Particle Decay Mode Percentages

[jfy4]

Hi everyone,

I find the following table from WolframAlpha concerning the probability of various decay modes of the pion $\pi^{+}$.

My question is: Are these probabilities calculated, or are they numbers from numerous experiments?

Thanks,

 

[kith]

In principle, such decay rates can be calculated using Fermi's Golden Rule, which consists of two main components: the transition matrix element, which can be calculated using Feynman diagrams, and the phase space factor, which roughly corresponds to how many possibilities exist for the final state. (see p. 204 of Griffiths' book)

To understand the branching ratios in the case of the pion, you have to be familiar with the weak interaction, especially the concept of helicity. Kinematically, the electron channel should be favoured. Actually, the muon channel is favoured. You can read about it in Griffiths, p. 321.

 

[Vanadium 50]

Those are measurements. If they were calculations, the last two entries would have numbers and not limits.

 

[jfy4]

Those are measurements. If they were calculations, the last two entries would have numbers and not limits.

Thanks, I should have been a little more specific in my question, I was really wondering what kith answered. That is, "is there a calculation such that the result says 'you get such-and-such decay mode 99.9% of the time, etc...' ?"

and it appears there is.

 

[Vanadium 50]

Not exactly. You can calculate the partial widths for various decays, but to get the branching fraction you need to divide that by the sum of all the partial widths of all possible decays.