We collected 19.4 days of data from four 750 g TeO2 bolometers, and in three of them we were able to set the energy threshold around 3 keV using a new analysis technique. We found a background rate ranging from 25 cpd/keV/kg at 3 keV to 2 cpd/keV/kg at 25 keV, and a peak at 4.7 keV. The origin of this peak is presently unknown, but its presence is confirmed by a reanalysis of 62.7 kg.days of data from the finished CUORICINO experiment. Finally, we report the expected sensitivities of the CUORE0 (52 bolometers) and CUORE (988 bolometers) experiments to a WIMP annual modulation signal.
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