#
On the Suppression of the Dark Matter-Nucleon Scattering Cross Section in the SE_{6}SSM

## Abstract

**:**

## 1. Introduction

## 2. The SE${}_{\mathbf{6}}$SSM

## 3. Dark Matter Nucleon Scattering Cross-section

## 4. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**Left**) The coupling ${g}_{h\chi \chi}$ and (

**Right**) the cross-section ${\sigma}_{SI}$ as a function of ${f}_{11}$ for ${\tilde{f}}_{11}=-0.5$, $tan\beta =2$, ${\tilde{\mu}}_{1}=2\phantom{\rule{0.166667em}{0ex}}\mathrm{TeV}$, ${\mu}_{11}=200\phantom{\rule{0.166667em}{0ex}}\mathrm{GeV}$ (solid lines), and ${\mu}_{11}=1\phantom{\rule{0.166667em}{0ex}}\mathrm{TeV}$ (dashed lines). The dotted lines correspond to the approximate expression for ${g}_{h\chi \chi}$ (20).

**Figure 2.**(

**Left**) The coupling ${R}_{Z11}$ and (

**Right**) the cross-section ${\sigma}^{p,n}$ as a function of ${f}_{11}$ for ${\tilde{f}}_{11}=-0.5$, $tan\beta =2$, ${\tilde{\mu}}_{1}=2\phantom{\rule{0.166667em}{0ex}}\mathrm{TeV}$, ${\mu}_{11}=200\phantom{\rule{0.166667em}{0ex}}\mathrm{GeV}$ (solid lines), and ${\mu}_{11}=1\phantom{\rule{0.166667em}{0ex}}\mathrm{TeV}$ (dashed lines). The upper solid and upper dashed lines represent ${\sigma}^{p}$ while lower solid and lower dashed lines are associated with ${\sigma}^{n}$. The dotted lines correspond to the approximate expression for ${R}_{Z11}$ (27).

**Table 1.**The $U{\left(1\right)}_{Y}$ and $U{\left(1\right)}_{N}$ charges of matter supermultiplets in the SE${}_{6}$SSM. The superfields ${N}_{i}^{c}$, ${\varphi}_{i}$, and $\varphi $ have zero $U{\left(1\right)}_{Y}$ and $U{\left(1\right)}_{N}$ charges.

${\mathit{Q}}_{\mathit{i}}$ | ${\mathit{u}}_{\mathit{i}}^{\mathit{c}}$ | ${\mathit{d}}_{\mathit{i}}^{\mathit{c}}$ | ${\mathit{L}}_{\mathit{i}},{\mathit{L}}_{4}$ | ${\mathit{e}}_{\mathit{i}}^{\mathit{c}}$ | ${\mathit{S}}_{\mathit{i}},\mathit{S}$ | ${\mathit{H}}_{\mathit{\alpha}}^{\mathit{u}},{\mathit{H}}_{\mathit{u}}$ | ${\mathit{H}}_{\mathit{\alpha}}^{\mathit{d}},{\mathit{H}}_{\mathit{d}}$ | ${\mathit{D}}_{\mathit{i}}$ | ${\overline{\mathit{D}}}_{\mathit{i}}$ | ${\overline{\mathit{L}}}_{4}$ | $\overline{\mathit{S}}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

$\sqrt{\frac{5}{3}}{Q}_{i}^{Y}$ | $\frac{1}{6}$ | $-\frac{2}{3}$ | $\frac{1}{3}$ | $-\frac{1}{2}$ | 1 | 0 | $\frac{1}{2}$ | $-\frac{1}{2}$ | $-\frac{1}{3}$ | $\frac{1}{3}$ | $\frac{1}{2}$ | 0 |

$\sqrt{40}{Q}_{i}^{N}$ | 1 | 1 | 2 | 2 | 1 | 5 | $-2$ | $-3$ | $-2$ | $-3$ | $-2$ | $-5$ |

**Table 2.**Transformation properties of different supermultiplets under the discrete symmetries ${\tilde{Z}}_{2}^{H}$, ${Z}_{2}^{M}$ and ${Z}_{2}^{E}$. The signs + and − correspond to the states which are even and odd under different ${Z}_{2}$ symmetries.

${\mathit{Q}}_{\mathit{i}},{\mathit{u}}_{\mathit{i}}^{\mathit{c}},{\mathit{d}}_{\mathit{i}}^{\mathit{c}},{\mathit{L}}_{\mathit{i}},{\mathit{e}}_{\mathit{i}}^{\mathit{c}},{\mathit{N}}_{\mathit{i}}^{\mathit{c}}$ | ${\overline{\mathit{D}}}_{\mathit{i}},{\mathit{D}}_{\mathit{i}},{\mathit{H}}_{\mathit{\alpha}}^{\mathit{d}},{\mathit{H}}_{\mathit{\alpha}}^{\mathit{u}},{\mathit{S}}_{\mathit{i}},{\mathit{\varphi}}_{\mathit{i}}$ | ${\mathit{H}}_{\mathit{d}},{\mathit{H}}_{\mathit{u}},\mathit{S},\overline{\mathit{S}},\mathit{\varphi}$ | ${\mathit{L}}_{4},{\overline{\mathit{L}}}_{4}$ | |
---|---|---|---|---|

${\tilde{Z}}_{2}^{H}$ | − | − | + | + |

${Z}_{2}^{M}$ | − | + | + | − |

${Z}_{2}^{E}$ | + | − | + | − |

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Nevzorov, R. On the Suppression of the Dark Matter-Nucleon Scattering Cross Section in the SE_{6}SSM. *Symmetry* **2022**, *14*, 2090.
https://doi.org/10.3390/sym14102090

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Nevzorov R. On the Suppression of the Dark Matter-Nucleon Scattering Cross Section in the SE_{6}SSM. *Symmetry*. 2022; 14(10):2090.
https://doi.org/10.3390/sym14102090

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Nevzorov, Roman. 2022. "On the Suppression of the Dark Matter-Nucleon Scattering Cross Section in the SE_{6}SSM" *Symmetry* 14, no. 10: 2090.
https://doi.org/10.3390/sym14102090