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FIG. 6: Statistical fitting of the electron and nuclear recoil populations using the WIMP-search (upper panel) and AmBe 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 y” (thin blue line) and a maximum likelihood (ML) method with the Poisson distribution as 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, )(S$2/51) 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 AmBe recoil data, which is used to define the acceptance region [u-20,:], between the vertical dashed lines. The number of electron recoils observed to be leaking into this region, novs, is compared with the estimated number, nea, from the ML fits. The total number of events expected in the acceptance region is 11.6+3.0.

Figure 6 Statistical fitting of the electron and nuclear recoil populations using the WIMP-search (upper panel) and AmBe 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 y” (thin blue line) and a maximum likelihood (ML) method with the Poisson distribution as 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, )(S$2/51) 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 AmBe recoil data, which is used to define the acceptance region [u-20,:], between the vertical dashed lines. The number of electron recoils observed to be leaking into this region, novs, is compared with the estimated number, nea, from the ML fits. The total number of events expected in the acceptance region is 11.6+3.0.

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FIG. 1: Segment of the high-sensitivity summed waveform for a neutron elastic scattering event with S1= 5 keVee, showing a small primary pulse (S1) preceding a large secondary pulse (S2). Some PMT after-pulsing and, possibly, single electron emission can be seen following $2. Note that only excursions >3 rms on individual channels are added into the summed waveform. See later text for more detailed discussion of some of these points.
FIG. 1: Segment of the high-sensitivity summed waveform for a neutron elastic scattering event with S1= 5 keVee, showing a small primary pulse (S1) preceding a large secondary pulse (S2). Some PMT after-pulsing and, possibly, single electron emission can be seen following $2. Note that only excursions >3 rms on individual channels are added into the summed waveform. See later text for more detailed discussion of some of these points.
FIG. 2: Response to an external °’ Co 7-ray source in the com- bined energy channel, exploiting $1 and S2 anti-correlation. One day’s experimental data are shown in blue with statis- tical error bars. The simulation result is indicated in red 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.
FIG. 2: Response to an external °’ Co 7-ray source in the com- bined energy channel, exploiting $1 and S2 anti-correlation. One day’s experimental data are shown in blue with statis- tical error bars. The simulation result is indicated in red 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.
FIG. 3: Distribution in the horizontal plane of events from the °’Co source on the left and from the AmBe source on the right. The source positions are different for each image and neither is centred. 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 centres and envelopes).
FIG. 3: Distribution in the horizontal plane of events from the °’Co source on the left and from the AmBe source on the right. The source positions are different for each image and neither is centred. 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 centres and envelopes).
FIG. 4: Expected mean number of $1 photoelectrons as a function of the mean pulse area observed in the central chan- nel in the array. The expected signal is the mean of the Pois- son distribution obtained by counting the frequency of ‘zeros’, ie. the absence of any response.
FIG. 4: Expected mean number of $1 photoelectrons as a function of the mean pulse area observed in the central chan- nel in the array. The expected signal is the mean of the Pois- son distribution obtained by counting the frequency of ‘zeros’, ie. the absence of any response.
FIG. 5: Calibration of the nuclear recoil response with an AmBe neutron source, plotted as the discrimination param- eter (log;, ($2/51)) as a function of ‘electron-equivalent en- ergy’ (ie. using the Sl channel calibrated by °’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 ~40 keVee is due to inelastic neu- tron scattering off 1?°Xe nuclei.
FIG. 5: Calibration of the nuclear recoil response with an AmBe neutron source, plotted as the discrimination param- eter (log;, ($2/51)) as a function of ‘electron-equivalent en- ergy’ (ie. using the Sl channel calibrated by °’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 ~40 keVee is due to inelastic neu- tron scattering off 1?°Xe nuclei.
FIG. 7: Double-logarithmic plot of Fig. 5 showing the nu- clear recoil population obeying the power-law trend indicated by the yellow line; the behaviour of the inelastic line from 129Xe is markedly different, as this is dominated by charge recombination of the 40 keV y-ray rather than the small nu- clear recoil component of the deposited energy. Approximate thresholds for $1 (3-fold software trigger) and for S2 (hard- ware trigger) are also indicated. From this it can be seen that the $2 hardware trigger corresponds to $1=0.5 keVee for nuclear recoils.
