IDENTIFICACIÓN DE LAS CATEGORÍAS DE ANÁLISIS

face events

Since there were no changes to background rates between Runs 123–124 and Runs 125–128, we could use surface events from the entire unblinded R123-4 WIMP-search dataset and directly compare with calibration surface events to quantify systematic differences. Two studies have shown systematic differences on the same two fronts [171, 172]:

1. Energy: The most important systematic difference between calibration and WIMP-search surface events is energy distribution. As shown in Figure 6.15, WIMP-search data has a larger fraction of events at low energy, compared to calibration data. This is important because low-energy surface events have a longer slow-timing tail than high-energy events, as shown in Figure 6.16.

2. Ionization yield: ZIPs have a slightly different response to phonon-side surface events com- pared to charge-side surface events. This was shown for phonon-energy partition in Figure 4.7, but is also true for phonon timing and ionization yield. Charge-side surface events have higher ionization yield, but a longer slow-timing tail than phonon-side surface events, as shown in Figure 6.17 for calibration data. Thus the other important systematic difference between WIMP-search data and calibration data arises from the difference in numbers of phonon-side and charge-side events between the two datasets. The ratio of charge-side to phonon-side

10 20 30 40 50 60 70 80 90 100 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Recoil Energy (keV)

Normalized counts

Calibration WIMP−search

Figure 6.15: Left: Recoil energy spectrum of surface events from the 12 inner germanium detectors used for WIMP search in Runs 125–128. The blue curve shows calibration surface events and the red curve shows WIMP-search surface events within the nuclear-recoil band for Runs 123–124.

0 5 10 15 10−4 10−3 10−2 Normalized pdel+pminrt Normalized counts 10−30 keV 30−100 keV

Figure 6.16: Tail distribution of corrected pminrt+pdel normalized by subtracting the mean for calibration surface events. The blue line is the tail for low-energy events (10–30 keV), and the red line is the tail for higher-energy events (30–100 keV).

surface events in the WIMP-search nuclear-recoil band is larger compared to the ratio of charge-side to phonon-side surface events in calibration data as seen by comparing figures 6.17 and 6.18. −40 −2 0 2 4 6 8 10 12 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Normalized Ionization yield (σ

NR) Relative fractions P Q 0 5 10 15 10−4 10−3 10−2 Normalized pdel+pminrt Normalized counts P Q

Figure 6.17: Left: Yield distribution (normalized by nuclear-recoil-band standard deviation), for charge-side (red) and phonon-side (black) surface events in calibration data. Right: Tail distribution of correctedpminrt+pdelnormalized by subtracting the mean for charge-side (red) and phonon-side (black) calibration surface events. Both distributions are summed over the 12 internal germanium detectors used for this WIMP search.

−40 −2 0 2 4 6 8 10 12 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Normalized Ionization yield (σ_NR)

Relative fractions

P Q

Figure 6.18: Yield distribution (normalized by nuclear-recoil-band standard deviation), for charge- side (red) and phonon-side (black) surface events in WIMP-search data from Runs 123–124, summed over the 12 internal germanium detectors used for WIMP search in Runs 125–128. The ratio of charge-side to phonon-side surface events is different in this distribution compared with that of calibration data displayed in Figure 6.17.

6.6.4

Estimating leakage, accounting for systematic differences

To account for the systematic differences between WIMP-search and calibration data explained above, I proposed the following estimator for surface-event leakage on a detector,ni, after consulting

with Jeff Filippini and Sunil Golwala: ni=Ni X e,f b(e,fi) s (i) e,f (6.1)

where Ni is the expected number of single-scatter surface events on the i-th detector, b (i) e,f is the

detector-specific passage fraction measured on calibration data for energy bin e and detector face

f, ands(e,fi) is the detector-specific measured fraction of events of that class in WIMP-search data.

In effect, this formula takes the calibration-measured leakage in each of the bins and reweights it in accordance with the occurrence of that type of event in WIMP-search data. The surface events of the WIMP-search data from Runs 123–124 were taken and divided into four bins to computese,f:

Charge-side with energy 10–30 keV; charge-side with energy 30–100 keV; phonon-side with energy 10–30 keV; phonon-side with energy 30–100 keV [172]. Since there were no WIMP candidates in Runs 123–124, the count of events passing WIMP-candidate cuts except for the timing cut provided a direct measurement of the background rates of the detectors. That scaled by the livetime for Runs 125–128 provided Ni. Thus, by measuring be,f on calibration data as a function of timing

discriminator such aspminrt+pdel, one could setni for each detector to the desired level.

This last step turned out to be a little complicated. Even with the large statistics of the undivided

133_{Ba-calibration dataset, some categories of surface events such as low-energy charge-side events had}

poor statistics. So, to estimatebe,f in far-out regions of the tails, we decided to fit the distribution

tails. It had been shown that the tails could be fit fairly well using generalized Pareto distributions [173]. Thus a Pareto fit was performed on the last_∼10 events of the CDF of the distribution, and the remainder was smoothed using a gaussian kernel. Then the two pieces were matched using a cubic-spline interpolation. The resulting fits were better than anyone expected. A sample is pictured in Figure 6.19. We then verified that by applying this scheme to calibration data for Runs 123–124, we could correctly match the WIMP-search leakage prediction from calibration data to that from WIMP-search sidebands for Runs 123–124 [174].