Please, I'd need some help. Although I am not sure if this is again the correct thread, but since it concerns muon decay I bring it here. So...(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to find out why the differential below, in spherical cordinates becomes:

[itex]d^{3}p_{\bar{v_{e}}}=-\frac{E_{\bar{v_{e}}} E_{v_{μ}}}{E_{e}} dE_{\bar{v_{e}}} dE_{v_{μ}} dφ (0)[/itex]

I already have derived the equation:

[itex] E_{v_{μ}}^{2}= E_{\bar{v_{e}}}^{2}+E_{e}^{2}+2E_{\bar{v_{e}}}E_{e}cosθ (1)[/itex]

I also have the conservation of energy due to delta function:

[itex] E_{v_{μ}}= m_{μ}-E_{\bar{v_{e}}}-E_{e} (2)[/itex]

I stop in a very bad position not knowing how to continue:

[itex]d^{3}p_{\bar{v_{e}}}= p_{\bar{v_{e}}}^{2} dp_{\bar{v_{e}}} dcosθ dφ=E_{\bar{v_{e}}}^{2} dE_{\bar{v_{e}}} dcosθ dφ [/itex]

How would you recommend I continue? I would try to differentiate the [itex](1)[/itex] but it has also cosθ and generally a mess is happening. I also could try to differentiate [itex](2)[/itex] but I would get weird results not coinciding with [itex](0)[/itex]

Any suggestion?

(the mass of muon only exists, in the game, so the electron and neutrinos' masses are neglected, and thus their energies are equal to their momentum's magnitudes)

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# Muon decay calculation

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