Search

It is known from Zhu's results that under modular transformations, correlators of rational $C_2$-cofinite vertex operator algebras transform like Jacobi forms. We investigate the modular transformation properties of VOA correlators that have zero modes inserted. We derive recursion relations for such correlators and use them to establish modular transformation properties. We find that correlators with only zero modes transform like quasi-modular forms, and mixed correlators with both zero modes and vertex operators transform like quasi-Jacobi forms. As an application of our results, we introduce algebras of higher weight fields whose zero mode correlators mimic the properties of those of weight 1 fields. We also give a simplified proof of the weight 1 transformation properties originally proven by Miyamoto.

The Cryogenic Underground Observatory for Rare Events (CUORE) is a detector array comprised by 988 5$\;$cm$\times$5$\;$cm$\times$5$\;$cm TeO$_2$ crystals held below 20 mK, primarily searching for neutrinoless double-beta decay in $^{130}$Te. Unprecedented in size amongst cryogenic calorimetric experiments, CUORE provides a promising setting for the study of exotic through-going particles. Using the first tonne-year of CUORE's exposure, we perform a search for hypothesized fractionally charged particles (FCPs), which are well-motivated by various Standard Model extensions and would have suppressed interactions with matter. No excess of FCP candidate tracks is observed over background, setting leading limits on the underground FCP flux with charges between $e/24-e/5$ at 90\% confidence level. Using the low background environment and segmented geometry of CUORE, we establish the sensitivity of tonne-scale sub-Kelvin detectors to diverse signatures of new physics., Comment: 7 pages, 5 figures

We present the model we developed to reconstruct the CUORE radioactive background based on the analysis of an experimental exposure of 1038.4 kg yr. The data reconstruction relies on a simultaneous Bayesian fit applied to energy spectra over a broad energy range. The high granularity of the CUORE detector, together with the large exposure and extended stable operations, allow for an in-depth exploration of both spatial and time dependence of backgrounds. We achieve high sensitivity to both bulk and surface activities of the materials of the setup, detecting levels as low as 10 nBq kg$^{-1}$ and 0.1 nBq cm$^{-2}$, respectively. We compare the contamination levels we extract from the background model with prior radio-assay data, which informs future background risk mitigation strategies. The results of this background model play a crucial role in constructing the background budget for the CUPID experiment as it will exploit the same CUORE infrastructure.

The main goal of the CRESST-III experiment is the direct detection of dark matter particles via their scattering off target nuclei in cryogenic detectors. In this work we present the results of a Silicon-On-Sapphire (SOS) detector with a mass of 0.6$\,$g and an energy threshold of (6.7$\, \pm \,$0.2)$\,$eV with a baseline energy resolution of (1.0$\, \pm \,$0.2)$\,$eV. This allowed for a calibration via the detection of single luminescence photons in the eV-range, which could be observed in CRESST for the first time. We present new exclusion limits on the spin-independent and spin-dependent dark matter-nucleon cross section that extend to dark matter particle masses of less than 100$\,$MeV/c$^{2}$., Comment: 10 pages, 8 figures

This paper deals with the problem of clustering data returned by a radar sensor network that monitors a region where multiple moving targets are present. The network is formed by nodes with limited functionalities that transmit the estimates of target positions (after a detection) to a fusion center without any association between measurements and targets. To solve the problem at hand, we resort to model-based learning algorithms and instead of applying the plain maximum likelihood approach, due to the related computational requirements, we exploit the latent variable model coupled with the expectation-maximization algorithm. The devised estimation procedure returns posterior probabilities that are used to cluster the huge amount of data collected by the fusion center. Remarkably, we also consider challenging scenarios with an unknown number of targets and estimate it by means of the model order selection rules. The clustering performance of the proposed strategy is compared to that of conventional data-driven methods over synthetic data. The numerical examples point out that the herein proposed solutions can provide reliable clustering performance overcoming the considered competitors., Comment: 12 pages 14 figures

