Low-mass dark matter search with CDMSlite

The SuperCDMS experiment is designed to directly detect weakly interacting massive particles (WIMPs) that may constitute the dark matter in our Galaxy. During its operation at the Soudan Underground Laboratory, germanium detectors were run in the CDMSlite mode to gather data sets with sensitivity specifically for WIMPs with masses $<10\mathrm{GeV}/c^2$. In this mode, a higher detector-bias voltage is applied to amplify the phonon signals produced by drifting charges. This paper presents studies of the experimental noise and its effect on the achievable energy threshold, which is demonstrated to be as low as $56{\mathrm{eV}}_{\mathrm{ee}}$ (electron equivalent energy). The detector-biasing configuration is described in detail, with analysis corrections for voltage variations to the level of a few percent. Detailed studies of the electric-field geometry, and the resulting successful development of a fiducial parameter, eliminate poorly measured events, yielding an energy resolution ranging from $\sim 9{\mathrm{eV}}_{\mathrm{ee}}$ at 0 keV to $101{\mathrm{eV}}_{\mathrm{ee}}$ at $\sim 10{\mathrm{keV}}_{\mathrm{ee}}$. New results are derived for astrophysical uncertainties relevant to the WIMP-search limits, specifically examining how they are affected by variations in the most probable WIMP velocity and the Galactic escape velocity. These variations become more important for WIMP masses below $10\mathrm{GeV}/c^2$. Finally, new limits on spin-dependent low-mass WIMP-nucleon interactions are derived, with new parameter space excluded for WIMP masses $\lesssim 3\mathrm{GeV}/c^2$.

Figure 1

Differential rates for WIMP recoils on a germanium target as functions of recoil energy. WIMPs with a WIMP-nucleon spin-independent cross section of ${10}^{-41}{\mathrm{cm}}^2$ and masses of 2, 5, and $10\mathrm{GeV}/c^2$ are considered. The bands encompassing each curve are computed by varying the astrophysical parameters of the dark matter halo within known observational uncertainties. The vertical lines designate example nuclear-recoil thresholds of 0.5 and 2 keV, respectively.

Figure 2

Schematic showing the general coverage of the four phonon read-out channels ($A–D$) overlaying the sensor pattern for the CDMSlite detector. The sensors on the bottom side are exclusively used for applying the high-voltage bias (HV) and are not read out. All sensors on the top side are held at ground.

Figure 3

Spin-independent WIMP-nucleon cross section 90% upper limits from CDMSlite Run 1 (red dotted curve with red uncertainty band) [11] and Run 2 (black solid curve with orange uncertainty band) [12] compared to the other (more recent) most sensitive results in this mass region: CRESST-II (magenta dashed curve) [33], which is more sensitive than CDMSlite Run 2 for $m_{\mathrm{WIMP}}\lesssim 1.7\mathrm{GeV}/c^2$, and PandaX-II (green dot-dashed curve) [34], which is more sensitive than CDMSlite Run 2 for $m_{\mathrm{WIMP}}\gtrsim 4\mathrm{GeV}/c^2$. The Run 1 uncertainty band gives the conservative bounding values due to the systematic uncertainty in the nuclear-recoil energy scale. The Run 2 band additionally accounts for the uncertainty on the analysis efficiency and gives the 95% uncertainty on the limit.

Figure 4

Total combined trigger and analysis efficiencies for Run 1 (red dotted curve) and Run 2 (black solid curve with orange 68% uncertainty band). The implementation of a fiducial-volume cut is primarily responsible for the reduction in efficiency at high recoil energies between the two analyses.

Figure 5

Measured efficiency-corrected spectra for Run 1 (red dotted curve) and Run 2 (gray shaded area). The ${}^{71}\mathrm{Ge}$-activation peaks at 10.37 and $1.30{\mathrm{keV}}_{\mathrm{ee}}$ are prominent in both spectra, and the peak at $0.16{\mathrm{keV}}_{\mathrm{ee}}$ is additionally visible in the Run 2 spectrum. The ${}^{65}\mathrm{Zn}$ $K$-shell electron-capture peak is also visible at $8.89{\mathrm{keV}}_{\mathrm{ee}}$ in the Run 1 spectrum. Inset: an enlargement of the spectra below $2{\mathrm{keV}}_{\mathrm{ee}}$ with bins five times smaller and the runs’ analysis thresholds given by the extended and labeled tick marks.

