  The most sensitive process able to probe the Majorana nature of neutrinos and
discover Lepton Number Violation is the neutrino-less double beta decay. Thanks
to the excellent energy resolution, efficiency and intrinsic radio-purity,
cryogenic calorimeters are primed for the search for this process. A novel
approach able to improve the sensitivity of the current experiments is the
rejection of $\alpha$ interactions, that represents the dominant background
source. In TeO$_2$ calorimeters, $\alpha$ particles can be tagged as, in
contrast to electrons, they do not emit Cherenkov light. Nevertheless, the very
low amount of detected Cherenkov light undermines the complete rejection of
$\alpha$ background. In this paper we compare the results obtained in previous
measurements of the TeO$_2$ light yield with a detailed Monte Carlo simulation
able to reproduce the number of Cherenkov photons produced in $\beta/\gamma$
interactions within the calorimeter and their propagation in the experimental
set-up. We demonstrate that the light yield detectable from a
$5\times5\times5$~cm$^{3}$ TeO$_2$ bolometer can be increased by up to 60% by
increasing the surface roughness of the crystal and improving the light
detector design. Moreover, we study the possibility to disentangle $\alpha$,
$\beta$ and $\gamma$ interactions, which represent the ultimate background
source. Unfortunately $\gamma$ rejection is not feasible but $\alpha$ rejection
can be achieved exploiting high sensitivity light detectors.
