# Pion Decay

1. Oct 22, 2013

### stefan10

1. The problem statement, all variables and given/known data

(a) Consider that decay when the pion is at rest. Find the speed β of the muon and the energy $E_{v}$ of the neutrino. (Work in general algebraic terms, and set c=1. Plug in numerical values as late as possible! You may find it useful to define a quantity $r=m_{\pi}/m_{\mu}$

2. Relevant equations

1. $E^2 = M^2 + P^2$

2. $β_{\mu} = P_{\mu}/E_{\mu}$

3. The attempt at a solution

By conservation of momentum $P_{\mu} = - P_{\nu}$

By conservation of energy $E_{\mu} + E_{\nu} = m_{\pi}$

Using Equation 1 and the fact the mass of the neutrino is zero. I go through algebra to get

$E_{\nu} = \frac{m_{\pi}}{2} - \frac{m_{\mu}^2}{2 m_{\pi}}$

I'm unsure how I can find the momentum and energy of the muon from there without going into long algebraic computations. Is there an easier way? Thank you.

2. Oct 23, 2013

### Simon Bridge

You now the mass of the neutrino is not zero right? But it may be OK to neglect it.

Not really. The hint is the shortcut.

Once you start you'll find the calculations are not all that bad.