# New Projections for Dark Matter Searches with Paleo-Detectors

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## Abstract

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## 1. Introduction

## 2. Dark Matter Signals in Paleo-Detectors

`SRIM`[105,106] to calculate stopping powers. The left panel of Figure 1 shows the range of the different constituent nuclei in gypsum [Ca(SO${}_{4})\phantom{\rule{-0.166667em}{0ex}}\xb7\phantom{\rule{-0.166667em}{0ex}}2$(H${}_{2}$O)] as an example. (Note that we do not show the range of H in Figure 1 since we do not expect ions with charge $Z\le 2$ (in particular, H and He) to produce lasting damage tracks in most materials; see the discussion in [36]). We see that a 1 keV recoil gives rise to a track a few nm long, while a 100 keV recoil produces a track with a length of a few hundred nm.

- High-resolution readout scenario: We assume that 10 mg of material can be read out with a track length resolution of ${\sigma}_{x}=1\phantom{\rule{0.166667em}{0ex}}$nm. This scenario may be achievable with Helium Ion Beam Microscopy (HIBM) combined with pulsed-laser and fast-ion-beam ablation techniques [46,47,53,54,55,56]. As we will see, this scenario is advantageous for low-mass (${m}_{\chi}\lesssim 10\phantom{\rule{0.166667em}{0ex}}$GeV$/{c}^{2}$) WIMP searches.
- High-exposure readout scenario: We assume that 100 g of material can be read out with ${\sigma}_{x}=15\phantom{\rule{0.166667em}{0ex}}$nm. This scenario could be realized via Small Angle X-ray scattering (SAXs) tomography at a synchrotron facility [48,49,50]; it is better suited for heavier (${m}_{\chi}\gtrsim 10\phantom{\rule{0.166667em}{0ex}}$GeV$/{c}^{2}$) WIMP searches.

## 3. Backgrounds

- Cosmogenics: In order to mitigate backgrounds from cosmic rays, minerals to be used as paleo-detectors must have been shielded by a large overburden for as long as they have been recording nuclear damage tracks (just as conventional direct detection experiments are operated in deep underground laboratories). Paleo-detectors require only (at most) a few kg of target material rather than actively operating a tonne-scale experiment; such modest amounts of materials can be sourced from even greater depths than those of existing underground laboratories. One promising source of samples is (existing) boreholes drilled for geological R&D or oil exploration. For example, for an overburden of 5 km rock, the cosmogenic-muon-induced neutron flux is $\mathcal{O}\left({10}^{2}\right)\phantom{\rule{0.166667em}{0ex}}{\mathrm{cm}}^{-2}\phantom{\rule{0.166667em}{0ex}}{\mathrm{Gyr}}^{-1}$ [110], leading to negligible backgrounds for the purposes of a paleo-detector. We note that at depths $\gtrsim 6\phantom{\rule{0.166667em}{0ex}}$km rock, backgrounds from atmospheric neutrinos producing neutrons in the vicinity of the target become comparable to the backgrounds from cosmogenic muons [111]. We also note that paleo-detector samples can be stored near the surface after extraction from deep in the Earth before readout. For example, the cosmogenic-muon-induced neutron flux in a ∼50 m deep storage facility is ≲$0.2\phantom{\rule{0.166667em}{0ex}}{\mathrm{cm}}^{-2}\phantom{\rule{0.166667em}{0ex}}{\mathrm{yr}}^{-1}$.
- Astrophysical Neutrinos: Neutrinos scattering off nuclei in a paleo-detector sample give rise to nuclear damage tracks. We include neutrinos from the Sun, supernovae, and the interactions of cosmic rays with the Earth’s atmosphere in our background modeling. We take the solar and atmospheric neutrino fluxes from Reference [112]. Because of the long integration times, paleo-detectors are sensitive not only to neutrinos from supernovae in far-away galaxies throughout our Universe (the Diffuse Supernova Neutrino Background, DSNB), but also to neutrinos from local supernovae—the supernova rate in the Milky Way is estimated to be 2–3 per 100 years [113,114,115,116,117,118]. We compute the DSNB spectrum and the contribution from Galactic supernovae as in Reference [76]; see also References [118,119,120,121,122]. The neutrino-induced background is dominated by solar neutrinos at track lengths below ∼100 nm, with supernova neutrinos giving the largest contributions for tracks of a few 100 nm, before atmospheric neutrinos dominate the neutrino-induced backgrounds at even longer track lengths. Note that while neutrino-induced nuclear recoils are a background for DM searches, they can also be an interesting signal for paleo-detectors; see References [76,77,78].
- Radiogenics: Any natural mineral used as a paleo-detector will contain trace amounts of radioactive materials. In order to mitigate radiogenic backgrounds, it is crucial to use minerals with as low a concentration of radioactive elements as possible. The most important radioactive isotope for paleo-detectors is ${}^{238}\mathrm{U}$. Typical minerals formed in the Earth’s crust have ${}^{238}\mathrm{U}$ concentrations of order ${C}^{238}$ ∼ ${10}^{-6}\phantom{\rule{0.166667em}{0ex}}$g/g, leading to prohibitively large backgrounds for DM searches. However, minerals that constitute so-called Ultra Basic Rocks (UBRs), formed from the material of the Earth’s mantle, and Marine Evaporites (MEs), formed from evaporated sea water, have typical ${}^{238}\mathrm{U}$ concentrations orders of magnitude lower [123,124,125,126,127,128,129], (see also Reference [36] and especially the discussion in the appendix of Reference [76]). As in previous works on paleo-detectors [35,36,37,76,77], we will assume benchmark ${}^{238}\mathrm{U}$ concentrations of ${C}^{238}={10}^{-10}\phantom{\rule{0.166667em}{0ex}}$g/g for UBRs and ${C}^{238}={10}^{-11}\phantom{\rule{0.166667em}{0ex}}$g/g for MEs.

`SOURCES-4A`[132] to compute the neutron spectra from spontaneous fission and $(\alpha ,n)$-reactions of $\alpha $’s from all $\alpha $-decaying nuclei in the ${}^{238}\mathrm{U}$ decay chain; note that the contributions from spontaneous fission and ($\alpha ,n$)-reactions to the neutron flux are typically of the same order of magnitude, and the precise balance depends on the chemical composition of the target. From the neutron spectra, we calculate the induced nuclear recoil spectra using

`TENDL-2017`[133,134,135,136] neutron-nucleus cross sections tabulated in the

`JANIS4.0`[137] database. (We take only elastic neutron-nucleus scattering into account; this yields a conservative estimate of the background because neutrons typically lose a larger fraction of their energies through inelastic processes than in elastic scattering. Note also that our Monte Carlo simulation of the nuclear recoils induced by radiogenic neutrons has been validated with a calculation of the nuclear recoils induced by the same neutron spectra with

`FLUKA`[138,139,140] in Reference [77] for the particular case of a halite target.) The neutron-induced backgrounds are strongly suppressed in target materials containing hydrogen: since neutrons and H nuclei have approximately the same mass, neutrons lose a large fraction of their energy in a single interaction with hydrogen, leading to efficient moderation of the radiogenic neutrons even if hydrogen comprises only a small fraction of the atoms in the target material [35,36].

