Exclusion limits on the WIMP-nucleon cross section from the first run of the Cryogenic Dark Matter Search in the Soudan Underground Laboratory

D. S. Akerib et al. (CDMS Collaboration)

Phys. Rev. D 72, 052009 – Published 30 September 2005

Abstract

The Cryogenic Dark Matter Search (CDMS-II) employs low-temperature Ge and Si detectors to seek weakly interacting massive particles (WIMPs) via their elastic-scattering interactions with nuclei. Simultaneous measurements of both ionization and phonon energy provide discrimination against interactions of background particles. For recoil energies above 10 keV, events due to background photons are rejected with $> 99.99 %$ efficiency. Electromagnetic events very near the detector surface can mimic nuclear recoils because of reduced charge collection, but these surface events are rejected with $> 96 %$ efficiency by using additional information from the phonon pulse shape. Efficient use of active and passive shielding, combined with the 2090 m.w.e. overburden at the experimental site in the Soudan mine, makes the background from neutrons negligible for this first exposure. All cuts are determined in a blind manner from in situ calibrations with external radioactive sources without any prior knowledge of the event distribution in the signal region. Resulting efficiencies are known to $\sim 10 %$ . A single event with a recoil of 64 keV passes all of the cuts and is consistent with the expected misidentification rate of surface electron recoils. Under the assumptions for a standard dark matter halo, these data exclude previously unexplored parameter space for both spin-independent and spin-dependent WIMP-nucleon elastic scattering. The resulting limit on the spin-independent WIMP-nucleon elastic-scattering cross section has a minimum of $4 \times 10^{- 43} {cm}^{2}$ at a WIMP mass of $60 GeV c^{- 2}$ . The minimum of the limit for the spin-dependent WIMP-neutron elastic-scattering cross section is $2 \times 10^{- 37} {cm}^{2}$ at a WIMP mass of $50 GeV c^{- 2}$ .

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Received 5 July 2005

DOI:https://doi.org/10.1103/PhysRevD.72.052009

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Vol. 72, Iss. 5 — 1 September 2005

