# Hadronic and Hadron-Like Physics of Dark Matter

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. New Stable Hadrons

#### 2.1. Gauge Structure of Chiral-Symmetrical Model with New Quarks

- to interpret the field ${V}_{\mu}$ as a new non-standard abelian field which mixes with ${V}_{\mu}^{3}$ in analogy with the standard procedure,
- to assume that ${V}_{\mu}$ is standard abelian field which does not mix with ${V}_{\mu}^{3}$.

#### 2.2. The Extension of Standard Quark Sector with Stable Singlet Quark

#### 2.3. Constraints on the New Quarks Following from the Precision Electroweak Measurements

#### 2.4. Composition of New Heavy Hadrons and Long-Distance Interactions with Nucleons

#### 2.5. The Properties of New Heavy Particles and Hadronic Dark Matter

## 3. Hypercolor Extensions of Standard Model

#### 3.1. Lagrangian and Global Symmetry of Symplectic QCD with ${n}_{F}=2,$ 3 Hyperquark Flavors

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

#### 3.2. Linear Sigma Model as an Effective Field Theory of Constituent H-Quarks

#### 3.2.1. Interactions of the Constituent H-Quarks with H-Hadrons and the Electroweak Gauge Bosons

#### 3.2.2. Interactions of the (Pseudo)scalar Fields with the Electroweak Gauge Bosons

#### 3.2.3. Self-Interactions and Masses of the (Pseudo)Scalar Fields

#### 3.2.4. Accidental Symmetries

#### 3.3. Physics and Cosmology of Hypercolor SU(4) and SU(6) Models

- (1)
- large ${E}_{T,mis}$ reaction due to production of stable ${\tilde{\pi}}^{0}$ and neutrino from ${\tilde{\pi}}^{\pm}$ and/or ${W}^{\pm}$ decays, or two leptons from charged H-pion and W decays (this is reaction of associated production, $W,\phantom{\rule{0.166667em}{0ex}}{\tilde{\pi}}^{\pm},\phantom{\rule{0.166667em}{0ex}}{\tilde{\pi}}^{0}$ final state of the process);
- (2)
- large ${E}_{T,mis}$ due to creation of two stable ${\tilde{\pi}}^{0}$ and neutrino from decay of charged H-pions, ${\tilde{\pi}}^{\pm}$, one lepton from ${\tilde{\pi}}^{\pm}$ and two quark jets from ${W}^{\pm}$ decay (the same final state with particles $W,\phantom{\rule{0.166667em}{0ex}}{\tilde{\pi}}^{\pm},\phantom{\rule{0.166667em}{0ex}}{\tilde{\pi}}^{0}$);
- (3)
- large ${E}_{T,mis}$ due to two stable neutral H-pions and neutrino from charged H-pion decay, two leptons (virtual Z, and ${\tilde{\pi}}^{+},\phantom{\rule{0.166667em}{0ex}}{\tilde{\pi}}^{-}$ in the final state);
- (4)
- large ${E}_{T,mis}$ due to two final neutral H-pions and neutrino from ${\tilde{\pi}}^{\pm}$, one lepton which originated from virtual W, ${\tilde{\pi}}^{+},\phantom{\rule{0.166667em}{0ex}}{\tilde{\pi}}^{0}$ final states.

## 4. Dark Atom Physics and Cosmology

#### 4.1. Dark Atoms Structure, Effects and Probes

#### 4.2. Models of Stable Multiple Charged Particles

#### 4.2.1. Double Cherged Stable Particles of Fourth Generation

^{4}$He$ in atom-like state of O-helium [127]. Origin of X-particles with larger charges seem highly unprobable in this model.

#### 4.2.2. Stable Charged Techniparticles in Walking Technicolor

^{4}$H{e}^{++}$ nuclei and form O-helium atoms, dominating in the observed dark matter. If both $TB$ and ${L}^{\prime}$ are conserved a two-component techni-O-helium dark matter scenario is possible.

