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**[SOLVED] Relativity and pi-meson decay**

## Homework Statement

A [tex]\pi[/tex] meson of mass [tex]m_{\pi}[/tex] at rest, decays into a muon of mass [tex]m_{\mu}[/tex] and a neutrino of zero rest mass, [tex]m_{v}=0[/tex]. Find the momentum of the muon.

## Homework Equations

I think this is the right equation though I'm not sure if I should use four vectors.

[tex]E^{2}=(pc)^{2}+(mc^{2})^2[/tex]

## The Attempt at a Solution

Total energy before the decay is the same as the total energy after the decay, so,

[tex]E_{\pi}=m_{\pi}c^{2}[/tex]

[tex]E_{\mu}=P_{\mu}c+m_{\mu}c^{2}[/tex]

[tex]E_{v}=P_{v}c[/tex]

Giving a total energy of,

[tex]E_{\pi}=E_{\mu}+E_{v}[/tex]

[tex]m_{\pi}c^{2}=P_{v}c+P_{\mu}c+m_{\mu}c^{2}[/tex]

So the momentum is,

[tex]P_{\mu}=m_{\pi}c-P_{v}-m_{\mu}c[/tex]

I have a horrid feeling this is all wrong as it seems too easy. Please could someone let me know if I'm wrong in my reasoning?

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