Paleo-detectors: Searching for dark matter with ancient minerals

We explore paleo-detectors as an approach to the direct detection of weakly interacting massive particle (WIMP) dark matter radically different from conventional detectors. Instead of instrumenting a (large) target mass in a laboratory in order to observe WIMP-induced nuclear recoils in real time, the approach is to examine ancient minerals for traces of WIMP-nucleus interactions recorded over timescales as large as 1 Gyr. Here, we discuss the paleo-detector proposal in detail, including background sources and possible target materials. In order to suppress backgrounds induced by radioactive contaminants such as uranium, we propose to use minerals found in marine evaporites or in ultrabasic rocks. We estimate the sensitivity of paleo-detectors to spin-independent and spin-dependent WIMP-nucleus interactions. The sensitivity to low-mass WIMPs with masses $m_{\chi }\lesssim 10\mathrm{GeV}$ extends to WIMP-nucleon cross sections many orders of magnitude smaller than current upper limits. For heavier WIMPs with masses $m_{\chi }\gtrsim 30\mathrm{GeV}$ cross sections a factor of a few to $\sim 100$ smaller than current upper limits can be probed by paleo-detectors.

Figure 1

Top: Track length $x_T$ as a function of nuclear recoil energy $E_R$ for the different target nuclei in nchwaningite [${\mathrm{Mn}}_2^{2+}{\mathrm{SiO}}_3(\mathrm{OH}{)}_2·({\mathrm{H}}_2\mathrm{O})$] calculated with SRIM. Bottom: Relative difference of $x_T^{\mathrm{ana}}(E_R)$ from the semianalytic calculation and $x_T^{\mathrm{SRIM}}$ calculated with SRIM. Note that for hydrogen the relative difference is rescaled by a factor $1/10$. For recoil energies outside of $0.1\mathrm{keV}\lesssim E_R\lesssim 100\mathrm{keV}$ the differences between the semianalytic calculation and the SRIM results become sizable. Further, the two computations differ widely for low-$Z$ nuclei such as hydrogen. As discussed further in the text, this stems from the semianalytic calculation being matched to experimental data only for larger-$Z$ nuclei and recoil energies $0.1\mathrm{keV}\lesssim E_R\lesssim 100\mathrm{keV}$, while the SRIM results describe experimental data well for larger/smaller recoil energies and a larger variety of nuclei.

Figure 2

Track length spectra from recoiling nuclei in halite (NaCl; top left), epsomite [$\mathrm{Mg}({\mathrm{SO}}_4)·7({\mathrm{H}}_2\mathrm{O})$; top right], olivine [${\mathrm{Mg}}_{1.6}{\mathrm{Fe}}_{0.4}^{2+}({\mathrm{SiO}}_4)$; bottom left], and nickelbischofite [${\mathrm{NiCl}}_2·6({\mathrm{H}}_2\mathrm{O})$; bottom right] induced by the neutrino ($\nu$) and neutron ($n$) background and WIMPs with $m_{\chi }=\{5,50,500\}\mathrm{GeV}$, assuming ${\sigma }_p^{\mathrm{SI}}={10}^{-45}{\mathrm{cm}}^2$. The vertical gray line indicates the track length of 72 keV ${}^{234}\mathrm{Th}$ nuclei from $({}^{238}\mathrm{U}\to {}^{234}\mathrm{Th}+\alpha )$ decays. Halite and epsomite are MEs for which we assume a ${}^{238}\mathrm{U}$ concentration of $C^{238}=0.01\mathrm{ppb}$ in weight while for the UBRs olivine and nickelbischofite we assume $C^{238}=0.1\mathrm{ppb}$. See Sec. 4 for a discussion of the background sources.