Many of the most sensitive physics experiments searching for rare events, like neutrinoless double beta ($0\nu\beta\beta$) decay and dark matter interactions, rely on cryogenic macro-calorimeters operating at the mK-scale. Located underground at the Gran Sasso National Laboratory (LNGS), in central Italy, CUORE (Cryogenic Underground Observatory for Rare Events) is one of the leading experiments for the search of $0\nu\beta\beta$ decay, implementing the low-temperature calorimetric technology. We present a novel multi-detector analysis to correlate environmental phenomena with the low-frequency noise of low-temperature calorimeters. Indeed, the correlation of marine and seismic data with data from a pair of CUORE detectors indicates that cryogenic detectors are sensitive not only to intense vibrations generated by earthquakes, but also to the much fainter vibrations induced by marine microseisms in the Mediterranean Sea due to the motion of sea waves. Proving that cryogenic macro-calorimeters are sensitive to such environmental sources of noise opens the possibility of studying their impact on the detectors physics-case sensitivity. Moreover, this study could pave the road for technology developments dedicated to the mitigation of the noise induced by marine microseisms, from which the entire community of cryogenic calorimeters can benefit.

The matter-antimatter asymmetry underlines the incompleteness of the current understanding of particle physics. Neutrinoless double-beta ($0\nu \beta\beta$) decay may help explain this asymmetry, while unveiling the Majorana nature of the neutrino. The CUORE experiment searches for $0\nu \beta\beta$ decay of $^{130}$Te using a tonne-scale cryogenic calorimeter operated at milli-kelvin temperatures. We report no evidence for $0\nu \beta\beta$ decay and place a lower limit on the half-life of T$_{1/2}$ $>$ 3.8 $\times$ 10$^{25}$ years (90% C.I.) with over 2 tonne$\cdot$year TeO$_2$ exposure. The tools and techniques developed for this result and the 5 year stable operation of nearly 1000 detectors demonstrate the infrastructure for a next-generation experiment capable of searching for $0\nu \beta\beta$ decay across multiple isotopes.

In recent times, the sensitivity of low-mass direct dark matter searches has been limited by unknown low energy backgrounds close to the energy threshold of the experiments known as the low energy excess (LEE). The CRESST experiment utilises advanced cryogenic detectors constructed with different types of crystals equipped with Transition Edge Sensors (TESs) to measure signals of nuclear recoils induced by the scattering of dark matter particles in the detector. In CRESST, this low energy background manifests itself as a steeply rising population of events below 200 eV. A novel detector design named doubleTES using two identical TESs on the target crystal was studied to investigate the hypothesis that the events are sensor-related. We present the first results from two such modules, demonstrating their ability to differentiate between events originating from the crystal's bulk and those occurring in the sensor or in its close proximity., Comment: 10 pages, 13 figures

Cryogenic scintillating calorimeters are ultrasensitive particle detectors for rare event searches, particularly for the search for dark matter and the measurement of neutrino properties. These detectors are made from scintillating target crystals generating two signals for each particle interaction. The phonon (heat) signal precisely measures the deposited energy independent of the type of interacting particle. The scintillation light signal yields particle discrimination on an event-by-event basis. This paper presents a likelihood framework modeling backgrounds and a potential dark matter signal in the two-dimensional plane spanned by phonon and scintillation light energies. We apply the framework to data from CaWO$_4$-based detectors operated in the CRESST dark matter search. For the first time, a single likelihood framework is used in CRESST to model the data and extract results on dark matter in one step by using a profile likelihood ratio test. Our framework simultaneously fits (neutron) calibration data and physics (background) data and allows combining data from multiple detectors. Although tailored to CaWO$_4$-targets and the CRESST experiment, the framework can easily be expanded to other materials and experiments using scintillating cryogenic calorimeters for dark matter search and neutrino physics., Comment: 18 pages, 11 figures, additional figures and data in ancillary files (on arXiv or at journal reference)

