Liquid argon light collection and veto modeling in GERDA Phase II

Abstract

The ability to detect liquid argon scintillation light from within a densely packed high-purity germanium detector array allowed the Gerda experiment to reach an exceptionally low background rate in the search for neutrinoless double beta decay of ${}^{76}$ Ge. Proper modeling of the light propagation throughout the experimental setup, from any origin in the liquid argon volume to its eventual detection by the novel light read-out system, provides insight into the rejection capability and is a necessary ingredient to obtain robust background predictions. In this paper, we present a model of the Gerda liquid argon veto, as obtained by Monte Carlo simulations and constrained by calibration data, and highlight its application for background decomposition.

Fig. 1

LAr veto instrumentation concept. Transport of light signals towards the PMTs or SiPMs relies on WLS processes in the TPB layers or optical fibers. Several potential light paths are indicated. Support structure details, electronics as well as individual fibers are not drawn

Fig. 2

Simplified light collection chain. This one-dimensional representation depicts the main material properties that affect the light collection with the Gerda fiber-SiPM instrumentation. The overall light collection efficiency for the primary VUV photon is of $\mathcal{O}$(0.1)%. In real life, effects like shadowing, reflections and optical coverage enter the game

Fig. 3

Emission spectra (solid lines) and absorption length (dashed lines) of indicated materials. The primary emission from the LAr follows a simple Gaussian distribution centered at 128 nm. Its absorption length connects to larger wavelength with an ad-hoc exponential scaling. Absorption and re-emission appears in TPB and the polystyrene fiber material. Nylon is only transparent to larger wavelength

Fig. 4

Binomial repopulation. a The pmf ${\Lambda }_s[m](\epsilon )$ defined in Eq. 4 can be obtained for any value of the detection efficiency $\epsilon$ from the unaltered simulation output. The example shows the pmf for a specific SiPM channel as obtained for ${}^{228}$Th decays in a calibration source at the top of the array (see also Tab. 1) depositing 2615 ± 10 keV in the HPGe detectors. The result is plotted for a selection of efficiency values, reported in the bottom panel. b The panel shows the non-linear dependence of the light detection probability ${\Lambda }_s$ (defined in Eq. 5). The color coding relates data points with corresponding distributions in the top panel

Fig. 5

Data/Monte Carlo comparison. a Projected distribution of the LAr energy depositions for simulated ${}^{208}$Tl 2615 keV FEP-events from a calibration source at position 8405 mm. Darker circles correspond to the volume occupied by the HPGe detectors. b Photon detection probability $\xi$ in the same region. c Top panel: the energy spectrum of the ${}^{228}$Th data corresponding to figure a, before the LAr veto cut, compared to the Monte Carlo prediction. The pdf is normalized to reproduce the total count rate in data. Despite small shape discrepancies, the predicted LAr veto survival probability (bottom panel) matches the data over a wide range of energies, even far from the model optimization energy region (gray band). A variable binning is adopted for visualization purposes

Fig. 6

Modification of the photon detection probability $\xi (\overrightarrow{x})$ through analytical power-law distortions defined in Eq. 8. a Inhomogeneities that are present in the nominal map are amplified with increasing $\alpha$, leading to a more homogeneous ($\alpha <1$, i.e. less color contrast) or less homogeneous ($\alpha >1$, i.e. more color contrast) response. b The probability ratio from two sample points $x_1$ and $x_2$, outside and within the array, highlights this modification (black data points). The comparison of an altered germanium reflectivity (magenta data points) shows how the distortions conservatively exceed $\pm 50\%$ on the reflectivity

Fig. 7

Probability density functions (pdfs, normalized to the number of simulated primary decays) for a representative selection of background and signal event sources in the Gerda Phase II setup as detected by HPGe detectors and surviving the LAr veto cut, as predicted by the model presented in this document. Model uncertainties are shown as bands of lighter color. pdfS before the cut [28] (dotted lines) are overlaid for comparison. The reader is referred to [, Figure 1] for a detailed documentation of the simulated setup. A variable binning is adopted for visualization purposes

Fig. 8

Background decomposition of the first 61.4 kg years of data from Gerda Phase II surviving the LAr veto cut (black dots). The veto model is applied to the existing background pdfs before the cut [28] folding in the probability map $\xi (\overrightarrow{x})$ . Data before the cut is shown as a light blue filled histogram. Shaded bands constructed with the maximally distorted probability maps provide a visualization of the systematic uncertainty affecting each pdf