Data taken during the final shallow-site run of the first tower of the Cryogenic Dark Matter Search (CDMS II) detectors have been reanalyzed with improved sensitivity to small energy depositions. Four ~224 g germanium and two ~105 g silicon detectors were operated at the Stanford Underground Facility (SUF) between December 2001 and June 2002, yielding 118 live days of raw exposure. Three of the germanium and both silicon detectors were analyzed with a new low-threshold technique, making it possible to lower the germanium and silicon analysis thresholds down to the actual trigger thresholds of ~1 keV and ~2 keV, respectively. Limits on the spin-independent cross section for weakly interacting massive particles (WIMPs) to elastically scatter from nuclei based on these data exclude interesting parameter space for WIMPs with masses below 9 GeV/c^2. Under standard halo assumptions, these data partially exclude parameter space favored by interpretations of the DAMA/LIBRA and CoGeNT experiments data as WIMP signals, and exclude new parameter space for WIMP masses between 3 GeV/c^2 and 4 GeV/c^2.
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