Recently low-mass dark matter direct searches have been hindered by a low energy background, drastically reducing the physics reach of the experiments. In the CRESST-III experiment, this signal is characterised by a significant increase of events below 200 eV. As the origin of this background is still unknown, it became necessary to develop new detector designs to reach a better understanding of the observations. Within the CRESST collaboration, three new different detector layouts have been developed and they are presented in this contribution., Comment: 8 pages, 4 figures

Diamond operated as a cryogenic calorimeter is an excellent target for direct detection of low-mass dark matter candidates. Following the realization of the first low-threshold cryogenic detector that uses diamond as absorber for astroparticle physics applications, we now present the resulting exclusion limits on the elastic spin-independent interaction cross-section of dark matter with diamond. We measured two 0.175 g CVD (Chemical Vapor Deposition) diamond samples, each instrumented with a W-TES. Thanks to the energy threshold of just 16.8 eV of one of the two detectors, we set exclusion limits on the elastic spin-independent interaction of dark matter particles with carbon nuclei down to dark matter masses as low as 0.122 GeV/c2. This work shows the scientific potential of cryogenic detectors made from diamond and lays the foundation for the use of this material as target for direct detection dark matter experiments., Comment: 6 pages, 6 figures

Using CaWO$_4$ crystals as cryogenic calorimeters, the CRESST experiment searches for nuclear recoils caused by the scattering of potential Dark Matter particles. A reliable identification of a potential signal crucially depends on an accurate background model. In this work we introduce an improved normalisation method for CRESST's model of the electromagnetic backgrounds. Spectral templates, based on Geant4 simulations, are normalised via a Bayesian likelihood fit to experimental background data. Contrary to our previous work, no assumption of partial secular equilibrium is required, which results in a more robust and versatile applicability. Furthermore, considering the correlation between all background components allows us to explain 82.7% of the experimental background within [1 keV, 40 keV], an improvement of 18.6% compared to our previous method., Comment: 24 pages, 14 figures, submitted to EPJC

We report on the results obtained with the global CUPID-0 background model, which combines the data collected in the two measurement campaigns for a total exposure of 16.6 kg$\times$yr. We identify with improved precision the background sources in the region of interest for neutrinoless double $\beta$-decay, making more solid the foundations for the background budget of the next-generation CUPID experiment. Relying on the excellent data reconstruction, we measure the two-neutrino double $\beta$-decay half-life of $^{82}$Se with unprecedented accuracy: $T_{1/2}^{2\nu} = [8.69 \pm 0.05 \textrm{(stat.)}~^{+0.09}_{-0.06} \textrm{(syst.)}] \times 10^{19}~\textrm{yr}$.

CUPID is a next-generation bolometric experiment aiming at searching for neutrinoless double-beta decay with ~250 kg of isotopic mass of $^{100}$Mo. It will operate at $\sim$10 mK in a cryostat currently hosting a similar-scale bolometric array for the CUORE experiment at the Gran Sasso National Laboratory (Italy). CUPID will be based on large-volume scintillating bolometers consisting of $^{100}$Mo-enriched Li$_2$MoO$_4$ crystals, facing thin Ge-wafer-based bolometric light detectors. In the CUPID design, the detector structure is novel and needs to be validated. In particular, the CUORE cryostat presents a high level of mechanical vibrations due to the use of pulse tubes and the effect of vibrations on the detector performance must be investigated. In this paper we report the first test of the CUPID-design bolometric light detectors with NTD-Ge sensors in a dilution refrigerator equipped with a pulse tube in an above-ground lab. Light detectors are characterized in terms of sensitivity, energy resolution, pulse time constants, and noise power spectrum. Despite the challenging noisy environment due to pulse-tube-induced vibrations, we demonstrate that all the four tested light detectors comply with the CUPID goal in terms of intrinsic energy resolution of 100 eV RMS baseline noise. Indeed, we have measured 70--90 eV RMS for the four devices, which show an excellent reproducibility. We have also obtained outstanding energy resolutions at the 356 keV line from a $^{133}$Ba source with one light detector achieving 0.71(5) keV FWHM, which is -- to our knowledge -- the best ever obtained when compared to $\gamma$ detectors of any technology in this energy range., Comment: Prepared for submission to JINST; 16 pages, 7 figures, and 1 table

