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This is a past (3rd year university level) exam question, so I hope it's ok that I didn't post this in the homework section even if it's set out like a homework question.

The Question:

Suppose we are observing the collision

Anti-electron-neutrino + electron ---> W-minus boson

What energy has the Anti-Electron-Neutrino, to produce the W particle?

Relavant equations and data:

mass of electron = 0.511 MeV/c^2

mass of W-minus boson = 80.403 GeV/c^2

Four-momentum equation

[tex]S = -(\overrightarrow{{p_{e}}}+\overrightarrow{{p_{\nu }}})^{2} = -(cp_{e}+cp_{\nu })^{2}+(E_{e}+E_{\nu})^{2}[/tex]

Thoughts so far:

My understanding is that the four-momentum is always conserved so I have to equate the initial four-momentum to the final four-momentum using the assumption that the electron and the W boson have no kinetic energy.

[tex]S_{initial} = -c^{2}p_{\nu }^{2} + E_{\nu }^{2}[/tex]

[tex]S_{final} = ((m_{W^{-}}) c^{2})^{2}[/tex]

to the initial four-momentum becomes zero since

cp = E

So I'm not sure how to carry on, the energy of the neutrino can't be zero!?

Thanks to anyone who helps

xoLouLouox

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# Conservation of four momentum

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