Title: First Results from CUORE: A Search for Lepton Number Violation via $0νββ$ Decay of $^{130}$Te,
Abstract: The CUORE experiment, a ton-scale cryogenic bolometer array, recently began
operation at the Laboratori Nazionali del Gran Sasso in Italy. The array
represents a significant advancement in this technology, and in this work we
apply it for the first time to a high-sensitivity search for a
lepton-number--violating process: $^{130}$Te neutrinoless double-beta decay.
Examining a total TeO$_2$ exposure of 86.3 kg$\cdot$yr, characterized by an
effective energy resolution of (7.7 $\pm$ 0.5) keV FWHM and a background in the
region of interest of (0.014 $\pm$ 0.002) counts/(keV$\cdot$kg$\cdot$yr), we
find no evidence for neutrinoless double-beta decay. The median statistical
sensitivity of this search is $7.0\times10^{24}$ yr. Including systematic
uncertainties, we place a lower limit on the decay half-life of
$T^{0\nu}_{1/2}$($^{130}$Te) > $1.3\times 10^{25}$ yr (90% C.L.). Combining
this result with those of two earlier experiments, Cuoricino and CUORE-0, we
find $T^{0\nu}_{1/2}$($^{130}$Te) > $1.5\times 10^{25}$ yr (90% C.L.), which is
the most stringent limit to date on this decay. Interpreting this result as a
limit on the effective Majorana neutrino mass, we find $m_{\beta\beta}<(110 -
520)$ meV, where the range reflects the nuclear matrix element estimates
employed.