Complete event-by-event $\alpha$/$\gamma(\beta)$ separation in a full-size TeO$_2$ CUORE bolometer by simultaneous heat and light detection

The CUORE project began recently a search for neutrinoless double-beta decay ($0\nu\beta\beta$) of $^{130}$Te with a $\mathcal{O}$(1 ton) TeO$_2$ bolometer array. In this experiment, the background suppression relies essentially on passive shielding, material radiopurity and anti-coincidences. The lack of particle identification in CUORE makes $\alpha$ decays at the detector surface the dominant background, at the level of $\sim$0.01 counts/(keV kg y) in the region of interest ($Q$-value of $0\nu\beta\beta$ of the order of 2.5 MeV). In the present work we demonstrate, for the first time with a CUORE-size (5$\times$5$\times$5 cm) TeO$_2$ bolometer and using the same technology as CUORE for the readout of the bolometric signals, an efficient $\alpha$ particle discrimination (99.9\%) with a high acceptance of the $0\nu\beta\beta$ signal (about 96\%). This unprecedented result was possible thanks to the superior performance (10 eV RMS baseline noise) of a Neganov-Luke-assisted germanium bolometer used to detect a tiny (70 eV) light signal dominated by $\gamma$($\beta$)-induced Cherenkov radiation in the TeO$_2$ detector. The obtained results represent a major breakthrough towards the TeO$_2$-based version of CUPID, a ton-scale cryogenic $0\nu\beta\beta$ experiment proposed as a follow-up to CUORE with particle identification.