## 4. Sensitivity Forecasts

`swordfish`package [143,144,145]. In the remainder of this section, we describe a profile likelihood ratio-based approach to calculate the projected sensitivity of paleo-detectors to a DM signal with a spectral analysis. As we will see, one advantage of using this statistical approach is that we can easily incorporate the effect of background mismodeling into our sensitivity forecast. We show results for the sensitivity forecasts in Figure 3, Figure 4 and Figure 5.

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Bertone, G.; Hooper, D. History of dark matter. Rev. Mod. Phys.
**2018**, 90, 045002. [Google Scholar] [CrossRef] [Green Version] - Jungman, G.; Kamionkowski, M.; Griest, K. Supersymmetric dark matter. Phys. Rep.
**1996**, 267, 195–373. [Google Scholar] [CrossRef] [Green Version] - Arcadi, G.; Dutra, M.; Ghosh, P.; Lindner, M.; Mambrini, Y.; Pierre, M.; Profumo, S.; Queiroz, F.S. The waning of the WIMP? A review of models, searches, and constraints. Eur. Phys. J. C
**2018**, 78, 203. [Google Scholar] [CrossRef] - Roszkowski, L.; Sessolo, E.M.; Trojanowski, S. WIMP dark matter candidates and searches—Current status and future prospects. Rep. Prog. Phys.
**2018**, 81, 066201. [Google Scholar] [CrossRef] [Green Version] - Drukier, A.; Stodolsky, L. Principles and Applications of a Neutral Current Detector for Neutrino Physics and Astronomy. Phys. Rev. D
**1984**, 30, 2295. [Google Scholar] [CrossRef] - Goodman, M.W.; Witten, E. Detectability of Certain Dark Matter Candidates. Phys. Rev. D
**1985**, 31, 3059. [Google Scholar] [CrossRef] [PubMed] - Drukier, A.K.; Freese, K.; Spergel, D.N. Detecting Cold Dark Matter Candidates. Phys. Rev. D
**1986**, 33, 3495–3508. [Google Scholar] [CrossRef] [PubMed] - Spergel, D.N. The Motion of the Earth and the Detection of Wimps. Phys. Rev. D
**1988**, 37, 1353. [Google Scholar] [CrossRef] [PubMed] - Collar, J.I.; Avignone, F.T. Diurnal modulation effects in cold dark matter experiments. Phys. Lett. B
**1992**, 275, 181–185. [Google Scholar] [CrossRef] - Akerib, D.S.; Alsum, S.; Araújo, H.M.; Bai, X.; Bailey, A.J.; Balajthy, J.; Beltrame, P.; Bernard, E.P.; Bernstein, A.; Biesiadzinski, T.P.; et al. Results from a search for dark matter in the complete LUX exposure. Phys. Rev. Lett.
**2017**, 118, 021303. [Google Scholar] [CrossRef] [PubMed] - Agnes, P.; Albuquerque, I.; Alexander, T.; Alton, A.; Araujo, G.; Ave, M.; Back, H.; Baldin, B.; Batignani, G.; Biery, K.; et al. DarkSide-50 532-day Dark Matter Search with Low-Radioactivity Argon. Phys. Rev. D
**2018**, 98, 102006. [Google Scholar] [CrossRef] [Green Version] - Collaboration, X.; Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Anthony, M.; Arneodo, F.; Baudis, L.; et al. Dark Matter Search Results from a One Ton-Year Exposure of XENON1T. Phys. Rev. Lett.
**2018**, 121, 111302. [Google Scholar] [CrossRef] [Green Version] - Wang, Q.; Abdukerim, A.; Chen, W.; Chen, X.; Chen, Y.; Cheng, C.; Cui, X.; Fan, Y.; Fang, D.; Fu, C.; et al. Results of dark matter search using the full PandaX-II exposure. Chin. Phys. C
**2020**, 44, 125001. [Google Scholar] [CrossRef] - Angloher, G.; Bento, A.; Bucci, C.; Canonica, L.; Defay, X.; Erb, A.; von Feilitzsch, F.; Iachellini, N.F.; Gorla, P.; Gütlein, A.; et al. Results on light dark matter particles with a low-threshold CRESST-II detector. Eur. Phys. J. C
**2016**, 76, 25. [Google Scholar] [CrossRef] [Green Version] - Armengaud, E.; Arnaud, Q.; Augier, C.; Benoît, A.; Berge, L.; Bergmann, T.; Billard, J.; Blümer, J.; de Boissiere, T.; Bres, G.; et al. Constraints on low-mass WIMPs from the EDELWEISS-III dark matter search. JCAP
**2016**, 5, 19. [Google Scholar] [CrossRef] - Agnese, R.; Anderson, A.; Aralis, T.; Aramaki, T.; Arnquist, I.; Baker, W.; Balakishiyeva, D.; Barker, D.; Thakur, R.B.; Bauer, D.; et al. Low-mass dark matter search with CDMSlite. Phys. Rev. D
**2018**, 97, 022002. [Google Scholar] [CrossRef] [Green Version] - Petricca, F.; Angloher, G.; Bauer, P.; Bento, A.; Bucci, C.; Canonica, L.; Defay, X.; Erb, A.; v Feilitzsch, F.; Iachellini, N.F.; et al. First results on low-mass dark matter from the CRESST-III experiment. J. Phys. Conf. Ser.
**2020**, 1342, 012076. [Google Scholar] [CrossRef] - Armengaud, E.; Augier, C.; Benoît, A.; Benoit, A.; Bergé, L.; Billard, J.; Broniatowski, A.; Camus, P.; Cazes, A.; Chapellier, M.; et al. Searching for low-mass dark matter particles with a massive Ge bolometer operated above-ground. Phys. Rev. D
**2019**, 99, 082003. [Google Scholar] [CrossRef] [Green Version] - Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Amaro, F.; Anthony, M.; Arazi, L.; Arneodo, F.; Balan, C.; Barrow, P.; et al. Physics reach of the XENON1T dark matter experiment. JCAP
**2016**, 1604, 27. [Google Scholar] [CrossRef] [Green Version] - Mount, B.J.; Hans, S.; Rosero, R.; Yeh, M.; Chan, C.; Gaitskell, R.J.; Huang, D.Q.; Makkinje, J.; Malling, D.C.; Pangilinan, M.; et al. LUX-ZEPLIN (LZ) Technical Design Report. arXiv
**2017**, arXiv:1703.09144. [Google Scholar] - Aalbers, J.; Agostini, F.; Alfonsi, M.; Amaro, F.; Amsler, C.; Aprile, E.; Arazi, L.; Arneodo, F.; Barrow, P.; Baudis, L.; et al. DARWIN: Towards the ultimate dark matter detector. JCAP
**2016**, 1611, 17. [Google Scholar] [CrossRef] - Aalseth, C.E.; Acerbi, F.; Agnes, P.; Albuquerque, I.; Alexander, T.; Alici, A.; Alton, A.; Antonioli, P.; Arcelli, S.; Ardito, R.; et al. DarkSide-20k: A 20 tonne two-phase LAr TPC for direct dark matter detection at LNGS. Eur. Phys. J. Plus
**2018**, 133, 131. [Google Scholar] [CrossRef] - Amaudruz, P.A.; Baldwin, M.; Batygov, M.; Beltran, B.; Bina, C.; Bishop, D.; Bonatt, J.; Boorman, G.; Boulay, M.G.; Broerman, B.; et al. Design and Construction of the DEAP-3600 Dark Matter Detector. Astropart. Phys.
**2019**, 108, 1–23. [Google Scholar] [CrossRef] [Green Version] - Daw, E.; Dorofeev, A.; Fox, J.; Gauvreau, J.-L.; Ghag, C.; Harmon, L.; Harton, J.; Gold, M.; Lee, E.; Loomba, D.; et al. The DRIFT Directional Dark Matter Experiments. EAS Publ. Ser.
**2012**, 53, 11–18. [Google Scholar] [CrossRef] - Cappella, F.; Bernabei, R.; Belli, P.; Caracciolo, V.; Cerulli, R.; Danevich, F.; d’Angelo, A.; Di Marco, A.; Incicchitti, A.; Poda, D.; et al. On the potentiality of the ZnWO
_{4}anisotropic detectors to measure the directionality of Dark Matter. Eur. Phys. J. C**2013**, 1, 2276. [Google Scholar] [CrossRef] [Green Version] - Battat, J.B.; Brack, J.; Daw, E.; Dorofeev, A.; Ezeribe, A.; Gauvreau, J.-L.; Gold, M.; Harton, J.; Landers, J.; Law, E.; et al. First background-free limit from a directional dark matter experiment: Results from a fully fiducialised DRIFT detector. Phys. Dark Univ.
**2015**, 9–10, 1–7. [Google Scholar] [CrossRef] - Riffard, Q.; Billard, J.; Bosson, G.; Bourrion, O.; Guillaudin, O.; Lamblin, J.; Mayet, F.; Muraz, J.-F.; Richer, J.-P.; Santos, D.; et al. Dark Matter directional detection with MIMAC. In Proceedings of the 48th Rencontres de Moriond on Very High Energy Phenomena in the Universe, La Thuile, Italy, 9–16 March 2013; pp. 227–230. [Google Scholar]
- Santos, D.; Bosson, G.; Bouly, J.; Bourrion, O.; Fourel, C.; Guillaudin, O.; Lamblin, J.; Mayet, F.; Muraz, J.; Richer, J.; et al. MIMAC: MIcro-tpc MAtrix of Chambers for dark matter directional detection. J. Phys. Conf. Ser.
**2013**, 469, 012002. [Google Scholar] [CrossRef] - Monroe, J. Status and Prospects of the DMTPC Directional Dark Matter Experiment. EAS Publ. Ser.
**2012**, 53, 19–24. [Google Scholar] [CrossRef] [Green Version] - Leyton, M. Directional dark matter detection with the DMTPC m
^{3}experiment. J. Phys. Conf. Ser.**2016**, 718, 042035. [Google Scholar] [CrossRef] - Miuchi, K.; Nishimura, H.; Hattori, K.; Higashi, N.; Ida, C.; Iwaki, S.; Kabuki, S.; Kubo, H.; Kurosawa, S.; Nakamura, K.; et al. First underground results with NEWAGE-0.3a direction-sensitive dark matter detector. Phys. Lett. B
