Measurement of the directional sensitivity of DMTPC detectors

The Dark Matter Time Projection Chamber (DMTPC) is a direction-sensitive detector designed to measure the direction of recoiling $^{19}$F and $^{12}$C nuclei in low-pressure CF$_4$ gas using optical and charge readout systems. In this paper, we employ measurements from two DMTPC detectors, with operating pressures of 30-60 torr, to develop and validate a model of the directional response and performance of such detectors as a function of recoil energy. Using our model as a benchmark, we formulate the necessary specifications for a scalable directional detector with sensitivity comparable to that of current-generation counting (non-directional) experiments, which measure only recoil energy. Assuming the performance of existing DMTPC detectors, as well as current limits on the spin-dependent WIMP-nucleus cross section, we find that a 10-20 kg scale direction-sensitive detector is capable of correlating the measured direction of nuclear recoils with the predicted direction of incident dark matter particles and providing decisive (3$\sigma$) confirmation that a candidate signal from a non-directional experiment was indeed induced by elastic scattering of dark matter particles off of target nuclei.