Matrix elemnet of pion decay

In summary, the hadronic matrix element for pion decay (Pi+->mu+ neutrino) is given by <0|ubar gamma[mu](1-gamma[5])d|pion>, where only the axial and pseudoscalar current contribute due to the vector current not being able to connect a state of unnatural parity to the hadronic vacuum. However, for pion decay (Pi+>Pi0 mu+ neutrino), the vector current does contribute, while the axial current contribution vanishes due to the state of unnatural parity going to another state of unnatural parity. It should be noted that the decay \pi^+ \rightarrow \pi^0 + \mu^+ + \nu is not allowed due to
  • #1
plasmon
36
1
I have studied that the hadronic matrix element of pion decay
(Pi+->mu+ anti muon neutrino) is given as
<0|ubar gamma[mu](1-gamma[5])d|pion>.
The vector current does not seem to contribute, because it cannot connect a state of unnatural parity to hadronic vacuum. Only the axial and pseudoscalar current seems to conribute.
Similarly for pion decay
(Pi+>Pi0 mu+ anti muon neutrino) is given as
<0|ubar gamma[mu](1-gamma[5])d|pion>.
Now The vector current does contribute. The axial current contribution seems to vanish now because a state of unnatural parity is going to unnatural parity!

I do not understand this abstract kind of reasoning.
 
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  • #2
[tex]\pi^+ \rightarrow \pi^0 + \mu^+ + \nu[/tex]

is not an allowed decay, check conservation of energy.

Correction: it should be a muon neutrino- not anti-neutrino. Negatively charged leptons are considered particles, positively charged leptons are anti-particles. Merely convention. Ah yes... latex does not update with the correction.
 
Last edited:
  • #3

The matrix element of pion decay is a mathematical representation of the process by which a pion particle decays into a muon and an anti-muon neutrino. In this process, the hadronic matrix element represents the interaction between the quarks in the pion and the leptons in the final state.

The first equation given in the content shows that the hadronic matrix element for the decay of a positively charged pion into a muon and an anti-muon neutrino involves the axial and pseudoscalar current. This is because the vector current cannot connect a state of unnatural parity (such as the pion) to the hadronic vacuum. Only currents that conserve parity (such as the axial and pseudoscalar currents) can contribute to this process.

However, in the second equation, the pion decays into a neutral pion, a muon, and an anti-muon neutrino. In this case, the vector current can contribute because it can connect a state of unnatural parity (the neutral pion) to the hadronic vacuum. This means that the axial current contribution vanishes, as it would be going from a state of unnatural parity to another state of unnatural parity.

The reasoning behind this is purely mathematical and abstract, as it involves understanding the properties of different currents and their interactions with different states. It may seem complex, but it is an important aspect of understanding and predicting particle decay processes.
 

1. What is the matrix element of pion decay?

The matrix element of pion decay is a mathematical representation of the transition between a pion particle in its initial state and its final state after decay. It is an important quantity in particle physics that describes the probability of a pion decaying into other particles.

2. How is the matrix element of pion decay calculated?

The matrix element of pion decay is calculated using a combination of theoretical models and experimental data. The process involves calculating the decay amplitude, which is then used to determine the matrix element through a series of mathematical equations and calculations.

3. What is the significance of the matrix element of pion decay?

The matrix element of pion decay is significant because it provides valuable information about the fundamental interactions between particles. It also allows for the testing and validation of theoretical models and helps to improve our understanding of the underlying laws of nature.

4. How does the matrix element of pion decay relate to the Standard Model of particle physics?

The matrix element of pion decay is a crucial component of the Standard Model, which is the current theoretical framework used to describe the fundamental particles and their interactions. It is used to calculate the decay rates of pion particles, which can then be compared to experimental data to test the predictions of the Standard Model.

5. What are some applications of the matrix element of pion decay?

The matrix element of pion decay has various applications in particle physics research. It is used in the study of particle interactions, the development of new theoretical models, and the testing of the Standard Model. It also has practical applications, such as in medical imaging techniques that use pion decay to produce images of the human body.

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