# New Physics of Strong Interaction and Dark Universe

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## Abstract

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## 1. Introduction

## 2. New Physics from QCD and QCD-Like Models

#### 2.1. General Features of New Physics of Strong Interactions in Dark Cosmology

#### 2.1.1. New Stable Quarks

#### 2.1.2. QCD-Like Models

- The chiral symmetry $\mathrm{SU}{(3)}_{\mathrm{L}}\times \mathrm{SU}{(3)}_{\mathrm{R}}$;
- SU(4) subgroup corresponding to the two-flavor model without singlet H-quark S;
- Two-flavor chiral group $\mathrm{SU}{(2)}_{\mathrm{L}}\times \mathrm{SU}{(2)}_{\mathrm{R}}$, which is a subgroup of both former subgroups.

- Explicitly—by the electroweak and Yukawa interactions, (9) and (11), and the H-quark masses;
- Dynamically—by H-quark condensate [52,53]:$$\begin{array}{c}\langle \overline{Q}Q+\overline{S}S\rangle =\frac{1}{2}\langle {\overline{P}}_{\mathrm{L}}{M}_{0}{P}_{\mathrm{R}}+{\overline{P}}_{\mathrm{R}}{M}_{0}^{\u2020}{P}_{\mathrm{L}}\rangle ,\phantom{\rule{2.em}{0ex}}{P}_{\mathrm{R}}=\omega {P}_{\mathrm{L}}{}^{\mathrm{C}},\phantom{\rule{2.em}{0ex}}{M}_{0}=\left(\begin{array}{ccc}0& \epsilon & 0\\ \epsilon & 0& 0\\ 0& 0& \epsilon \end{array}\right).\end{array}$$

#### 2.2. Exotic States of New Colored Objects

#### 2.2.1. Fractons

#### 2.2.2. Fractionally Charged States in QCD-Like Models

#### 2.2.3. Multiple Charged States in QCD and QCD-Like Models

#### 2.3. Strongly Interacting Dark Matter Candidates

#### 2.3.1. Stable Heavy Quark Hadrons

#### 2.3.2. Dark Atoms with Primordial Helium

## 3. New Physics of Strong Interaction in the Galaxy

#### 3.1. New Components of Cosmic Rays

#### 3.1.1. UHECR Interaction with Dark Matter

**Region 1**: ${M}_{\tilde{\sigma}}>2{m}_{{\tilde{\pi}}^{0}}$ and $u\ge {M}_{\tilde{\sigma}}$. At small angles of mixing, ${s}_{\theta}$, and large masses of H-pions it is possible to obtain a significant fraction of H-pions.

**Region 2**: the same relation between ${M}_{\tilde{\sigma}},\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}{m}_{{\tilde{\pi}}^{0}},\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}u$ but the H-pion mass is smaller, ${m}_{\tilde{\pi}}\approx $ 300–600 GeV, H-pion fraction is small here.

**Region 3**: ${M}_{\tilde{\sigma}}<2{m}_{\tilde{\pi}}$. This domain is always possible and it is presented in all figures. Note, decay $\tilde{\sigma}\to \tilde{\pi}\tilde{\pi}$ is prohibited. H-pion fraction in the DM relic can be large if the mass ${m}_{{\tilde{\pi}}^{0}}$ is large and the mixing angle is small. In Figure 2 and Figure 3, we illustrate the regions changing for lower values of the v.e.v. u and $sin\theta $.

#### 3.1.2. Creation of New Components in the UHECR Sources

#### 3.2. Multimessenger Probes for New Physics Effects

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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1. |

**Figure 1.**Numerical solution of kinetic equations system in a phase diagram in terms of ${M}_{\tilde{\sigma}}$ and ${m}_{\tilde{\pi}}$, other parameters are also indicated.

**Figure 2.**Analogous phase diagram in terms of ${M}_{\tilde{\sigma}}$ and ${m}_{\tilde{\pi}}$, but for much smaller u.

**Figure 3.**Phase diagram in terms of ${M}_{\tilde{\sigma}}$ and ${m}_{\tilde{\pi}}$, the same u but the mixing is smaller.

