Run 2 at Northwestern

HVEV RUN 3 AT NEXUS

3.2 Previous HVeV Science

3.2.2 Run 2 at Northwestern

The second run using an HVeV detector used an updated design focused on im- proving the phonon energy resolution. The detector utilized had the same mass and volume as Run 1, but achieved energy resolution equivalent to 3 eV with a voltage

Figure 3.4: A photo of the NF-C detector in the copper and PCB (FR-4) housing used for Run 3. The detector face is visible through a window in the center of the PCB. The calipers show the housing as being∼6 cm wide. Wire-bonds connecting to the readout pads of the detector can be seen to the left of the detector.

Figure 3.5: The dark-matter-electron scattering limits produced by HVeV Run 1 (from [40]). Red lines are the limits. The narrow pink region around each limit is the limit’s uncertainty from varying the ionization model. The excluded regions are shaded in a transparent red. The parameter space excluded below 4 MeV was world-leading when Run 1 was published. (Left) The limit for scattering via a heavy mediator. (Right) The limit for scattering via a light mediator.

bias of 100 V (set using 5%-coverage bias electrodes). The resultant ionization res- olution was equivalent to 0.03𝑒⁻ℎ⁺pairs. The detector was run in an above-ground adiabatic demagnetization refrigerator (at Northwestern University), which required daily cycling in order to maintain a temperature between 50 and 52 mK for 10-12

Figure 3.6: The dark-photon absorption limit produced by HVeV Run 1 (from [40]).

The red line is the limit. The narrow pink region around the limit is the uncertainty from varying the ionization model and the photoelectric cross section. The excluded region is shaded in a transparent red.

hours each day. Outside these times, the fridge remained at 4 K. The run achieved a greater exposure of 1.2 gram-days after cuts [26].

Laser calibration data was taken each day after cooldown to account for the effects of fridge cycling on the calibration. Laser data was also taken for a range of fridge temperatures, in order to correct for temperature variation within the measured range. Time periods when the fridge temperature drifted outside the calibration range were removed.

Adjacent to its HVeV detector, Run 2 operated a veto detector designed to pickup RF background signals from the lab environment. The analysis removed all HVeV- detector events that were close in time to significant signals in the veto detector.

It is statistically unlikely for weakly-interacting dark-matter to produce recoils in multiple detectors simultaneously (compared to radiogenic, cosmogenic, or RF backgrounds), so removing coincident events preferentially lowers the background rate. This type of cut is known as a live-time cut since the data and associated live- time were removed together. Alternatively, data-quality cuts remove events on the basis that the event was poorly characterized. Data-quality cuts lower the efficiency of the search since they quantify the experiment’s inability to characterize all events precisely. The Run 2 veto detector was a second silicon wafer instrumented with a single TES. The transition temperature of the veto TES was near the fridge operating temperature, causing the veto detector to perform poorly and have only a small effect on the analysis.

Unlike Run 1, the Run 2 signal model considered effects we refer to as charge- trapping (CT) and impact ionization (II). Charge-trapping occurs when an electron or hole traveling through the crystal is captured by an oppositely ionized donor or ac- ceptor impurity in the crystal. Donor (acceptor) impurities have donated (accepted) an electron to the conduction band, leaving the impurity positively (negatively) charged and capable of capturing an electron (hole). Conversely, impact ionization occurs when a traveling electron or hole frees a charge carrier that was previously captured by a donor or acceptor impurity. Since these effects remove or add charge carriers partway through the NTL-production process, they create events with non- quantized NTL-phonon energy that appear outside the typical𝑒⁻ℎ⁺ peaks. CT and II are visualized in Figure 3.7.

For Run 2, charge-trapping and impact-ionization were assumed to occur with fixed probabilities. The CT probability was defined as the probability that an 𝑒⁻ℎ⁺ pair loses one of its charge carriers. The II probability was defined as the probability that an𝑒⁻ℎ⁺ pair produces one additional charge carrier. The model assumed that only one of the two processes could occur for a given𝑒⁻ℎ⁺ pair, and otherwise the pair would produce the full NTL-phonon energy [43]. The Run 2 probabilities were measured (using laser data) to be 11±3% and 2⁺₋³₂% for CT and II, respectively [26]. When the Run 1 detector was characterized using the same model, its CT was observed to be significantly lower at 0.713±0.093% [44]. The Run 1 detector’s II was comparable to Run 2 at 1.576±0.110%. The Run 1 probabilities were only

Figure 3.7: A diagram of charge transport in a voltage-biased detector. (from [42]).

In each case, we see a bulk event that produces 1 𝑒⁻ℎ⁺ pair. On the left, the pair travels (in opposite directions) all the way across the detector. This will produce phonon energy equivalent to𝑒𝑉_bias. Many of such events will form the 1-𝑒⁻ℎ⁺peak in the energy spectrum. In the middle, we see examples of one charge carrier being trapped by an oppositely ionized donor or acceptor impurity (charge trapping). Such cases will produce< 𝑒𝑉_biasof energy. On the right, we see examples of one charge carrier freeing a similar charge carrier that was previously captured by a donor or acceptor impurity (impact ionization). Such cases will produce> 𝑒𝑉_biasof energy.

measured after the Run 1 analysis and were therefore not used. Both probabilities were sufficiently low that we would not expect including them to significantly change the Run 1 limits.

The electron-scattering and dark-photon-absorption exclusion limits produced by the Run 2 analysis can be seen in Figures 3.8 and 3.9, respectively. For most of the mass range, the Run 2 limits were slightly worse than those of Run 1 (despite Run 2 having improved energy resolution and≥ 2× exposure). The weaker limits were actually the result of the Run 2 detector’s higher CT rate and using a more conservative limit-setting method. Specifically, Run 2 used a Poisson limit-setting method rather than the Optimum-Interval (OI) method used by Run 1. The OI method was found to be highly dependent on the expected signal spectral (including CT and II effects) and therefore produced problematic systematic uncertainties. The Poisson method is more robust to uncertainty in CT and II because it only considers events within the quantized peaks.

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Figure 3.8: The dark-matter-electron scattering limits produced by HVeV Run 2 (from [26]). Blue lines are the Run 2 limits. The narrow light-blue region around each limit is the limit’s uncertainty from varying the ionization model. (Left) The limit for scattering via a heavy mediator. (Right) The limit for scattering via a light mediator.

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Figure 3.9: The dark-photon absorption limit produced by HVeV Run 2 (from [26]).

The blue line is the limit. The narrow light-blue region around the limit is the uncertainty from varying the ionization model and the photoelectric cross section.

like particles (ALPs) down to an ALP mass of 1.2 eV. This limit was world-leading among direct detection experiments, but remains significantly less sensitive than the limit imposed by stellar-cooling observations (𝑔_{𝑎 𝑒} ≲ 10⁻¹³, see Figure 2.16).

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Figure 3.10: The ALP-absorption limit produced by HVeV Run 2 (from [26]). The blue line is the limit. The narrow light-blue region around the limit is the uncertainty from varying the ionization model and the photoelectric cross section. The entire region remains significantly less sensitive than the limit imposed by stellar-cooling observations (𝑔_{𝑎 𝑒} ≲ 10⁻¹³).