Several uncertainties and simplifications of the analysis method and of the parameters that enter in the calculation of the 2νββ-decay half-life contribute to the systematic uncertainty. This includes: (1) the approximative LAr veto, (2) the background mod- eling after anti-coincidence cut and (3) the uncertainties on the active masses of the germanium detectors which are expected to dominate.
In the following, the main uncertainties are discussed and an attempt is made to provide systematic errors. However, it has to be noted that at some indicated points, the approach is simplified and should be revised in the future.
LAr veto suppression
The measured LAr veto survival fraction for all detector channels is drawn inFig. 8.7. It varies between 58% and 81%. For each string it can be observed that the LAr veto reaches the strongest suppression for the topmost detectors and the LAr veto suppression is the least for the detectors placed in the middle of a string (see Fig. D.5
for a sketch of the detector array and detector channel numbers).
To great extent, this behavior is reproduced by the individual scaling on the counts of the40K and42K FEP in the energy spectrum of each detector. However, the LAr veto suppression efficiency is assumed to be homogeneous, independent on the germanium
8.2. TWO-NEUTRINO DOUBLE-BETA DECAY HALF-LIFE T2ν1/2 OF 76GE
Figure 8.7: Survival fraction after LAr veto in energy window from 600 keV to 1300 keV.
detector position. Thus, this scaling does take not into account that the suppression factors measured by the top detectors are higher because of a stronger veto efficiency by the SiPMs. This fact has been discussed for the LAr commissioning run with a 228Th calibration source (Sec. 7.2.1). The statistics of the calibration source measurement of the full array did not allow to use the survival efficiency histograms (compareFig. 8.4) measured by each single detector. Moreover, the energy dependent survival efficiency of a 228Th calibration source measurement does not fully imitate the suppression that is reached in case of 40K, 42K and 228Th placed in different positions and materials than the calibration source.
The systematic uncertainty which is induced by this approach has been evaluated in a threefold way: (1) The uncertainty on the suppression of the40K,42K and228Th back- ground components and their impact on the 2νββ-decay half-life measurement has been determined by using a survival efficiency histogram from the LAr commissioning run. The suppression factors that were reached were approximately twice as high as in case of the measurement with the full detector array. As a result, a systematic uncertainty of σLAr veto = 0.02 · 1021yr for the BEGe and the semi-coaxial dataset has been calculated.
(2) The228Ac background component had been scaled down by applying a cut on the energy deposition in LAr of 100 keV. To deduce the systematic uncertainty induced by a more or less efficient LAr veto cut, this threshold has been varied by a factor two. The associated systematic uncertainty is calculated to σLAr veto, Ac228 = 0.01 · 1021yr.
(3) Since the same cut has been applied to the 2νββ energy spectra, the energy thresh- old has been equally varied by a factor two. This approach results in a systematic uncertainty on the measured half-life of σSF,2νββ = 0.01 · 1021yr.
CHAPTER 8. MEASUREMENT OF THE 2νββ-DECAY HALF-LIFE OF 76GE
Active mass determination of germanium detectors
Uncorrelated and correlated uncertainties have been assigned to the active masses of the BEGe detectors accounting for uncertainties in Monte Carlo physics processes, γ- ray source, detector and cryostat, data collection and analysis methods [107]. However, since the correlated uncertainties are small in comparison to the uncorrelated ones, they are, for simplicity, added in quadrature and treated as uncorrelated uncertainty in the following discussion.
The uncertainties on the active volume of the germanium detectors lead to a sys- tematic uncertainty of σAV = 0.04 · 1021yr in the case of the BEGe dataset and
σAV = 0.11 · 1021yr in the case of the semi-coaxial dataset. This corresponds to un-
certainties below 2.0% and ≈ 5.7% in the measurement of the 2νββ-decay half-life by the BEGe and semi-coaxial detectors, respectively. The numbers reflect the enormous effort that has been put in the characterization of the new Phase II BEGe detectors, providing a more accurate measurement of the active volume [107].
Adding the uncertainty on the active mass of RG2 (≈ 6%) in quadrature to the statistical uncertainty, the measured half-life of this detector deviates only by 2.1σ from the central T1/22ν value. Consequently, no significant tension between the detector measurement and the measurement by the complete semi-coaxial dataset is observed.
Background model
The background model developed on the datasets after anti-coincidence takes only close-by sources into account [128]. Obviously, the statistics after six month of data taking of a ultra-low background experiment, such as Gerda do not allow to disen- tangle contributions of the same isotope placed close-by or medium far away from the Germanium detector array.
In the case of the strongest background contributors in the 2νββ analysis window,
40K and42K, the fit is strongly constraint by the counts in the FEP’s. In the background
model only40K in the mini-shroud is included, although a contribution from40K in the fibers is expected from screening measurements. The difference of the peak-to-Compton ratio of these two background components impacts the measurement of the half-life by attributing more or less events to 2νββ-decays in the analysis window.
Figure 8.8: Energy spectra in-
duced by 40K in the mini-shrouds (blue) and in the fibers (green) in
the BEGe detectors. The spectra
are normalized to the same number of counts in the FEP.
8.2. TWO-NEUTRINO DOUBLE-BETA DECAY HALF-LIFE T2ν1/2 OF 76GE
For the BEGe dataset the peak-to-Compton ratio in the energy range from 600 to 1300 keV of 40K in the mini-shroud was calculated to 1.0000 : 0.0075. The energy spectra of 40K in the mini-shrouds and in the fibers are depicted in Fig. 8.8. The peak-to-Compton ratio for the fibers is determined to 1.0000 : 0.0109. Assuming the most extreme case of having the whole background arising from the fibers and not the mini-shrouds would assign 45 and 38 less counts as 2νββ-events in the 600 to 1300 keV energy window of the BEGe and semi-coaxial dataset, respectively. The associated uncertainty is < 0.5%.