# Power Laws and Elementary Particle Decays

## Abstract

**:**

^{−21}s), using data available from the Particle Data Group. This set of states seems to be divided into three groups, in each of which the two quantities can be correlated through a remarkably accurate power law. Although this fact does not represent anything new compared to the predictions of the Standard Model, it nevertheless reveals an unexpected order structure in the set of particle decays, emerging from such predictions.

## 1. Introduction

^{−21}s) into three groups in each of which the following power laws hold, with slightly different values of the parameters:

_{0}is completely arbitrary and we choose it equal to the time taken by the light to travel the classic radius of the electron, so as to express A with a comfortable value; E

_{0}= ħ/θ

_{0}. It is evident that starting from M it is possible, through (3) and (4), to derive both θ and n, and then T. It is therefore possible to derive T from M through auxiliary parameters, while it does not appear possible, as we will show, to derive directly T as a function of M. Relations (3) and (4) therefore express a relation between lifetimes and masses.

^{−n}. Let us now consider the particular instant t to which the following relation holds:

## 2. The Decays of Elementary Particles

^{−}with a lifetime of about 15 minutes. It is well known that the slowness of this decay is due to the small phase space factor: the mass of the neutron is almost equal to that of the final state of transformation, which is the proton. For this anomaly we will exclude the neutron from our subsequent considerations. The remaining decays are, as one can immediately see from the plot, grouped in a way dependent on the quark composition or on the lepton flavor. Point 2 is the muon; points 3–5 represent pseudoscalar mesons (including the K

_{0L}) composed of quarks u, d, s; points 6–12 represent the baryons (more the K

_{0S}) composed of quarks u, d, s; points 13–17 represent hadrons with the bottom (b) as the heavier quark; points 18–25 represent hadrons with charm (c) as the heavier quark; they also include tau. All these states decay through weak interactions, which induce the transmutation of the heavier quark into a quark of lower mass.

## 3. Power Laws

^{2}= 0.998

^{2}= 0.995

^{2}= 0.991

_{0S}) they reach the two orders. In any case, considering that the lifetimes of states 2–34 span about 15 orders of magnitude, it can be argued that the agreement is satisfactory.

_{0}), obtained from the experimental data through (5) and (2), is plotted as a function of (Mc

^{2}/E

_{0}) in a doubly logarithmic scale. The representative points of the states 2–16, 17–25 and 26–34 are reported in three different colors and shapes (respectively diamonds, squares and triangles), in order to facilitate the distinction between families. The three fitting lines of the single families, Equation (3), are also reported. The reader can compare with Figure 2 and note the difference in correlation with the new variable.

## 4. Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Particle | Mass (MeV) | Measured Width (MeV) | n (Equation (5)) | n (Equation (4)) | Calculated Width (MeV) | Calc/Meas Width | |
---|---|---|---|---|---|---|---|

1 | n | 9.40 × 10^{2} | 7.43 × 10^{−25} | 96.11 | |||

2 | μ | 1.06 × 10^{2} | 3.00 × 10^{−16} | 63.78 | 64.76 | 3.17 × 10^{−16} | 1.06 |

3 | π^{±} | 1.40 × 10^{2} | 2.53 × 10^{−14} | 57.64 | 63.51 | 9.77 × 10^{−16} | 3.86 × 10^{−2} |