An array of twelve 0.28 kg lithium molybdate (LMO) low-temperature bolometers equipped with 16 bolometric Ge light detectors, aiming at optimization of detector structure for CROSS and CUPID double-beta decay experiments, was constructed and tested in a low-background pulse-tube-based cryostat at the Canfranc underground laboratory in Spain. Performance of the scintillating bolometers was studied depending on the size of phonon NTD-Ge sensors glued to both LMO and Ge absorbers, shape of the Ge light detectors (circular vs. square, from two suppliers), in different light collection conditions (with and without reflector, with aluminum coated LMO crystal surface). The scintillating bolometer array was operated over 8 months in the low-background conditions that allowed to probe a very low, $\mu$Bq/kg, level of the LMO crystals radioactive contamination by $^{228}$Th and $^{226}$Ra., Comment: Prepared for submission to JINST; 23 pages, 9 figures, and 4 tables

New-generation direct searches for low mass dark matter feature detection thresholds at energies well below 100 eV, much lower than the energies of commonly used X-ray calibration sources. This requires new calibration sources with sub-keV energies. When searching for nuclear recoil signals, the calibration source should ideally cause mono-energetic nuclear recoils in the relevant energy range. Recently, a new calibration method based on the radiative neutron capture on $^{182}$W with subsequent de-excitation via single $\gamma$-emission leading to a nuclear recoil peak at 112 eV was proposed. The CRESST-III dark matter search operated several CaWO$_{4}$-based detector modules with detection thresholds below 100 eV in the past years. We report the observation of a peak around the expected energy of 112 eV in the data of three different detector modules recorded while irradiated with neutrons from different AmBe calibration sources. We compare the properties of the observed peaks with Geant-4 simulations and assess the prospects of using this for the energy calibration of CRESST-III detectors., Comment: 8 pages, 4 figures; submitted to Phys. Rev. D

Hyperspectral target detection is a task of primary importance in remote sensing since it allows identification, location, and discrimination of target features. To this end, the reflectance maps, which contain the spectral signatures and related abundances of the materials in the observed scene, are often used. However, due to the low spatial resolution of most hyperspectral sensors, targets occupy a fraction of the pixel and, hence, the spectra of different sub-pixel targets (including the background spectrum) are mixed together within the same pixel. To solve this issue, in this paper, we adopt a generalized replacement model accounting for multiple sub-pixel target spectra and formulate the detection problem at hand as a binary hypothesis test where under the alternative hypothesis the target is modeled in terms of a linear combination of endmembers whose coefficients also account for the presence of the background. Then, we devise detection architectures based upon the generalized likelihood ratio test where the unknown parameters are suitably estimated through procedures inspired by the maximum likelihood approach. The performances of the proposed decision schemes are evaluated by means of both synthetic as well as real data and compared with an analogous counterpart by showing the effectiveness of the proposed procedure., Comment: 12 pages, 8 figures

We present limits on the spin-independent interaction cross section of dark matter particles with silicon nuclei, derived from data taken with a cryogenic calorimeter with 0.35 g target mass operated in the CRESST-III experiment. A baseline nuclear recoil energy resolution of $(1.36\pm 0.05)$ eV$_{\text{nr}}$, currently the lowest reported for macroscopic particle detectors, and a corresponding energy threshold of $(10.0\pm 0.2)$ eV$_{\text{nr}}$ have been achieved, improving the sensitivity to light dark matter particles with masses below 160 MeV/c$^2$ by a factor of up to 20 compared to previous results. We characterize the observed low energy excess, and we exclude noise triggers and radioactive contaminations on the crystal surfaces as dominant contributions., Comment: 8 pages, 5 figures; precised the position of the calibration source in Fig. 1; extended the discussion about the observed energy spectrum; added the DM limit curve to ancillary files. Published in Phys. Rev. D

