Directional statistics for realistic weakly interacting massive particle direct detection experiments

The direction dependence of the event rate in WIMP direct detection experiments provides a powerful tool for distinguishing WIMP events from potential backgrounds. We use a variety of (nonparametric) statistical tests to examine the number of events required to distinguish a WIMP signal from an isotropic background when the uncertainty in the reconstruction of the nuclear recoil direction is included in the calculation of the expected signal. We consider a range of models for the Milky Way halo, and also study rotational symmetry tests aimed at detecting nonsphericity/isotropy of the Milky Way halo. Finally we examine ways of detecting tidal streams of WIMPs. We find that if the senses of the recoils are known then of order ten events will be sufficient to distinguish a WIMP signal from an isotropic background for all of the halo models considered, with the uncertainties in reconstructing the recoil direction only mildly increasing the required number of events. If the senses of the recoils are not known the number of events required is an order of magnitude larger, with a large variation between halo models, and the recoil resolution is now an important factor. The rotational symmetry tests require of order a thousand events to distinguish between spherical and significantly triaxial halos, however a deviation of the peak recoil direction from the direction of the solar motion due to a tidal stream could be detected with of order a hundred events, regardless of whether the sense of the recoils is known.

Figure 1

Simulated pixel readout in the xy plane from a 40 keV recoil. The strength of the signal in each pixel is obtained by integrating the voltage pulse for that pixel. The actual recoil track is shown by the solid line. The ellipse results from the moment analysis and its long axis gives the reconstructed direction.

Figure 2

Time averaged WIMP flux (top) and S Recoil rate above 20 keV (bottom) in Galactic ($l$, $b$) coordinates for halo model 1 and ${\rho }_0=0.3{\mathrm{GeV}\mathrm{cm}}^{-3}$, $m_{\chi }=100\mathrm{GeV}$, and ${\sigma }_{\chi p}={10}^{-6}\mathrm{pb}$.

Figure 3

As Fig. 2 for model 3 (logarithmic ellipsoidal model with $p=0.9$, $q=0.8$, and $\beta =0.4$).

Figure 4

As Fig. 2 for model 12 (standard halo model with a 25% contribution to the local WIMP density from a tidal stream with properties given in Sec. 2a2).

Figure 5

Variation of the angle (in degrees) between the mean recoil directions of the standard halo and the standard halo plus a tidal stream with ${\overrightarrow{v}}_{\mathrm{str}}=(-65.0,135.0,-250.0){\mathrm{km}\mathrm{s}}^{-1}$ function of the fraction of the local WIMP density contributed by the stream, ${\rho }_{\mathrm{str}}/{\rho }_0$.