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Decay ratio

  • Thread starter GoodKopp
  • Start date
  • #1
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Homework Statement



Give a simple estimate of the ratio of decay rates for [tex]K^+ \rightarrow e^+ \nu_e / K^+ \rightarrow \mu^+ \nu_\mu.[/tex]

Homework Equations



Fermi's Golden Rule for decay width [tex]\Gamma = \hbar W = 2\pi (dn/dE_f)|M_{if}|^2.[/tex]

For comparison, from the PDG, [tex]\Gamma / \Gamma_i[/tex] are [tex]1.55 \pm 0.07 \times 10^{-5}[/tex] and [tex]63.44 \pm 0.14[/tex] for [tex]K^+ \rightarrow e^+ \nu_e[/tex] and [tex]K^+ \rightarrow \mu^+ \nu_\mu[/tex], respectively.

The Attempt at a Solution



[tex]\frac{\Gamma (K^+ \rightarrow e^+ \nu_e)}{\Gamma (K^+ \rightarrow \mu^+ \nu_\mu)} = \frac{\frac{dn}{dE} e^+ \nu_e}{\frac{dn}{dE} \mu^+ \nu_\mu}[/tex]

[tex]\frac{dn}{dE} = \frac{dn}{dp} \frac{dp}{dE}[/tex]

Am I going about this the right way? Where do I go from here?
 
Last edited:

Answers and Replies

  • #2
pam
455
1
You have to include a very strong dependence on the e or mu mass.
This comes from the weak interaction.
The same factor comes up in pi decay.
 

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