CUORE---the Cryogenic Underground Observatory for Rare Events---is an experiment searching for the neutrinoless double-beta ($0\nu\beta\beta$) decay of $^{130}$Te, based at the Laboratori Nazionali del Gran Sasso in Italy. The detector consists of 988 5$\times$5$\times$5 cm$^3$ TeO$_2$ crystals operated as bolometers at temperatures of $\sim$10 mK inside the world's largest and most powerful dilution refrigerator. CUORE began physics data collection in the spring of 2017, and has recently released its first limit on the $0\nu\beta\beta$ decay half-life of $^{130}$Te from 24 kg $\cdot$ y isotope exposure ($\sim$2 months live time). This result---T$^{0\nu}_{1/2} > 1.5 \cdot 10^{25}$ y (Bayesian) and T$^{0\nu}_{1/2} > 2.3 \cdot 10^{25}$ y (Frequentist) at $90 \%$ C.L.---is the most stringent to date and, together with two alternative analyses necessary to calculate it, forms the centerpiece of this thesis. In the future, with five years of live time, CUORE is projected to reach a median sensitivity of $9 \cdot 10^{25}$ y on this half-life. Besides the main physics conclusions, in this work I present an analysis modeling the spectral line shape of the bolometer, which is used for constructing the region of interest fit PDF. Additionally, I discuss the major CUORE hardware projects to which I have contributed in a significant way. Specifically, these are our world-leading cryostat, a cryogenic feedback temperature control system, a radon-free detector installation environment, and a room temperature detector calibration system.

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This dissertation describes an experimental search for neutrinoless double beta (0νββ) decay of ^{130}Te. An observation of 0νββ decay would establish that neutrinos are Majorana fermions and would constrain the neutrino mass scale. The data analyzed were collected by two bolometric experiments: CUORICINO and an R&D experiment for CUORE known as the Three Towers Test. Both experiments utilized arrays of TeO_{2} crystals operated as bolometers at ∼10 mK in a dilution refrigerator. The bolometers measured the energy deposited by particle interactions in the crystals by recording the induced change in crystal temperature. Between the two experiments, there were 81 TeO_{2} bolometers used in the analysis, each of which was an independent detector of nuclear decays as well as a source of ^{130}Te. The experiments were conducted underground at a depth of about 3300 meters water equivalent in Hall A of the Laboratori Nazionali del Gran Sasso in Assergi, Italy, in order to shield the detectors from cosmic rays. The data analyzed represent an exposure of 19.9 kg · y of ^{130}Te (18.6 kg · y from CUORICINO and 1.3 kg · y from the Three Towers Test). In addition to the combined analysis of the two experiments, an analysis of CUORICINO data alone is presented in order to compare with an independent analysis being carried out by collaborators at the Univerity of Milano-Bicocca.

No signal due to 0νββ decay is observed, and therefore a limit on the partial half-life for the decay is set. From a simultaneous fit to the 81 independent detectors, the rate of 0νββ decay of ^{130}Te is measured to be Γ^{0νββ}(^{130}Te) = (-0.6 ± 1.4 (stat.) ± 0.4 (syst.)) × 10^{-25} y^{-1}, which corresponds to a lower limit on the partial half-life for 0νββ decay of ^{130}Te of T_{1/2}^{0νββ}(^{130}Te) > 3.0 × 10^{24} y (90% C.L.). Converting the half-life limit to an upper limit on the effective Majorana neutrino mass, m_{ββ}, using a set of recent nuclear matrix element calculations results in m_{ββ} < 0.25–0.68 eV (90% C.L.), where the range reflects the spread of calculated nuclear matrix element values. These results disagree by at least 1.2σ, depending on the nuclear matrix element calculation, with a claim of observation of 0νββ decay of ^{76}Ge, assuming that the dominant mechanism driving 0νββ decay is the exchange of light Majorana neutrinos.

This thesis describes the design, operation and results of an

experimental search for neutrinoless double beta decay (0$\nu\beta\beta$) of

$^{130}$Te using the CUORE-0 detector.

The discovery of 0$\nu\beta\beta$ would have profound implications for particle

physics and our understanding of the Universe. Its discovery would

demonstrate the violation of lepton number and imply that neutrinos

are Majorana fermions and therefore their own anti-particles. Combined

with other experimental results, the discovery of 0$\nu\beta\beta$ could also

have implications for understanding the absolute neutrino mass scale

as well as the presently unknown neutrino mass hierarchy.

The CUORE experiment is a ton-scale search for 0$\nu\beta\beta$ in $^{130}$Te

expected to begin operation in late 2015. The first stage of

this experiment is a smaller 39-kg active-mass detector called CUORE-0. This

detector contains 11~kg of $^{130}$Te and operates in the Laboratori

Nazionali del Gran Sasso lab in Italy from 2013 -- 2015.

The results presented here are based on a $^\text{nat}$TeO$_2$

exposure of 35.2~kg$\cdot$yr, or 9.8~kg$\cdot$yr exposure of $^{130}$Te collected

between 2013 -- 2015. We see no evidence of 0$\nu\beta\beta$ and place an

upper limit on the 0$\nu\beta\beta$ decay rate of

$\Gamma_{0\nu\beta\beta}<0.25\times10^{-24}$~yr$^{-1}$ (90\% C.L.),

corresponding to a lower limit on the half-life of

$T^{0\nu}_{1/2}>2.8\times10^{24}$~yr (90\% C.L.).

We combine the present result with the results of previous searches in

$^{130}$Te. Combining it with the 1.2~kg$\cdot$yr $^{130}$Te exposure from the

Three Towers Test run we place a half-life limit of

$T_{1/2}^{0\nu}>3.3\times10^{24}$~yr (90\% C.L.). And combining these

results with the 19.75~kg$\cdot$yr $^{130}$Te exposure from CUORE-0ino, we place

the strongest limit on the 0$\nu\beta\beta$ half-life of $^{130}$Te to date, at

$T^{0\nu}_{1/2}>4.5\times10^{24}$~yr (90\% C.L.). Using the present

nuclear matrix element calculations for $^{130}$Te, this result

corresponds to a 90\% upper limit range on the effective Majorana

mass of $m_{\beta\beta}<250-710$~meV.