Lawrence Berkeley National Laboratory

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 $\Gamma_\text{0$\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.