Directional dark matter by polar angle direct detection and application of columnar recombination

We report a systematic study on the directional sensitivity of a direct dark matter detector that detects the polar angle of a recoiling nucleus. A weakly interacting massive particle (WIMP)-mass independent method is used to obtain the sensitivity of a general detector in an isothermal galactic dark matter halo. By using two-dimensional distributions of energy and polar angle, a detector without head-tail information with 6.3 times the statistics is found to achieve the same performance level as a full three-dimensional tracking dark matter detector. Optimum operation orientations are obtained for various experimental configurations, with detectors that are space- or Earth-fixed, have head-tail capability or not, and use energy information or not. Earth-fixed detectors are found to have best sensitivity when the polar axis is oriented at a 45 degree angle from the Earth’s pole. With background contamination that mimics the WIMP signal’s energy distribution, the performance is found to decrease at a rate less than the decrease of signal purity. The WIMP-mass dependence of the performance of a detector with various energy thresholds that uses gaseous xenon as target material is reported. We find that with a $5\times {10}^{-46}{\mathrm{cm}}^2$ spin-independent WIMP-nucleon cross-section and a 30 GeV WIMP, a $770\mathrm{kg}·\mathrm{year}$’s exposure with a polar detector of 10 keV threshold can make a three sigma discovery of directional WIMPs in the isothermal galactic dark matter halo. For a columnar recombination detector, experimental considerations are discussed.

Figure 1

Schematic plot of an Earth-fixed detector shown as a rectangular box.

Figure 2

Median $q$ values on solid markers as a function of cosine of the angle between the detector $z$ axis and the WIMP wind direction for general space-fixed detectors. Head-tail polar and angular only detectors correspond to up and down triangles. Axial polar and angular only detectors correspond to circles and diamonds. The event number for head-tail configuration is 200, different from 50 events for axial configuration, in order to fit in a single plot.

Figure 3

Median $q$ values on open markers as a function of angle ${\theta }_D$ between detector $z$ axis and Earth’s pole, for Earth-fixed detectors. General head-tail polar and angular only detectors with 50 events correspond to up and down triangles. General axial polar and angular only detectors with 200 events correspond to circles and diamonds. For a standard axial xenon detector of 3 keV threshold with 200 observed events, four graphs for WIMP masses of 20, 30, 50 and 100 GeV are shown as blue squares with decreasing sizes. These graphs are fitted using an empirical function $q_{\text{med}}=Q\cos (\alpha ({\theta }_D-{\theta }_D^0))$ that are superimposed as red solid curves for a standard axial xenon detector, and as red dashed and dotted curves for general axial polar and angular only detectors.

Figure 4

Median $q$ values versus numbers of observed events for all detector types in their optimal orientations. Solid squares represent a standard space-fixed axial xenon detector. Other symbol markers are explained in Figs. 2 and 3. The fitted linearly proportional lines are superimposed. Blue dashed lines represent axial xenon detectors configured at 30 GeV WIMP and 3 keV threshold.

Figure 5

Sensitivity ratio over that for pure signal case, as a function of signal purity defined as the ratio of signal component over all events in the data set. For each detector type, data points are normalized to a constant number of signal events. Space- and Earth-fixed polar detectors under axial and head-tail configurations are shown when placed in each one’s optimal orientation.

Figure 6

Median $q$ values as a function of WIMP mass for axial xenon detectors, normalized to 200 events of point interaction. From the top to bottom, the dashed, dotted and dot-dashed lines corresponds to the 3, 10 and 30 keV energy threshold. The best orientations on space-fixed ($\cos {\theta }_0=1$, main plot) and Earth-fixed (${\theta }_D=45°$, inset plot) basis are used.