# How to determine the decay mode probability of a pion

• rwooduk
In summary: I'm not quite at quantum field theory level yet, but in essence i think we agree that decay mode is independent of energy :-)Even in its rest frame, the pion will have mass... so it can decay into an electron and an electron antineutrino.In summary, the primary decay mode of a pion, with probability 0.999877, is a purely leptonic decay into an anti-muon and a muon neutrino. The second most common decay mode of a pion, with probability 0.000123, is also a leptonic decay into an electron and the corresponding electron antineutr
rwooduk
Hi,

Given the initial energy of a pion is it possible to calculate the probability and mode of its decay?

Ive looked everywhere for a relevant formula but everywhere simply states the probability and mode...

Wiki "The primary decay mode of a pion, with probability 0.999877, is a purely leptonic decay into an anti-muon and a muon neutrino"... "The second most common decay mode of a pion, with probability 0.000123, is also a leptonic decay into an electron and the corresponding electron antineutrino."

I considered doing some sort of conservation of energy / momentum, but how am i supposed to do that if i don't know what it decays into?

ive spent at least two hours trying to find an equation, i found something called the "branching ratio" is that at all related?

any direction on this would be appreciated.

There is no rule to determine the decay modes. In principle, a particle can decay in every final state allowed by conservation laws. First of all the total mass of the final state must be lighter than the decay particle. Then the right quantum numbers must be conserved (total angular momentum, lepton number and so forth).

Once you chose what particular final state you want to study you can compute the decay width for that particular final state using the Quantum Field Theory methods. A good reference on how to actually do this kind of calculation can be:

De Wit - Field Theory in Particule Physics (Chapter 3)

Is a very practical book that shows you how to compute cross sections and decay widths.

I hope this is useful

1 person
That's very very useful! Thank you!

The decay is truly random. There is no way to tell ahead of time which of the possible outcomes will actually happen. All you can tell are the probabilities of each possible outcome.

1 person
The energy of the pion does not matter - in particular, you can always consider it in its rest frame.

Branching ratios are exactly the probabilities of the decay modes you are looking for.

1 person
mfb said:
The energy of the pion does not matter - in particular, you can always consider it in its rest frame.

Branching ratios are exactly the probabilities of the decay modes you are looking for.

if the energy of the pion is completely independent of its decay mode then that again that answers my question because the only information given in the question is the pions total energy. So finding the main decay mode calculatively would not be possible.

Thanks all!

rwooduk said:
if the energy of the pion is completely independent of its decay mode then that again that answers my question because the only information given in the question is the pions total energy. So finding the main decay mode calculatively would not be possible.
You are contradicting yourself here.

Calculating the main decay modes is possible with theoretical physics (quantum field theory). And those decay modes are completely independent of the energy of the pion in our lab frame (the pion just does not care about our lab).

mfb said:
You are contradicting yourself here.

Calculating the main decay modes is possible with theoretical physics (quantum field theory). And those decay modes are completely independent of the energy of the pion in our lab frame (the pion just does not care about our lab).

hmm I'm not quite at quantum field theory level yet, but in essence i think we agree that decay mode is independent of energy :-)

Even in its rest frame, the pion will have mass...

## 1. What is a pion?

A pion is a subatomic particle made up of a combination of an up quark and an anti-down quark. It is a type of meson and is represented by the symbol π.

## 2. How does a pion decay?

A pion can decay in two ways: into a muon and a neutrino, or into an electron and a neutrino. These decays are known as the muon mode and electron mode, respectively.

## 3. What is the decay mode probability of a pion?

The decay mode probability of a pion is the likelihood that it will decay through the muon mode or electron mode. This probability is determined by the properties of the pion, such as its mass and lifetime.

## 4. How do scientists determine the decay mode probability of a pion?

Scientists use experimental data and mathematical models to determine the decay mode probability of a pion. This involves studying the properties of pions and their decays in particle accelerators and other experiments.

## 5. Why is it important to determine the decay mode probability of a pion?

Knowing the decay mode probability of a pion is crucial for understanding the behavior of subatomic particles and for making predictions about their interactions. It also helps scientists test and refine current theories of particle physics.

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