Figure 6

Templates used for the standard OF, NSOF, and 2T-fit algorithms for CDMSlite analysis. The green solid curve is the single trace used for the OF, NSOF, and 2T-fit slow templates, which is derived from averaging high-energy traces. In the 2T fit, the slow template’s amplitude carries the main energy information. The 2T-fit fast template (orange dotted), is derived by considering the differences between the slow template and the traces used in the slow template’s derivation. In the 2T fit, the fast template’s amplitude captures the position information from the signal trace. The maxima of the amplitudes (Ampl.) are scaled to unity in the figure.

Figure 7

Results of the 2T-fit algorithm for an example event chosen from the ${}^{71}\mathrm{Ge}$ $L$-shell capture peak in Run 2. The traces and fits from all four phonon channels, labeled A–D (where channel A is the outer ring) are given. For each channel, the raw trace (blue solid) is compared to the final total fit (black dashed) which is a linear combination of the slow (green solid) and fast (orange dotted) templates. The channel with the largest fast-template amplitude, channel B for this event, is the channel of which the sensors are closest to the initial recoil.

Figure 8

NSOF-fit energy estimator as a function of the 2T-fit fast-template amplitude from the summed trace. The high-density band of events is the ${}^{71}\mathrm{Ge}$ $K$-shell activation line. Residual position dependence is reflected in the slope of the band. This dependence is corrected according to the straight-line fit shown by the solid line. The location of the peak at $\sim 155{\mathrm{keV}}_{\mathrm{t}}$ is discussed in Sec. 5a.

Figure 9

Baseline resolution (top) and the corresponding SNR (bottom) as a function of the applied bias potential. Each point represents a single 3 h long data set taken prior to Run 2. The resolution and SNR increase and decrease, respectively, past $\sim 70\mathrm{V}$ in applied bias. The average uncertainty for each point is $3.6{\mathrm{eV}}_{\mathrm{t}}$ for the resolution and 0.39 for the SNR. The additional variation seen at a given bias is likely a result of time dependence of the noise. For reference, $1{\mathrm{keV}}_{\mathrm{t}}\approx 66{\mathrm{eV}}_{\mathrm{ee}}$.

Figure 10

Top: total phonon energy, or noise, as a function of time since biasing in Run 1. The noise decays quasiexponentially with time; four example events are given by noncircular markers. The first and last 500 traces are highlighted in light and dark orange, respectively. The noise distribution is offset from $0{\mathrm{keV}}_{\mathrm{t}}$ as the energy-estimating algorithm tends to fit to upward noise fluctuations. For reference, $1{\mathrm{keV}}_{\mathrm{t}}\approx 66{\mathrm{eV}}_{\mathrm{ee}}$. Middle: raw traces of the events marked in the top panel. Traces are shifted by 100 nA with respect to each other for clarity. Bottom: power spectral densities (PSDs) for the noise at the start (light orange) and end (dark orange) of the series. The earlier traces have more power below $\sim 10\mathrm{kHz}$.

Figure 11

Baseline noise distribution for series that were prebiased (gray area) and series that were not prebiased (red curve) taken at potential differences of $51/60/66\mathrm{V}$ (top/middle/bottom). The Gaussian-equivalent widths (see Sec. 4a) of the distributions with ${\sigma }_{\mathrm{w}}$ and without ${\sigma }_{\mathrm{wo}}$ prebiasing are also given, in ${\mathrm{keV}}_{\mathrm{t}}$. The thinner distribution widths for prebiased series compared to nonprebiased series demonstrates the effect of prebiasing. For reference, $1{\mathrm{keV}}_{\mathrm{t}}\approx 66{\mathrm{eV}}_{\mathrm{ee}}$.

