- #1
stefan10
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Homework Statement
(a) Consider that decay when the pion is at rest. Find the speed β of the muon and the energy [itex]E_{v}[/itex] 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 [itex]r=m_{\pi}/m_{\mu} [/itex]
Homework Equations
1. [itex] E^2 = M^2 + P^2 [/itex]
2. [itex] β_{\mu} = P_{\mu}/E_{\mu} [/itex]
The Attempt at a Solution
By conservation of momentum [itex] P_{\mu} = - P_{\nu} [/itex]
By conservation of energy [itex] E_{\mu} + E_{\nu} = m_{\pi} [/itex]
Using Equation 1 and the fact the mass of the neutrino is zero. I go through algebra to get
[itex] E_{\nu} = \frac{m_{\pi}}{2} - \frac{m_{\mu}^2}{2 m_{\pi}} [/itex]
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.