Directional Sensitivity in Light-Mass Dark Matter Searches with Single-Electron-Resolution Ionization Detectors

We propose a method using solid state detectors with directional sensitivity to dark matter interactions to detect low-mass weakly interacting massive particles (WIMPs) originating from galactic sources. In spite of a large body of literature for high-mass WIMP detectors with directional sensitivity, no available technique exists to cover WIMPs in the mass range $<1\mathrm{GeV}/c^2$. We argue that single-electron-resolution semiconductor detectors allow for directional sensitivity once properly calibrated. We examine the commonly used semiconductor material response to these low-mass WIMP interactions.

Figure 1

Threshold displacement energy surface in different crystal directions in Ge (top) and Si (bottom) determined from classical MD simulations illustrated with a Mollweide projection. These plots represent the averages over the eight threshold surface data sets. Darker regions correspond to a lower energy threshold and, hence, a higher differential rate (see Fig. 2).

Figure 2

(Top) Normalized integrated rate with respect to the mean over one day for a $300\mathrm{MeV}/c^2$ WIMP at the SNOLAB site. (Bottom) Angular distribution of the differential rate per steradian for a nucleon cross section of ${10}^{-39}{\mathrm{cm}}^2$ over one day for a $300\mathrm{MeV}/c^2$ WIMP at the SNOLAB site. Each angle plot corresponds to a local extremum of the integrated rate.

Figure 3

Angular distribution of the differential rate per steradian for a Ge detector assuming a nucleon cross section of ${10}^{-39}{\mathrm{cm}}^2$ for several WIMP masses at 4:00 on September 6, 2015. As the WIMP mass increases, the differential rate angular spread increases due to the Maxwell-Boltzmann velocity distribution and hard-sphere scattering acting in conjunction with the energy thresholds (see Fig. 1).

Figure 4

Normalized rms of the rate modulation (left axis, thin lines) and mean rate (right axis, thick lines) as a function of the dark matter mass for Ge (blue lines) and Si (red lines). A WIMP-nucleon cross section of ${10}^{-39}{\mathrm{cm}}^2$ is assumed. The normalized rms modulation error is given by the shaded regions. The mean rate error is negligible and consequently not included. The thick and thin dashed curves show the normalized rms modulation and mean rate, respectively, given thresholds half of those used for the solid curves.