4 | K_{0L} | 4.98 × 10^{2} | 1.27 × 10^{−14} | 60.53 | 58.11 | 1.34 × 10^{−13} | 1.06 × 10 |

5 | K^{±} | 4.94 × 10^{2} | 5.33 × 10^{−14} | 58.41 | 58.14 | 1.30 × 10^{−13} | 2.44 |

6 | Ξ_{0} | 1.31 × 10^{3} | 2.27 × 10^{−12} | 54.3 | 54.31 | 4.61 × 10^{−12} | 2.03 |

7 | Λ | 1.12 × 10^{3} | 2.50 × 10^{−12} | 53.92 | 54.91 | 2.63 × 10^{−12} | 1.05 |

8 | Ξ^{−} | 1.32 × 10^{3} | 4.02 × 10^{−12} | 53.47 | 54.28 | 4.73 × 10^{−12} | 1.18 |

9 | Σ^{−} | 1.20 × 10^{3} | 4.46 × 10^{−12} | 53.17 | 54.64 | 3.37 × 10^{−12} | 7.55 × 10^{−1} |

10 | Ω | 1.67 × 10^{3} | 8.02 × 10^{−12} | 52.79 | 53.39 | 1.09 × 10^{−11} | 1.36 |

11 | Σ^{+} | 1.19 × 10^{3} | 8.25 × 10^{−12} | 52.24 | 54.67 | 3.27 × 10^{−12} | 3.96 × 10^{−1} |

12 | K_{0S} | 4.98× 10^{2} | 7.38 × 10^{−12} | 51.12 | 58.11 | 1.34 × 10^{−13} | 1.82 × 10^{−2} |

13 | B^{±} | 5.28 × 10^{3} | 4.28× 10^{−10} | 48.59 | 49.26 | 5.57 × 10^{−10} | 1.30 |

14 | B_{0} | 5.28 × 10^{3} | 4.39 × 10^{−10} | 48.56 | 49.26 | 5.57 × 10^{−10} | 1.27 |

15 | B_{0S} | 5.38 × 10^{3} | 4.92 × 10^{−10} | 48.41 | 49.19 | 5.93 × 10^{−10} | 1.21 |

16 | Λ_{0b} | 5.64 × 10^{3} | 6.16 × 10^{−10} | 48.15 | 49.03 | 6.93 × 10^{−10} | 1.13 |

17 | B_{c}_{+} | 6.29 × 10^{3} | 1.42 × 10^{−9} | 47.07 | 45.59 | 7.82 × 10^{−9} | 5.51 |

18 | D^{±} | 1.87 × 10^{3} | 6.24 × 10^{−10} | 46.49 | 44.50 | 4.84 × 10^{−9} | 7.75 |

19 | D_{s}^{±} | 1.97 × 10^{3} | 1.41 × 10^{−9} | 45.36 | 44.54 | 4.94 × 10^{−9} | 3.50 |

20 | Ξ_{c}^{+} | 2.47 × 10^{3} | 1.88 × 10^{−9} | 45.26 | 44.74 | 5.41 × 10^{−9} | 2.88 |

21 | D_{0} | 1.86 × 10^{3} | 1.59 × 10^{−9} | 45.09 | 44.49 | 4.83 × 10^{−9} | 3.04 |

22 | τ | 1.78 × 10^{3} | 2.23 × 10^{−9} | 44.52 | 44.45 | 4.74 × 10^{−9} | 2.13 |

23 | Λ_{c}^{+} | 2.29 × 10^{3} | 3.30 × 10^{−9} | 44.31 | 44.68 | 5.25 × 10^{−9} | 1.59 |

24 | Ξ_{c}_{0} | 2.47 × 10^{3} | 5.85 × 10^{−9} | 43.57 | 44.74 | 5.41 × 10^{−9} | 9.25 × 10^{−1} |

25 | Ω_{c}_{0} | 2.70 × 10^{3} | 9.50 × 10^{−9} | 43 | 44.82 | 5.61 × 10^{−9} | 5.90 × 10^{−1} |

26 | π_{0} | 1.35× 10^{2} | 7.85 × 10^{−6} | 28.38 | 24.65 | 1.82 × 10^{−4} | 2.32 × 10 |

27 | η | 5.47× 10^{2} | 1.20 × 10^{−3} | 22.84 | 22.67 | 2.69 × 10^{−3} | 2.24 |

28 | Σ_{0} | 1.19 × 10^{3} | 8.91 × 10^{−3} | 20.95 | 21.63 | 1.14 × 10^{−2} | 1.28 |

29 | γ(3S) | 1.04 × 10^{4} | 2.63 × 10^{−2} | 22.62 | 18.99 | 5.46 × 10^{−1} | 2.08 × 10 |

30 | γ(2S) | 1.00 × 10^{4} | 4.40 × 10^{−2} | 21.77 | 19.04 | 5.10 × 10^{−1} | 1.16 × 10 |

31 | γ(1S) | 9.46 × 10^{3} | 5.25 × 10^{−2} | 21.41 | 19.10 | 4.63 × 10^{−1} | 8.82 |

32 | J/ψ(1S) | 3.10 × 10^{3} | 8.80 × 10^{−2} | 18.88 | 20.42 | 6.49 × 10^{−2} | 7.38 × 10^{−1} |

33 | D*^{±} | 2.01 × 10^{3} | 9.60 × 10^{−2} | 18.08 | 20.96 | 2.97 × 10^{−2} | 3.10 × 10^{−1} |

34 | J/ψ(2S) | 3.69 × 10^{3} | 3.37 × 10^{−1} | 17.06 | 20.21 | 8.86 × 10^{−2} | 2.63 × 10^{−1} |

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Chiatti, L.
Power Laws and Elementary Particle Decays. *Sci* **2020**, *2*, 17.
https://doi.org/10.3390/sci2010017

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Chiatti L.
Power Laws and Elementary Particle Decays. *Sci*. 2020; 2(1):17.
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Chiatti, Leonardo.
2020. "Power Laws and Elementary Particle Decays" *Sci* 2, no. 1: 17.
https://doi.org/10.3390/sci2010017