Figure 12

Top: Run 2 noise distribution. The electronic-noise distribution is centered at $\sim 0{\mathrm{keV}}_{\mathrm{t}}$ while the low-frequency noise distribution dominates from $0.5–1.5{\mathrm{keV}}_{\mathrm{t}}$. For reference, $1{\mathrm{keV}}_{\mathrm{t}}\approx 66{\mathrm{eV}}_{\mathrm{ee}}$. Middle: raw (thin light blue solid) and filtered (thick black dotted) trace from a typical low-frequency noise event compared to the standard-event template (thick green solid), derived from high-energy ${}^{71}\mathrm{Ge}$ $K$-shell events. The difference in pulse shape is most evident between 0 and 2 ms. Bottom: power spectral densities (PSDs) for 500 low-frequency (light blue) and electronic (dark blue) noise traces. The low-frequency noise population has more power below $\sim 1\mathrm{kHz}$.

Figure 13

Number of low-energy triggered events for Run 2 Period 1 in the two-dimensional plane of cryocooler time, ${\widehat{t}}_{-}$, and calendar time in 2014. The color scale is logarithmic with empty bins mapped to black. The rate of low-frequency noise injection evolved throughout the run because of the deterioration of the cryocooler, ranging from 0 to $>1000$ counts per bin. The boundaries of the eight time blocks defined after applying a smoothing filter to the histogram are given in the bar labeled “Blocks” above the plot.

Figure 14

Template traces for the standard OF (green solid) and low-frequency noise (orange dotted) fits. The templates were generated by averaging many events’ pulse shapes, which removed uncorrelated noise. Details of the low-frequency noise template generation are discussed in the text, and the standard OF template definition is discussed in Sec. 2c. The maxima of the amplitudes (Ampl.) are scaled to unity in the figure.

Figure 15

$\mathrm{\Delta }{\chi }_{\mathrm{LF}}^2$ as a function of total phonon energy for time blocks 2 (top) and 7 (bottom) showing the three portions of the low-frequency noise rejection cut (dotted) with the defining portion at any given energy darkened. Low-frequency noise events cluster near $\sim 1{\mathrm{keV}}_{\mathrm{t}}$, while good events fall on a downward opening parabola. The major difference between the two subplots is the difference in low-frequency noise: time block 2 shows low noise, while time block 7 is more noisy. Events above any portion of the cut are rejected (light blue), while those below are retained (dark blue). Time block 2 is relatively less noisy, while time block 7 is relatively more noisy. The contour portion in block 2 cuts more loosely ($2.5\sigma$) than in block 7 ($5\sigma$) because of the changing low-frequency noise environment throughout the run. A preselection cut removing events with unusually high NSOF ${\chi }^2$ values has been applied in these figures and, for reference, $1{\mathrm{keV}}_{\mathrm{t}}\approx 66{\mathrm{eV}}_{\mathrm{ee}}$.

Figure 16

Efficiency of the pulse-shape based cuts for Run 2 Period 1 (top) and Period 2 (bottom) as a function of electron-equivalent energy. Almost all loss in efficiency is due to the low-frequency noise cut, with the sharp drop in efficiency below $100{\mathrm{eV}}_{\mathrm{ee}}$ due to the kernel-density-estimate portion of that cut. The insets give an enlargement in the $\mathcal{O}(100{\mathrm{eV}}_{\mathrm{ee}})$ range, where the systematic uncertainty from varying the pulse shape, shown by the error bars, is largest. The average statistical uncertainty for each bin, due to the number of traces simulated, is 1.2%.

Figure 17

Reconstructed energy probability distribution function (PDF) of noise-only events in Run 2 (blue solid, left vertical axis) with the corresponding cumulative distribution function (CDF) (orange dotted, right vertical axis). The $1\sigma$-equivalent is taken as half the distance between the 15.87th and 84.13th percentiles (dark purple dashed) and is $9.26\pm 0.11{\mathrm{eV}}_{\mathrm{ee}}$.

Figure 18

Width of four points in the Run 2 energy spectrum (red points), the best-fit curve (black), and 68% uncertainty band (orange). The bottom panel is an enlargement of the top panel below $1.5{\mathrm{keV}}_{\mathrm{ee}}$.

Figure 19

Binned trigger efficiency without (top) and with (bottom) a cut on cryocooler timing for Run 2 Periods 1 (left) and 2 (right). Using the cryocooler information noticeably improved the Period 1 measurement while marginally improving that for Period 2. The best-fit error function (black dashed curve) and its 68% uncertainty (gray shaded) are given in the bottom row for each period.