Figure 3

Binned recoil spectra (upper panels) and ratio of signal ($S$) to background ($B$) events per bin (lower panels) in epsomite [$\mathrm{Mg}({\mathrm{SO}}_4)·7({\mathrm{H}}_2\mathrm{O})$], assuming an exposure of $0.01\mathrm{kg}\mathrm{Myr}$ and a ${}^{238}\mathrm{U}$ concentration of $C^{238}=0.01\mathrm{ppb}$ in weight. The colored lines are for WIMPs with (5, 10, 15, 50) GeV mass assuming a WIMP-nucleon cross section of ${\sigma }_n^{\mathrm{SI}}={10}^{-42}{\mathrm{cm}}^2$ as indicated in the legend. Upper panels: The solid, dashed, and dash-dotted black lines are for the neutrino ($\nu$), neutron ($n$), and single-$\alpha$ ($1\alpha$) induced background spectra, respectively. The gray shaded bands around the respective lines indicate the statistical and systematic errors, added in quadrature, of the respective backgrounds. Note that the uncertainty bands of multiple backgrounds overlap where the shaded area appears darker. Lower panels: Ratio of signal ($S$) to total background ($B$) events per bin. The gray shaded area indicates the relative uncertainty of the total background per bin, i.e., the ratio of the (quadratic sum of the statistical and systematic errors of all components)/(sum of all background events) per bin. The signal-to-noise ratio, as defined in Eq. (32), per bin is obtained by dividing $S/B$ for the respective signal with the relative uncertainty of the background. The left panels show spectra calculated with low-$Z$ tracks, i.e., under the assumption that tracks from low-$Z$ nuclei, including hydrogen, are visible. Thus, the single-$\alpha$ induced background can be rejected based on the appearance of the $\alpha$-tracks. The spectra in the right panels are calculated without low-$Z$ tracks. Thus, we assume that low-$Z$ nuclei such as hydrogen and helium ($\alpha$-particles) do not leave visible tracks. Hence, the monochromatic ${}^{234}\mathrm{Th}$ recoils from the single-$\alpha$ background appear as broadened spectra due to the finite track length resolution.

Figure 4

Same as Fig. 3 but for an exposure of $100\mathrm{kg}\mathrm{Myr}$ and assuming a track length resolution of ${\sigma }_x=15\mathrm{nm}$. WIMP signal are shown for masses of (5, 50, 500, 5000) GeV and assuming WIMP-nucleon cross sections of $({10}^{-42},{10}^{-47},{10}^{-46},{10}^{-47}){\mathrm{cm}}^2$, respectively. Note that the bin-width is 10 nm instead of 1 nm in Fig. 3 and that the scales of the axes are different.

Figure 5

Sensitivity projection for spin-independent (SI) WIMP-nucleon scattering cross sections. The different colors are for different target materials: Three examples of MEs, halite (NaCl), gypsum [$\mathrm{Ca}({\mathrm{SO}}_4)·2({\mathrm{H}}_2\mathrm{O})$], and epsomite [$\mathrm{Mg}({\mathrm{SO}}_4)·7({\mathrm{H}}_2\mathrm{O})$] and three examples of UBRs, olivine [${\mathrm{Mg}}_{1.6}{\mathrm{Fe}}_{0.4}^{2+}({\mathrm{SiO}}_4)$], nchwaningite [${\mathrm{Mn}}_2^{2+}{\mathrm{SiO}}_3(\mathrm{OH}{)}_2·({\mathrm{H}}_2\mathrm{O})$], and nickelbischofite [${\mathrm{NiCl}}_2·6({\mathrm{H}}_2\mathrm{O})$]. For reference, the light gray line indicates the conventional neutrino floor for Xe direct detection experiments [134]. The shaded area shows current direct detection limits [5, 9, 11, 12]. For the left (right) panels we assume a track length resolution of ${\sigma }_x=1\mathrm{nm}$ (${\sigma }_x=15\mathrm{nm}$) and an exposure of $ϵ=0.01\mathrm{kg}\mathrm{Myr}$ ($ϵ=100\mathrm{kg}\mathrm{Myr}$). The top panels are for the low-$Z$ tracks scenario where we include tracks from all nuclei. The bottom panels are for the without low-$Z$ tracks scenario, for which we assume only tracks with $Z\ge 3$ to give rise to reconstructible tracks. We use ${}^{238}\mathrm{U}$ concentrations of $C^{238}=0.01\mathrm{ppb}$ in weight for MEs and $C^{238}=0.1\mathrm{ppb}$ for UBRs.