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Figure 1
Diagram of Tower 1. The tower has four temperature stages (4 K, 600 mK, 50 mK, and base). The cold electronics for the ionization channels (FETs) and phonon channels (SQUIDs) are mounted on the top of the tower, which has surfaces at 4 K and 600 mK. The six ZIP detectors are arranged in the bottom portion of the tower with 2 mm separation and no intervening material. The two Si ZIPs (Z4 and Z6) are indicated by a darker shade.
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Figure 2
Top view and side view of the CDMS-II shielding and veto. The detector volume is referred to as the “icebox.” As shown, the stem to the right of the detector volume is the “cold stem” and connects the detectors and the copper cans to the cryostat. The stem to the left of the detector volume is the “electronics stem” and contains the wiring that connects the cold electronics to the room-temperature electronics.
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Figure 3
Ionization energy versus recoil energy for detector Z5 (Ge). Black dots correspond to calibration events from a ${}^{133}{Ba}$ source (emits gammas only) and gray dots correspond to calibration events from a ${}^{252}{Cf}$ source (emits gammas and neutrons).
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Figure 4
Ionization yield versus recoil for detector Z5 (Ge). Black dots correspond to calibration events from a ${}^{133}{Ba}$ source (emits gammas only) and gray dots correspond to calibration events from a ${}^{252}{Cf}$ source (emits gammas and neutrons). The upper distribution of events are bulk electron recoils which define the “electron-recoil band.” The lower distribution of events are nuclear recoils which define the “nuclear-recoil band.”
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Figure 5
Diagram of a CDMS ZIP detector. (a) The “ionization side” of the detector with a large inner electrode and an outer guard ring electrode. (b) The “phonon side,” divided into four quadrants labeled A, B, C, and D, each consisting of 37 dies of 28 QETs. The convention for the $x − y$ axes is shown. The area outside the cells consists of a passive Al/W grid that is patterned sparsely (10% area coverage) to minimize athermal-phonon absorption while maintaining field uniformity for the ionization measurement. (c) One of the 37 dies constituting a single phonon channel; each die contains 28 QETs. (d) One of the QETs consisting of a $1 μ m$ -wide tungsten strip connected to 8 aluminum fins.
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Figure 6
Peak phonon delay versus ionization yield for detector Z5. Events from a ${}^{252}{Cf}$ source (emits both gammas and neutrons) are shown as gray dots. Events from a ${}^{133}{Ba}$ source (emits gammas only) are shown as black dots. Surface electron recoils from the ${}^{133}{Ba}$ calibration appear as a low-yield tail and having smaller peak phonon delays. Lines for a typical cut excluding events with high yield or low peak phonon delay are shown.
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Figure 7
CDMS-II data acquisition layout showing the various hardware components in relation to the detector and veto systems. When a detector triggers, various detector and veto elements are read out to form an event. Monitoring processes run continuously to monitor the health of the detector, veto, and cryogenics components.
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Figure 8
Live-time before (gray) and after (black) application of the data-quality cut described in Sec. 5b1. The short regions of down-time correspond to episodes of electronics problems and unintended detector warming above 1 K.
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Figure 9
Phonon trigger efficiencies for some of the ZIP detectors. Black dots with error bars show the trigger efficiency for the detector Z3 (Ge). The other points are plotted without error bars to avoid confusion. Triangles correspond to the trigger efficiency for Z5 (Ge), and diamonds correspond to the efficiency of Z4 (Si), which has the worst efficiency of all the Tower 1 ZIPs.
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Figure 10
Comparison of the measured ${}^{133}{Ba}$ charge spectrum (dots with error bars) and the Monte Carlo simulation (gray line) for the Ge detector Z3 (top) and the Si detector Z4 (bottom). The expected lines for this source are at 276 keV, 303 keV, 356 keV, and 384 keV.
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Figure 11
Comparison of measured ${}^{252}{Cf}$ neutron recoil spectrum (dots with error bars) and Monte Carlo simulation (gray line) for coadded Ge detectors (top) and Si detectors (bottom). The level of agreement suggests that the phonon measurement of the recoil energy is unquenched.
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Figure 12
Plot of ionization energy versus recoil energy for events during the WIMP search after the initiation of an old-air purge between the outer copper can and the surrounding mu-metal shield. Alphas (black dots) interacting in the detectors are easily identified. Nonlinearity in the phonon energy response at high energies is evident in the gammas (gray dots). This nonlinearity results in the recoil energy of the alphas being underestimated by about a factor of 2.
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Figure 13
Measured gamma spectra in the coadded Ge detectors along with Monte Carlo simulations of the most likely contributions: U/Th/K on the inner polyethylene (dotted), U/Th/K on the Cu cans (thin gray), Rn outside the mu-metal shield (thick black), and the sum of all these contributions (thick gray).
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Figure 14
Charge-collection efficiency as a function of depth from the surface of a Germanium ZIP at a 3.0 V ionization bias, as derived from Monte Carlo simulations and analysis of ${}^{109}{Cd}$ data.
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Figure 15
Depth distributions for simulated surface events (10–100 keV) corresponding to ${}^{133}{Ba}$ single scatters (dashed light gray), ${}^{133}{Ba}$ nearest neighbor doubles (solid light gray), ${}^{133}{Ba}$ beta-beta doubles (dark gray) and ${}^{40}K$ singles (black). The ${}^{133}{Ba}$ simulation results are normalized to all events. The ${}^{40}K$ simulation results have been scaled down by a factor of $\sim 100$ for easier comparison with the results from the ${}^{133}{Ba}$ simulations. The horizontal thin black line indicates the expected distribution for events interacting uniformly throughout the entire detector.