FIG. 7: Double-logarithmic plot of Fig. 5 showing the nu- clear recoil population obeying the power-law trend indicated by the yellow line; the behaviour of the inelastic line from 129Xe is markedly different, as this is dominated by charge recombination of the 40 keV y-ray rather than the small nu- clear recoil component of the deposited energy. Approximate thresholds for $1 (3-fold software trigger) and for S2 (hard- ware trigger) are also indicated. From this it can be seen that the $2 hardware trigger corresponds to $1=0.5 keVee for nuclear recoils.
FIG. 8: Comparison of the skew-Gaussian mean and standard deviations for the '®”Cs and WIMP-search data-sets calcu- lated from the ML-fit parameters (the horizontal error bars indicate the bin width).
FIG. 8: Comparison of the skew-Gaussian mean and standard deviations for the '®”Cs and WIMP-search data-sets calcu- lated from the ML-fit parameters (the horizontal error bars indicate the bin width).
FIG. 9: Combined scatter plot of log;,($2/S1) as a function of energy from the two calibration data-sets, ‘°”Cs and AmBe. The upper population corresponds to low-energy Compton electrons and the narrower, lower one to nuclear recoils pro- duced by neutron elastic scattering.
FIG. 9: Combined scatter plot of log;,($2/S1) as a function of energy from the two calibration data-sets, ‘°”Cs and AmBe. The upper population corresponds to low-energy Compton electrons and the narrower, lower one to nuclear recoils pro- duced by neutron elastic scattering.
FIG. 10: Electron recoil background measured during the fully-shielded science run. The differential spectrum is shown superimposed on the Monte Carlo prediction [3] us- ing GEANT4 [16] without rescaling. The latter includes a dominant 10.5 evts/kg/day/keVee (‘dru’) from the photomul- tipliers, y-rays from the lead ‘castle’ (0.7 dru), G-particles from *Kr (0.2 dru) and 7-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 optimised for the WIMP-search run.
FIG. 10: Electron recoil background measured during the fully-shielded science run. The differential spectrum is shown superimposed on the Monte Carlo prediction [3] us- ing GEANT4 [16] without rescaling. The latter includes a dominant 10.5 evts/kg/day/keVee (‘dru’) from the photomul- tipliers, y-rays from the lead ‘castle’ (0.7 dru), G-particles from *Kr (0.2 dru) and 7-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 optimised for the WIMP-search run.
FIG. 11: Scatter plot of log,,($2/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 keVee and wn — 20n < log,)($2/S1) < pin, where fin is the energy-dependent mean of the nuclear recoils (thin red line bordered by the blue curves at a tlon). These are all located near the upper boundary, between ~5-15 keVee.
FIG. 11: Scatter plot of log,,($2/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 keVee and wn — 20n < log,)($2/S1) < pin, where fin is the energy-dependent mean of the nuclear recoils (thin red line bordered by the blue curves at a tlon). These are all located near the upper boundary, between ~5-15 keVee.
FIG. 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 Figure 3. The reconstructed location of the 7 events in the acceptance region is indicated. The measured distribution of the overall background is consistent with de- tailed Monte Carlo simulations of that expected from the in- strument activity which is dominated by the photomultipliers.
FIG. 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 Figure 3. The reconstructed location of the 7 events in the acceptance region is indicated. The measured distribution of the overall background is consistent with de- tailed Monte Carlo simulations of that expected from the in- strument activity which is dominated by the photomultipliers.
FIG. 13: Differential energy spectra for the AmBe elas- tic recoil population in $1 electron-equivalent units (°"Co- calibrated S1). The main calibration data (shaded blue his- togram) 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 threshold- ing effects are expected. The dashed red curve is the result of the nuclear recoil non-linearity analysis described in the text, which results in the energy conversion indicated by the markers at the top of the figure.
FIG. 13: Differential energy spectra for the AmBe elas- tic recoil population in $1 electron-equivalent units (°"Co- calibrated S1). The main calibration data (shaded blue his- togram) 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 threshold- ing effects are expected. The dashed red curve is the result of the nuclear recoil non-linearity analysis described in the text, which results in the energy conversion indicated by the markers at the top of the figure.
