Calibration of the Gerda experiment

Abstract

The GERmanium Detector Array (Gerda) collaboration searched for neutrinoless double- $\beta$ decay in ${}^{76}$ Ge with an array of about 40 high-purity isotopically-enriched germanium detectors. The experimental signature of the decay is a monoenergetic signal at $Q_{\beta \beta }$ $=2039.061\left(7\right)$ keV in the measured summed energy spectrum of the two emitted electrons. Both the energy reconstruction and resolution of the germanium detectors are crucial to separate a potential signal from various backgrounds, such as neutrino-accompanied double- $\beta$ decays allowed by the Standard Model. The energy resolution and stability were determined and monitored as a function of time using data from regular ${}^{228}$ Th calibrations. In this work, we describe the calibration process and associated data analysis of the full Gerda dataset, tailored to preserve the excellent resolution of the individual germanium detectors when combining data over several years.

Fig. 1

Combined Phase II energy spectrum for ${}^{228}$Th calibration data for all enriched detectors of BEGe, coaxial, and IC type after rebinning to 3 keV. The inset shows the fit to the 2.6 MeV line in the spectrum of the detector GD91A before the 2018 upgrade with 0.3 keV binning, with the components of the fit drawn separately (linear and step backgrounds are combined). The energies of the nine peaks that typically contribute to the formation of calibration curves are labelled

Fig. 2

Fitting the residuals of the calibration curve with a quadratic function, as shown for detector ANG2 for the calibration on 15th October 2018

Fig. 3

FWHM of the FEP as a function of time for detector GD76B, one of the BEGe detectors. Each data point comes from one calibration run. The full data acquisition period is divided into three partitions, shown in solid circle (blue), triangle (green), and diamond (red), respectively. The time of the 2018 upgrade is represented by the dashed line. A second partition (shown in triangles) began directly afterwards with a coincident improvement in resolution. A third partition (shown in diamonds) was created due to the jump in resolution in January 2019 when a hardware change took place

Fig. 4

Distribution of FWHM resolution at ${\text{Q}}_{\beta \beta }$ per detector partition. The detector partitions with resolutions > 6 keV are due to two coaxial detectors whose resolutions degraded after the 2018 upgrade

Fig. 5

Comparison of simplified Gaussian signal model (dashed blue) to the more detailed Gaussian mixture signal model (solid black) of the FEP, for DTDs formed of the partitions of BEGe (left), coaxial (middle) and IC (right) detectors. Red lines show Gaussian shaped peaks for individual partitions, which have been rescaled by a factor of 20/5/1 for the BEGe/Coax/IC detectors for visibility

Fig. 6

Effective resolution curves for BEGe (purple), coaxial (blue) and IC (green) DTDs. Open points indicate broadened lines not used to form the resolution curves, namely the double- and single-escape peaks of the 2.6 MeV line due to ${}^{208}$Tl decay. Square markers indicate the exposure-weighted resolutions of the lines in physics data due to ${}^{40}$K (1460.8 keV) and ${}^{42}$K (1524.7 keV) decays

Fig. 7

Resolution of the 1524.7 keV ${}^{42}$K line as measured from physics data and extracted from calibration data, for each detector partition. The red line shows the case of perfect agreement