kopp) ±2 σ expected •T=1year, t0=152.5 day (ﬁxed) 3 sigma t0 = 152.5 day (Jun. 2nd) XMASS2013 ω = 2π/T (T = 365.24. day) CDMS-Si •V0 = 232 km/sec, Vesc = 544 km/s CoGeNT (2013) 3 XMASS 2016 •ρDM = 0.3 GeV/cm XMASS(This work) • 2D ﬁRng (Sme and energy bin ) LUX XENON1T 5sigma low mass •DAMA/LIBRA region is excluded by annual modulaSon search. <1.9 x 10-41cm2 (90% CL) @ 8GeV

Masaki Yamashita 10 Model Independent Case

Amplitude 10-3 •Searching for without any model assumption. Experiment (counts/day/kg/keVee) • Fixed parameter : t0 = 152.5 day (Jun. 2nd) , T = 365.24. day • Null hypotheses p-value: 0.11 (1.6σ), previous work (2.5σ). DAMA/LIBRA(2013) [email protected] keVee 1.67±0.73 ( 2.0-5.8 keVee), • => Upper limit. Most stringent amplitude for modulation search. XENON100(2017) <3.1 90CL (when models assumed, the relation btw NaI and Xe might be changed) XMASS-I (2017) < 1.3-3.2 (2-6 keVee) 90CL

2014. Jan 2015. Jan 2016. Jan ] ee V

ke 1.0 - 1.5 keVee

0.8 g/ k / 1.0-1.5 keVee ay

d Nuclear Recoil Energy [keVnr] / s t n

ou 5 10 15 20 25 30 [c

]

0.7 ate 0.04 R ee e]

e Expected ± 1σ

V 0.03 e 0.4 Expected 2 k 1.5 - 2.0 keVee ± σ 1.5-2.0 keVee 0.02 g/ DAMA/LIBRA (2013)

k DAMA / 0.35 y 0.01 a d / 0.25

ts 0 2.0-2.5 keVee n 2.0 - 2.5 keVee

ou -0.01

c 0.2 [ t0 = 152.5 day (Jun. 2nd) e -0.02 at XeorNaI(Tl) ω = 2π/T (T = 365.24. day) R 0.15 -0.03 2.5 - 3.0 keVee 2.5-3.0 keVee -0.04 0.10 0 2 4 6 8 10 12 14 16 18 20 Amplitude[events/day/kg/keV Energy[keV ] 0 200 2.7400 years600 800 1000 ee Day fromDay from Jan/2014Jan/2014 Masaki Yamashita 11 Power Spectrum •To ﬁnd any period in the data in the energy range of 1-6 keVee.

•Phase t0 is a free parameter. •⊿Χ2= Χ2(null) - Χ2(periodic hypotheses) •Test statistic to evaluate significance. •Global significance: the maximum ⊿Χ2 in the range to take into account `look elsewhere effect’. •No significant period was found between 20 and 600 days.

1 year

2 60 χ

Expected ± 1σ (local) ∆ 50 Expected ± 2σ (local) Expected 1σ (global) NDF = 10 40 Expected 2σ (global) 30 20 10

102 Period[days] Masaki Yamashita 12 Conclusion and Summary

•It is important to look for any signal (not only nuclear recoil) for dark matter search. •XMASS-I carried out annual modulation search with 2.7 years of data. (800 live days x 832 kg) •We did not ﬁnd any modulation signals – <1.9 x 10-41cm2 (90% CL) @ 8GeV – < 1.3-3.2 x 10-3 counts/day/kg/days (2-6 keVee) 90CL •We did not ﬁnd any particular period between 20 - 600 days in the energy region of 1-6keVee.

Masaki Yamashita 13