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CUORE, an array of 988 TeO$_2$ bolometers, is about to be one of the mostsensitive experiments searching for neutrinoless double-beta decay. Itssensitivity could be further improved by removing the background from $\alpha$radioactivity. A few years ago it has been pointed out that the signal from$\beta$s can be tagged by detecting the emitted Cherenkov light, which is notproduced by $\alpha$s. In this paper we confirm this possibility. For the firsttime we measured the Cherenkov light emitted by a CUORE crystal, and found itto be 100 eV at the $Q$-value of the decay. To completely reject the $\alpha$background, we compute that one needs light detectors with baseline noise below20 eV RMS, a value which is 3-4 times smaller than the average noise of thebolometric light detectors we are using. We point out that an improved lightdetector technology must be developed to obtain TeO$_2$ bolometric experimentsable to probe the inverted hierarchy of neutrino masses.

TeO$_2$ bolometers with Cherenkov signal tagging: towards next-generation neutrinoless double beta decay experiments