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Abstract We report the in-situ 3D reconstruction of through-going muons in the CUORE experiment, a cryogenic calorimeter array searching for neutrinoless double beta ($$0\nu \beta \beta $$ $0\nu \beta \beta$ ) decay, leveraging the segmentation of the detector. Due to the slow time response of the detector, time-of-flight estimation is not feasible. Therefore, the track reconstruction is performed using a multi-objective optimization algorithm that relies on geometrical information from the detector as a whole. We measure the integral flux of cosmic-ray muons underground at theLaboratori Nazionali del Gran Sasso, and find our value to be in good agreement with other experiments that have performed a similar measurement. To our knowledge, this work represents the first demonstration of 3D particle tracking and reconstruction of through-going muons with per-event angular determination in a millikelvin cryogenic detector array. The analysis performed for this work will be critical for validating the muon-related background in CUPID, a next-generation$$0\nu \beta \beta $$ $0\nu \beta \beta$ experiment, and for follow-up studies on detector response and on delayed products induced by cosmic-ray muons. 

A calorimetric detector for minimally disruptive measurements of atomic hydrogen beams is described. The calorimeter measures heat released by the recombination of hydrogen atoms into molecules on a thin wire. As a demonstration, the angular distribution of a beam with a peak intensity of$$\approx 10^{16} \,{\textrm{atoms}}/{(\textrm{cm}^2 \textrm{s})}$$ $\approx {10}^{16}\text{atoms}/\left({\text{cm}}^2\text{s}\right)$ is measured by translating the wire across the beam. The data agree well with an analytic model of the beam from the thermal hydrogen atom source. Using the beam shape model, the relative intensity of the beam can be determined to 5% precision or better at any angle. Graphical abstract 

Abstract CUPID is a next-generation bolometric experiment to search for neutrinoless double-beta decay ($$0\nu \beta \beta $$ $0\nu \beta \beta$ ) of¹⁰⁰Mo using Li$$_2$$ $_2^{}$ MoO$$_4$$ $_4^{}$ scintillating crystals. It will operate 1596 crystals at$$\sim $$ $\sim$ 10 mK in the CUORE cryostat at the Laboratori Nazionali del Gran Sasso in Italy. Each crystal will be facing two Ge-based bolometric light detectors for$$\alpha $$ $\alpha$ rejection. We compute the discovery and the exclusion sensitivity of CUPID to$$0\nu \beta \beta $$ $0\nu \beta \beta$ in a Frequentist and a Bayesian framework. This computation is done numerically based on pseudo-experiments. For the CUPIDbaselinescenario, with a background and an energy resolution of$$1.0 \times 10^{-4}$$ $1.0\times {10}^{-4}$ counts/keV/kg/yr and 5 keV FWHM at the Q-value, respectively, this results in a Bayesian exclusion sensitivity (90% c.i.) of$$\hat{T}_{1/2} > 1.6 \times 10^{27} \ \textrm{yr}$$ ${\hat{T}}_{1/2}>1.6\times {10}^{27}\text{yr}$ , corresponding to the effective Majorana neutrino mass of$$\hat{m}_{\beta \beta } < \ 9.6$$ ${\hat{m}}_{\beta \beta }<9.6$ –$$28 \ \textrm{meV}$$ $28\text{meV}$ . The Frequentist discovery sensitivity (3$$\sigma $$ $\sigma$ ) is$$\hat{T}_{1/2}= 1.0 \times 10^{27} \ \textrm{yr}$$ ${\hat{T}}_{1/2}=1.0\times {10}^{27}\text{yr}$ , corresponding to$$\hat{m}_{\beta \beta }= \ 12$$ ${\hat{m}}_{\beta \beta }=12$ –$$36 \ \textrm{meV}$$ $36\text{meV}$ . 

We present the analysis techniques developed to explore the keV-scale energy region of the Cryogenic Underground Observatory for Rare Events (CUORE) experiment, based on more than 2 metric ton yr of data collected over five years. By prioritizing a stricter selection over a larger exposure, we are able to optimize data selection for thresholds at 10 keV and 3 keV with 691 kg yr and 11 kg yr of data, respectively. We study how the performance varies among the 988-detector array with different detector characteristics and data-taking conditions. We achieve an average baseline resolution of $2.54\pm 0.14\mathrm{keV}$ FWHM and $1.18\pm 0.02\mathrm{keV}$ FWHM for the data selection at 10 keV and 3 keV, respectively. The analysis methods employed reduce the overall background by about an order of magnitude, reaching $2.06\pm 0.05\mathrm{counts}/\left(\mathrm{keV}\mathrm{kg}\mathrm{days}\right)$ and $16\pm 2\mathrm{counts}/\left(\mathrm{keV}\mathrm{kg}\mathrm{days}\right)$ at the thresholds of 10 keV and 3 keV. We evaluate for the first time the near-threshold reconstruction efficiencies of the CUORE experiment, and find these to be $50\pm 2\%$ and $26\pm 4\%$ at 10 keV and 3 keV, respectively. This analysis provides crucial insights into rare decay studies, new physics searches, and keV-scale background modeling with CUORE. We demonstrate that ton-scale cryogenic calorimeters can operate across a wide energy range, from keV to MeV, establishing their scalability as versatile detectors for rare event and dark matter physics. These findings also inform the optimization of future large mass cryogenic calorimeters to enhance the sensitivity to low-energy phenomena. 

