The Search for Neutrinoless Double Beta Decay in $^{130}$Te With CUORE-0

This thesis describes the design, operation and results of anexperimental 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 particlephysics and our understanding of the Universe. Its discovery woulddemonstrate the violation of lepton number and imply that neutrinosare Majorana fermions and therefore their own anti-particles. Combinedwith other experimental results, the discovery of 0$\nu\beta\beta$ could alsohave implications for understanding the absolute neutrino mass scaleas well as the presently unknown neutrino mass hierarchy.The CUORE experiment is a ton-scale search for 0$\nu\beta\beta$ in $^{130}$Teexpected to begin operation in late 2015. The first stage ofthis experiment is a smaller 39-kg active-mass detector called CUORE-0. Thisdetector contains 11~kg of $^{130}$Te and operates in the LaboratoriNazionali 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 collectedbetween 2013 -- 2015. We see no evidence of 0$\nu\beta\beta$ and place anupper 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 theThree 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 theseresults with the 19.75~kg$\cdot$yr $^{130}$Te exposure from CUORE-0ino, we placethe 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 presentnuclear matrix element calculations for $^{130}$Te, this resultcorresponds to a 90\% upper limit range on the effective Majoranamass of $m_{\beta\beta}<250-710$~meV