TABLE I: Energy-independent efficiency factors and thresh- olds due to hardware and software actions. Efficiency fig- ures are constant over the WIMP recoil range. Numbers following the entries refer back to the list of software oper- ations itemised in Section HIB. The total effective exposure is 127.8 kg-days.
TABLE I: Energy-independent efficiency factors and thresh- olds due to hardware and software actions. Efficiency fig- ures are constant over the WIMP recoil range. Numbers following the entries refer back to the list of software oper- ations itemised in Section HIB. The total effective exposure is 127.8 kg-days.
FIG. 14: Energy-dependent part of the nuclear recoil de- tection efficiency as deduced empirically by comparing the two experimental AmBe spectra shown in Fig. 13. The ‘low- threshold’ run was taken with a lower hardware trigger thresh- old; in addition, software quality cuts were relaxed, along with the $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 S2 hardware trigger in the low-threshold AmBe run was half of that used in the science data-set and thus cor- responded to $1 =0.25 keVee, and the S1 pulse finding algo- rithms only required a 2-fold detection above 1/3 p.e. giving a nominal software threshold of $1=1.1keVee. Hence above S1=2keVee (the lower WIMP acceptance box boundary) the ‘low-threshold’ data-set has near-unity efficiency. “AJl thresholds are quoted here in terms of the S1 signal in keVee for nuclear recoils. The equivalent nuclear recoil energy, keVnr, depends on the conversion between keVee and keVnr. For the re- lationship shown in Section IIID 2, 11 ionisation electrons corre- sponds to < 7keVnr
FIG. 14: Energy-dependent part of the nuclear recoil de- tection efficiency as deduced empirically by comparing the two experimental AmBe spectra shown in Fig. 13. The ‘low- threshold’ run was taken with a lower hardware trigger thresh- old; in addition, software quality cuts were relaxed, along with the $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 S2 hardware trigger in the low-threshold AmBe run was half of that used in the science data-set and thus cor- responded to $1 =0.25 keVee, and the S1 pulse finding algo- rithms only required a 2-fold detection above 1/3 p.e. giving a nominal software threshold of $1=1.1keVee. Hence above S1=2keVee (the lower WIMP acceptance box boundary) the ‘low-threshold’ data-set has near-unity efficiency. “AJl thresholds are quoted here in terms of the S1 signal in keVee for nuclear recoils. The equivalent nuclear recoil energy, keVnr, depends on the conversion between keVee and keVnr. For the re- lationship shown in Section IIID 2, 11 ionisation electrons corre- sponds to < 7keVnr
FIG. 15: The derived energy-dependent behaviour of Les ¢-Sn. 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.
FIG. 15: The derived energy-dependent behaviour of Les ¢-Sn. 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.
FIG. 16: The WIMP search box with the vertical axis remapped onto nuclear recoil percentiles. This is done us- ing the S2/S1 distribution from the AmBe 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.
FIG. 16: The WIMP search box with the vertical axis remapped onto nuclear recoil percentiles. This is done us- ing the S2/S1 distribution from the AmBe 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.
FIG. 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 in- teraction. For comparison, the experimental results from XENON10 [10, 27] and CDMS-II [28] are also shown. Note that the XENON10 curve is a 1-sided limit, corresponding ap- proximately to an 85% confidence 2-sided limit [10]. CDMS-II and our result are both 90% 2-sided limits. The hatched ar- eas show 68% and 95% confidence regions for the neutralino- proton scattering cross-section with flat priors as calculated in Constrained MSSM [30].
FIG. 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 in- teraction. For comparison, the experimental results from XENON10 [10, 27] and CDMS-II [28] are also shown. Note that the XENON10 curve is a 1-sided limit, corresponding ap- proximately to an 85% confidence 2-sided limit [10]. CDMS-II and our result are both 90% 2-sided limits. The hatched ar- eas show 68% and 95% confidence regions for the neutralino- proton scattering cross-section with flat priors as calculated in Constrained MSSM [30].
Related topics:
PhysicsQuantum PhysicsElastic ScatteringConfidence LimitTime Projection ChamberElementary ParticlesWeakly Interacting Massive Particle
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