# Particle Decay Mode Percentages

• jfy4
In summary, The table from WolframAlpha shows the probability of various decay modes of the pion \pi^{+}. It is calculated using Fermi's Golden Rule, which involves the transition matrix element and the phase space factor. The electron channel should be favored kinematically, but the muon channel is actually favored due to the weak interaction and the concept of helicity. The last two entries in the table are measurements, not calculations, as indicated by the use of limits instead of numbers. However, calculations can be done to determine the partial widths for various decays, but the branching fraction requires dividing by the sum of all partial widths.
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,

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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.

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

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.

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.

## 1. What is particle decay mode percentage?

Particle decay mode percentage refers to the probability of a specific particle decaying into different combinations of other particles. It is used to describe the relative likelihood of different decay products.

## 2. How is particle decay mode percentage measured?

Particle decay mode percentage is typically measured by analyzing the data collected from particle collisions in accelerators such as the Large Hadron Collider. By comparing the number of observed decay events with the expected number based on theoretical predictions, scientists can determine the percentage of each decay mode.

## 3. Why is particle decay mode percentage important?

Particle decay mode percentage is important because it provides valuable information about the fundamental properties of particles and their interactions. It can also help validate or disprove theories and models in particle physics.

## 4. Can particle decay mode percentage change over time?

Yes, particle decay mode percentage can change over time as our understanding of particle physics evolves and new particles are discovered. It can also vary depending on the energy of the particle collisions.

## 5. How is particle decay mode percentage used in practical applications?

Particle decay mode percentage is used in practical applications such as medical imaging and cancer therapy. By understanding the decay modes of particles, scientists can develop new technologies and treatments that utilize these particles' unique properties.

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