Figure 20

Phonon energy as a function of run time for Run 1. The overdensity around $120{\mathrm{keV}}_{\mathrm{t}}$ is from the 10.37 keV $K$-shell electron-capture products. Gaps exist because of unstable conditions. The different colors/orientations of the triangles indicate the four time periods which were fit to independent polynomials in the gain-correcting piecewise fit. The horizontal line indicates the peak’s expected location (under the assumptions made for the Run 1 analysis; see main text) with departures of 5% and 10% indicated by the bands. The measured energy of the line shows up to 15% variation over the course of the run.

Figure 21

$K$-shell activation peak (cluster at $150–160{\mathrm{keV}}_{\mathrm{t}}$) in Run 2 as a function of time without (top) and with (bottom) corrections for gain variations. ${}^{252}\mathrm{Cf}$ calibrations occurred in February, May, and September/October. The horizontal lines indicate the means of the two peak distributions.

Figure 22

Difference in electric potential between the final locations of electrons and holes (color map), after propagating through the crystal, as a function of their initial position in the detector. A single vertical slice of the detector, perpendicular to the circular top and bottom faces (see Fig. 2) and along an arbitrary radius ($R$ coordinate, with 0 at the center of the detector) is shown. To uniformly cover the crystal, the squared radius is sampled, and thus $R^2$ is plotted. The top of the crystal (along the $Z$ coordinate) is at 70 V, and the bottom is at 0 V. The copper housing (not shown at high $R^2$) surrounding the detector is also at 0 V, and a small gap exists between it and the sidewall. This causes the total potential difference experienced by drifting charges to be $<70\mathrm{V}$ in regions where field lines terminate on the sidewall. Radii with $R^2<800{\mathrm{mm}}^2$ experience the full 70 V potential difference and are not shown.

Figure 23

${}^{71}\mathrm{Ge}$ $K$-shell peak in the Run 2 data, with no fiducial-volume cut, compared to the results of the electric-field study. The study simulates peak events on top of a flat Compton background before applying a smearing function. The smeared low-energy tail observed in the data is replicated in the simulation.

Figure 24

Position of Run 2 events using the energy partition coordinates. Events in the full energy range are gray, while those between 100 and $200{\mathrm{eV}}_{\mathrm{ee}}$ are highlighted in black. The population at low energy is clearly clustered in position.

Figure 25

2T-fit-based radial parameter as a function of energy for Run 2 Period 1 (top) and Period 2 (bottom). The vertical clusters are the ${}^{71}\mathrm{Ge}$-activation lines, and the horizontal band at high radius contains reduced-amplification events. The radial cut thresholds are indicated by the blue dashed line, effectively removing events at high radius, including the low-energy cluster seen in Period 2.

Figure 26

Diagram showing the morphology of the expected event distribution in the radial-parameter versus reconstructed-energy plane from a monoenergetic homogeneously distributed source. The distribution is split (vertical solid lines) into nonpeak events $R$, with reduced NTL amplification, and peak events $P$. The latter group is further separated into inner peak events $P_i$, that pass the cut threshold (horizontal dotted line), and outer peak events $P_o$, that do not. In practice, the ${}^{71}\mathrm{Ge}$-activation peaks were considered and can be separated from background because of the known half-life of the isotope.

Figure 27

Radial fiducial-volume cut efficiency below $2{\mathrm{keV}}_{\mathrm{ee}}$ for Period 1 (top) and Period 2 (bottom). The efficiency at full NTL amplification ${\mathcal{E}}_2$ (orange triangles) as well as the total efficiency $\mathcal{E}$ (blue circles) are shown along with their respective uncertainties. The error bars on ${\mathcal{E}}_2$ encompass statistical uncertainty due to the available number of $L$-shell peak events used as simulation inputs (same for each energy simulated), statistical uncertainty due to the number of simulated events passing the cut (different for each energy simulated), and a systematic uncertainty due to the estimate of nonpeak background events simulated (same for each energy simulated). The error bars on $\mathcal{E}$ additionally contain a small statistical uncertainty from the computation of the efficiency to have full NTL amplification (same for each energy simulated).

