# An Overview of the Searches for the Violation of the Charge-Parity Symmetry in the Leptonic Sector

## Abstract

**:**

## 1. Introduction

- existence of baryon number violation,
- existence of Charge (C) and Charge-Parity (CP) symmetry violations,
- departure from thermal equilibrium.

## 2. Quark Mixing and CP Violation

## 3. Neutrino Mixing and CP Violation

^{12}GeV to 10

^{15}GeV, N cannot be created in particle accelerators. On the other hand, such particles could be produced after the Big Bang when the temperature of the early universe was still very high and their numbers were effectively frozen once the temperature decreased. N could then decay both to charged leptons and antileptons. However, if leptonic CP violation exists, these decays would not have the same rates, leading eventually to an asymmetry between the number of leptons and antileptons that, in turn, could be converted into baryon–antibaryon asymmetry.

## 4. Neutrino Oscillations

## 5. Experimental Landscape

## 6. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BAU | Baryon Asymmetry of Universe |

CP | Charge Parity |

LBL | Long BaseLine |

IO | Inverted Ordering |

NO | Normal Ordering |

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**Figure 1.**Asymmetry averaged over an energy window given by the full width at half maximum of ${\nu}_{e}$ (${\overline{\nu}}_{e}$) appearance probabilities, computed with Equation (26), as a function of the baseline. A constant density of 2.8 $\mathrm{g}{\mathrm{cm}}^{-3}$ is assumed and the values of other oscillation parameters (${\theta}_{ij}$ and $\mathsf{\Delta}{m}_{ij}^{2}$), apart from ${\delta}_{CP}$, are taken from [8,9]. Asymmetry is shown for the two possible neutrino mass orderings with the bands indicating variation from different possible ${\delta}_{CP}$ values.

**Figure 2.**The first maximum of ${\nu}_{\mu}\to {\nu}_{e}$ (${\overline{\nu}}_{\mu}\to {\overline{\nu}}_{e}$) appearance probability shown in solid (dashed) curves for a set of values of ${\delta}_{CP}$ as a function of (anti)neutrino energy for a baseline of 1300 km computed with Equation (26). The panel on the left (right) is for normal (inverted) neutrino mass ordering. A constant density of 2.8 $\mathrm{g}{\mathrm{cm}}^{-3}$ is assumed, and the values of other oscillation parameters (${\theta}_{ij}$ and $\mathsf{\Delta}{m}_{ij}^{2}$), apart from ${\delta}_{CP}$, are taken from [8,9].

**Figure 3.**The number of events ${\nu}_{e}$ like events from running in $\nu $ beam versus $\overline{\nu}$ beam modes is taken from [34]. The region in grey corresponds to the best fit values of oscillation parameters based on the collected data, while the somewhat elliptical coloured contours indicate expected event numbers in each category under different hypothesis for ${sin}^{2}{\theta}_{23}$, ${\delta}_{CP}$, and the sign of mass ordering.

**Figure 4.**T2K, NOvA, and Super-Kamiokande 90% confidence level contours in the ${sin}^{2}{\theta}_{23}$-${\delta}_{CP}$ parameter plane for normal (

**left panel**) and inverted (

**right panel**) mass ordering taken from [34]. The best fit point for each experiment is denoted by a cross.

**Figure 5.**The fraction of ${\delta}_{CP}$ parameter space for which CP conservation could be excluded with $3\sigma $ (black) or $5\sigma $ confidence level from [39]. Prior knowledge of mass ordering is assumed.

**Figure 6.**Sensitivity to ${\delta}_{CP}=-\pi /2$ and the coverage of ${\delta}_{CP}$ parameter space as a function of time at different significance levels assuming normal mass ordering from [41]. Horizontal arrows indicate progressive second-phase improvements such as further addition of two detector modules (FD-3, FD-4), the upgrade of near detector facility (MCND) for improvement of systematic uncertainties, or the beam power upgrade.

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**MDPI and ACS Style**

Galymov, V.
An Overview of the Searches for the Violation of the Charge-Parity Symmetry in the Leptonic Sector. *Symmetry* **2024**, *16*, 130.
https://doi.org/10.3390/sym16010130

**AMA Style**

Galymov V.
An Overview of the Searches for the Violation of the Charge-Parity Symmetry in the Leptonic Sector. *Symmetry*. 2024; 16(1):130.
https://doi.org/10.3390/sym16010130

**Chicago/Turabian Style**

Galymov, Vyacheslav.
2024. "An Overview of the Searches for the Violation of the Charge-Parity Symmetry in the Leptonic Sector" *Symmetry* 16, no. 1: 130.
https://doi.org/10.3390/sym16010130