Terrestrial effects on dark matter-electron scattering experiments

A well-studied possibility is that dark matter may reside in a sector secluded from the Standard Model, except for the so-called photon portal: kinetic mixing between the ordinary and dark photons. Such interactions can be probed in dark matter direct detection experiments, and new experimental techniques involving detection of dark matter–electron scattering offer new sensitivity to sub-GeV dark matter. Typically however it is implicitly assumed that the dark matter is not altered as it traverses the Earth to arrive at the detector. In this paper we study in detail the effects of terrestrial stopping on dark photon models of dark matter, and find that they significantly reduce the sensitivity of XENON10 and DAMIC. In particular we find that XENON10 only excludes masses in the range (5–3000) MeV while DAMIC only probes (20–50) MeV. Their corresponding cross section sensitivity is reduced to a window of cross sections between $(5\times {10}^{-38}–{10}^{-30}){\mathrm{cm}}^2$ for XENON10 and a small window around $\sim {10}^{-31}{\mathrm{cm}}^2$ for DAMIC. We also examine implications for a future DAMIC run.

Figure 1

Flowchart of the MC simulation algorithm.

Figure 2

Example trajectories ($z$-component only) as a function of the number of scattering events. The depth is 1400 m, corresponding to the underground depth of the experimental facilities of the LNGS. The DM-proton scattering cross section is ${\sigma }_p\approx {10}^{-28}{\mathrm{cm}}^2$, the critical value for $m_X=5\mathrm{MeV}$. For further description we refer to the text.

Figure 3

Comparison of the analytical and numerical description of energy loss due to elastic scatterings on oxygen nuclei for ${\sigma }_p={10}^{-32}{\mathrm{cm}}^2$ and $d=10\mathrm{km}$. The upper panel shows the average energy loss as a function of $m_X$ in the MC simulations compared to the analytic prediction. The lower panel shows the relative deviations between the two.

Figure 4

XENON and DAMIC constraints including the effects of nuclear stopping. The estimated DAMIC limits for the 2012 data and for the projection have been taken from Fig. 1 of [11]. The $11e^{-}$ and $2e^{-}$ are the experiments’ thresholds, the minimal number of electron-hole pairs, which lead to a detection. However they also correspond directly to certain energy thresholds.