Projected Sensitivity of Paleo-Detectors to Dark Matter Effective Interactions with Nuclei

Abstract

Paleo-detectors are a proposed experimental technique for direct detection (DD) of dark matter (DM) via the read-out of DM-induced nuclear recoil tracks in natural minerals. The large detector mass required for the sensitivity of conventional DD experiments to rare events is replaced by the exposure of paleo-detectors to DM-induced nuclear recoils over geological timescales. In this paper, we extend previous theoretical predictions for canonical spin-independent coherent and spin-dependent scattering (proportional to $A^2$ and the spin of the nucleus, respectively). We estimate the sensitivity of paleo-detectors to interactions between weakly interacting massive particle (WIMP) DM and nuclei within the framework of a Non-Relativistic Effective Field Theory (NREFT), considering isoscalar couplings to nucleons for both elastic and inelastic scattering. Taking into account cosmogenic, astrophysical and radiogenic backgrounds, we project the 90% confidence-level (CL) upper limits on the isoscalar NREFT coupling constants for both scattering types. We consider representative read-out scenarios and examine several target minerals. The projected sensitivities of paleo-detectors are compared with the 90% CL limits from the XENON100, LUX-ZEPLIN, and PandaX-II experiments, as well as with the 95% Bayesian credible region of the 2D marginalized posterior distribution from SuperCDMS. For DM masses from 1 GeV-10 GeV, paleo-detectors are projected to have sensitivity superior to that of conventional experiments for WIMP-nucleus interactions via all NREFT operators, largely independent of read-out scenario or target mineral. For DM masses from 10 GeV-5 TeV, we find that the sensitivity of paleo-detectors is projected to be comparable to or better than that of conventional experiments for WIMP-nucleus interactions via several NREFT operators, depending on the read-out scenario and target mineral.

Figures (20)

• Figure 1: Differential track production rate $dR/d(\ln x_T)$ for elastic scattering, given per unit exposure and per logarithmic interval in track length, shown as a function of the track length $x_T$ for the spin-independent NREFT operators $\mathcal{O}_{1}^{s}$, $\mathcal{O}_{5}^{s}$, $\mathcal{O}_{8}^{s}$, and $\mathcal{O}_{11}^{s}$ and for a variety of target minerals. We note that $\mathcal{O}^{s}_{1}$ is the standard spin-independent case considered by many direct detection experiments. The calculations assume isoscalar interactions ($c^{p}=c^{n}$). Results are shown for gypsum and halite with ${}^{238}$U concentrations of $10^{-11}\ \mathrm{g/g}$, and for olivine and muscovite with ${}^{238}$U concentrations of $10^{-10}\ \mathrm{g/g}$. The DM mass is fixed at $500\ \mathrm{GeV}/c^{2}$. For comparison, we also show background spectra induced by neutrinos ($\nu$), radiogenic neutrons ($n$), and ${}^{238}\text{U}\to{}^{234}\text{Th}+\alpha$ recoils (${}^{234}\text{Th}$); see Sec. \ref{['background']}. For the normalization of the DM track production spectra, we set the NREFT coupling constants to $(c^{s}_{1}\ m_{v}^{2})^{2}=4\cdot10^{-9}$, $(c^{s}_{5}\ m_{v}^{2})^{2}=2.5$, $(c^{s}_{8}\ m_{v}^{2})^{2}=1.5\cdot10^{-2}$, and $(c^{s}_{11}\ m_{v}^{2})^{2}=5\cdot10^{-6}$, where $m_{v} = 246.2\ \mathrm{GeV}$ denotes the electroweak mass scale. These values are chosen to be compatible with the upper limits from the LUX–ZEPLIN experiment LZ:2023lvz.
