Dark matter spin determination with directional direct detection experiments

If dark matter has spin 0, only two WIMP-nucleon interaction operators can arise as leading operators from the nonrelativistic reduction of renormalizable single-mediator models for dark matter-quark interactions. Based on this crucial observation, we show that about 100 signal events at next generation directional detection experiments can be enough to enable a $2\sigma$ rejection of the spin 0 dark matter hypothesis in favor of alternative hypotheses where the dark matter particle has spin $1/2$ or 1. In this context, directional sensitivity is crucial since anisotropy patterns in the sphere of nuclear recoil directions depend on the spin of the dark matter particle. For comparison, about 100 signal events are expected in a ${\mathrm{CF}}_4$ detector operating at a pressure of 30 torr with an exposure of approximately 26,000 cubic-meter-detector days for WIMPs of 100 GeV mass and a WIMP-fluorine scattering cross section of 0.25 pb. Comparable exposures require an array of cubic meter time projection chamber detectors.

Figure 1

Left panel. Normalized angular distribution of signal events as a function of the nuclear recoil direction for selected WIMP-nucleon interactions. For spin 0 WIMPs, most of the nuclear recoils are expected at $\cos \theta =-1$, i.e., in a direction opposite to the Earth’s motion in the galactic rest frame. For WIMP-nucleon interactions which are illustrative for spin 1 or spin $1/2$ dark matter, most of the nuclear recoil events are expected in rings around $\cos \theta =-1$. Right panel. Normalized energy spectrum of signal events as a function of the nuclear recoil energy for selected WIMP-nucleon interactions.

Figure 2

Mollweide projection of 1000 nuclear recoil events simulated under the ${\mathcal{H}}_5^{s=1}$ (left panel) and ${\mathcal{H}}_7^{s=1/2}$ (right panel) hypotheses. The sphere of nuclear recoil direction has been discretized according to HEALPix’s pixelization scheme. In the simulation, we have assumed $N_{\mathrm{pix}}=768$ pixels. The color code follows the number of recoil events per pixel.

Figure 3

Probability density functions times $N_S$: $N_{S}f(q_0|{\mathit{d}}_{{\mathcal{H}}_1^{s=0}})$ in left panel and $N_{S}f(q_0|{\mathit{d}}_{{\mathcal{H}}_{10}^{s=0}})$ in the right panel. Histograms have been obtained from 10000 pseudo-experiments characterized by $N_S=1000$ and ${\mathcal{H}}_A={\mathcal{H}}_7^{s=1/2}$. Nuclear recoil energies and directions have been simulated as explained in Sec. 3. For illustrative purposes, a fitting distribution has been superimposed to the histograms.

Figure 4

Statistical significance with which nuclear recoil energies and directions, $\mathit{d}$, simulated under the hypothesis ${\mathcal{H}}_5^{s=1}$ (left panel) and ${\mathcal{H}}_7^{s=1/2}$ (right panel) allow to reject the hypotheses ${\mathcal{H}}_1^{s=0}$ (blue curve) and ${\mathcal{H}}_{10}^{s=0}$ (green curve) as a function of the number of signal events $N_S$. For values of $N_S$ such that both ${\mathcal{H}}_1^{s=0}$ and ${\mathcal{H}}_{10}^{s=0}$ can be rejected, the spin 0 WIMP hypothesis can also be rejected. To each curve in the figure, we have associated shaded binomial error bands, i.e. $\mathrm{\Delta }p=\sqrt{p(1-p)/N}$, with $N=10000$.

Figure 5

Same as for Fig. 4, but now with $E_{\mathrm{th}}=5\mathrm{keV}$ instead of $E_{\mathrm{th}}=20\mathrm{keV}$.

Figure 6

Same as for Fig. 4, but now with: $E_{\mathrm{th}}=5\mathrm{keV}$, $E_{\max }=50\mathrm{keV}$ and no angular information (left panel); $E_{\mathrm{th}}=50\mathrm{keV}$, $E_{\max }=100\mathrm{keV}$ and angular information (right panel).