The CRESST experiment employs cryogenic calorimeters for the sensitive measurement of nuclear recoils induced by dark matter particles. The recorded signals need to undergo a careful cleaning process to avoid wrongly reconstructed recoil energies caused by pile-up and read-out artefacts. We frame this process as a time series classification task and propose to automate it with neural networks. With a data set of over one million labeled records from 68 detectors, recorded between 2013 and 2019 by CRESST, we test the capability of four commonly used neural network architectures to learn the data cleaning task. Our best performing model achieves a balanced accuracy of 0.932 on our test set. We show on an exemplary detector that about half of the wrongly predicted events are in fact wrongly labeled events, and a large share of the remaining ones have a context-dependent ground truth. We furthermore evaluate the recall and selectivity of our classifiers with simulated data. The results confirm that the trained classifiers are well suited for the data cleaning task., Comment: 12 pages, 8 figures, 6 tables

The Monster Lie algebra $\mathfrak m$ is a quotient of the physical space of the vertex algebra $V=V^\natural\otimes V_{1,1}$, where $V^\natural$ is the Moonshine module vertex operator algebra of Frenkel, Lepowsky, and Meurman, and $V_{1,1}$ is the vertex algebra corresponding to the rank 2 even unimodular lattice $\textrm{II}_{1,1}$. We construct vertex algebra elements that project to bases for subalgebras of $\mathfrak m$ isomorphic to $\mathfrak{gl}_{2}$, corresponding to each imaginary simple root, denoted $(1,j)$ for $j>0$. Our method requires the existence of pairs of primary vectors in $V^{\natural}$ satisfying some natural conditions, which we prove. We show that the action of the Monster finite simple group $\mathbb{M}$ on the subspace of primary vectors in $V^\natural$ induces an $\mathbb{M}$-action on the set of $\mathfrak{gl}_2$ subalgebras corresponding to a fixed imaginary simple root. We use the generating function for dimensions of subspaces of primary vectors of $V^\natural$ to prove that this action is non-trivial for small values of $j$., Comment: Final version, to appear in the Journal of Pure and Applied Algebra

We present the first search for the Majoron-emitting modes of the neutrinoless double $\beta$ decay ($0\nu\beta\beta\chi_0$) using scintillating cryogenic calorimeters. We analysed the CUPID-0 Phase I data using a Bayesian approach to reconstruct the background sources activities, and evaluate the potential contribution of the $^{82}$Se $0\nu\beta\beta\chi_0$. We considered several possible theoretical models which predict the existence of a Majoron-like boson coupling to the neutrino. The energy spectra arising from the emission of such bosons in the neutrinoless double $\beta$ decay have spectral indices $n=$ 1, 2, 3 or 7. We found no evidence of any of these decay modes, setting a lower limit (90% of credibility interval) on the half-life of 1.2 $\times$ 10$^{23}$ yr in the case of $n=$ 1, 3.8 $\times$ 10$^{22}$ yr for $n=$ 2, 1.4 $\times$ 10$^{22}$ yr for $n=$ 3 and 2.2 $\times$ 10$^{21}$ yr for $n=$ 7. These are the best limits on the $0\nu\beta\beta\chi_0$ half-life of the $^{82}$Se, and demonstrate the potentiality of the CUPID-0 technology in this field.

