# Directional Observation of Cold Dark Matter Particles (WIMP) in Light Target Experiments

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## Abstract

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## 1. Introduction

## 2. Scheme of WIMP Elastic Interaction with Detector Material. Energy and Angular Distributions of Recoil Nuclei

## 3. Scheme of Track Modeling in GEANT4

## 4. Models of Cold Dark Matter (WIMP) in micrOMEGAs. Constraints on WIMP Fluxes for Various Models

## 5. Elastic Interaction of Solar Neutrinos with Detector Material as a Directional Background for WIMP Observations

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**General scheme of WIMP elastic interaction with a target nucleus, in which a recoil nucleus is produced. WIMP velocities before the interaction follow a Maxwell distribution with an average velocity 220 km/s and $\sigma =156$ km/s.

**Figure 2.**Distributions of ${10}^{5}$ simulated hydrogen (H) recoil nuclei over their energies ${E}_{rec}$ and the projection of a 3D recoil nucleus incidence angle on a 2D detector plane $tg{\theta}_{z}$ for various WIMP masses.

**Figure 3.**Distributions of ${10}^{5}$ simulated carbon (C) recoil nuclei over their energies ${E}_{rec}$ and the projection of a 3D recoil nucleus incidence angle on a 2D detector plane $tg{\theta}_{z}$ for various WIMP masses.

**Figure 4.**Distributions of ${10}^{5}$ simulated fluorine (F) recoil nuclei over their energies ${E}_{rec}$ and the projection of a 3D recoil nucleus incidence angle on a 2D detector plane $tg{\theta}_{z}$ for various WIMP masses.

**Figure 5.**Examples of tracks of hydrogen (H) (

**left**plot) and carbon (C) (

**right**plot) nuclei in the nuclear emulsion obtained using the GEANT4 Nuclear Recoil Physics List. Red dots represent track points, the blue line is the least squares best fit of track points. The units are nm.

**Figure 6.**Distributions of model hydrogen (H) (

**left**) and carbon (C) (

**right**) nuclei tracks over the lengths of their track lengths in the emulsion.

**Figure 7.**Distributions of model hydrogen (H) and carbon (C) nuclei tracks over the angle between the primary direction of a recoil nucleus and the direction obtained as best fit of their track points in the nuclear emulsion. These distributions determine the extent of scattering of recoil nuclei as they propagate through the emulsion material. The left figure shows the case for (H), the right—for (C).

**Figure 8.**Distributions of track lengths in the nuclear emulsion (

**left**) and the propane target (

**right**) for hydrogen and carbon recoil nuclei for WIMPs with masses 10 and 100 GeV.

**Figure 9.**Angular distributions relative to the direction <<toward the Cygnus constellation>> of tracks in a nuclear emulsion (

**left**) and in liquid propane (

**right**) for hydrogen and carbon recoil nuclei for WIMPs with masses of 10 and 100 GeV. Only tracks with a length greater than 80 nm are considered.

**Figure 10.**Track length distributions for carbon and fluorine recoil nuclei in ${\mathrm{C}}_{3}{\mathrm{F}}_{}$ for WIMPs with masses 10 and 100 GeV.

**Figure 11.**Distributions over the angles between the track and the direction <<toward the Cygnus constellation>> in ${\mathrm{C}}_{3}{\mathrm{F}}_{8}$ for carbon and fluorine recoil nuclei and WIMP masses 10 and 100 GeV.

**Figure 12.**Cross sections of the NMSSM [27] WIMP interactions with nucleons and constraints set by the CRESST [30], DarkSide [32], and XENON1T [33] experiments (

**left**). Number of the NMSSM WIMP events per kg of target (H,C,N,O) per day with the account of the relic density $\Omega \xb7{\mathrm{h}}^{2}$ (

**right**).

**Figure 13.**IDM simulations vs. experimental constraints. Blue points denote different IDM variants (for different choice of model parameters) in the “DM mass—relic density” parameter space. Red lines denote the contemporary constraints on the value of $\Omega \xb7{\mathrm{h}}^{2}$.

**Figure 14.**Cross sections for interactions of DM particles of the IDM with nucleons for different masses vs. the existing experimental constraints set by XENON1T [30], DarkSide [32], and CRESST [33] (

**left**). Number of DM-nucleon interactions per kg of target per day for various light targets (H,C,N,O) for different DM particle masses and $\Omega \xb7{\mathrm{h}}^{2}<0.12$ (

**right**).

**Figure 15.**Distributions of the recoil nuclei from solar neutrino interactions over neutrino energies and recoil nuclei track lengths. The points represent simulated hydrogen (H) and carbon (C) recoil nuclei events in nuclear emulsion and propane. A cut (minimal track length ∼2 nm) has been applied to all the simulated tracks. This cut is motivated by GEANT4 capabilities.

**Figure 16.**Distribution of track lengths of hydrogen (H) and carbon (C) recoil nuclei from solar neutrino interactions in nuclear emulsion, ${\mathrm{C}}_{3}{\mathrm{H}}_{8}$ and ${\mathrm{C}}_{3}{\mathrm{F}}_{8}$.

**Figure 17.**Estimates of number of WIMP and neutrino events in the emulsion, ${\mathrm{C}}_{3}{\mathrm{H}}_{8}$, and ${\mathrm{C}}_{3}{\mathrm{F}}_{8}$.

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**MDPI and ACS Style**

Anokhina, A.; Gulyaeva, V.; Khalikov, E.; Kurochkin, E.; Roganova, T.; Ursov, E.; Vidulin, I.
Directional Observation of Cold Dark Matter Particles (WIMP) in Light Target Experiments. *Universe* **2021**, *7*, 215.
https://doi.org/10.3390/universe7070215

**AMA Style**

Anokhina A, Gulyaeva V, Khalikov E, Kurochkin E, Roganova T, Ursov E, Vidulin I.
Directional Observation of Cold Dark Matter Particles (WIMP) in Light Target Experiments. *Universe*. 2021; 7(7):215.
https://doi.org/10.3390/universe7070215

**Chicago/Turabian Style**

Anokhina, Anna, Vasilisa Gulyaeva, Emil Khalikov, Evgeny Kurochkin, Tatiana Roganova, Eduard Ursov, and Ivan Vidulin.
2021. "Directional Observation of Cold Dark Matter Particles (WIMP) in Light Target Experiments" *Universe* 7, no. 7: 215.
https://doi.org/10.3390/universe7070215