Max Electron Energy from Muon Relativistic Decay

In summary, the process of muon decay involves a muon at rest decaying into an electron and two massless neutrinos. The maximum possible energy of the electron can be determined by considering its motion opposite to the two neutrinos, which are both moving in the same direction. This can be solved mathematically by conserving energy and momentum, resulting in three equations and six unknowns. Boosting into different frames may provide more equations, but there may be a simpler approach to solving this problem.
  • #1
eep
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Consider the process of muon decay: muon (at rest) -> electron + 2 neutrinos. Assuming the neutrinos are massless and the muon decays from rest, what is the maximum possible electron energy? We are given the mass of the muon, the mass of the electron, and are told to treat the neutrinos as being massless (E = pc).

My intuition tells me that the electron will have maximum energy when it is moving opposite to the two neutrinos, both moving in the same direction. I'm not too sure how to show this mathematically, however. Obviously, momentum and energy need to be conserved but by doing this I end up with 3 equations (Energy conservation, parallel momentum conservation, perpendicular momentum conservation) but six unknowns (speed of electron in parallel direction, speed of election in perp direction, momentum of first neutrino in parallel direction, perp direction, momentum of second neutrino in parallel, perp direction).

I figure by doing some boosts into different frames I can get more equations, but is there a simpler way of approaching this? I can post more details if needed but I think the question is pretty straightforward.
 
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  • #2
[tex]2p+\sqrt{4p^2+m^2}=M[/tex].
 
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Related to Max Electron Energy from Muon Relativistic Decay

1. What is the significance of the "Max Electron Energy from Muon Relativistic Decay"?

The "Max Electron Energy from Muon Relativistic Decay" is an important concept in particle physics. It refers to the maximum energy that an electron can obtain from the decay of a muon, a subatomic particle that is unstable and decays into an electron, a neutrino, and an antineutrino.

2. How is the Max Electron Energy from Muon Relativistic Decay calculated?

The Max Electron Energy from Muon Relativistic Decay is calculated using the formula Emax = (mμ^2 - mν^2) / (2mμ), where mμ is the mass of the muon and mν is the mass of the neutrino. This equation takes into account the conservation of energy and momentum in the decay process.

3. What is the relationship between the Max Electron Energy from Muon Relativistic Decay and the muon's half-life?

The Max Electron Energy from Muon Relativistic Decay is directly related to the muon's half-life. As the half-life of a muon decreases, the maximum energy that can be obtained from its decay also decreases. This is because a shorter half-life means the muon decays faster, resulting in less time for the electron to gain energy from the decay process.

4. Can the Max Electron Energy from Muon Relativistic Decay be exceeded?

No, the Max Electron Energy from Muon Relativistic Decay is a fundamental limit and cannot be exceeded. This is due to the laws of conservation of energy and momentum, which dictate that the total energy and momentum before and after the decay must be the same.

5. What applications does the concept of Max Electron Energy from Muon Relativistic Decay have?

The concept of Max Electron Energy from Muon Relativistic Decay has various applications in particle physics research. It can be used to study the properties of muons and other subatomic particles, as well as to test the validity of the laws of conservation of energy and momentum. It also has practical applications in medical imaging techniques such as positron emission tomography (PET), which uses the decay of muons to produce images of internal body structures.

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