• Figure 2: Differential track production rate $dR/d(\ln x_T)$ for inelastic scattering, given per unit exposure and per logarithmic interval in track length, shown as a function of the track length $x_T$ for the spin-independent NREFT operators $\mathcal{O}_{1}^{s}$, $\mathcal{O}_{5}^{s}$, $\mathcal{O}_{8}^{s}$, and $\mathcal{O}_{11}^{s}$ and for a variety of target minerals. The calculations assume isoscalar interactions ($c^{p}=c^{n}$). The DM mass is fixed at $500\ \mathrm{GeV}/c^{2}$. In the left panel, the DM mass splitting is $\delta_{m}=50\ \mathrm{keV}/c^{2}$. The NREFT coupling constants are set to $(c^{s}_{1} m_{v}^{2})^{2}=1.5\cdot10^{-8}$, $(c^{s}_{5} m_{v}^{2})^{2}=5$, $(c^{s}_{8} m_{v}^{2})^{2}=5.6\cdot10^{-2}$, and $(c^{s}_{11} m_{v}^{2})^{2}=1.2\cdot10^{-5}$, where $m_{v}=246.2\ \mathrm{GeV}$ denotes the electroweak mass scale. In the right panel, the DM mass splitting is $\delta_{m}=100\ \mathrm{keV}/c^{2}$. The coupling constants are set to $(c^{s}_{1} m_{v}^{2})^{2}=1.3\cdot10^{-7}$, $(c^{s}_{5} m_{v}^{2})^{2}=1.4\cdot10^{1}$, $(c^{s}_{8} m_{v}^{2})^{2}=3.7\cdot10^{-1}$, and $(c^{s}_{11} m_{v}^{2})^{2}=5.4\cdot10^{-5}$. In both panels, the values for the coupling constants are chosen to be compatible with the upper limits for inelastic WIMP--nucleon scattering from the LUX--ZEPLIN experiment LZ:2023lvz. For comparison, background spectra induced by neutrinos ($\nu$), radiogenic neutrons ($n$), and ${}^{238}\text{U}\to{}^{234}\text{Th}+\alpha$ recoils (${}^{234}\text{Th}$) are also shown; see Sec. \ref{['background']}. Results are presented for gypsum with a ${}^{238}$U concentration of $10^{-11}\,\mathrm{g/g}$.
• Figure 3: Elastic Scattering. Upper panels: track length spectra (number of tracks binned by track length) for the spin–independent NREFT operators $\mathcal{O}^{s}_{1}$, $\mathcal{O}^{s}_{5}$, $\mathcal{O}^{s}_{8}$, and $\mathcal{O}^{s}_{11}$ in gypsum, assuming the case of elastic, isoscalar interactions ($c^{p}=c^{n}$). Note the DM spectra for $\mathcal{O}^{s}_{1}$ (blue line) and $\mathcal{O}^{s}_{8}$ (orange line) are nearly identical in both panels. Left panel: High Resolution (HR) scenario, with a read-out resolution of $\sigma_{x}=1\ \mathrm{nm}$ and a mineral mass of $M=10\ \mathrm{mg}$. The DM mass is set to $m_{\chi}=5\ \mathrm{GeV}/c^{2}$. For the normalization of the DM track production spectra, we set the NREFT coupling constants to $(c^{s}_{1} m_{v}^{2})^{2}=9.5\cdot10^{-3}$, $(c^{s}_{5} m_{v}^{2})^{2}=5.7\cdot10^{8}$, $(c^{s}_{8} m_{v}^{2})^{2}=3.7\cdot10^{4}$, and $(c^{s}_{11} m_{v}^{2})^{2}=4\cdot10^{2}$, where $m_{v}=246.2\ \mathrm{GeV}$ denotes the electroweak mass scale. These values are chosen to be compatible with the upper limits from the SuperCDMS experiment SuperCDMS:2022crd. Right panel: High Exposures (HE) scenario, with $\sigma_{x}=15\ \mathrm{nm}$, $M=100\ \mathrm{g}$, $m_{\chi}=500\ \mathrm{GeV}/c^{2}$, and $(c^{s}_{1} m_{v}^{2})^{2}=4\cdot10^{-9}$, $(c^{s}_{5} m_{v}^{2})^{2}=2.5$, $(c^{s}_{8} m_{v}^{2})^{2}=1.5\cdot10^{-2}$, and $(c^{s}_{11} m_{v}^{2})^{2}=5\cdot10^{-6}$, compatible with the upper limits from the LUX--ZEPLIN experiment LZ:2023lvz. For comparison, background spectra induced by neutrinos ($\nu$), radiogenic neutrons ($n$), and ${}^{238}\text{U}\to{}^{234}\text{Th}+\alpha$ recoils (${}^{234}\text{Th}$) are also shown; see Sec. \ref{['background']}. Here, we include shaded bands around background components, representing the combined statistical (Poisson) and systematic uncertainties in the background predictions. In the HE scenario, these uncertainties are much smaller than the background event rates, so the corresponding bands are extremely narrow and effectively invisible in the plots. Bottom panels: Colored lines show the ratio of signal events from the spin–independent NREFT operators ($S_{i}$) to background events ($B_{i}$) in each bin. The sand–colored band indicates the relative uncertainty ($\delta B_i/B_i$) for the number of background events per bin, such that the ratio of the colored lines to the upper edge of the sand-colored band gives an estimate of the signal-to-noise ratio ($S_i/\delta B_i$) in each bin. Results are presented for gypsum with a ${}^{238}$U concentration of $10^{-11}\,\mathrm{g/g}$. The ratio $S_i/B_i$ is largest at shorter (longer) track lengths for lower (higher) DM masses, where neutrino (neutron) backgrounds dominate, as shown in the left (right) panel.