Figure 28

Run 1 low-energy spectrum showing both single- (gray shaded) and multiple-scatter (red line) events. Below the $L$-shell peak, the shape of the multiple-scatter spectrum is statistically compatible with the shape of the single-scatter spectrum.

Figure 29

Effect on the Run 2 best-fit limit from varying the Galactic escape velocity $v_{\mathrm{esc}}$ in the Maxwellian halo model while keeping all other parameters constant. Curves shown are the median values of the 2007 and 2014 RAVE survey results at $544\mathrm{km}{\mathrm{s}}^{-1}$ (black solid) and $533\mathrm{km}{\mathrm{s}}^{-1}$ (red dotted), respectively, as well as the 90% confidence bounds of the 2014 result at $492\mathrm{km}{\mathrm{s}}^{-1}$ (green dashed) and $587\mathrm{km}{\mathrm{s}}^{-1}$ (purple dot-dashed). The inset shows an enlargement below WIMP masses of $2\mathrm{GeV}/c^2$. Varying $v_{\mathrm{esc}}$ changes the lowest WIMP mass that can produce recoils above threshold, while the impact on the limit at higher masses is negligible.

Figure 30

Effect on the Run 2 best-fit limit from varying the most probable WIMP velocity ${\mathrm{\Theta }}_0$ in the Maxwellian halo model while keeping all other parameters constant. Curves shown are for the SHM value of $220\mathrm{km}{\mathrm{s}}^{-1}$ (black solid) and the upper and lower bounds of the measured values at $270\mathrm{km}{\mathrm{s}}^{-1}$ (green dashed) and $196\mathrm{km}{\mathrm{s}}^{-1}$ (purple dot-dashed). Varying ${\mathrm{\Theta }}_0$ changes where the most sensitive part of the curve lies in addition to slight changes in the lowest accessible WIMP mass. The effect is largest for the lowest WIMP masses, vertically shifting the limit by up to an order of magnitude in either direction.

Figure 31

The 95% (orange) uncertainty band on the best-fit Run 2 spin-independent limit (black solid) due to the uncertainties in the most probable WIMP velocity ($v_0$) and the Galactic escape velocity ($v_{\mathrm{esc}}$) used in the SHM. The 2014 RAVE survey $v_{\mathrm{esc}}$ distribution is sampled, and thus the best-fit curve substituting the 2014 median value into the SHM is given for consistency (red dotted). The black and red-dotted curves are the same as in Fig. 29, where an enlargement at low WIMP mass is given. The best-fit limit computed using the alternative velocity distribution of Eq. (26) is also presented (blue dashed).

Figure 32

Upper limits on the spin-dependent free neutron ${\sigma }_n^{\mathrm{SD}}$ (left) and free proton ${\sigma }_p^{\mathrm{SD}}$ (right) WIMP scattering cross sections in the proton- and neutron-only models, respectively. For both, the median (90% C.L.) (thick black solid curve) upper limit from CDMSlite Run 2 is compared to other selected direct-detection limits from PANDAX-II (thick-green dotted curve) [61], LUX (thick-green dot-dashed curve) [62], XENON100 (thick-green dashed curve) [63], PICO-60 (magenta upward triangles) [64], PICO-2L (magenta downward triangles) [65], PICASSO (purple dot-dashed band) [66], CDEX-0 (thin-red dashed curve) [67, 68], and CDEX-1 (thin-red solid curve) [68]. The orange band surrounding the Run 2 result is the 95% uncertainty interval on the upper limit. The Run 2 limits are the most sensitive for $m_{\mathrm{WIMP}}\lesssim 4$ and $\lesssim 2\mathrm{GeV}/c^2$ for the neutron- and proton-only models, respectively.

Figure 33

Median (90% C.L.) upper limit and associated 95% uncertainty (thick black solid curve and orange bands) on the WIMP-nucleon coupling coefficients $a_p$ and $a_n$ from CDMSlite Run 2 for WIMP masses of 2 (top left), 5 (top right), 10 (bottom left), and 20 (bottom right) $\mathrm{GeV}/c^2$. Areas outside the ellipses are excluded for each WIMP mass.