Results from the first science run of the ZEPLIN-III dark matter search experiment

The ZEPLIN-III experiment in the Palmer Underground Laboratory at Boulby uses a 12 kg two-phase xenon time-projection chamber to search for the weakly interacting massive particles (WIMPs) that may account for the dark matter of our Galaxy. The detector measures both scintillation and ionization produced by radiation interacting in the liquid to differentiate between the nuclear recoils expected from WIMPs and the electron-recoil background signals down to $\sim 10\mathrm{keV}$ nuclear-recoil energy. An analysis of $847\mathrm{kg}·\mathrm{days}$ of data acquired between February 27, 2008, and May 20, 2008, has excluded a WIMP-nucleon elastic scattering spin-independent cross section above $8.1\times {10}^{-8}\mathrm{pb}$ at $60\mathrm{GeV}{c}^{-2}$ with a 90% confidence limit. It has also demonstrated that the two-phase xenon technique is capable of better discrimination between electron and nuclear recoils at low-energy than previously achieved by other xenon-based experiments.

Figure 1

Segment of the high-sensitivity summed waveform for a neutron elastic scattering event with $\mathrm{S}1=5\mathrm{keVee}$, showing a small primary pulse ($\mathrm{S}1$) preceding a large secondary pulse ($\mathrm{S}2$). Some PMT afterpulsing and, possibly, single-electron emission can be seen following $\mathrm{S}2$. Note that only excursions $>3\mathrm{rms}$ on individual channels are added into the summed waveform. See later text for more detailed discussion of some of these points.

Figure 2

Response to an external ${}^{57}\mathrm{Co}$ $\gamma$ ray source in the combined energy channel, exploiting $\mathrm{S}1$ and $\mathrm{S}2$ anticorrelation. One day’s experimental data are shown in as the solid (blue) line with statistical error bars. The simulation result is indicated in the filled (red) histograms: the solid histogram shows the bare energy deposits and the shaded one shows the result of Gaussian smearing with the energy resolution indicated in the figure.

Figure 3

Distribution in the horizontal plane of events from the ${}^{57}\mathrm{Co}$ source on the left and from the Am-Be source on the right. The source positions are different for each image and neither is centered. In both cases the volume distribution is as expected from Monte Carlo simulations, given the location of each source. Interaction vertices can be seen out to the edge of the fiducial volume at a radius of 150 mm (red circle). The outer circle shows the edge of the liquid xenon target. Each PMT is marked by two smaller circles (PMT centers and envelopes).

Figure 4

Expected mean number of $\mathrm{S}1$ photoelectrons as a function of the mean pulse area observed in the central channel in the array. The expected signal is the mean of the Poisson distribution obtained by counting the frequency of “zeros,” i.e., the absence of any response.

Figure 5

Calibration of the nuclear-recoil response with an Am-Be neutron source, plotted as the discrimination parameter [${log}_{10}(S2/S1)$] as a function of “electron-equivalent energy” (i.e., using the $\mathrm{S}1$ channel calibrated by ${}^{57}\mathrm{Co}$). The lines show the trends of the mean and standard deviation of energy-binned log-normal fits to the recoil population. The distinct population above $\sim 40\mathrm{keVee}$ is due to inelastic neutron scattering off ${}^{129}\mathrm{Xe}$ nuclei.

Figure 6

Statistical fitting of the electron and nuclear-recoil populations using the WIMP search (upper panel) and Am-Be data sets (lower panel). Three 1 keVee wide bins are shown: lowest, intermediate, and highest energies accepted. The electron-recoil population was fitted with a skew-Gaussian function using both the minimum ${\chi }^2$ (thin blue line) and a maximum likelihood (ML) method with the Poisson distribution as the estimator (thick red line). The latter fit is more appropriate to data with low statistics (including zeros) in the tails of the populations as it uses a Poisson distribution as an estimator. Note that the entire population can be fitted (all energy bins, across the entire ${log}_{10}(S2/S1)$ range). The ML best fit parameters are indicated, along with the mean and standard deviation of the skew Gaussian. The lower panels show the log-normal fits to the Am-Be recoil data, which is used to define the acceptance region [$\mu -2\sigma$, $\mu$], between the vertical dashed lines. The number of electron recoils observed to be leaking into this region, $n_{\mathrm{obs}}$, is compared with the estimated number, $n_{\mathrm{cal}}$, from the ML fits. The total number of events expected in the acceptance region is $11.6\pm 3.0$.

Figure 7

Double-logarithmic plot of Fig. 5 showing the nuclear-recoil population obeying the power-law trend indicated by the solid (yellow) line with a power-law index of $+0.45$; the behavior of the inelastic line from ${}^{129}\mathrm{Xe}$ is markedly different, as this is dominated by charge recombination of the 40 keV $\gamma$ ray rather than the small nuclear-recoil component of the deposited energy. Approximate thresholds for $S1$ (3-fold software trigger) and for $S2$ (hardware trigger) are also indicated. From this it can be seen that the $S2$ hardware trigger corresponds to $S1=0.5\mathrm{keVee}$ for nuclear recoils.