CRESST is a leading direct detection sub-$\mathrm{GeVc}^{-2}$ dark matter experiment. During its second phase, cryogenic bolometers were used to detect nuclear recoils off the $\mathrm{CaWO}_4$ target crystal nuclei. The previously established electromagnetic background model relies on secular equilibrium (SE) assumptions. In this work, a validation of SE is attempted by comparing two likelihood-based normalisation results using a recently developed spectral template normalisation method based on Bayesian likelihood. We find deviations from SE; further investigations are necessary to determine their origin., Comment: Part of special issue: ICRM-LLRMT22 8th International Conference on Radionuclide Metrology - Low Level Radioactivity Measurement and Techniques, 6 pages, 3 figures

The CRESST experiment observes an unexplained excess of events at low energies. In the current CRESST-III data-taking campaign we are operating detector modules with different designs to narrow down the possible explanations. In this work, we show first observations of the ongoing measurement, focusing on the comparison of time, energy and temperature dependence of the excess in several detectors. These exclude dark matter, radioactive backgrounds and intrinsic sources related to the crystal bulk as a major contribution., Comment: 10 pages, 5 figures; to be published in IDM2022 proceedings; corrected several minor typos

In the past decades, numerous experiments have emerged to unveil the nature of dark matter, one of the most discussed open questions in modern particle physics. Among them, the CRESST experiment, located at the Laboratori Nazionali del Gran Sasso, operates scintillating crystals as cryogenic phonon detectors. In this work, we present first results from the operation of two detector modules which both have 10.46 g LiAlO$_2$ targets in CRESST-III. The lithium contents in the crystal are $^6$Li, with an odd number of protons and neutrons, and $^7$Li, with an odd number of protons. By considering both isotopes of lithium and $^{27}$Al, we set the currently strongest cross section upper limits on spin-dependent interaction of dark matter with protons and neutrons for the mass region between 0.25 and 1.5 GeV/c$^2$., Comment: 9 pages, 8 figures

We determine the level two Zhu algebra for the Heisenberg vertex operator algebra $V$ for any choice of conformal element. We do this using only the following information for $V$: the internal structure of $V$; the level one Zhu algebra of $V$ already determined by the second author, along with Vander Werf and Yang; and the information the lower level Zhu algebras give regarding irreducible modules. We are able to carry out this calculation of the level two Zhu algebra for $V$ with this minimal information by employing the general results and techniques for determining generators and relations for higher level Zhu algebras for a vertex operator algebra, as developed previously by the authors in "On generators and relations for higher level Zhu algebras and applications", by Addabbo and Barron, J. Algebra, 2023. In particular, we show that the level $n$ Zhu algebras for the Heisenberg vertex operator algebra become noncommutative at level $n=2$. We also give a conjecture for the structure of the level $n$ Zhu algebra for the Heisenberg vertex operator algebra, for any $n >2$., Comment: 65 pages; minor typos corrected; some calculations shortened

CUPID-0, an array of Zn$^{82}$Se cryogenic calorimeters, was the first medium-scale demonstrator of the scintillating bolometers technology. The first project phase (March 2017 - December 2018) allowed the most stringent limit on the neutrinoless double beta decay half-life of the isotope of interest, $^{82}$Se, to be set. After a six months long detector upgrade, CUPID-0 began its second and last phase (June 2019 - February 2020). In this letter, we describe the search for neutrinoless double beta decay of $^{82}$Se with a total exposure (phase I + II) of 8.82 kg$\times$yr of isotope. We set a limit on the half-life of $^{82}$Se to the ground state of $^{82}$Kr of T$^{0\nu}_{1/2}$($^{82}$Se)$>$ 4.6$\times \mathrm{10}^{24}$ yr (90\% credible interval), corresponding to an effective Majorana neutrino mass m$_{\beta\beta} <$ (263 -- 545) meV. We also set the most stringent lower limits on the neutrinoless decays of $^{82}$Se to the 0$_1^+$, 2$_1^+$ and 2$_2^+$ excited states of $^{82}$Kr, finding 1.8$\times$10$^{23}$ yr, 3.0$\times$10$^{23}$ yr, 3.2$\times$10$^{23}$ yr (90$\%$ credible interval) respectively.

