# On Mikheyev–Smirnov–Wolfenstein Resonance Widths

## Abstract

**:**

## 1. Introduction

## 2. Framework and Definitions

## 3. Half-Widths with Respect to the Variable $\mathit{y}$

## 4. Full Consideration of the Resonance Width

## 5. Applications

^{3}with an electron fraction number ${Y}_{e}\approx 0.5$ and Avogadro constant, ${N}_{A}$, as ${N}_{e}={Y}_{e}{\rho}_{m}{N}_{A}$. From Equation (4), the resonance energy is

## 6. Discussion

## Funding

## Conflicts of Interest

## Abbreviations

PMNS | Pontecorvo—Maki—Nakagawa—Sakata |

MSW | Mikheyev—Smirnov—Wolfenstein |

## References

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**Figure 2.**The difference between the upper and lower curves presents the absolute half-width dependence, with respect to $tan2\theta $.

**Figure 3.**The total width dependence, with respect to the parameter $\theta $ for the variable y (solid line) and maximal width for the variable x (dashed line).

**Figure 4.**Resonance shapes (solid lines for ${P}_{2}=1/2$) for the mixing parameters $\pi /100$ (

**a**), $2\pi /25$ (

**b**), and $\pi /4$ (

**c**). Dashed lines correspond to Equation (16), and the dots show the absolute maxima.

**Figure 5.**Comparison of the minimal width of the medium in units of ${d}_{0}$ from Equation (21) (dashed line) and direct calculations (solid line).

**Figure 6.**Resonance shape of the probability distribution (solid lines for ${P}_{2}=1/2$) for the atmospheric neutrinos in Earth. Dashed line corresponds to Equation (16) and dot shows absolute maximum.

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**MDPI and ACS Style**

Chizhov, M.
On Mikheyev–Smirnov–Wolfenstein Resonance Widths. *Symmetry* **2022**, *14*, 176.
https://doi.org/10.3390/sym14010176

**AMA Style**

Chizhov M.
On Mikheyev–Smirnov–Wolfenstein Resonance Widths. *Symmetry*. 2022; 14(1):176.
https://doi.org/10.3390/sym14010176

**Chicago/Turabian Style**

Chizhov, Mihail.
2022. "On Mikheyev–Smirnov–Wolfenstein Resonance Widths" *Symmetry* 14, no. 1: 176.
https://doi.org/10.3390/sym14010176