**Table 1.**The lightest (pseudo)scalar H-hadrons in $\mathrm{Sp}(2{\chi}_{\tilde{c}})$ model with two and three flavors of H-quarks (in the limit of vanishing mixings). The lower half of the table lists the states present only in the three-flavor version of the model containing the singlet H-quark S. T is the weak isospin. $\tilde{G}$ denotes hyper-G-parity of a state. $\tilde{B}$ is the H-baryon number. ${Q}_{\mathrm{em}}$ is the electric charge (in units of the positron charge $e=\left|e\right|$). The H-quark charges are ${Q}_{\mathrm{em}}^{U}=({Y}_{Q}+1)/2$, ${Q}_{\mathrm{em}}^{D}=({Y}_{Q}-1)/2$, and ${Q}_{\mathrm{em}}^{S}={Y}_{S}$, which is seen from (22).

State | H-Quark Current | ${\mathit{T}}^{\tilde{\mathit{G}}}({\mathit{J}}^{\mathbf{PC}})$ | $\tilde{\mathit{B}}$ | ${\mathit{Q}}_{\mathbf{em}}$ |
---|---|---|---|---|

$\sigma $ | $\overline{Q}Q+\overline{S}S$ | ${0}^{+}({0}^{++})$ | 0 | 0 |

$\eta $ | $i\left(\overline{Q}{\gamma}_{5}Q+\overline{S}{\gamma}_{5}S\right)$ | ${0}^{+}({0}^{-+})$ | 0 | 0 |

${a}_{k}$ | $\overline{Q}{\tau}_{k}Q$ | ${1}^{-}({0}^{++})$ | 0 | $\pm 1$, 0 |

${\pi}_{k}$ | $i\overline{Q}{\gamma}_{5}{\tau}_{k}Q$ | ${1}^{-}({0}^{-+})$ | 0 | $\pm 1$, 0 |

A | ${\overline{Q}}^{\mathrm{C}}\epsilon \omega Q$ | ${0}^{\phantom{+}}({0}^{-\phantom{+}})$ | 1 | ${Y}_{Q}$ |

B | $i{\overline{Q}}^{\mathrm{C}}\epsilon \omega {\gamma}_{5}Q$ | ${0}^{\phantom{+}}({0}^{+\phantom{+}})$ | 1 | ${Y}_{Q}$ |

f | $\overline{Q}Q-2\overline{S}S$ | ${0}^{+}({0}^{++})$ | 0 | 0 |

${\eta}^{\prime}$ | $i\left(\overline{Q}{\gamma}_{5}Q-2\overline{S}{\gamma}_{5}S\right)$ | ${0}^{+}({0}^{-+})$ | 0 | 0 |

${\mathcal{K}}^{\u2605}$ | $\overline{S}Q$ | ${\frac{1}{2}}^{\phantom{+}}({0}^{+\phantom{+}})$ | 0 | ${Y}_{Q}/2-{Y}_{S}\pm 1/2$ |

$\mathcal{K}$ | $i\overline{S}{\gamma}_{5}Q$ | ${\frac{1}{2}}^{\phantom{+}}({0}^{-\phantom{+}})$ | 0 | ${Y}_{Q}/2-{Y}_{S}\pm 1/2$ |

$\mathcal{A}$ | ${\overline{S}}^{\mathrm{C}}\omega Q$ | ${\frac{1}{2}}^{\phantom{+}}({0}^{-\phantom{+}})$ | 1 | ${Y}_{Q}/2+{Y}_{S}\pm 1/2$ |

$\mathcal{B}$ | $i{\overline{S}}^{\mathrm{C}}\omega {\gamma}_{5}Q$ | ${\frac{1}{2}}^{\phantom{+}}({0}^{+\phantom{+}})$ | 1 | ${Y}_{Q}/2+{Y}_{S}\pm 1/2$ |

**Table 2.**List of possible integer charged techniparticles. Candidates for even charged constituents of dark atoms are marked bold [10].

