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XENON1T dark matter data analysis: Signal and background models and statistical inference

E. Aprile et al. (XENON Collaboration)
Phys. Rev. D 99, 112009 – Published 27 June 2019
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  • INTRODUCTION
  • DETECTOR RESPONSE MODEL
  • BACKGROUND AND DARK MATTER SIGNAL MODELS
  • INFERENCE WITH XENON1T DATA
  • SUMMARY
  • ACKNOWLEDGMENTS
    • References

    Abstract

    The XENON1T experiment searches for dark matter particles through their scattering off xenon atoms in a 2 metric ton liquid xenon target. The detector is a dual-phase time projection chamber, which measures simultaneously the scintillation and ionization signals produced by interactions in target volume, to reconstruct energy and position, as well as the type of the interaction. The background rate in the central volume of XENON1T detector is the lowest achieved so far with a liquid xenon-based direct detection experiment. In this work we describe the response model of the detector, the background and signal models, and the statistical inference procedures used in the dark matter searches with a 1  metric ton×year exposure of XENON1T data, that leads to the best limit to date on WIMP-nucleon spin-independent elastic scatter cross section for WIMP masses above 6  GeV/c2.

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    • Received 28 February 2019

    DOI:https://doi.org/10.1103/PhysRevD.99.112009

    © 2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Particle dark matter
    1. Techniques
    Dark matter detectors
    Particles & Fields

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    Issue

    Vol. 99, Iss. 11 — 1 June 2019

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    Images

    • Figure 1
      Figure 1

      Mean photon and charge yields of NR (upper panels) and ER (lower panels) in the XENON1T calibration data fit (details of the fit are in Sec. 2c). The blue solid line and shaded region represent the point estimation and 15%–85% credible region, respectively, of the posterior. Data points for upper panels are from fixed-angle neutron scattering measurements [22, 23, 24, 25, 26, 27, 28]. Results of XENON100 [17] using data—Monte Carlo (MC) matching on the Am241Be calibration method are shown with the red solid line and shaded region. The best fit from NEST v2.0 [21] is shown with the black solid line. The measurements from [19, 20, 29, 30] are shown along with the best fit of NEST v2.0 [21] in lower panels. The vertical dashed blue lines indicate the energy threshold for XENON1T NR and ER calibrations, below which the detection efficiency drops to less than 10%.

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    • Figure 2
      Figure 2

      The cS1 spectra of the SR1 data (black bars) and the signal response models (blue) for Rn220, AmBe241, and D-D generator are shown in panel A, B, and C, respectively. Solid lines represent the median of the posterior, and the shaded regions show the 15.4% to 84.6% credible regions of the posterior. The accidental coincidence, ER contamination, single NR scatter (NR SS), and multiple NR scatter (NR MS) components are shown in magenta, gold, red and green, respectively.

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    • Figure 3
      Figure 3

      The cS2b distributions in different cS1 ranges of the SR1 data (black bars) and the signal response model (blue) for Rn220, AmBe241 and D-D generator, from left to right, respectively. The figure description is the same as in Fig. 2.

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    • Figure 4
      Figure 4

      Variations in log10(cS2b) distributions as γer (top panel) and Δr (bottom panel) vary, from the 2.3% to 50.0%, and then to 97.7% percentile of the signal model posterior, in different cS1 ranges.

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    • Figure 5
      Figure 5

      Spatial (left panel) and (cS1, cS2b) (right panel) distribution of identified multiple neutron scatters in SR0 and SR1 DM search data, along with blinded DM search data (ER events) shown in black dots. The solid circles in the left panel represent the primary (largest cS2b) scatter positions while the hollow circles show the positions of the secondary scatters. The solid or dashed black line connects the scatters that are in the same event. XENON1T TPC boundaries are shown as solid gray lines. Different volumes defined in [9], 0.65 t (dashed green), 0.9 t (dashed blue) and 1.3 t (solid magenta), are shown. In the right panel, the 1σ, 2σ, and 3σ contours of the expected distribution of neutron multiple scatters are shown as solid, dashed and dotted purple lines, respectively. Solid purple circles show the primary (cS1, cS2b) of the identified neutron multiple scatters in DM data. As a comparison, the shaded black regions display the 1σ (dark) and 2σ (light) probability density percentiles of the ER background component for SR1.

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    • Figure 6
      Figure 6

      Illustration of the surface background distributions in cS1 and Log10(cS2b), with projections on each axis showing the expected distribution within the entire analysis space (blue), and in the reference region for the entire 1.3 metric ton FV (brown), and the inner 1 metric ton (green). The reference region lies between the NR median and −2σ quantile lines, marked by red and black lines, respectively.

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    • Figure 7
      Figure 7

      Illustration of the accidental coincidence background distribution in cS1 and log10(cS2b), with projections on each axis showing the expected distribution within the entire analysis space (blue), and in the reference region for 1.3 metric ton FV. The reference region lies between the NR median and −2σ quantile lines, marked by red and black lines, respectively.

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    • Figure 8
      Figure 8

      The main panel shows the 1σ (dashed line) and 2σ contours of the WIMP signal model in (cS1, cS2b) space, for WIMP mass of 10  GeV/c2 (red), 50  GeV/c2 (violet), and 200  GeV/c2 (blue), respectively. The lower right inset shows the differential energy rate, which is in unit of tyu, for these three WIMP masses, with an assumed WIMP-nucleon cross section of 10−45  cm2. The upper left inset shows the rate uncertainty of WIMP signal model as a function of WIMP mass.

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    • Figure 9
      Figure 9

      Distribution of the lower (blue) and upper (gray) toy-MC limits on a 50  GeV/c2 WIMP cross section. The upper (lower) limits are drawn as a cumulative (complementary cumulative) distribution, to show the fraction of limits that include a certain cross section. The corresponding signal expectation value is shown on the upper horizontal axis. The toy-MC did not include a true signal, indicated with a dashed orange line at 0. All upper limits are above 0, and 0.93 of lower limits are equal to 0, giving a total estimated coverage of 0.93 for the 500 toy-MCs used in this example, part of the dataset used for Fig. 11. As the cross section is constrained to be non-negative, the survival fraction below 0 is 1. Green solid and dot-dashed lines show the median upper limit and 1σ sensitivity band.

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    • Figure 10
      Figure 10

      Illustration of the effect of a mismodeling term on the ER model for a slice of parameter space 20<cS1<30  PE, projected onto cS2b. The upper curve shows the ER model for safeguard fractions −0.01, 0 and 0.01, showing how a positive (negative) mismodeling term raises (lowers) the signal-like tail of the ER model with respect to the nominal model in blue. The lower panel shows Δmm, the difference between each model and the nominal, demonstrating both the effect on the tail at low cS2b and the opposite at higher cS2b, due to the normalization of the PDF.

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    • Figure 11
      Figure 11

      Figure displaying the coverage of confidence intervals for the spin-independent 1 metric ton-year analysis and a 50  GeV/c2 WIMP. Error bars indicate 1σ confidence intervals around the best estimate. Orange squares show the result using the profile construction, while the blue circles show the coverage of the XENON1T analysis including the 3σ threshold for reporting upper limits. The upper and lower x-axes show the WIMP cross section and expectation (setting ε=1), respectively, and the green band and line highlight the sensitivity and 1  sigma band of upper limits for the analysis.

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