Calculation of particle life span

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SUMMARY

The discussion establishes a definitive relationship between the inverse fine-structure constant (alpha) and the life span of elementary particles, specifically through the decay process μ → e + νe + νμ, which is governed by weak interactions. It highlights that the weak coupling constant G is related to the mass of the W boson (MW) and the coupling constant g, which is closely linked to the fine structure constant. The weak and electromagnetic interactions are unified under the electroweak interaction framework, emphasizing the significance of the weak mixing angle (θW) in this relationship.

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  • Understanding of weak interactions in particle physics
  • Familiarity with the electroweak theory
  • Knowledge of particle decay processes
  • Basic concepts of coupling constants and their significance
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Is there a relationship between the inverse fine-structure constant (alpha) and the life span of elementary particles?
 
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Indirectly yes. Decays of the elementary particles such as μ → e + νe + νμ are governed by the weak interaction. The original description of the weak interactions was in terms of a weak coupling constant G. We now know that the weak and the electromagnetic interactions are two aspects of a single electroweak interaction, and G ~ g2/MW2 where MW is the mass of the W boson and g is a coupling constant that differs from the fine structure constant only by a small factor: g sin θW = e where θW is the weak mixing angle.
 
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