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Pulse Shape Model for a Light Enhanced Phonon Detector

This paper introduces a new pulse shape model explaining deviations in early COSINUS prototype detectors, revealing that light absorption in the carrier crystal creates a light-enhanced phonon signal that enables particle discrimination with a single channel and informs the design of the final remote TES detector.

Original authors: G. Angloher, M. R. Bharadwaj, A. Böhmer, S. Braun, M. R. Cababie, I. Colantoni, I. Dafinei, N. Di Marco, C. Dittmar, F. Ferella, F. Ferroni, S. Fichtinger, A. Filipponi, M. Friedl, D. Fuchs, L. Gai, M

Published 2026-10-21

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: G. Angloher, M. R. Bharadwaj, A. Böhmer, S. Braun, M. R. Cababie, I. Colantoni, I. Dafinei, N. Di Marco, C. Dittmar, F. Ferella, F. Ferroni, S. Fichtinger, A. Filipponi, M. Friedl, D. Fuchs, L. Gai, M. Gapp, M. Heikinheimo, K. Heim, M. N. Hughes, K. Huitu, M. Kellermann, A. Mancuso, L. Pagnanini, F. Petricca, C. Petrucci, S. Pirro, F. Pröbst, G. Profeta, A. Puiu, F. Reindl, K. Schäffner, J. Schieck, P. Schreiner, C. Schwertner, P. Settembri, K. Shera, M. Stahlberg, A. Stendahl, M. Stukel, C. Tresca, S. Yue, V. Zema, Y. Zhu, L. Ziegele, N. Zimmermann, O. Schulz

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep in the quiet, frigid silence of an underground laboratory, scientists are listening for the faintest whispers of the universe. They are hunting for dark matter, the invisible substance that makes up most of the matter in the cosmos but refuses to interact with light. To catch a glimpse of it, researchers use detectors made of special crystals cooled to temperatures colder than deep space. When a particle strikes the crystal, it deposits a tiny amount of energy, creating a ripple of heat called a phonon. By measuring this heat with extreme precision, scientists can identify what kind of particle hit the crystal. The challenge is distinguishing between the rare, heavy particles they are looking for and the constant rain of background radiation that creates similar, but slightly different, signals.

The COSINUS collaboration, a team of physicists working with sodium iodide crystals, set out to build such a detector. Their goal was to verify results from a famous experiment that claimed to have seen dark matter, using the same target material but with a new method to tell particle types apart. They built a prototype where the sensor, a tiny device capable of feeling the slightest temperature change, was not placed directly on the main crystal. Instead, it was mounted on a separate, smaller crystal that was glued to the main one. This design was meant to protect the delicate sensor from the harsh manufacturing process, but when the team turned on their detectors, the signals they received did not look like anything they had seen before. The pulses of heat arrived with a strange shape, and the team could not separate the heavy particle hits from the background noise as they had hoped.

The researchers realized that their initial design had created an unexpected side effect. The separate crystal holding the sensor was not just a passive mount; it was actively participating in the detection process. When a particle hit the main crystal, it produced flashes of light. Because the separate crystal was made of a material that absorbs this light, it caught the photons and converted their energy into heat. This created a second, faster pulse of heat that arrived at the sensor almost at the same time as the heat from the main crystal. The sensor was not just measuring the hit on the main crystal; it was measuring a combination of the main hit and the light absorbed by the carrier crystal. This accidental mixing of signals turned the detector into what the team calls a "light-enhanced phonon detector."

By developing a new mathematical model to describe this specific behavior, the team found that the strange pulse shapes were not a flaw, but a feature. The model showed that the signal was a superposition of two distinct events: the direct impact of the particle and the subsequent absorption of light in the carrier. This insight explained why the standard models failed to fit the data and why the team could not distinguish between different particle types using their original analysis. In a standard detector, heavy particles produce less light than lighter ones, creating a clear separation in the data. However, in this light-enhanced setup, the light-induced heat signal was so strong that it overwhelmed the subtle differences caused by the particle type, making all events look similar.

The team then used a sophisticated statistical method to fit their new model to the actual data recorded from their prototypes. They analyzed thousands of events, separating them into those caused by electrons and those caused by neutrons, which mimic the heavy particles they seek. The results confirmed that their model accurately described the physics of the detector. More importantly, they discovered that even though the light signal dominated the total energy reading, the specific shape of the pulse still held the key to identifying the particle. By looking closely at the ratio between the light-induced part of the signal and the direct particle-induced part, they could successfully tell the difference between the two types of events.

This finding transforms the way these detectors can be used. Previously, distinguishing particle types required two separate channels: one to measure the heat and another to measure the light. The new analysis shows that a single channel, if understood correctly, can do the job of both. The researchers demonstrated that by analyzing the detailed shape of the heat pulse alone, they could achieve the same particle discrimination that usually requires a second detector. This simplifies the design of future experiments and opens the door to more sensitive searches for dark matter. The work suggests that what looked like a confusing experimental error was actually a new way to listen to the universe, turning a complex problem into a powerful tool for discovery.

