# Pion Decay

## Homework Statement

(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 $r=m_{\pi}/m_{\mu}$

## Homework Equations

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

2. $β_{\mu} = P_{\mu}/E_{\mu}$

## 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.

## Answers and Replies

Related Introductory Physics Homework Help News on Phys.org
Simon Bridge