Pulse-shape discrimination against low-energy Ar-39 beta decays in liquid argon with 4.5 tonne-years of DEAP-3600 data

Abstract

The DEAP-3600 detector searches for the scintillation signal from dark matter particles scattering on a 3.3 tonne liquid argon target. The largest background comes from ${}^{39}\text{Ar}$ beta decays and is suppressed using pulse-shape discrimination (PSD). We use two types of PSD estimator: the prompt-fraction, which considers the fraction of the scintillation signal in a narrow and a wide time window around the event peak, and the log-likelihood-ratio, which compares the observed photon arrival times to a signal and a background model. We furthermore use two algorithms to determine the number of photons detected at a given time: (1) simply dividing the charge of each PMT pulse by the mean single-photoelectron charge, and (2) a likelihood analysis that considers the probability to detect a certain number of photons at a given time, based on a model for the scintillation pulse shape and for afterpulsing in the light detectors. The prompt-fraction performs approximately as well as the log-likelihood-ratio PSD algorithm if the photon detection times are not biased by detector effects. We explain this result using a model for the information carried by scintillation photons as a function of the time when they are detected.

Fig. 1

The distributions of mainly ${}^{39}\text{Ar}$ $\beta$ decay events for each of the four PSD parameters as a function of energy. The 50% (blue) and 90% (brown) nuclear recoil acceptance lines are also shown. Some events are expected above the ${}^{39}\text{Ar}$ population because only a subset of the WIMP analysis cuts are used

Fig. 2

The PP distributions for events at 120 $N_{\text{nsc}}$ (approximately 19.65 ${\text{keV}}_{\mathrm{ee}}$ to 19.82 ${\text{keV}}_{\mathrm{ee}}$) are shown together with the effective model fits. The bin width is 0.0025 and there are $2.8·{10}^7$ events in each histogram. The vertical dashed red line marks the $F_{\text{prompt}}$ value above which the trigger efficiency is 99.5%. The brown (blue) line marks a nuclear recoil acceptance of 90% (50%). The lower panel shows the relative deviation between the model and the data

Fig. 3

The relative difference, (model-data)/data, for each of the four PSD parameters. The only significant deviations between model and data are at the edge of the distributions, where several systematic effects bias the event count (see Sect. 5.4). The black contour shows, for each $N_{\text{nsc}}$ slice, the first bin when going from the center of the population to higher/lower values of the PP where the absolute value of the difference between model and data is more than 10%

Fig. 4

a The $F_{\text{prompt}}^{\text{nsc}}$ distributions at 110 $N_{\text{nsc}}$ are shown for ${}^{39}\text{Ar}$ $\beta$ events (background), together with the model fit, and for simulated ${}^{40}\text{Ar}$ recoil events (signal). b The background leakage probability (based on the fit model to ${}^{39}\text{Ar}$ data) and signal acceptance (based on signal MC) as a function of the PSD parameter is shown

Fig. 5

Leakage probabilities for each PP as a function of NRA for events at a 110 $N_{\text{nsc}}$(approximately 17.46 ${\text{keV}}_{\mathrm{ee}}$ to 17.61 ${\text{keV}}_{\mathrm{ee}}$) and at b 130 $N_{\text{nsc}}$(approximately 19.65 ${\text{keV}}_{\mathrm{ee}}$ to 19.82 ${\text{keV}}_{\mathrm{ee}}$). Statistical error bars, where not visible, are smaller than the marker size

Fig. 6

The leakage probability as a function of $N_{\text{nsc}}$ at a 50% and b 90% NRA. Statistical error bars, where not visible, are smaller than the marker size

Fig. 7

A study of three effects that lead to systematic uncertainties on the leakage probabilities. The green up-triangles show the nominal leakage probability for $F_{\text{prompt}}^{\text{nsc}}$ from the 2D fit (the curve is the same as in Fig. 5). The pink down-triangles use the results from the 1D fit instead. The purple boxes are obtained with the 1D fit where the upper fit limit was reduced from 0.6 to 0.55 to exclude bins with fewer than 10 events. The points overlap, indicating that the fit procedure does not significantly change the leakage predictions. The brown curve uses an ${}^{40}\text{Ar}$ distribution modified to account for energy resolution differences between MC and real data [10]

Fig. 8

The upper two figures show the time evolution of the leakage probabilities at 110 $N_{\text{nsc}}$ and 130 $N_{\text{nsc}}$ for $F_{\text{prompt}}^{\text{nsc}}$ at 50% NRA. The triplet lifetimes in the third figure are determined by using the full mathematical model of the ${}^{39}\text{Ar}$ scintillation pulse shape [22]. The observed triplet lifetime strongly depends on the state variables of the detector, e.g. temperature, pressure, or impurities diffused from the detector into the liquid argon. A change in the triplet lifetime is expected to influence the shape of the PP distribution and hence causes the PP distribution of the whole data set to be a superposition of distributions with slightly different parameters

Fig. 9

The $L_{\text{recoil}}$ weight-functions from Eq. (6) calculated for photon detection PDFs that take into account different components of the detector response are shown. The blue solid line considers only the LAr scintillation (Argon), the pink long-dashed line adds dark noise (DN), the green short-dash line includes the slow component of TPB fluorescence (TPB), and the purple dot-dash line adds afterpulsing (AP). This is compared to the equivalent weight function used in the $F_{\text{prompt}}$ PP (yellow dotted line). The insert zooms in on the time region from $-$ 50 to 200 ns; for reasons of legibility, only three of the lines are shown here. Note that the detector’s time resolution is included in the PDFs the photon weights are based on. The weight can be interpreted as follows: PE detected at times where $w(t)>0$ strengthen the NR hypothesis, while PE detected where $w(t)<0$ strengthen the ER hypothesis