**2010**, 686, 11–17. [Google Scholar] [CrossRef] [Green Version] - Nakamura, K.; Miuchi, K.; Tanimori, T.; Kubo, H.; Takada, A.; Parker, J.D.; Mizumoto, T.; Mizumura, Y.; Nishimura, H.; Sekiya, H.; et al. Direction-sensitive dark matter search with gaseous tracking detector NEWAGE-0.3b’. PTEP
**2015**, 2015, 043F01. [Google Scholar] [CrossRef] [Green Version] - Battat, J.; Ezeribe, A.; Gauvreau, J.-L.; Harton, J.; Lafler, R.; Law, E.; Lee, E.; Loomba, D.; Lumnah, A.; Miller, E.; et al. Low Threshold Results and Limits from the DRIFT Directional Dark Matter Detector. Astropart. Phys.
**2017**, 91, 65–74. [Google Scholar] [CrossRef] [Green Version] - Vahsen, S.E.; O’Hare, C.A.J.; Lynch, W.A.; Spooner, N.J.C.; Baracchini, E.; Barbeau, P.; Battat, J.B.R.; Crow, B.; Deaconu, C.; Eldridge, C.; et al. CYGNUS: Feasibility of a nuclear recoil observatory with directional sensitivity to dark matter and neutrinos. arXiv
**2020**, arXiv:2008.12587. [Google Scholar] - Baum, S.; Drukier, A.K.; Freese, K.; Górski, M.; Stengel, P. Searching for Dark Matter with Paleo-Detectors. Phys. Lett. B
**2020**, 803, 135325. [Google Scholar] [CrossRef] - Drukier, A.K.; Baum, S.; Freese, K.; Górski, M.; Stengel, P. Paleo-detectors: Searching for Dark Matter with Ancient Minerals. Phys. Rev. D
**2019**, 99, 043014. [Google Scholar] [CrossRef] [Green Version] - Edwards, T.D.P.; Kavanagh, B.J.; Weniger, C.; Baum, S.; Drukier, A.K.; Freese, K.; Górski, M.; Stengel, P. Digging for dark matter: Spectral analysis and discovery potential of paleo-detectors. Phys. Rev. D
**2019**, 99, 043541. [Google Scholar] [CrossRef] [Green Version] - Fleischer, R.L.; Price, P.B.; Walker, R.M.; Hubbard, E.L. Track Registration in Various Solid-State Nuclear Track Detectors. Phys. Rev.
**1964**, 133, A1443–A1449. [Google Scholar] [CrossRef] - Fleischer, R.L.; Price, P.B.; Walker, R.M. Tracks of Charged Particles in Solids. Science
**1965**, 149, 383–393. [Google Scholar] [CrossRef] - Fleischer, R.L.; Price, P.B.; Walker, R.M. Solid-state track detectors: Applications to nuclear science and geophysics. Ann. Rev. Nucl. Part. Sci.
**1965**, 15, 1–28. [Google Scholar] [CrossRef] - Guo, S.L.; Chen, B.L.; Durrani, S. Chapter 3—Solid-State Nuclear Track Detectors. In Handbook of Radioactivity Analysis, 4th ed.; L’Annunziata, M.F., Ed.; Academic Press: Amsterdam, The Netherland, 2020; pp. 307–407. [Google Scholar] [CrossRef]
- Gradstein, F.M.; Ogg, J.G.; Schmitz, M.D.; Ogg, G.M. (Eds.) The Geologic Time Scale; Elsevier: Amsterdam, The Netherlands, 2012. [Google Scholar] [CrossRef]
- Gallagher, K.; Brown, R.; Johnson, C. Fission Track Analysis and its Applications to Geological Problems. Annu. Rev. Earth Planet. Sci.
**1998**, 26, 519–572. [Google Scholar] [CrossRef] - van den Haute, P.; de Corte, F. (Eds.) Advances in Fission-Track Geochronology; Springer: Berlin/Heidelberg, Germany, 1998. [Google Scholar] [CrossRef]
- Toulemonde, M.; Assmann, W.; Dufour, C.; Meftah, A.; Studer, F.; Trautmann, C. Experimental Phenomena and Thermal Spike Model Description of Ion Tracks in Amorphisable Inorganic Insulators. In Ion Beam Science: Solved and Unsolved Problems, Mat. Fys. Medd. Dan. Vid. Selsk.; Sigmund, P., Ed.; Det Kongelige Danske Videnskabernes Selskab: Copenhagen, Denmark, 2006; Volume 52, p. 263. [Google Scholar]
- Hill, R.; Notte, J.A.; Scipioni, L. Chapter 2—Scanning Helium Ion Microscopy. In Advances in Imaging and Electron Physics; Hawkes, P.W., Ed.; Elsevier: Amsterdam, The Netherlands, 2012; Volume 170, pp. 65–148. [Google Scholar] [CrossRef]
- van Gastel, R.; Hlawacek, G.; Zandvliet, H.J.; Poelsema, B. Subsurface analysis of semiconductor structures with helium ion microscopy. Microelectron. Reliab.
**2012**, 52, 2104–2109. [Google Scholar] [CrossRef] - Rodriguez, M.; Li, W.; Chen, F.; Trautmann, C.; Bierschenk, T.; Afra, B.; Schauries, D.; Ewing, R.; Mudie, S.; Kluth, P. SAXS and TEM investigation of ion tracks in neodymium-doped yttrium aluminium garnet. Nucl. Instrum. Methods Phys. Res. Sect. Beam Interact. Mater. Atoms.
**2014**, 326, 150–153. [Google Scholar] [CrossRef] - Schaff, F.; Bech, M.; Zaslansky, P.; Jud, C.; Liebi, M.; Guizar-Sicairos, M.; Pfeiffer, F. Six-dimensional real and reciprocal space small-angle X-ray scattering tomography. Nature
**2015**, 527, 353. [Google Scholar] [CrossRef] [PubMed] - Holler, M.; Diaz, A.; Guizar-Sicairos, M.; Karvinen, P.; Färm, E.; Härkönen, E.; Ritala, M.; Menzel, A.; Raabe, J.; Bunk, O. X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution. Sci. Rep.
**2014**, 4, 3857. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bartz, J.; Zeissler, C.; Fomenko, V.; Akselrod, M. An imaging spectrometer based on high resolution microscopy of fluorescent aluminum oxide crystal detectors. Radiat. Meas.
**2013**, 56, 273–276. [Google Scholar] [CrossRef] - Kouwenberg, J.; Kremers, G.; Slotman, J.; Woltenbeek, H.; Houtsmuller, A.; Denkova, A.; Bos, A. Alpha particle spectroscopy using FNTD and SIM super-resolution microscopy. J. Microsc.
**2018**, 270, 326–334. [Google Scholar] [CrossRef] [Green Version] - Joens, M.S.; Huynh, C.; Kasuboski, J.M.; Ferranti, D.; Sigal, Y.J.; Zeitvogel, F.; Obst, M.; Burkhardt, C.J.; Curran, K.P.; Chalasani, S.H.; et al. Helium Ion Microscopy (HIM) for the imaging of biological samples at sub-nanometer resolution. Sci. Rep.
**2013**, 3, 3514. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Echlin, M.P.; Straw, M.; Randolph, S.; Filevich, J.; Pollock, T.M. The TriBeam system: Femtosecond laser ablation in situ SEM. Mater. Charact.
**2015**, 100, 1–12. [Google Scholar] [CrossRef] - Pfeifenberger, M.J.; Mangang, M.; Wurster, S.; Reiser, J.; Hohenwarter, A.; Pfleging, W.; Kiener, D.; Pippan, R. The use of femtosecond laser ablation as a novel tool for rapid micro-mechanical sample preparation. Mater. Des.
**2017**, 121, 109–118. [Google Scholar] [CrossRef] - Randolph, S.J.; Filevich, J.; Botman, A.; Gannon, R.; Rue, C.; Straw, M. In situ femtosecond pulse laser ablation for large volume 3D analysis in scanning electron microscope systems. J. Vac. Sci. Technol.
**2018**, 36, 06JB01. [Google Scholar] [CrossRef] - Goto, E. On the Observation of Magnetic Monopoles. J. Phys. Soc. Jpn.
**1958**, 13, 1413–1418. [Google Scholar] [CrossRef] - Goto, E.; Kolm, H.H.; Ford, K.W. Search for Ferromagnetically Trapped Magnetic Monopoles of Cosmic-Ray Origin. Phys. Rev.
**1963**, 132, 387. [Google Scholar] [CrossRef] - Fleischer, R.L.; Jacobs, I.S.; Schwarz, W.M.; Price, P.B.; Goodell, H.G. Search for Multiply Charged Dirac Magnetic Poles. Phys. Rev.
**1969**, 177, 2029–2035. [Google Scholar] [CrossRef] - Fleischer, R.L.; Hart, H.R.; Jacobs, I.S.; Price, P.B.; Schwarz, W.M.; Aumento, F. Search for magnetic monopoles in deep ocean deposits. Phys. Rev.
**1969**, 184, 1393–1397. [Google Scholar] [CrossRef] - Fleischer, R.L.; Price, P.B.; Woods, R.T. Search for tracks of massive, multiply charged magnetic poles. Phys. Rev.
**1969**, 184, 1398–1401. [Google Scholar] [CrossRef] [Green Version] - Alvarez, L.W.; Eberhard, P.H.; Ross, R.R.; Watt, R.D. Search for Magnetic Monopoles in the Lunar Sample. Science
**1970**, 167, 701–703. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kolm, H.H.; Villa, F.; Odian, A. Search for Magnetic Monopoles. Phys. Rev. D
**1971**, 4, 1285. [Google Scholar] [CrossRef] - Eberhard, P.H.; Ross, R.R.; Alvarez, L.W.; Watt, R.D. Search for Magnetic Monopoles in Lunar Material. Phys. Rev. D
**1971**, 4, 3260. [Google Scholar] [CrossRef] [Green Version] - Ross, R.R.; Eberhard, P.H.; Alvarez, L.W.; Watt, R.D. Search for Magnetic Monopoles in Lunar Material Using an Electromagnetic Detector. Phys. Rev. D
**1973**, 8, 698. [Google Scholar] [CrossRef] [Green Version] - Price, P.B.; Guo, S.l.; Ahlen, S.P.; Fleischer, R.L. Search for GUT Magnetic Monopoles at a Flux Level Below the Parker Limit. Phys. Rev. Lett.
**1984**, 52, 1265. [Google Scholar] [CrossRef] - Kovalik, J.M.; Kirschvink, J.L. New Superconducting Quantum Interface Device Based Constraints on the Abundance of Magnetic Monopoles Trapped in Matter: An Investigation of Deeply Buried Rocks. Phys. Rev. A
**1986**, 33, 1183–1187. [Google Scholar] [CrossRef] [Green Version] - Price, P.B.; Salamon, M.H. Search for Supermassive Magnetic Monopoles Using Mica Crystals. Phys. Rev. Lett.
**1986**, 56, 1226–1229. [Google Scholar] [CrossRef] [Green Version] - Ghosh, D.; Chatterjea, S. Supermassive magnetic monopoles flux from the oldest mica samples. Europhys. Lett.
**1990**, 12, 25–28. [Google Scholar] [CrossRef] - Jeon, H.; Longo, M.J. Search for magnetic monopoles trapped in matter. Phys. Rev. Lett.