The most sensitive direct neutrino mass searches today are based on measurement of the end point of the β spectrum of tritium to infer limits on the mass of the unobserved neutrino. To avoid the smearing associated with the distribution of molecular final states in the T-He molecule, the next generation of these experiments will need to employ atomic (T) rather than molecular (T2) tritium sources, at currents of at least 1015 atoms per second. Following production, atomic T can be trapped in gravitational and/or magnetic bottles for β spectrum experiments, if and only if it can first be cooled to millikelvin temperatures. Accomplishing this cooling presents substantial technological challenges. The Project 8 collaboration is developing a technique based on magnetic evaporative cooling along a beamline (MECB) for the purpose of cooling T to feed a magnetogravitational trap that also serves as a cyclotron radiation emission spectroscope. Initial tests of the approach are planned in a pathfinder apparatus using atomic Li. This paper presents a method for analyzing the dynamics of the MECB technique and applies these calculations to the design of systems for cooling and slowing of atomic Li and T. A scheme is outlined that could provide a current of T at the millikelvin temperatures required for the Project 8 neutrino mass search. 

Cyclotron Radiation Emission Spectroscopy (CRES) is a technique for precision measurements of kinetic energies of charged particles, pioneered by the Project 8 experiment to measure the neutrino mass using the tritium end-point method. It was recently employed for the first time to measure the molecular tritium spectrum and place a limit on the neutrino mass using a cubic-centimeter-scale detector. Future direct neutrino mass experiments are developing the technique to overcome the systematic and statistical limitations of current detectors. This paper describes one such approach, namely the use of antenna arrays for CRES in free space. Phenomenology, detector design, simulation, and performance estimates are discussed, culminating with an example design with a projected sensitivity of mβ < 0.04 eV/c2. Prototype antenna array measurements are also shown for a demonstrator-scale setup as a benchmark for the simulation. By consolidating these results, this paper serves as a comprehensive reference for the development and performance of antenna arrays for CRES. 

Abstract Vibrations from experimental setups and the environment are a persistent source of noise for low-temperature calorimeters searching for rare events, including neutrinoless double beta (0νββ) decay or dark matter interactions. Such noise can significantly limit experimental sensitivity to the physics case under investigation. Here, we report the detection of marine microseismic vibrations using mK-scale calorimeters. This study employs a multi-device analysis correlating data from CUORE, the leading experiment in the search for 0νββdecay with mK-scale calorimeters, and the Copernicus Earth Observation program, revealing the seasonal impact of Mediterranean Sea activity on CUORE’s energy thresholds, resolution, and sensitivity over four years. The detection of marine microseisms underscores the need to address faint environmental noise in ultra-sensitive experiments. Understanding how such noise couples to the detector and developing mitigation strategies is essential for next-generation experiments. We demonstrate one such strategy: a noise decorrelation algorithm implemented in CUORE using auxiliary sensors, which reduces vibrational noise and improves detector performance. Enhancing sensitivity to 0νββdecay and to rare events with low-energy signatures requires identifying unresolved noise sources, advancing noise reduction methods, and improving vibration suppression systems, all of which inform the design of next-generation rare event experiments. 

Abstract The objective of the cyclotron radiation emission spectroscopy (CRES) technology is to build precise particle energy spectra. This is achieved by identifying the start frequencies of charged particle trajectories which, when exposed to an external magnetic field, leave semi-linear profiles (called tracks) in the time–frequency plane. Due to the need for excellent instrumental energy resolution in application, highly efficient and accurate track reconstruction methods are desired. Deep learning convolutional neural networks (CNNs) - particularly suited to deal with information-sparse data and which offer precise foreground localization—may be utilized to extract track properties from measured CRES signals (called events) with relative computational ease. In this work, we develop a novel machine learning based model which operates a CNN and a support vector machine in tandem to perform this reconstruction. A primary application of our method is shown on simulated CRES signals which mimic those of the Project 8 experiment—a novel effort to extract the unknown absolute neutrino mass value from a precise measurement of tritiumβ⁻-decay energy spectrum. When compared to a point-clustering based technique used as a baseline, we show a relative gain of 24.1% in event reconstruction efficiency and comparable performance in accuracy of track parameter reconstruction.