# Charge Asymmetry of New Stable Families in Baryon Asymmetrical Universe

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## Abstract

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## 1. Introduction

## 2. Balance between Baryon and Dark Matter Densities Due to Sphaleron Transitions

#### 2.1. Model

#### 2.2. Chemical Potentials

- ${\mu}_{uL/R},{\mu}_{dL/R}$ for all left-/right-handed and up-/down-like quarks, correspondingly;
- ${\mu}_{eL/R}$ for all charged leptons;
- $\mu ={\sum}_{i}{\mu}_{{\nu}_{i}L}$, ${\mu}_{{\nu}_{i}R}$, i=e, $\mu $, $\tau $ for left-/right-handed neutrino;
- ${\mu}_{W}$ for ${W}^{-}$, note that the chemical potential of neutral vector boson is vanishing;
- ${\mu}_{0}$ and ${\mu}_{-}$ for the Higgs doublet.

- ${\mu}_{UL/R},{\mu}_{DL/R}$ for left-/right-handed U and D correspondingly;
- ${\mu}_{EL/R},{\mu}_{NL/R}$ for left-/right-handed E and N correspondingly.

- for any up-/down-like right fermion “i”$${\mu}_{iR}={\mu}_{iL}\pm {\mu}_{0};$$
- for particle “i” with isospin projection −1/2 and corresponding particle “j” with isospin projection 1/2$${\mu}_{i}={\mu}_{j}+{\mu}_{W};$$

#### 2.3. Equations

#### 2.4. Density Rate

#### 2.5. Non-Equal Masses

- both ratios strongly depend on the mass difference of U and D quarks, but hardly depend on the mass of the heavy electron E;
- the ratio $\frac{{\mathsf{\Omega}}_{DM}}{{\mathsf{\Omega}}_{b}}$ is suppressed if D quark is too heavy. This fact can be used to correct the result obtained in the approximation of equal masses;
- standard lepton to baryon asymmetry increases.

## 3. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The ratio of dark and baryonic matter densities for the case of sphaleron transition when freezing out temperature is above the temperature of the EWPT: ${T}_{*}>{T}_{c}$. The observed ratio plotted according to PLANCK collaboration data [31]. In this work the equal masses approximation was used.

**Figure 2.**The ratio of dark and baryonic matter densities for the case of sphaleron transition when freezing out temperature is below the temperature of the EWPT: ${T}_{*}<{T}_{c}$. The observed ratio plotted according to PLANCK collaboration data [31]. In this paper the equal masses approximation was used.

**Figure 3.**The absolute value of lepton number density to baryon number density ratio for ${T}_{*}>{T}_{c}$ (

**right**) and for ${T}_{*}<{T}_{c}$ (

**left**). The approximation of equal masses was used. Dark matter density provided only by anti-clusters $\overline{U}\overline{U}\overline{U}$.

**Figure 4.**The ratio of the dark and baryonic matter densities (

**left column**) and the ratio of the lepton and baryon number densities (

**right column**) for different masses of heavy fermions.

**Top row:**sphaleron transitions freeze out before EWPT.

**Bottom row:**sphaleron transitions freeze out after EWPT. The red dot corresponds to the value obtained in the approximation of equal masses.

Particle | Mass | Charge q | Charge y | New Lepton Number | New Baryon Number |
---|---|---|---|---|---|

U | ∼1 TeV | $\frac{2}{3}$ | $-\frac{1}{3}$ | 0 | $\frac{1}{3}$ |

D | ∼1 TeV | $-\frac{1}{3}$ | $-\frac{1}{3}$ | 0 | $\frac{1}{3}$ |

E | ∼1 TeV | $-1$ | 1 | 1 | 0 |

N | ∼50 GeV | 0 | 1 | 1 | 0 |

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**MDPI and ACS Style**

Beylin, V.A.; Khlopov, M.Y.; Sopin, D.O.
Charge Asymmetry of New Stable Families in Baryon Asymmetrical Universe. *Symmetry* **2023**, *15*, 657.
https://doi.org/10.3390/sym15030657

**AMA Style**

Beylin VA, Khlopov MY, Sopin DO.
Charge Asymmetry of New Stable Families in Baryon Asymmetrical Universe. *Symmetry*. 2023; 15(3):657.
https://doi.org/10.3390/sym15030657

**Chicago/Turabian Style**

Beylin, Vitaly A., Maxim Yu. Khlopov, and Danila O. Sopin.
2023. "Charge Asymmetry of New Stable Families in Baryon Asymmetrical Universe" *Symmetry* 15, no. 3: 657.
https://doi.org/10.3390/sym15030657