Probing light WIMPs with directional detection experiments

Ben Morgan and Anne M. Green

Phys. Rev. D 86, 083544 – Published 31 October 2012

Abstract

The CoGeNT and CRESST WIMP direct detection experiments have recently observed excesses of nuclear recoil events, while the DAMA/LIBRA experiment has a long-standing annual modulation signal. It has been suggested that these excesses may be due to light masses of $m_{χ} \sim 5 - 10 GeV$ , weakly interacting massive particles (WIMPs). The Earth’s motion with respect to the Galactic rest frame leads to a directional dependence in the WIMP scattering rate, providing a powerful signal of the Galactic origin of any recoil excess. We investigate whether direct detection experiments with directional sensitivity have the potential to observe this anisotropic scattering rate with the elastically scattering light WIMPs proposed to explain the observed excesses. We find that the number of recoils required to detect an anisotropic signal from light WIMPs at $5 σ$ significance varies from 7 to more than 190 over the set of target nuclei and energy thresholds expected for directional detectors. Smaller numbers arise from configurations where the detector is only sensitive to recoils from the highest-speed, and hence most anisotropic, WIMPs. However, the event rate above the threshold is very small in these cases, leading to the need for large experimental exposures to accumulate even a small number of events. To account for this sensitivity to the tail of the WIMP velocity distribution, whose shape is not well known, we consider two exemplar halo models spanning the range of possibilities. We also note that for an accurate calculation, the Earth’s orbital speed must be averaged over. We find that the exposures required to detect 10 GeV WIMPs at a WIMP-proton cross section of $10^{- 4} pb$ are of order $10^{3} kg day$ for a 20 keV energy threshold, within reach of planned directional detectors. Lower WIMP masses require higher exposures and/or lower energy thresholds for detection.

Received 27 August 2012

DOI:https://doi.org/10.1103/PhysRevD.86.083544

Authors & Affiliations

Ben Morgan¹ and Anne M. Green²

¹Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
²School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 86, Iss. 8 — 15 October 2012

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The minimum WIMP speed, $v_{\min }$ , which can cause a recoil of energy $E$ for ${}^{3}{He}$ (solid), C (dotted), F (short dashed), and S (long dashed) nuclei for $m_{χ} = 5$ and 10 GeV (top and bottom curves in each case, respectively). The horizontal dot-dashed lines show the maximum WIMP speeds in the lab, $v_{χ}^{\max } \approx v_{esc} + 248 km s^{- 1}$ , corresponding to the 90% upper and lower confidence limits on the escape speed from RAVE, $v_{esc}^{\max } = 608 km s^{- 1}$ and $v_{esc}^{\min } = 498 km s^{- 1}$ .Reuse & Permissions
Figure 2
The differential event rates assuming a Maxwellian speed distribution with a sharp cutoff at $v_{esc}^{\max } = 608 km s^{- 1}$ , a cross section $σ_{p} = 10^{- 4} pb$ , and a local WIMP density $ρ = 0.3 GeV {cm}^{- 3}$ , for $He$ (solid), C (dotted), F (short dashed), and S (long dashed) nuclei for $m_{χ} = 5$ , 7.5, and 10 GeV (from top to bottom at $E = 0 keV$ ).Reuse & Permissions
Figure 3
The speed integral $g (v_{\min })$ relative to that for the Maxwellian distribution, with a sharp cutoff at $v_{esc}^{\max } = 608 km s^{- 1}$ , including averaging over the Earth’s orbit. The solid line is for the $f (v)$ of Lisanti et al. [Eq. (4)], with $v_{esc}^{\min } = 498 km s^{- 1}$ , including the Earth’s orbit. The dotted and dashed lines are for the Maxwellian and Lisanti et al. distributions, respectively, neglecting the Earth’s orbit.Reuse & Permissions
Figure 4
The exposure required for a $5 σ$ rejection of isotropy as a function of the energy threshold, $E_{th}$ , for ${}^{3}{He}$ (top left), C (top right), F (bottom left), and S (bottom right) nuclei for $m_{χ} = 5$ , 7.5, and 10 GeV (crosses, stars, and triangles, respectively) for the Maxwellian $f (v)$ with a sharp cutoff at $v_{esc}^{\max } = 608 km s^{- 1}$ . Where a symbol is not displayed, the minimum WIMP speed corresponding to the energy threshold, $v_{\min } (E_{th})$ , for this WIMP and target mass combination exceeds the maximum WIMP speed in the lab frame, $v_{χ}^{\max }$ , and hence the event rate is zero.Reuse & Permissions
Figure 5
Same as Fig. 4, but for a S target nucleus only, comparing the exposures required for the $f (v)$ of Lisanti et al. [Eq. (4)] with $v_{esc}^{\min } = 498 km s^{- 1}$ (upper symbols) with those for the Maxwellian $f (v)$ with a sharp cutoff at $v_{esc}^{\max } = 608 km s^{- 1}$ (lower symbols). For $m_{χ} = 7.5 keV$ and $E_{th} = 5 keV$ , the exposures required for the two speed distributions are the same, and hence only one symbol is visible.Reuse & Permissions
Figure 6
Same as Fig. 5, but comparing the exposures required using the Bingham statistic (upper symbols) with those required using the Rayleigh statistic (lower symbols), in both cases for a S target nucleus using a Maxwellian $f (v)$ with a sharp cutoff at $v_{esc}^{\max } = 608 km s^{- 1}$ . For $m_{χ} = 10 GeV$ and $E_{th} = 5 keV$ , we have only been able to place a lower bound on the number of events—and hence the exposure—required with the Bingham statistic.Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology