First Results from CUORE: A Search for Lepton Number Violation via $0νββ$ Decay of $^130$Te

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 $m_\beta\beta<(140 - 400)$ meV, where the range reflects the nuclear matrix element estimates employed.