Beta/gamma and alpha backgrounds in CRESST-II Phase 2

The experiment CRESST-II aims at the detection of dark matter with scintillating CaWO$_4$ crystals operated as cryogenic detectors. Recent results on spin-independent WIMP-nucleon scattering from the CRESST-II Phase 2 allowed to probe a new region of parameter space for WIMP masses below 3 GeV/c$^2$. This sensitivity was achieved after background levels were reduced significantly. We present extensive background studies of a CaWO$_4$ crystal, called TUM40, grown at the Technische Universit\"at M\"unchen. The average beta/gamma rate of 3.51/[kg keV day] (1-40 keV) and the total intrinsic alpha activity from natural decay chains of $3.08\pm0.04$ mBq/kg are the lowest reported for CaWO$_4$ detectors. Contributions from cosmogenic activation, surface-alpha decays, external radiation and intrinsic alpha/beta emitters are investigated in detail. A Monte-Carlo based background decomposition allows to identify the origin of the majority of beta/gamma events in the energy region relevant for dark matter search.