Figure 6

Same as Fig. 5 but for SD scattering assuming neutron-only couplings. We show three examples of MEs: cattiite [${\mathrm{Mg}}_{2.92}{\mathrm{Fe}}_{0.01}({\mathrm{PO}}_4{)}_{2.01}·22.05({\mathrm{H}}_2\mathrm{O})$], epsomite [$\mathrm{Mg}({\mathrm{SO}}_4)·7({\mathrm{H}}_2\mathrm{O})$], and mirabilite [${\mathrm{Na}}_2({\mathrm{SO}}_4)·10({\mathrm{H}}_2\mathrm{O})$] and three examples of UBRs: baddeleyite (${\mathrm{ZrO}}_2$), nickelbischofite [${\mathrm{NiCl}}_2·6({\mathrm{H}}_2\mathrm{O})$], and phlogopite [${\mathrm{KMg}}_3{\mathrm{AlSi}}_3{\mathrm{O}}_{10}\mathrm{F}(\mathrm{OH})$]. As before, we assume ${}^{238}\mathrm{U}$ concentrations of $C^{238}=0.01\mathrm{ppb}$ in weight for MEs and $C^{238}=0.1\mathrm{ppb}$ for the UBRs baddeleyite and nickelbischofite. For phlogopite, we assume $C^{238}=0.01\mathrm{ppb}$, since large chunks of phlogopite with linear dimension of order 1m and $C^{238}\lesssim 0.01\mathrm{ppb}$ have been found in natural deposits [135]. The shaded area shows current upper limits from direct detection experiments [7, 136], and the light gray line indicates the neutrino-floor for SD neutron-only interactions in Xe [137]. Note that the lines corresponding to cattiite and epsomite overlap for a wide range of WIMP masses in all panels shown. In the top-right panel the lines for cattiite, epsomite, and phlogopite overlap for $m_{\chi }\gtrsim 30\mathrm{GeV}$.

Figure 7

Same as Fig. 5 but for SD scattering assuming proton-only couplings. We show three example of MEs: borax [${\mathrm{Na}}_2({\mathrm{B}}_4{\mathrm{O}}_5)(\mathrm{OH}{)}_4·8({\mathrm{H}}_2\mathrm{O})$], epsomite [$\mathrm{Mg}({\mathrm{SO}}_4)·7({\mathrm{H}}_2\mathrm{O})$], and mirabilite [${\mathrm{Na}}_2({\mathrm{SO}}_4)·10({\mathrm{H}}_2\mathrm{O})$] and three examples of UBRs: nchwaningite [${\mathrm{Mn}}_2^{2+}{\mathrm{SiO}}_3(\mathrm{OH}{)}_2·({\mathrm{H}}_2\mathrm{O})$], nickelbischofite [${\mathrm{NiCl}}_2·6({\mathrm{H}}_2\mathrm{O})$], and phlogopite [${\mathrm{KMg}}_3{\mathrm{AlSi}}_3{\mathrm{O}}_{10}\mathrm{F}(\mathrm{OH})$]. As before, we assume ${}^{238}\mathrm{U}$ concentrations of $C^{238}=0.01\mathrm{ppb}$ in weight for MEs and $C^{238}=0.1\mathrm{ppb}$ for the UBRs nchwaningite and nickelbischofite. For phlogopite, we assume $C^{238}=0.01\mathrm{ppb}$, since large samples of phlogopite with such concentrations have been found in natural deposits [135]. The shaded area shows current upper limits from direct detection experiments [6, 138], and the light gray line indicates the neutrino-floor for SD neutron-only interactions in ${\mathrm{C}}_3{\mathrm{F}}_8$ [137].