**1995**, 75, 1443–1446, Erratum in Phys. Rev. Lett.**1996**, 76, 159. [Google Scholar] [CrossRef] [Green Version] - Collar, J.I.; Zioutas, K. Limits on exotic heavily ionizing particles from the geological abundance of fullerenes. Phys. Rev. Lett.
**1999**, 83, 3097. [Google Scholar] [CrossRef] [Green Version] - Snowden-Ifft, D.P.; Freeman, E.S.; Price, P.B. Limits on dark matter using ancient mica. Phys. Rev. Lett.
**1995**, 74, 4133–4136. [Google Scholar] [CrossRef] [PubMed] - Collar, J.I.; Avignone, F.T., III. Nuclear tracks from cold dark matter interactions in mineral crystals: A Computational study. Nucl. Instrum. Meth.
**1995**, B95, 349. [Google Scholar] [CrossRef] [Green Version] - Engel, J.; Ressell, M.T.; Towner, I.S.; Ormand, W.E. Response of mica to weakly interacting massive particles. Phys. Rev. C
**1995**, 52, 2216–2221. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Snowden-Ifft, D.P.; Westphal, A.J. Unique signature of dark matter in ancient mica. Phys. Rev. Lett.
**1997**, 78, 1628–1631. [Google Scholar] [CrossRef] [Green Version] - Baum, S.; Edwards, T.D.P.; Kavanagh, B.J.; Stengel, P.; Drukier, A.K.; Freese, K.; Górski, M.; Weniger, C. Paleodetectors for Galactic supernova neutrinos. Phys. Rev. D
**2020**, 101, 103017. [Google Scholar] [CrossRef] - Jordan, J.R.; Baum, S.; Stengel, P.; Ferrari, A.; Morone, M.C.; Sala, P.; Spitz, J. Measuring Changes in the Atmospheric Neutrino Rate Over Gigayear Timescales. Phys. Rev. Lett.
**2020**, 125, 231802. [Google Scholar] [CrossRef] [PubMed] - Arellano, N.T.; Horiuchi, S. Measuring solar neutrinos over Gigayear timescales with Paleo Detectors. arXiv
**2021**, arXiv:2102.01755. [Google Scholar] - Rajendran, S.; Zobrist, N.; Sushkov, A.O.; Walsworth, R.; Lukin, M. A method for directional detection of dark matter using spectroscopy of crystal defects. Phys. Rev. D
**2017**, 96, 035009. [Google Scholar] [CrossRef] [Green Version] - Essig, R.; Mardon, J.; Slone, O.; Volansky, T. Detection of sub-GeV Dark Matter and Solar Neutrinos via Chemical-Bond Breaking. Phys. Rev. D
**2017**, 95, 056011. [Google Scholar] [CrossRef] [Green Version] - Budnik, R.; Chesnovsky, O.; Slone, O.; Volansky, T. Direct Detection of Light Dark Matter and Solar Neutrinos via Color Center Production in Crystals. Phys. Lett. B
**2018**, 782, 242–250. [Google Scholar] [CrossRef] - Cogswell, B.K.; Goel, A.; Huber, P. Passive low-energy nuclear recoil detection with color centers. arXiv
**2021**, arXiv:2104.13926. [Google Scholar] - Ebadi, R.; Mathur, A.; Tanin, E.H.; Tailby, N.D.; Marshall, M.C.; Ravi, A.; Trubko, R.; Fu, R.R.; Phillips, D.F.; Rajendran, S.; et al. Ultra-Heavy Dark Matter Search with Electron Microscopy of Geological Quartz. arXiv
**2021**, arXiv:2105.03998. [Google Scholar] - Baum, S.; DeRocco, W.; Edwards, T.D.P.; Kalia, S. Throwing Rocks at Dinosaurs: Time-varying Dark Matter Signals in Paleo-Detectors. To appear.
- Available online: https://github.com/sbaum90/paleoSpec (accessed on 10 June 2021).
- Available online: https://github.com/sbaum90/paleoSens (accessed on 10 June 2021).
- Engel, J. Nuclear form-factors for the scattering of weakly interacting massive particles. Phys. Lett. B
**1991**, 264, 114–119. [Google Scholar] [CrossRef] - Engel, J.; Pittel, S.; Vogel, P. Nuclear physics of dark matter detection. Int. J. Mod. Phys.
**1992**, E1, 1–37. [Google Scholar] [CrossRef] - Ressell, M.T.; Aufderheide, M.B.; Bloom, S.D.; Griest, K.; Mathews, G.J.; Resler, D.A. Nuclear shell model calculations of neutralino - nucleus cross-sections for Si-29 and Ge-73. Phys. Rev. D
**1993**, 48, 5519–5535. [Google Scholar] [CrossRef] [Green Version] - Bednyakov, V.A.; Simkovic, F. Nuclear spin structure in dark matter search: The Zero momentum transfer limit. Phys. Part. Nucl.
**2005**, 36, 131–152. [Google Scholar] [CrossRef] [Green Version] - Bednyakov, V.A.; Simkovic, F. Nuclear spin structure in dark matter search: The Finite momentum transfer limit. Phys. Part. Nucl.
**2006**, 37, S106–S128. [Google Scholar] [CrossRef] [Green Version] - Fan, J.; Reece, M.; Wang, L.T. Non-relativistic effective theory of dark matter direct detection. JCAP
**2010**, 1011, 42. [Google Scholar] [CrossRef] [Green Version] - Fitzpatrick, A.L.; Haxton, W.; Katz, E.; Lubbers, N.; Xu, Y. The Effective Field Theory of Dark Matter Direct Detection. JCAP
**2013**, 1302, 4. [Google Scholar] [CrossRef] [Green Version] - Helm, R.H. Inelastic and Elastic Scattering of 187-Mev Electrons from Selected Even-Even Nuclei. Phys. Rev.
**1956**, 104, 1466–1475. [Google Scholar] [CrossRef] - Lewin, J.D.; Smith, P.F. Review of mathematics, numerical factors, and corrections for dark matter experiments based on elastic nuclear recoil. Astropart. Phys.
**1996**, 6, 87–112. [Google Scholar] [CrossRef] [Green Version] - Duda, G.; Kemper, A.; Gondolo, P. Model Independent Form Factors for Spin Independent Neutralino-Nucleon Scattering from Elastic Electron Scattering Data. JCAP
**2007**, 0704, 12. [Google Scholar] [CrossRef] - Vietze, L.; Klos, P.; Menéndez, J.; Haxton, W.C.; Schwenk, A. Nuclear structure aspects of spin-independent WIMP scattering off xenon. Phys. Rev. D
**2015**, 91, 043520. [Google Scholar] [CrossRef] [Green Version] - Gazda, D.; Catena, R.; Forssén, C. Ab initio nuclear response functions for dark matter searches. Phys. Rev. D
**2017**, 95, 103011. [Google Scholar] [CrossRef] [Green Version] - Körber, C.; Nogga, A.; de Vries, J. First-principle calculations of Dark Matter scattering off light nuclei. Phys. Rev. C
**2017**, 96, 035805. [Google Scholar] [CrossRef] [Green Version] - Hoferichter, M.; Klos, P.; Menéndez, J.; Schwenk, A. Nuclear structure factors for general spin-independent WIMP-nucleus scattering. Phys. Rev. D
**2019**, 99, 055031. [Google Scholar] [CrossRef] [Green Version] - Koposov, S.E.; Rix, H.W.; Hogg, D.W. Constraining the Milky Way potential with a 6-D phase-space map of the GD-1 stellar stream. Astrophys. J.
**2010**, 712, 260–273. [Google Scholar] [CrossRef] [Green Version] - Piffl, T.; Scannapieco, C.; Binney, J.; Steinmetz, M.; Scholz, R.-D.; Williams, M.E.; De Jong, R.S.; Kordopatis, G.; Matijevič, G.; Bienayme, O.; et al. The RAVE survey: The Galactic escape speed and the mass of the Milky Way. Astron. Astrophys.
**2014**, 562, A91. [Google Scholar] [CrossRef] - Bovy, J.; Prieto, C.A.; Beers, T.C.; Bizyaev, D.; Da Costa, L.N.; Cunha, K.; Ebelke, G.L.; Eisenstein, D.J.; Frinchaboy, P.M.; Pérez, A.E.G.; et al. The Milky Way’s circular velocity curve between 4 and 14 kpc from APOGEE data. Astrophys. J.
**2012**, 759, 131. [Google Scholar] [CrossRef] [Green Version] - Freese, K.; Lisanti, M.; Savage, C. Colloquium: Annual modulation of dark matter. Rev. Mod. Phys.
**2013**, 85, 1561–1581. [Google Scholar] [CrossRef] [Green Version] - Ziegler, J.F.; Biersack, J.P.; Ziegler, M.D. The Stopping and Range of Ions in Matter; Lulu Press Co.: Morrisville, NC, USA, 2007. [Google Scholar]
- Ziegler, J.F.; Ziegler, M.D.; Biersack, J.P. SRIM—The stopping and range of ions in matter. Nucl. Instrum. Methods Phys. Res. Sect. Beam Interact. Mater. Atoms.
**2010**, 268, 1818–1823. [Google Scholar] [CrossRef] [Green Version] - Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Antochi, V.C.; Angelino, E.; Arneodo, F.; Barge, D.; et al. Light Dark Matter Search with Ionization Signals in XENON1T. Phys. Rev. Lett.
**2019**, 123, 251801. [Google Scholar] [CrossRef] [Green Version] - Hirose, S. (JAMSTEC, Yokohama, Japan). Personal communication, 2021. [Google Scholar]
- Brown, E. (Rensselaer Polytechnic Institute, Troy, NY, USA). Personal communication, 2021. [Google Scholar]
- Mei, D.; Hime, A. Muon-induced background study for underground laboratories. Phys. Rev. D
