- #1
ncs22
- 6
- 0
Show that the phase space factor [tex]\rho \propto p^2 dp/dE [/tex] for the decay [tex]\pi\rightarrow \mu + \upsilon[/tex] is
[tex]\rho \propto \frac{({m_\pi}^2 - {m_\mu}^2)^2}{{m_\pi}^3}E_\mu [/tex]
where E is the total energy.I can show that [tex]p^2 = ({m_\pi}^2 - {m_\mu}^2)^2/4{m_\pi}^2[/tex]
but then I get stuck, I don't know how to evaluate dp/dE and I'm not sure what p here is referring to i.e. which particle and in which frame. I worked out the above expression for p2 taking it to be the energy for the muon (or neutrino) in the center of mass frame.
[tex]\rho \propto \frac{({m_\pi}^2 - {m_\mu}^2)^2}{{m_\pi}^3}E_\mu [/tex]
where E is the total energy.I can show that [tex]p^2 = ({m_\pi}^2 - {m_\mu}^2)^2/4{m_\pi}^2[/tex]
but then I get stuck, I don't know how to evaluate dp/dE and I'm not sure what p here is referring to i.e. which particle and in which frame. I worked out the above expression for p2 taking it to be the energy for the muon (or neutrino) in the center of mass frame.