Decay rate of the muon

The muon is a heavy cousin of the electron and decays into an electron and two neutrinos \begin{equation*} \mu \to e + \nu_{\mu} + \bar{\nu}_e \end{equation*} The decay rate of the muon is calculated in section 10.2 in Griffiths [1]. To calculate the decay rate $\Gamma$ one needs to calculate a 6-dimensional integral coming from 3 particles times 3 momentum integrals with momentum conservation. The calculation of this integral in Griffiths is quite lengthy and I do not have much insight about it. I have questions like

• Could I have calculated the integral in a different order than the one in Griffiths?
• Could one still calculate the result analytically if more particles were produced in the decay?
• Is there a faster way to obtain the result?

I therefore decided to calculate $\Gamma$ in a different way. My calculation is motivated by [2]. I set the mass of the electron $e$, of the muon neutrino $\nu_{\mu}$ and of the electron anti neutrino $\bar{\nu}_e$ to zero.

Resonance in pseudoscalar Yukawa theory

A post with calculations in pseudoscalar Yukawa theory and plots of cross sections to illustrate a resonance.

Scattering in Yukawa theory

I illustrate the cross section of the scattering $e^+ e^- \to e^+ e^-$ in Yukawa theory.