**2006**, 73, 053004. [Google Scholar] [CrossRef] [Green Version] - Aharmim, B.; Ahmed, S.; Andersen, T.; Anthony, A.; Barros, N.; Beier, E.; Bellerive, A.; Beltran, B.; Bergevin, M.; Biller, S.; et al. Measurement of the Cosmic Ray and Neutrino-Induced Muon Flux at the Sudbury Neutrino Observatory. Phys. Rev. D
**2009**, 80, 012001. [Google Scholar] [CrossRef] [Green Version] - O’Hare, C.A.J. Can we overcome the neutrino floor at high masses? Phys. Rev. D
**2020**, 102, 063024. [Google Scholar] [CrossRef] - Cappellaro, E.; Barbon, R.; Turatto, M. Supernova statistics. Springer Proc. Phys.
**2005**, 99, 347–354. [Google Scholar] [CrossRef] - Diehl, R.; Halloin, H.; Kretschmer, K.; Lichti, G.G.; Schönfelder, V.; Strong, A.W.; Kienlin, A.; Wang, W.; Jean, P.; Knödlseder, J.; et al. Radioactive Al-26 and massive stars in the galaxy. Nature
**2006**, 439, 45–47. [Google Scholar] [CrossRef] [Green Version] - Strumia, A.; Vissani, F. Neutrino masses and mixings and …. arXiv
**2006**, arXiv:hep-ph/0606054. [Google Scholar] - Li, W.; Chornock, R.; Leaman, J.; Filippenko, A.V.; Poznanski, D.; Wang, X.; Ganeshalingam, M.; Mannucci, F. Nearby supernova rates from the Lick Observatory Supernova Search—III. The rate-size relation, and the rates as a function of galaxy Hubble type and colour. Mon. Not. R. Astron. Soc.
**2011**, 412, 1473–1507. [Google Scholar] [CrossRef] [Green Version] - Botticella, M.T.; Smartt, S.J.; Kennicutt, R.C., Jr.; Cappellaro, E.; Sereno, M.; Lee, J.C. A comparison between star formation rate diagnostics and rate of core collapse supernovae within 11 Mpc. Astron. Astrophys.
**2012**, 537, A132. [Google Scholar] [CrossRef] [Green Version] - Adams, S.M.; Kochanek, C.S.; Beacom, J.F.; Vagins, M.R.; Stanek, K.Z. Observing the Next Galactic Supernova. Astrophys. J.
**2013**, 778, 164. [Google Scholar] [CrossRef] [Green Version] - Beacom, J.F. The Diffuse Supernova Neutrino Background. Ann. Rev. Nucl. Part. Sci.
**2010**, 60, 439–462. [Google Scholar] [CrossRef] [Green Version] - Billard, J.; Strigari, L.; Figueroa-Feliciano, E. Implication of neutrino backgrounds on the reach of next generation dark matter direct detection experiments. Phys. Rev. D
**2014**, 89, 023524. [Google Scholar] [CrossRef] [Green Version] - Madau, P.; Dickinson, M. Cosmic Star Formation History. Ann. Rev. Astron. Astrophys.
**2014**, 52, 415–486. [Google Scholar] [CrossRef] [Green Version] - Strolger, L.G.; Dahlen, T.; Rodney, S.A.; Graur, O.; Riess, A.G.; McCully, C.; Ravindranath, S.; Mobasher, B.; Shahady, A.K. The Rate of Core Collapse Supernovae to Redshift 2.5 From The CANDELS and CLASH Supernova Surveys. Astrophys. J.
**2015**, 813, 93. [Google Scholar] [CrossRef] [Green Version] - Thomson, S.; Wardle, G. Coloured natural rocksalts: A study of their helium contents, colours and impurities. Geochim. Cosmochim. Acta
**1954**, 5, 169–184. [Google Scholar] [CrossRef] - Condie, K.C.; Kuo, C.S.; Walker, R.M.; Murthy, V.R. Uranium Distribution in Separated Clinopyroxenes from Four Eclogites. Science
**1969**, 165, 57–59. [Google Scholar] [CrossRef] - Adams, J.A.S.; Osmond, J.K.; Rogers, J.J.W. The geochemistry of thorium and uranium. Phys. Chem. Earth
**1959**, 3, 298–348. [Google Scholar] [CrossRef] - Seitz, M.; Hart, S. Uranium and boron distributions in some oceanic ultramafic rocks. Earth Planet. Sci. Lett.
**1973**, 21, 97–107. [Google Scholar] [CrossRef] - Dean, W.E. Section 5 Trace and Minor Elements in Evaporites. In Marine Evaporites; SEPM Society for Sedimentary Geology: Tulsa, OK, USA, 1987. [Google Scholar] [CrossRef]
- Yui, M.; Kikawada, Y.; Oi, T.; Honda, T.; Nozaki, T. Abundance of Uranium and Thorium in Rock Salts. Radioisotopes
**1998**, 47, 488–492. [Google Scholar] [CrossRef] [Green Version] - Sanford, W.; Doughten, M.; Coplen, T.; Hunt, A.; Bullen, T. Evidence for high salinity of Early Cretaceous sea water from the Chesapeake Bay crater. Nature
**2013**, 503, 252–256. [Google Scholar] [CrossRef] [PubMed] - Collar, J.I. Comments on ‘limits on dark matter using ancient mica’. Phys. Rev. Lett.
**1996**, 76, 331. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Snowden-Ifft, D.P.; Freeman, E.S.; Price, P.B. Snowden-Ifft, Freemen, and Price Reply (A Reply to the Comment by Juan I Collar). Phys. Rev. Lett.
**1996**, 76, 332. [Google Scholar] [CrossRef] [PubMed] - SOURCES 4A: A Code for Calculating (Alpha, n), Spontaneous Fission, and Delayed Neutron Sources and Spectra; Technical Report LA-13639-MS; Los Alamos National Lab.: Los Alamos, NM, USA, 1999. [CrossRef] [Green Version]
- Koning, A.J.; Rochman, D. Modern Nuclear Data Evaluation with the TALYS Code System. Nucl. Data Sheets
**2012**, 113, 2841–2934. [Google Scholar] [CrossRef] - Rochman, D.; Koning, A.J.; Sublet, J.C.; Fleming, M.; Bauge, E.; Hilaire, S.; Romain, P.; Morillon, B.; Duarte, H.; Goriely, S.; et al. The TENDL library: Hope, reality and future. In Proceedings of the International Conference on Nuclear Data for Science and Technology, Bruges, Belgium, 11–16 September 2016. [Google Scholar]
- Sublet, J.C.; Koning, A.J.; Rochman, D.; Fleming, M.; Gilbert, M. TENDL-2015: Delivering Both Completeness and Robustness. In Proceedings of the Advances in Nuclear Nonproliferation Technology and Policy Conference, Santa Fe, NM, USA, 25–30 September 2015. [Google Scholar]
- Fleming, M.; Sublet, J.C.; Kopecky, J.; Rochman, D.; Koning, A.J. Probing Experimental and Systematic Trends of the Neutron-Induced TENDL-2014 Nuclear Data Library; CCFE report UKAEA-R: Abingdon, UK, October 2015. [Google Scholar]
- Soppera, N.; Bossant, M.; Dupont, E. JANIS 4: An Improved Version of the NEA Java-based Nuclear Data Information System. Nucl. Data Sheets
**2014**, 120, 294–296. [Google Scholar] [CrossRef] [Green Version] - Ferrari, A.; Sala, P.R.; Fasso, A.; Ranft, J. FLUKA: A Multi-Particle TRANSPORT code (Program Version 2005); CERN-2005-010, SLAC-R-773, INFN-TC-05-11; Menlo Park, CA, USA; SLAC National Accelerator Lab.: Menlo Park, CA, USA, 2005. [Google Scholar] [CrossRef] [Green Version]
- Böhlen, T.T.; Cerutti, F.; Chin, M.P.W.; Fassò, A.; Ferrari, A.; Ortega, P.G.; Mairani, A.; Sala, P.R.; Smirnov, G.; Vlachoudis, V. The FLUKA Code: Developments and Challenges for High Energy and Medical Applications. Nucl. Data Sheets
**2014**, 120, 211–214. [Google Scholar] [CrossRef] [Green Version] - Battistoni, G.; Ferrari, A.; Lantz, M.; Sala, P.R.; Smirnov, G.I. A neutrino-nucleon interaction generator for the FLUKA Monte Carlo code. In Proceedings of the 12th International Conference on Nuclear Reaction Mechanisms, CERN-Proceedings-2010-001, Varenna, Italy, 15–19 June 2009; pp. 387–394. [Google Scholar]
- Povinec, P.P. New ultra-sensitive radioanalytical technologies for new science. J. Radioanal. Nucl. Chem.
**2018**, 316, 893–931. [Google Scholar] [CrossRef] [Green Version] - Povinec, P.; Benedik, L.; Breier, R.; Ješkovský, M.; Kaizer, J.; Kameník, J.; Kochetov, O.; Kučera, J.; Loaiza, P.; Nisi, S.; et al. Ultra-sensitive radioanalytical technologies for underground physics experiments. J. Radioanal. Nucl. Chem.
**2018**, 318, 677–684. [Google Scholar] [CrossRef] - Edwards, T.D.P.; Weniger, C. A Fresh Approach to Forecasting in Astroparticle Physics and Dark Matter Searches. JCAP
**2018**, 1802, 21. [Google Scholar] [CrossRef] [Green Version] - Edwards, T.D.P.; Weniger, C. swordfish: Efficient Forecasting of New Physics Searches without Monte Carlo. arXiv
**2017**, arXiv:1712.05401. [Google Scholar] - Available online: https://github.com/cweniger/swordfish (accessed on 10 June 2021).
- Cowan, G.; Cranmer, K.; Gross, E.; Vitells, O. Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C
**2011**, 71, 1554, Erratum in Eur. Phys. J. C**2013**, 73, 2501. [Google Scholar] [CrossRef] [Green Version] - Billard, J.; Mayet, F.; Santos, D. Assessing the discovery potential of directional detection of dark matter. Phys. Rev. D
**2012**, 85, 035006. [Google Scholar] [CrossRef] [Green Version] - Conrad, J. Statistical Issues in Astrophysical Searches for Particle Dark Matter. Astropart. Phys.
**2015**, 62, 165–177. [Google Scholar] [CrossRef] [Green Version] - Wilks, S.S. The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses. Annals Math. Statist.
**1938**, 9, 60–62. [Google Scholar] [CrossRef] - Agnes, P.; Albuquerque, I.; Alexander, T.; Alton, A.; Araujo, G.; Asner, D.M.; Ave, M.; Back, H.O.; Baldin, B.; Batignani, G.; et al. Low-Mass Dark Matter Search with the DarkSide-50 Experiment. Phys. Rev. Lett.
**2018**, 121, 081307. [Google Scholar] [CrossRef] [Green Version] - Ruppin, F.; Billard, J.; Figueroa-Feliciano, E.; Strigari, L. Complementarity of dark matter detectors in light of the neutrino background. Phys. Rev. D
**2014**, 90, 083510. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**(