• Figure 4: Inelastic Scattering. Upper panels: track length spectra (number of tracks binned by track length) for the spin–independent NREFT operators $\mathcal{O}^{s}_{1}$, $\mathcal{O}^{s}_{5}$, $\mathcal{O}^{s}_{8}$, and $\mathcal{O}^{s}_{11}$ in gypsum for the case of inelastic, isoscalar interactions ($c^{p}=c^{n}$), and a DM mass of $m_{\chi}=500\ \mathrm{GeV}/c^{2}$. The HE scenario is considered, with a read-out resolution of $\sigma_{x}=15\ \mathrm{nm}$ and a mineral mass of $M=100\ \mathrm{g}$. In the left panel, the mass splitting is $\delta_{m}=50\ \mathrm{keV}/c^{2}$. The NREFT coupling constants are set to $(c^{s}_{1} m_{v}^{2})^{2}=1.5\cdot10^{-8}$, $(c^{s}_{5} m_{v}^{2})^{2}=5$, $(c^{s}_{8} m_{v}^{2})^{2}=5.6\cdot10^{-2}$, and $(c^{s}_{11} m_{v}^{2})^{2}=1.2\cdot10^{-5}$, where $m_{v}=246.2\ \mathrm{GeV}$ denotes the electroweak mass scale. In the right panel, the mass splitting is $\delta_{m}=100\ \mathrm{keV}/c^{2}$. The coupling constants are set to $(c^{s}_{1} m_{v}^{2})^{2}=1.3\cdot10^{-7}$, $(c^{s}_{5} m_{v}^{2})^{2}=1.4\cdot10^{1}$, $(c^{s}_{8} m_{v}^{2})^{2}=3.7\cdot10^{-1}$, and $(c^{s}_{11} m_{v}^{2})^{2}=5.4\cdot10^{-5}$. In both panels, the values for the coupling constants are chosen to be compatible with the upper limits for inelastic WIMP--nucleon scattering from the LUX--ZEPLIN experiment LZ:2023lvz. For comparison, background spectra induced by neutrinos ($\nu$), radiogenic neutrons ($n$), and ${}^{238}\text{U}\to{}^{234}\text{Th}+\alpha$ recoils (${}^{234}\text{Th}$) are also shown; see Sec. \ref{['background']}. Here, we include shaded bands around background components, representing the combined statistical (Poisson) and systematic uncertainties in the background predictions. Bottom panels: Ratio of signal events from the spin–independent NREFT operators ($S_{i}$) to background events ($B_{i}$) in each bin (colored lines). The sand–colored band indicates the relative uncertainty ($\delta B_i/B_i$) for the number of background events per bin, such that the ratio of the colored lines to the upper edge of the sand-colored band gives an estimate of the signal-to-noise ratio ($S_i/\delta B_i$) in each bin. Results are presented for gypsum with a ${}^{238}$U concentration of $10^{-11}\,\mathrm{g/g}$. The ratio $S_i/B_i$ peaks at track lengths $x_T \sim 100~\mathrm{nm}$ for both mass splittings, $\delta_m = 50~\mathrm{keV}/c^{2}$ (left panel) and $\delta_m = 100~\mathrm{keV}/c^{2}$ (right panel). The signal-to-noise ratio is larger for $\delta_m = 50~\mathrm{keV}/c^{2}$, indicating improved sensitivity relative to current limits in this case.
• Figure 5: Projected 90% confidence level upper limits on the dimensionless isoscalar WIMP--nucleon NREFT coupling constants for elastic scattering, assuming a small exposure $M=10$ mg and $t_{ \text{age}} = 1$ Gyr, and a high read-out resolution $\sigma_{x}=1$ nm. The solid (dashed) lines indicate minerals with $C^{238}=10^{-11}$ g/g ($C^{238}=10^{-10}$ g/g), see Table \ref{['tab:U238_concentration']}. Black lines show the NREFT results from conventional direct detection experiments: the 90% confidence level upper limits from XENON100 XENON:2017fdd, LUX--ZEPLIN LZ:2023lvz, PandaX--II PandaX-II:2018woa, as well as the 95% Bayesian credible region of the two-dimensional marginalized posterior distribution from SuperCDMS SuperCDMS:2022crd. For elastic scattering, the HR scenario illustrates sensitivity of paleo-detectors to WIMP--nucleon cross sections below existing experimental direct detection bounds for $m_\chi \lesssim 10~\mathrm{GeV}/c^2$.