Kinetic Energy of Muon in Decay of Pi+ -> Mu+ + Nu_mu

In summary, the mc^2 for a pion and muon are 139.57 MeV and 105.66 MeV respectively. To find the kinetic energy of the muon in its decay from \pi^+ -> \mu^+ + \nu_{\mu} assuming the neutrino is massless, we must use the equation E^2 = p^2 + m^2. However, this equation can only be applied to individual vectors, not the whole system. In the case where there is a small neutrino mass, the equation becomes p = \sqrt{(m_{\pi})^2 - (m_{\mu}+m_{\nu})^2}. Therefore, your approach of
  • #1
indigojoker
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the mc^2 for a pion and muon are 139.57 MeV and 105.66 MeV respectively. Find the kinetic energy of the muon in its decay from [tex] \pi ^+ -> \mu^+ + \nu_{\mu} [/tex] assuming the neutrino is massless. Here's what I did:

Since [tex]E^2=p^2c^2+m^2c^4[/tex] and that c=1, then E, p and m have same units.

[tex]E^2 = p^2 +m^2[/tex]
[tex](139.57 MeV)^2 - (105.66MeV)^2 =p^2[/tex]
[tex]p=91.19MeV[/tex]

Also consider the case where there is a small neutrino mass:

[tex]E^2 = p^2 +m^2[/tex]
[tex](m_{\pi})^2 - (m_{\mu}+m_{\nu})^2 =p^2[/tex]
[tex]p=\sqrt{(m_{\pi})^2 - (m_{\mu}+m_{\nu})^2}[/tex]

I feel like there is ill logic here. Comments on my work would be appreciated.
 
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  • #2
There is ill logic. You are dealing with a three body problem. Think four vectors. (E_pion,p_pion)=(E_muon,p_muon)+(E_neutrino,p_neutrino). You can only apply E^2=p^2+m^2 to each individual vector, not somehow magically to the whole system.
 

What is the kinetic energy of the muon in the decay of Pi+ -> Mu+ + Nu_mu?

The kinetic energy of the muon in this decay process is dependent on various factors such as the mass and energy of the parent particle (Pi+) and the mass of the daughter particles (Mu+ and Nu_mu). It can be calculated using the equation: KE = (mPi+ - mMu+ - mNu_mu)c^2, where m represents the mass and c is the speed of light in a vacuum.

How does the kinetic energy of the muon change with different decay scenarios?

The kinetic energy of the muon will vary depending on the specific decay scenario. In some cases, the muon may have a higher kinetic energy if the parent particle has a larger mass and energy, while in other cases it may have a lower kinetic energy if the daughter particles have larger masses.

Is kinetic energy conserved in this decay process?

Yes, kinetic energy is conserved in this decay process. The total kinetic energy of the daughter particles (Mu+ and Nu_mu) will equal the kinetic energy of the parent particle (Pi+).

What other factors can affect the kinetic energy of the muon in this decay?

Aside from the masses and energies of the particles involved, other factors that can affect the kinetic energy of the muon in this decay include the angle of emission, the presence of external forces, and the presence of other particles in the decay environment.

How is kinetic energy related to the speed of the muon in this decay?

The kinetic energy of the muon is directly related to its speed in this decay process. As the muon gains kinetic energy, its speed will increase. However, the exact relationship between kinetic energy and speed will vary depending on the masses and energies of the particles involved.

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