**Left**): Range ${x}_{N}$ of different ions with initial energy ${E}_{R}$ in gypsum [Ca(SO${}_{4})\phantom{\rule{-0.166667em}{0ex}}\xb7\phantom{\rule{-0.166667em}{0ex}}2$(H${}_{2}$O)]. (

**Right**): Differential rate of tracks per track length and unit target mass in gypsum from a $5\phantom{\rule{0.166667em}{0ex}}$GeV/c${}^{2}$ and a $500\phantom{\rule{0.166667em}{0ex}}$GeV/c${}^{2}$ WIMP compared to background spectra induced by neutrinos ($\nu $), radiogenic neutrons (n), and ${}^{238}\mathrm{U}\to {}^{234}\mathrm{Th}+\alpha $ recoils (${}^{234}\mathrm{Th}$ ); see the discussion in Section 3. For the normalization of the WIMP DM spectra, we set the spin-independent WIMP-nucleon cross sections to ${\sigma}_{p}^{\mathrm{SI}}={10}^{-43}\phantom{\rule{0.166667em}{0ex}}{\mathrm{cm}}^{2}$ for the 5 GeV/c${}^{2}$ case and ${\sigma}_{p}^{\mathrm{SI}}={10}^{-46}\phantom{\rule{0.166667em}{0ex}}{\mathrm{cm}}^{2}$ for the 500 GeV/c${}^{2}$ case, compatible with current upper bounds [12,107].