One of the most energetic events in the Universe are core-collapse Supernovae (SNe), where almost all the star's binding energy is released as neutrinos. These particles are direct probes of the processes occurring in the stellar core and provide unique insights into the gravitational collapse. RES-NOVA will revolutionize how we detect neutrinos from astrophysical sources, by deploying the first ton-scale array of cryogenic detectors made from archaeological lead. Pb offers the highest neutrino interaction cross-section via coherent elastic neutrino-nucleus scattering (CE$\nu$NS). Such process will enable RES-NOVA to be equally sensitive to all neutrino flavors. For the first time, we propose to use archaeological Pb as sensitive target material in order to achieve an ultra-low background level in the region of interest (\textit{O}(1keV)). All these features make possible the deployment of the first cm-scale neutrino telescope for the investigation of astrophysical sources. In this contribution, we will characterize the radiopurity level and the performance of a small-scale proof-of-principle detector of RES-NOVA, consisting in a PbWO$_4$ crystal made from archaeological-Pb operated as cryogenic detector.

This paper is devoted to the performance analysis of the detectors proposed in the companion paper where a comprehensive design framework is presented for the adaptive detection of subspace signals. The framework addresses four variations on subspace detection: the subspace may be known or known only by its dimension; consecutive visits to the subspace may be unconstrained or they may be constrained by a prior probability distribution. In this paper, Monte Carlo simulations are used to compare the generalized likelihood ratio (GLR) detectors derived in [1] with estimate-and-plug (EP) approximations of the GLR detectors. Remarkably, the EP approximations appear here for the first time (at least to the best of the authors' knowledge). The numerical examples indicate that GLR detectors are effective for the detection of partially-known signals affected by inherent uncertainties due to the system or the operating environment. In particular, if the signal subspace is known, GLR detectors tend to outperform EP detectors. If, instead, the signal subspace is known only by its dimension, the performance of GLR and EP detectors is very similar., Comment: 10 pages, 10 figures

The Cryogenic Underground Observatory for Rare Events (CUORE) is the most sensitive experiment searching for neutrinoless double-beta decay ($0\nu\beta\beta$) in $^{130}\text{Te}$. CUORE uses a cryogenic array of 988 TeO$_2$ calorimeters operated at $\sim$10 mK with a total mass of 741 kg. To further increase the sensitivity, the detector response must be well understood. Here, we present a non-linear thermal model for the CUORE experiment on a detector-by-detector basis. We have examined both equilibrium and dynamic electro-thermal models of detectors by numerically fitting non-linear differential equations to the detector data of a subset of CUORE channels which are well characterized and representative of all channels. We demonstrate that the hot-electron effect and electric-field dependence of resistance in NTD-Ge thermistors alone are inadequate to describe our detectors' energy dependent pulse shapes. We introduce an empirical second-order correction factor in the exponential temperature dependence of the thermistor, which produces excellent agreement with energy-dependent pulse shape data up to 6 MeV. We also present a noise analysis using the fitted thermal parameters and show that the intrinsic thermal noise is negligible compared to the observed noise for our detectors., Comment: 34 pages, 14 figures, 6 tables

The Cryogenic Underground Observatory for Rare Events (CUORE) at Laboratori Nazionali del Gran Sasso of INFN in Italy is an experiment searching for neutrinoless double beta (0$\nu\beta\beta$) decay. Its main goal is to investigate this decay in $^{130}$Te, but its ton-scale mass and low background make CUORE sensitive to other rare processes as well. In this work, we present our first results on the search for \nbb decay of $^{128}$Te, the Te isotope with the second highest natural isotopic abundance. We find no evidence for this decay, and using a Bayesian analysis we set a lower limit on the $^{128}$Te \nbb decay half-life of T$_{1/2} > 3.6 \times 10^{24}$ yr (90\% CI). This represents the most stringent limit on the half-life of this isotope, improving by over a factor 30 the previous direct search results, and exceeding those from geochemical experiments for the first time.