Characterization of the Low Energy Excess using a NUCLEUS $Al_2O_3$ detector

Abstract

The NUCLEUS experiment aims to detect coherent elastic neutrino-nucleus scattering of reactor antineutrinos using low-threshold, gram-scale cryogenic calorimeters. Similar to other low-threshold experiments, NUCLEUS observes a sharp rise in the event rate below a few hundred eV, referred to as the low energy excess (LEE), whose origin remains yet unidentified. Building on results from the NUCLEUS testing and commissioning at the Technical University of Munich and from previous characterization campaigns, we present a comprehensive study of the background rate measured with a sapphire detector equipped with two transition-edge sensors under various experimental conditions. We find no evidence for a dependence of the LEE rate on the particle background level, whereas the results indicate that slower cooling-down procedures lead to lower initial LEE rates. The behavior of the LEE rate during the same cooldown is comparable across the measurements and is best described by a power law with a common exponent across datasets of $(-0.59 \pm 0.06)$, when time is expressed from the moment the detector reaches the 4 K temperature. These findings provide valuable guidance for future LEE mitigation strategies in the NUCLEUS experiment.

Figures (10)

• Figure 1: Left: Photograph of the double TES module. The [0.75]g Al$_2$O$_3$ crystal absorber, instrumented with two TESs, is mounted inside a copper housing. The detector is supported from below by three [1]mm sapphire spheres (indicated by the blue dashed circles) and secured from above by two bronze clamps, each resting on an additional sapphire sphere. Right: Schematic of the TES used in the NUCLEUS double TES detector. The purple color represents the tungsten layer, the gray the aluminum and the yellow the gold. The tungsten and aluminum structures have a small overlap and are evaporated onto an auxiliary $\mathrm{SiO_2}$ layer between the crystal and the films.
• Figure 2: Photographs of the NUCLEUS commissioning setup at TUM deployed in the UGL experimental site, with the cryostat open (left) and closed (right). Inside the cryostat, the detector box is mounted on a cryogenic spring pendulum serving as the vibration decoupling system WexSpring:2025. The detectors are read out by SQUIDs, and optical fibers provide the LED optical calibration DelCastello_LANTERN:2024lantern2. The shield (PE, Pb, and active MV layers) is installed inside and outside the cryostat, with the external layers assembled into two half-cubes mounted on rails (in the right panel, one of the half-cubes is visible). Table \ref{['tab:measurements']} indicates the shield configuration used in each of the considered measurements.
• Figure 3: Left: Energy sharing between the two TES channels at low energies. Events between the yellow dashed lines, defined by Eq. \ref{['eq:shared_cut']}, are classified as shared events. Signals appearing in only one TES within the coincidence window are identified as singles; the grey dashed lines indicate the triggering thresholds and define the singles-event selection. The solid yellow line shows the fit $E_\text{TES2} = r\cdot E_\text{TES1}$ used to extract the parameter $r$, which accounts for calibration mismatches. Center: Example coincident traces at energies around [100]eV from both TESs for the event populations identified in the left panel: shared events, where both sensors record a pulse, and singles, where only one sensor does. Typical pulse shapes from higher-energy particle events are shown as dashed lines. Right: Energy spectra, in dru ($\unit[1]{dru} = \unit[1]{counts/(keV\,kg\,d)}$), recorded during the NUCLEUS commissioning run LBR_paper, showing all triggered events (blue), shared events (yellow), singles (cyan), and negative triggers used to estimate the noise-induced trigger rate (red). The magenta shaded area marks the $[100,300]\,\mathrm{eV}$ interval used for the LEE estimate, while the green shaded area indicates the region used to evaluate the background $\mathrm{Rate}([1,3]\,\mathrm{keV})$. The vertical dashed gray line denotes the triggering threshold at $4\sigma_0$.
• Figure 4: Top: Correlation of the LEE rate ($R_\text{LEE}$) with the background rate in the keV region for different datasets. A dedicated test during the UGL2 cooldown was performed by opening the shield surrounding the detector. Under the hypothesis of a background-induced LEE, the $R_\text{LEE}$ was expected to increase; the opposite was observed. Bottom: Energy spectra of the two UGL2 datasets, showing an increase in the particle background rate in the keV region (shaded in green) when the shield is opened, while the LEE region (shaded in pink) exhibits the opposite behavior.
• Figure 5: Effect of the MV coincidence cut measured during the NUCLEUS commissioning run LBR_paper. Top: Measured energy spectra (solid histograms) before (yellow) and after (red) the application of the MV coincidence cut. The points show the Geant4 simulation results in the same range, before MV cut (blue) and after MV cut (cyan). Bottom: Best fit between toy model and data to extract the coincidence probability between the MV and the LEE spectrum.