Technical Summary: Pulse Shape Model for a Light Enhanced Phonon Detector

Problem Statement
The COSINUS collaboration developed composite cryogenic calorimeters using Sodium Iodide (NaI) as a target absorber and a separate carrier crystal (CdWO $_4$ or Al $_2$ O $_3$ ) to host the Transition Edge Sensor (TES). This "composite design" was necessary because NaI cannot withstand the high temperatures required for evaporating the tungsten TES directly onto the absorber. However, initial measurements with these prototypes revealed two significant discrepancies compared to standard cryogenic calorimeter behavior:

Pulse Shape Deviation: The recorded pulse shapes could not be described by the established thermal model for such detectors (Pröbst et al.), requiring the ad-hoc addition of an empirical exponential term.
Loss of Particle Discrimination: During neutron calibration, the detectors failed to distinguish nuclear recoils from electron recoils ( $e^-/\gamma$ ). In standard scintillating calorimeters, nuclear recoils produce less scintillation light (quenching), creating a distinct band in the Light Yield (LY) vs. Energy plot. This separation was absent in the composite prototypes.

Methodology
To address these anomalies, the authors proposed a new physical interpretation: the composite detectors function as Light Enhanced Phonon Detectors. The hypothesis posits that the carrier crystal, while opaque to NaI scintillation light, absorbs a fraction of this light. This absorption generates a secondary population of non-thermal phonons within the carrier, which are subsequently detected by the TES alongside the primary phonons from the absorber.

The authors extended the original two-component thermal model (Pröbst et al.) to a three-component system comprising the Absorber, Carrier, and TES.

Thermal Model: A system of differential equations was derived to describe the heat flow between the three components and the heat bath. Crucially, the model includes a power input term ( $P_\ell$ ) representing the energy deposited into the carrier by absorbed scintillation light, distinct from the power input ( $P_0$ ) from direct particle interactions in the absorber.
Analytical Solution: The system was solved analytically, yielding a pulse shape composed of multiple exponential terms representing non-thermal and thermal phonon populations.
Statistical Analysis: The model was fitted to experimental data from two prototypes, NaIce2 (CdWO $_4$ carrier) and NaIce6 (Al $_2$ O $_3$ carrier), using the Bayesian inference software package BAT.jl. This approach allowed for the sampling of the full posterior distribution to handle high-dimensional parameter spaces and strong degeneracies. The fits were performed directly on voltage waveforms, treating temperature-like quantities as voltage-equivalent units.

Key Results

Model Validation: The extended model successfully reproduced the observed pulse shapes, including the "extra" thermal component that previously required empirical addition. The analytical solution naturally generates this additional component through the coupling of the light-induced phonon population in the carrier.
Light-Dominated Regime: The fit results indicate that the phonon signal is dominated by the light-induced contribution ( $E^c_\ell \gg E_p$ ). The ratio of light-induced to absorber-induced phonon amplitudes ( $A_{max}/B_{max}$ ) was found to be significantly larger for NaIce2 (CdWO $_4$ carrier, lower light transmission) than for NaIce6 (Al $_2$ O $_3$ carrier, higher transmission), consistent with the optical properties of the materials.
Explanation of Missing Nuclear Recoil Band: Because the phonon signal is dominated by the light-induced component, the total phonon energy scales with the scintillation light yield. Since the external light detector also measures this light, the calculated Light Yield ( $LY = E^b_\ell / E_{ph}$ ) becomes approximately constant ( $LY \approx \kappa$ ) regardless of the particle type. This explains why nuclear recoils (which have reduced light yield) failed to separate from electron recoils in the LY plot; they were effectively "masked" by the light-induced phonon signal.
Particle Discrimination via Pulse Shape: Despite the failure of the standard LY method, the authors demonstrated that the pulse shape parameters themselves offer discrimination power. Specifically, the ratio $A_{max}/B_{max}$ (the peak amplitude of the light-induced contribution relative to the absorber-induced contribution) showed a clear separation between NTD-tagged neutron and $e^-/\gamma$ events in NaIce6. Neutron events exhibited lower values of this ratio, consistent with their reduced scintillation light output. In NaIce2, an outlier event in both $A_{max}/B_{max}$ and the inferred scintillation fraction $S$ was identified, suggesting the method's viability even without an independent neutron tag.

Significance and Claims
The paper claims that the "accidental" experimental finding of light absorption in the carrier has been turned into an opportunity for single-channel particle discrimination. By modeling the detector as a light-enhanced phonon detector, the authors provide a physical explanation for the previously anomalous pulse shapes and the lack of nuclear recoil bands.

The significance lies in demonstrating that a single-channel phonon detector, when analyzed with this specific pulse shape model, can distinguish particle types without requiring a separate, dedicated light detector. This insight laid the foundation for the development of the final remote TES (remoTES) design for the COSINUS experiment. The work validates the use of Bayesian inference for extracting physically interpretable parameters (such as phonon collection efficiencies and scintillation fractions) from complex thermal models in cryogenic detectors.

The authors remain modest regarding the immediate application of these results to large-scale data analysis, noting that the current Bayesian fitting method is computationally expensive and requires manual tuning for convergence. Future work is identified as necessary to quantify the discrimination power and energy threshold more precisely and to adapt the model for the final remoTES design.

Technical Summary: Pulse Shape Model for a Light Enhanced Phonon Detector

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