Figure 8

Comparison of the skew-Gaussian mean and standard deviations for the ${}^{137}\mathrm{Cs}$ and WIMP-search data sets calculated from the ML-fit parameters (the horizontal error bars indicate the bin width).

Figure 9

Combined scatter plot of ${log}_{10}(S2/S1)$ as a function of energy from the two calibration data sets, ${}^{137}\mathrm{Cs}$ and Am-Be. The upper population corresponds to low-energy Compton electrons and the narrower, lower one to nuclear recoils produced by neutron elastic scattering.

Figure 10

Electron-recoil background measured during the fully-shielded science run. The differential spectrum is shown superimposed on the Monte Carlo prediction [3] using GEANT4 [18] without rescaling. The latter includes a dominant $10.5\mathrm{evts}/\mathrm{kg}/\mathrm{day}/\mathrm{keVee}$ (“dru”) from the photomultipliers, $\gamma$ rays from the lead “castle” (0.7 dru), $\beta$ particles from ${}^{85}\mathrm{Kr}$ (0.2 dru), and $\gamma$ rays from ceramic feedthroughs (0.1 dru). The disagreement at high energies is caused by single-scatter selection in the data (but not in the simulation) and by the limited DAQ dynamic range which was optimized for the WIMP-search run.

Figure 11

Scatter plot of ${log}_{10}(S2/S1)$ as a function of energy for the entire 83-day data set of first science run. There are 7 events (large dots) in the WIMP-search region (thick red box), which extends from $2<E<16\mathrm{keVee}$ and ${\mu }_n-2{\sigma }_n<{log}_{10}(S2/S1)<{\mu }_n$, where ${\mu }_n$ is the energy-dependent mean of the nuclear recoils (thin red line bordered by the blue curves at $\pm 1{\sigma }_n$). These are all located near the upper boundary, between $\simeq 5–15\mathrm{keVee}$.

Figure 12

Horizontal distribution of events in the energy range 2–16 keVee for the science run data set produced in the same way as those in Fig. 3. The reconstructed location of the 7 events in the acceptance region is indicated. The measured distribution of the overall background is consistent with detailed Monte Carlo simulations of that expected from the instrument activity which is dominated by the photomultipliers.

Figure 13

Differential energy spectra for the Am-Be elastic recoil population in $\mathrm{S}1$ electron-equivalent units (${}^{57}\mathrm{Co}$ calibrated $\mathrm{S}1$). The main calibration data (shaded blue histogram) and the lower threshold data set described in the text (black) are compared with the Monte Carlo simulation using a constant conversion factor between nuclear-recoil and electron-equivalent energies (solid red curve). The ratio between these two curves is interpreted as an energy-dependent efficiency factor and occurs in the low-energy region where thresholding effects are expected. The dashed red curve is the result of the nuclear-recoil nonlinearity analysis described in the text, which results in the energy conversion indicated by the markers at the top of the figure.

Figure 14

Energy-dependent part of the nuclear-recoil detection efficiency as deduced empirically by comparing the two experimental Am-Be spectra shown in Fig. 13. The “low-threshold” run was taken with a lower hardware trigger threshold; in addition, software quality cuts were relaxed, along with the $\mathrm{S}1$ 3-fold requirement. A fit to the data is shown, with the WIMP acceptance box indicated by the thicker portion of the line. The $\mathrm{S}2$ hardware trigger in the low-threshold Am-Be run was half of that used in the science data set and thus corresponded to $S1=0.25\mathrm{keVee}$, and the $\mathrm{S}1$ pulse-finding algorithms only required a 2-fold detection above 1/3 PE giving a nominal software threshold of $S1=1.1\mathrm{keVee}$. Hence above $S1=2\mathrm{keVee}$ (the lower WIMP acceptance box boundary) the low-threshold data set has near-unity efficiency.

Figure 15

The derived energy-dependent behavior of $L_{\mathrm{eff}}\times S_n$. The thick curve shows the best fit to the data, but other curves producing very similar goodness-of-fit indicators are obtained within the envelope shown. The constraints become very weak outside the energy range shown.

Figure 16

The WIMP-search box with the vertical axis remapped onto nuclear-recoil percentiles. This is done using the $S2/S1$ distribution from the Am-Be calibration data. The positions of the 7 events falling within the box are shown as well as other events just outside the box. The horizontal dashed line separates the box into two regions with an area ratio of $1:4$.

Figure 17

90% confidence interval upper limit to the WIMP-nucleon elastic scattering cross section as derived from the first science run of ZEPLIN-III for a spin-independent interaction. For comparison, the experimental results from XENON10 [11, 29] and CDMS-II [30] are also shown. Note that the XENON10 curve is a one-sided limit, corresponding approximately to an 85% confidence two-sided limit [11]. CDMS-II and our result are both 90% two-sided limits. The hatched areas show 68% and 95% confidence regions for the neutralino-proton scattering cross section with flat priors as calculated in constrained minimal supersymmetry model [31].