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Sunday, July 31, 2016

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.

Friday, July 15, 2016

Resonance in pseudoscalar Yukawa theory

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

Friday, July 8, 2016

Scattering in Yukawa theory

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