#### 4.3. Effects of Hadronic Dark Matter

#### 4.3.1. Cosmology of Hadronic Dark Matter

^{2}is taken as the geometrical cross section for SIMP collisions with baryons. Therefore, SIMPs should not follow baryonic matter in formation of the baryonic objects. SIMPs can be captured only by sufficiently dense matter proto-object clouds and objects, like planets and stars (see [135]).

#### 4.3.2. Probes for Hadronic Dark Matter

#### 4.4. Open Problems of Hadronic Dark Matter

## 5. Composite Dark Matter in the Context of Cosmo–Particle Physics

^{6}–10

^{10}) GeV to provide masses for new fermions [22]. Analogously, an origin of heavy singlet quark as a consequence of the chain of transitions like $E\left(6\right)\to SO\left(10\right)\to SU\left(5\right)$ also stems from an additional Higgs doublet and corresponding symmetry breaking at a high scale. We suppose that both of these variants of heavy fermion emergence take place at the end of the inflation stage (or after it) due to some first Higgs transition. Then, massive non-stable states decay contributing to the quark-gluon plasma, while stable massive quarks go on interacting with photons. Later, after the second (electroweak) Higgs transition, remaining “light” quarks become massive, and (at the hadronic epoch) hadrons can be formed as bound states of the quarks. New “heavy-light” mesons also produced after the EW symmetry breaking. At the same time, we can just appeal to some special unknown dynamics which should break the symmetry at some higher scale. It may cause nontrivial features of cosmological scenario, which deserve further analysis.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Algebras su(6) and sp(6)

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${J}^{P}={0}^{-}$ | $T={\displaystyle \frac{1}{2}}$ | ${M}_{U}=\left({M}_{U}^{0}\phantom{\rule{0.166667em}{0ex}}{M}_{U}^{-}\right)$ | ${M}_{U}^{0}=\overline{U}u$, ${M}_{U}^{-}=\overline{U}d$ |

${J}^{P}={0}^{-}$ | $T={\displaystyle \frac{1}{2}}$ | ${M}_{D}=\left({M}_{D}^{+}\phantom{\rule{0.166667em}{0ex}}{M}_{D}^{0}\right)$ | ${M}_{D}^{+}=\overline{D}u$, ${M}_{D}^{0}=\overline{D}d$ |

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

$J={\displaystyle \frac{1}{2}}$ | $T=1$ | ${B}_{1D}=\left({B}_{1D}^{+}\phantom{\rule{0.166667em}{0ex}}{B}_{1D}^{0}\phantom{\rule{0.166667em}{0ex}}{B}_{1D}^{-}\right)$ | ${B}_{1D}^{+}=Duu,\phantom{\rule{0.166667em}{0ex}}{B}_{1D}^{-}=Ddd,{B}_{1D}^{0}=Dud$ |

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

$J={\displaystyle \frac{1}{2}}$ | $T={\displaystyle \frac{1}{2}}$ | ${B}_{2D}=\left({B}_{2D}^{0}\phantom{\rule{0.166667em}{0ex}}{B}_{2D}^{-}\right)$ | ${B}_{2D}^{0}=DDu,{B}_{2D}^{-}=DDd$ |

$J={\displaystyle \frac{3}{2}}$ | $T=0$ | $\left({B}_{3U}^{++}\right)$ | ${B}_{3U}^{++}=UUU$ |

$J={\displaystyle \frac{3}{2}}$ | $T=0$ | $\left({B}_{3D}^{-}\right)$ | ${B}_{3D}^{-}=DDD$ |

**Table 2.**The lightest (pseudo)scalar H-hadrons in $\mathrm{Sp}\left(2{\chi}_{\tilde{c}}\right)$ 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. T is the weak isospin. $\tilde{G}$ denotes hyper-G-parity of a state (see Section 3.2.4). $\tilde{B}$ 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 (67).

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

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

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

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

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

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

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

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

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

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

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

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

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

**Table 3.**List of possible integer charged techniparticles. Candidates for even charged constituents of dark atoms are marked bold.

q | $\mathit{UU}(\mathit{q}+1)$ | $\mathit{UD}\left(\mathit{q}\right)$ |
---|