Calculation of particle life span

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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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