**Figure 2.**Track length spectra for a 5 GeV/c${}^{2}$ and a 500 GeV/c${}^{2}$ WIMP compared to the background spectra induced by neutrinos ($\nu $), radiogenic neutrons (n), and ${}^{238}\mathrm{U}\to {}^{234}\mathrm{Th}+\alpha $ recoils (${}^{234}\mathrm{Th}$ ) after taking finite resolution effects into account. The left panels are for our high resolution scenario ($M=10\phantom{\rule{0.166667em}{0ex}}$mg of sample material read out with track length resolution of ${\sigma}_{x}=1\phantom{\rule{0.166667em}{0ex}}$nm), while the right panels are for the high exposure scenario ($M=100\phantom{\rule{0.166667em}{0ex}}$g, ${\sigma}_{x}=15\phantom{\rule{0.166667em}{0ex}}$nm). We assume that the samples have been recording tracks for ${t}_{\mathrm{age}}=1\phantom{\rule{0.166667em}{0ex}}$Gyr. In all panels, we use 100 logarithmically spaced bins between ${\sigma}_{x}/2\le x\le {10}^{3}\phantom{\rule{0.166667em}{0ex}}$nm; note that these bins and the scales of the axes differ between the left and the right panels. The upper panels show the number of tracks per bin from the respective sources. For the backgrounds, the shaded bands around the respective spectra show the associated error (systematic and statistical added in quadrature). The bottom panels show the ratio of the number of signal (${S}_{i}$) to the (summed) number of background (${B}_{i}$) events per bin, and the sand-colored shade shows the relative uncertainty of the total number of background events per bin. The signal-to-noise ratio per bin can be read off from the lower panels by dividing ${S}_{i}/{B}_{i}$ for the respective signal with the relative uncertainty of the background. For the normalization of the WIMP DM spectra, we set the spin-independent WIMP-nucleon cross sections to ${\sigma}_{p}^{\mathrm{SI}}={10}^{-43}\phantom{\rule{0.166667em}{0ex}}{\mathrm{cm}}^{2}$ for the 5 GeV/c${}^{2}$ case and ${\sigma}_{p}^{\mathrm{SI}}={10}^{-46}\phantom{\rule{0.166667em}{0ex}}{\mathrm{cm}}^{2}$ for the 500 GeV/c${}^{2}$ case, as in Figure 1.