q | $\mathit{UU}(\mathit{q}+1)$ | $\mathit{UD}(\mathit{q})$ | $\mathit{DD}(\mathit{q}-1)$ | ${\mathit{\nu}}^{\prime}({\displaystyle \frac{1-3\mathit{q}}{2}})$ | $\mathit{\zeta}({\displaystyle \frac{-1-3\mathit{q}}{2}})$ |
---|---|---|---|---|---|

1 | 2 | 1 | 0 | $-1$ | $-\mathbf{2}$ |

3 | 4 | 3 | 2 | $-\mathbf{4}$ | $-5$ |

5 | 6 | 5 | 4 | $-7$ | $-\mathbf{8}$ |

7 | 8 | 7 | 6 | $-\mathbf{10}$ | $-11$ |

${\mathit{J}}^{\mathit{P}}$ | T | Isotopic Content | Quark Content |
---|---|---|---|

${0}^{-}$ | $\frac{1}{2}$ | $M=({M}^{0}\phantom{\rule{0.166667em}{0ex}}{M}^{-})$ | ${M}^{0}=\overline{U}u$, ${M}^{-}=\overline{U}d$ |

$\frac{1}{2}$ | 1 | ${B}_{1}=({B}_{1}^{++}\phantom{\rule{0.166667em}{0ex}}{B}_{1}^{+}\phantom{\rule{0.166667em}{0ex}}{B}_{1}^{0})$ | ${B}_{1}^{++}=Uuu,{B}_{1}^{+}=Uud,{B}_{1}^{0}=Udd$ |

$\frac{1}{2}$ | $\frac{1}{2}$ | ${B}_{2}=({B}_{2}^{++}\phantom{\rule{0.166667em}{0ex}}{B}_{2}^{+})$ | ${B}_{2}^{++}=UUu,{B}_{2}^{+}=UUd$ |

$\frac{1}{2}$ | 0 | $({B}_{3}^{++})$ | ${B}_{3}^{++}=UUU$ |

${\mathit{N}}_{\mathit{a}}{\mathit{M}}_{\mathit{b}}\to {\mathit{N}}_{\mathit{c}}{\mathit{M}}_{\mathit{d}}$ | ${\Delta}_{\mathbf{ab}}=\mathit{f}(\Delta \mathit{M},\Delta \mathit{m})$ | Signum ${\Delta}_{\mathbf{ab}}$ |
---|---|---|

$p{M}^{0}\to n{M}^{+}$ | ${\Delta}_{p0}=\Delta M+\Delta m$ | ${\Delta}_{p0}>0$ (threshold) |

$n{M}^{+}\to p{M}^{0}$ | ${\Delta}_{n+}=-\Delta M-\Delta m$ | ${\Delta}_{n+}<0$ (non-threshold) |

$n{M}^{0}\to p{M}^{-}$ | ${\Delta}_{n0}=\Delta M-\Delta m$ | ${\Delta}_{n0}>0\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}(\Delta M>\Delta m)$ |

$p{M}^{-}\to n{M}^{0}$ | ${\Delta}_{p-}=-\Delta M+\Delta m$ | ${\Delta}_{p-}>0\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}(\Delta M<\Delta m)$ |

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**MDPI and ACS Style**

Beylin, V.; Khlopov, M.; Kuksa, V.; Volchanskiy, N.
New Physics of Strong Interaction and Dark Universe. *Universe* **2020**, *6*, 196.
https://doi.org/10.3390/universe6110196

**AMA Style**

Beylin V, Khlopov M, Kuksa V, Volchanskiy N.
New Physics of Strong Interaction and Dark Universe. *Universe*. 2020; 6(11):196.
https://doi.org/10.3390/universe6110196

**Chicago/Turabian Style**

Beylin, Vitaly, Maxim Khlopov, Vladimir Kuksa, and Nikolay Volchanskiy.
2020. "New Physics of Strong Interaction and Dark Universe" *Universe* 6, no. 11: 196.
https://doi.org/10.3390/universe6110196