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.