**Figure 3.**Projected 90% confidence level upper limits in the WIMP mass (${m}_{\chi}$)—spin-independent WIMP-nucleus scattering cross section (${\sigma}_{p}^{\mathrm{SI}}$) plane in the high-resolution (sample mass $M=10\phantom{\rule{0.166667em}{0ex}}$mg, track length resolution ${\sigma}_{x}=1\phantom{\rule{0.166667em}{0ex}}$nm; left panel) and high-exposure ($M=100\phantom{\rule{0.166667em}{0ex}}$g, ${\sigma}_{x}=15\phantom{\rule{0.166667em}{0ex}}$nm; right panel) readout scenarios. The different lines are for different target materials as indicated in the legend; see Table 1. The gray-shaded region of parameter space is disfavored by current upper limits from direct detection experiments [12,14,17,107,150], while the sand-colored region indicates the neutrino floor for a Xe-based experiment [151]. Colors and linestyles are the same in both panels.

**Figure 4.**Projected 90% confidence level exclusion limits in a gypsum [Ca(SO${}_{4})\phantom{\rule{-0.166667em}{0ex}}\xb7\phantom{\rule{-0.166667em}{0ex}}2$(H${}_{2}$O)] paleo-detector in the high-resolution (

**left**) and high-exposure (

**right**) readout scenarios. The black solid lines show the projected limit using the Poisson log-likelihood (see Equation (9))in our maximum likelihood ratio test, Equation (12), while the dashed lines show the projected upper limit if we instead use a ${\chi}^{2}$ distribution, Equation (14), for the log-likelihood. The differently colored dashed lines are for different assumptions regarding the relative systematic error of the background modeling parameterized by ${\Delta}_{\mathrm{Bkg}}^{\mathrm{sys}}$; see Equation (15). The gray and sand-colored shaded areas indicate current upper limits and the conventional neutrino floor in a Xe-based direct detection experiment, respectively; see Figure 3. Colors and linestyles are the same in both panels. Note that in the left panel, the ${\mathcal{L}}_{\mathrm{Poisson}}$, the ${\mathcal{L}}_{{\chi}^{2}}({\Delta}_{\mathrm{Bkg}}^{\mathrm{sys}}=0)$, and the ${\mathcal{L}}_{{\chi}^{2}}({\Delta}_{\mathrm{Bkg}}^{\mathrm{sys}}=0.01)$ lines are practically laying on top of each other.

**Figure 5.**Projected 90% confidence level exclusion limits in a gypsum [Ca(SO${}_{4})\phantom{\rule{-0.166667em}{0ex}}\xb7\phantom{\rule{-0.166667em}{0ex}}2$(H${}_{2}$O)] paleo-detector in the high-resolution (

**left**) and high-exposure (

**right**) readout scenarios for different assumptions on the ${}^{238}\mathrm{U}$ concentration ${C}^{238}$ controlling the radiogenic backgrounds. The solid black line shows the sensitivity with our fiducial value for marine evaporites, ${C}^{238}={10}^{-11}\phantom{\rule{0.166667em}{0ex}}$g/g, while the differently colored dashed lines show the projected upper limit for both larger and smaller ${C}^{238}$. The gray and sand-colored shaded areas indicate current upper limits and the conventional neutrino floor in a Xe-based direct detection experiment, respectively; see Figure 3. Colors and linestyles are the same in both panels.

**Table 1.**List of minerals considered in this work with their chemical composition and our fiducial assumption for the ${}^{238}\mathrm{U}$ concentration (${C}^{238}$) in radiopure samples of these minerals.

Mineral | Composition | Fiducial ${}^{238}$U Concentration [per Weight, g/g] |
---|---|---|

Halite | NaCl | ${10}^{-11}$ |

Gypsum | Ca(SO${}_{4})\phantom{\rule{-0.166667em}{0ex}}\xb7\phantom{\rule{-0.166667em}{0ex}}2$(H${}_{2}$O) | ${10}^{-11}$ |

Sinjarite | CaCl${}_{2}\phantom{\rule{-0.166667em}{0ex}}\xb7\phantom{\rule{-0.166667em}{0ex}}2($H${}_{2}$O) | ${10}^{-11}$ |

Olivine | Mg${}_{1.6}$Fe${}_{0.4}^{2+}$(SiO${}_{4}$) | ${10}^{-10}$ |

Phlogopite | KMg${}_{3}$AlSi${}_{3}$O${}_{10}$F(OH) | ${10}^{-10}$ |

Nchwaningite | Mn${}_{2}^{2+}$SiO${}_{3}$(OH)${}_{2}\phantom{\rule{-0.166667em}{0ex}}\xb7\phantom{\rule{-0.166667em}{0ex}}($H${}_{2}$O) | ${10}^{-10}$ |

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Baum, S.; Edwards, T. .; Freese, K.; Stengel, P.
New Projections for Dark Matter Searches with Paleo-Detectors. *Instruments* **2021**, *5*, 21.
https://doi.org/10.3390/instruments5020021

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Baum S, Edwards T , Freese K, Stengel P.
New Projections for Dark Matter Searches with Paleo-Detectors. *Instruments*. 2021; 5(2):21.
https://doi.org/10.3390/instruments5020021

**Chicago/Turabian Style**

Baum, Sebastian, Thomas D. P. Edwards, Katherine Freese, and Patrick Stengel.
2021. "New Projections for Dark Matter Searches with Paleo-Detectors" *Instruments* 5, no. 2: 21.
https://doi.org/10.3390/instruments5020021