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Figure 16
Plot of the time delay parameters $t_{Y}$ versus $t_{X}$ for detector Z5 with ${}^{133}{Ba}$ calibration data. The barrel shape of the plot indicates that this event reconstruction is nonlinear.
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Figure 17
Plot of the phonon partitioning parameter $P_{Y}$ versus $P_{X}$ for detector Z5 with ${}^{133}{Ba}$ calibration data. $P_{Y}$ and $P_{X}$ denote relative partitioning of the phonon energy as defined by Eq. (13).
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Figure 18
Plot of delay “radius,” $R = \sqrt{t_{X}^{2} + t_{Y}^{2}}$ , versus phonon partitioning parameter $P_{X}$ for $- 0.3 < P_{Y} < - 0.2$ . Events shown are for detector Z5 when exposed to a ${}^{133}{Ba}$ source.
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Figure 19
Plot of peak delay versus phonon partitioning parameter $P_{X}$ for the slice $- 0.3 < P_{Y} < - 0.2$ . Gray dots are uncorrected distributions and black dots are corrected distributions. The corrected peak delay has been rescaled to $3 μ s$ for easier comparison.
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Figure 20
Plot of peak risetime versus phonon partitioning parameter $P_{X}$ for the slice $- 0.3 < P_{Y} < - 0.2$ . Gray dots are uncorrected distributions and black dots are corrected distributions. The corrected peak risetime has been rescaled to $9.5 μ s$ for easier comparison.
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Figure 21
Plot of ionization yield versus $P_{X}$ for the slice $- 0.3 < P_{Y} < - 0.2$ . Gray dots are uncorrected distributions and black dots are corrected distributions. The corrected yield has been rescaled to 0.95 for easier comparison.
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Figure 22
Reduced $χ^{2}$ (for 4092 degrees of freedom) of the ionization pulse as given by the optimal-filter algorithm plotted against ionization energy (electron equivalent) from a ${}^{133}{Ba}$ calibration for detector Z3. Only events beneath the solid line pass the $χ^{2}$ cut. The faint upper band consists of events taken during the $\sim 5 %$ of the time that a noisy heater was on; see Fig. 23.
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Figure 23
Plot of the reduced $χ^{2}$ (for 4092 degrees of freedom) of the ionization pulse from the optimal-filter algorithm versus time of day for a ${}^{133}{Ba}$ calibration of detector Z3. Events are between 10–60 keVee. The events in the upper band of Fig. 22 are clearly localized in time. These excursions are correlated with the time a noisy heater was active.
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Figure 24
Efficiency of the ionization $χ^{2}$ cut for nuclear-recoil candidate events (see Sec. 5b3) in the Ge detector Z3. Note that the plot is versus recoil energy and not ionization.
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Figure 25
Ionization collected in the outer electrode versus ionization collected in the inner electrode using the optimal-filter (see Sec. 5a1) algorithm for Ge detector Z5. Calibration data taken with an external ${}^{133}{Ba}$ source are shown. Events between the two lines pass the fiducial-volume cut.
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Figure 26
Ionization collected in the outer electrode versus ionization collected in the inner electrode using the time-based fitting (see Sec. 5a1) algorithm for Ge detector Z5. Calibration data taken with an external ${}^{133}{Ba}$ source are shown. Events between the two lines pass the fiducial-volume cut.
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Figure 27
Efficiency of the fiducial-volume cut for detector Z5 (Ge). The black line corresponds to the Monte Carlo simulation of the ${}^{252}{Cf}$ neutron calibration estimate when the intended optimal-filter algorithm is used to estimate the ionization pulse amplitude. The gray line corresponds to the estimate when using the time-based fit. The black dots with error bars are estimates using the actual nuclear-recoil events due to neutrons from the ${}^{252}{Cf}$ calibration runs using the cuts for the current analysis. The roll-off above 60 keV is an artifact due to surface-electron contamination of the data set. Only the fiducial-volume cut for this detector (Z5) varied substantially ( $\sim 25 %$ reduction) with the time-based fit.
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Figure 28
Efficiency of the nuclear-recoil-band cut for the Ge detector Z3 (see Sec. 5b5).
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Figure 29
Efficiency of the ionization-threshold cut (see Sec. 5b6) on nuclear-recoil events. Black points with error bars indicate the efficiency as determined from data using nuclear recoils from the ${}^{252}{Cf}$ calibration runs. Diamonds correspond to the calculated efficiencies assuming that the yield is a Gaussian.
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Figure 30
Histogram of time from last veto hit for Tower 1 at the Stanford Underground Facility. An excess above the 5.7-kHz rate expected for uncorrelated events is seen for times near zero. The cut at $- 50 μ s$ is set in order to remove the excess for single scatters with recoil energies between 5–10 keV in Ge detectors Z2, Z3, and Z5 (solid dark gray curve); in Z1 (solid light gray line); and in the two Si detectors Z4 and Z6 (dashed gray line).
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Figure 31
Plot of phonon peak delay versus phonon peak risetime (defined in Sec. 5a1) for Ge detector Z5 in the 20–40 keV recoil bin. ${}^{252}{Cf}$ neutrons in the $2 σ$ nuclear-recoil band (gray) and ${}^{133}{Ba}$ surface electron recoils in the $4 σ$ nuclear-recoil band (black) are shown. The first step in determining the timing cuts is to set energy-independent cuts within the bin for each of these two parameters so that all of the surface electron recoils are rejected. Events below or to the left of the lines illustrating hypothetical cut values would be rejected.
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Figure 32
Plots of peak risetime (top) and peak delay (bottom) versus recoil energy for detector Z5 (Ge). Gray dots correspond to ${}^{252}{Cf}$ neutrons in the $2 σ$ nuclear-recoil band. Black dots correspond to ${}^{133}{Ba}$ surface electron recoils in the $4 σ$ nuclear-recoil band. The piecewise linear functions corresponding to the cut in each parameter are also shown. Events below either line are cut. For this detector, above $\sim 20 keV$ all of the discrimination comes from the peak delay.
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Figure 33
Efficiency of the phonon timing cut for the Ge detector Z3 (dots with error bars) and Si detector Z4 (gray diamonds). Error bars for the Si detector have been omitted to avoid confusion.
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Figure 34
Overall WIMP efficiency when cuts are applied. Light gray dashed line corresponds to application of data-quality, pile-up, and muon-veto cuts and, above 20 keV, overlaps with the light gray solid line which corresponds to imposing the ionization analysis threshold. Dark gray dashed line corresponds to application of the fiducial-volume cut. Dark gray solid line corresponds to the $2 σ$ nuclear-recoil-band cut. The black solid line corresponds to application of the phonon timing cuts and is the overall efficiency for our current analysis. The black dashed line is the overall efficiency for the initial analysis.
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Figure 35
Overall WIMP efficiency for the Si detector Z4. Dashed line corresponds to the efficiency for the initial analysis and the solid line is the efficiency for the current analysis. The two estimates differ by less than 1% since, for this detector, there was little difference between using the time-based pulse height algorithm and the optimal-filter algorithm.
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Figure 36
Events from the ${}^{252}{Cf}$ calibrations with recoils between 5–100 keV. Solid lines indicate the $2 σ$ nuclear-recoil bands. Dashed lines indicate the recoil (vertical) and ionization (curved) analysis thresholds. All the events shown satisfy all of the WIMP-search cuts (e.g. single scatter and fiducial volume), excluding the ionization yield and phonon timing cuts. Gray points fail the timing cuts and black points pass the timing cuts. Compare with Fig. 37 and 38. Note that the timing cut rejects $\sim 20 %$ of the events in the nuclear-recoil band while rejecting $≳ 75 %$ of the events in the electron-recoil band.
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Figure 37
Unvetoed single scatters in the fiducial volume for each of the six ZIP detectors of Tower 1. These data correspond to the current analysis of 52 live-days of the Run 118 WIMP search at Soudan. Solid lines indicate the $2 σ$ nuclear-recoil bands. Dashed lines indicate the recoil (vertical) and ionization (curved) analysis thresholds. Gray points fail the timing cuts and black points pass the timing cuts. A single event in Z5 with a 64 keV recoil satisfies all of the criteria for a WIMP candidate but is consistent with our expected misidentification of electron recoils near the surface. Compare with Fig. 36. Detector Z6 was not included in this analysis due to a known ${}^{14}C$ contamination.
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Figure 38
Unvetoed single-scatters in the fiducial volume for each of the six ZIP detectors of Tower 1. These data correspond to the initial analysis of 52 live-days of the Run 118 WIMP search at Soudan for which we inadvertently analyzed some of the ionization pulses using the time-based fit. Solid lines indicate the $2 σ$ nuclear-recoil-acceptance bands. Dashed lines indicate the recoil (vertical) and ionization (curved) analysis thresholds. Gray points fail the timing cuts and black points pass the timing cuts. This algorithm led to an overly severe fiducial-volume cut which rejected the event in Z5 that passed all of the other cuts. Compare with Fig. 36. Detector Z6 was not included in this analysis due to a known ${}^{14}C$ contamination.
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Figure 39
Experimental limits in the WIMP-nucleon cross section versus WIMP mass parameter space for spin-independent interactions. The cross section is normalized to a single nucleon. The region above the solid (dashed) black curve is excluded at 90% confidence by the current (initial) analysis of the CDMS-II Soudan WIMP search (Ge detectors). The upper thin black curve is the CDMS-II Soudan 90% C.L. exclusion limit for the Si detector. The solid gray curve is the EDELWEISS [72] exclusion limit. The dashed gray curve is the ZEPLIN I [80] exclusion limit. The $3 σ$ DAMA [73] detection region is shown in light gray. Plot courtesy of [81].
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Figure 40
Comparison of the current (solid curve) and initial (dashed curve) CDMS-II exclusion limits with predicted regions in the WIMP-nucleon cross section versus WIMP mass parameter space for spin-independent interactions. The cross section is normalized to a single nucleon. The light gray region corresponds to parameter space that is consistent with the standard constraints of the MSSM framework and measurements of the relic abundance of dark matter [66]. The two dark gray regions correspond to additional allowed parameter space under the relaxation of some of the grand unification constraints [67]. Plot courtesy of [81].
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Figure 41
Comparison of the current (solid curve) and initial (dashed curve) CDMS-II exclusion limits with predicted regions in the WIMP-nucleon cross section versus WIMP mass parameter space for spin-independent interactions. The cross section is normalized to a single nucleon. The two light gray regions correspond to parameter space allowed in the mSUGRA framework [68, 69]. The dark gray region and black $\times$ ’s correspond to allowed regions under the assumptions of split-SUSY [70, 71]. Plot courtesy of [81].
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Figure 42
CDMS-II (Tower 1) spin-dependent limits. Black lines are Ge limits, gray lines are Si limits. Dotted lines are proton limits and solid lines are neutron limits.
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Figure 43
Limits on WIMP-nucleon couplings ( $a_{p}$ and $a_{n}$ ) with a WIMP mass of $50 GeV c^{- 2}$ . The black curve is the Ge limit and the gray curve is the Si limit.
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